Leveraged ETF Return Dispersion

Introduction #

Over the past 15 years (or so), leveraged ETFs have become frequently used for trading equity indices, sectors, and other asset classes by the investor that is seeking to use leverage for excess exposure to those asset classes. The question remains, however, what happens to the returns of leveraged ETFs over an extended time horizon and is there an optimal leverage ratio for the long-term buy-and-hold investor that allows them to take advantage of leverage to increase the up-side returns, while avoiding catastrophic losses on the down-side? In this investigation, we will delve into these ideas and see what the data shows.

Python Imports #

# Standard Library
import os
import sys
import warnings

from pathlib import Path

# Data Handling
import pandas as pd

# Suppress warnings
warnings.filterwarnings("ignore")

# Add the source subdirectory to the system path to allow import config from settings.py
current_directory = Path(os.getcwd())
website_base_directory = current_directory.parent.parent.parent
src_directory = website_base_directory / "src"
sys.path.append(str(src_directory)) if str(src_directory) not in sys.path else None

# Import settings.py
from settings import config

# Add configured directories from config to path
SOURCE_DIR = config("SOURCE_DIR")
sys.path.append(str(Path(SOURCE_DIR))) if str(Path(SOURCE_DIR)) not in sys.path else None

# Add other configured directories
BASE_DIR = config("BASE_DIR")
CONTENT_DIR = config("CONTENT_DIR")
POSTS_DIR = config("POSTS_DIR")
PAGES_DIR = config("PAGES_DIR")
PUBLIC_DIR = config("PUBLIC_DIR")
SOURCE_DIR = config("SOURCE_DIR")
DATA_DIR = config("DATA_DIR")
DATA_MANUAL_DIR = config("DATA_MANUAL_DIR")

Python Functions #

Here are the functions needed for this project:

• load_data: Load data from a CSV, Excel, or Pickle file into a pandas DataFrame.
• pandas_set_decimal_places: Set the number of decimal places displayed for floating-point numbers in pandas.
• plot_histogram: Plot the histogram of a data set from a DataFrame.
• plot_scatter: Plot the data from a DataFrame for a specified date range and columns.
• plot_time_series: Plot the timeseries data from a DataFrame for a specified date range and columns.
• run_linear_regression: Run a linear regression using statsmodels OLS and return the results.
• summary_stats: Generate summary statistics for a series of returns.
• yf_pull_data: Download daily price data from Yahoo Finance and export it.

from load_data import load_data
from pandas_set_decimal_places import pandas_set_decimal_places
from plot_histogram import plot_histogram
from plot_scatter import plot_scatter
from plot_time_series import plot_time_series
from run_linear_regression import run_linear_regression
from summary_stats import summary_stats
from yf_pull_data import yf_pull_data

Data Overview #

For this exercise, we will investigate the long-term return relationships between the following:

• QQQ (Invesco QQQ Trust, Series 1) and TQQQ (ProShares UltraPro QQQ)
• SPY (SPDR S&P 500 ETF Trust) and UPRO (ProShares UltraPro S&P 500)

Just to clarify, any time we are referring to “close prices” in this analysis, we are referring to the partially-adjusted close prices that account for splits, but not dividends. Because we are dealing with leveraged ETFs, we want to focus on the pure returns due to change in price, but exclude the dividends, which are not leveraged in the same way as the price changes.

QQQ & TQQQ #

Acquire & Plot Data (QQQ) #

First, let’s get the data for QQQ. If we already have the desired data, we can load it from a local pickle file. Otherwise, we can download it from Yahoo Finance using the yf_pull_data function.

pandas_set_decimal_places(2)

yf_pull_data(
    base_directory=DATA_DIR,
    ticker="QQQ",
    adjusted=False,
    source="Yahoo_Finance",
    asset_class="Exchange_Traded_Funds",
    excel_export=True,
    pickle_export=True,
    output_confirmation=False,
)

qqq = load_data(
    base_directory=DATA_DIR,
    ticker="QQQ",
    source="Yahoo_Finance",
    asset_class="Exchange_Traded_Funds",
    timeframe="Daily",
    file_format="pickle",
)

# Rename columns to "QQQ_Close", etc.
qqq = qqq.rename(columns={
    "Adj Close": "QQQ_Adj_Close",
    "Close": "QQQ_Close",
    "High": "QQQ_High",
    "Low": "QQQ_Low",
    "Open": "QQQ_Open",
    "Volume": "QQQ_Volume"
})

display(qqq)

And the plot of the time series of partially adjusted close prices:

plot_time_series(
    df=qqq,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["QQQ_Close"],
    title="QQQ Close Price",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=2,
    x_tick_rotation=30,
    y_label="Price ($)",
    y_format="Decimal",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=False,
    export_plot=False,
    plot_file_name=None,
)

Acquire & Plot Data (TQQQ) #

Next, TQQQ:

yf_pull_data(
    base_directory=DATA_DIR,
    ticker="TQQQ",
    adjusted=False,
    source="Yahoo_Finance", 
    asset_class="Exchange_Traded_Funds", 
    excel_export=True,
    pickle_export=True,
    output_confirmation=False,
)

tqqq = load_data(
    base_directory=DATA_DIR,
    ticker="TQQQ",
    source="Yahoo_Finance", 
    asset_class="Exchange_Traded_Funds",
    timeframe="Daily",
    file_format="pickle",
)

# Rename columns to "TQQQ_Close", etc.
tqqq = tqqq.rename(columns={
    "Adj Close": "TQQQ_Adj_Close",
    "Close": "TQQQ_Close", 
    "High": "TQQQ_High", 
    "Low": "TQQQ_Low", 
    "Open": "TQQQ_Open", 
    "Volume": "TQQQ_Volume"
})

display(tqqq)

And the plot of the time series of partially adjusted close prices:

plot_time_series(
    df=tqqq,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["TQQQ_Close"],
    title="TQQQ Close Price",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=1,
    x_tick_rotation=30,
    y_label="Price ($)",
    y_format="Decimal",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=False,
    export_plot=False,
    plot_file_name=None,
)

Looking at the close prices doesn’t give us a true picture of the magnitude of the difference in returns due to the leverage. In order to see that, we need to look at the cumulative returns and the drawdowns.

Calculate & Plot Cumulative Returns, Rolling Returns, and Drawdowns (QQQ & TQQQ) #

Next, we will calculate the cumulative returns, rolling returns, and drawdowns. This involves aligning the data to start with the inception of TQQQ. For this excercise, we will not extrapolate the data for QQQ back to 1999, but rather just align the data from the inception of TQQQ in 2010.

etfs = ["QQQ", "TQQQ"]

# Merge dataframes and drop rows with missing values
qqq_tqqq_aligned = tqqq.merge(qqq, left_index=True, right_index=True, how='left')
qqq_tqqq_aligned = qqq_tqqq_aligned.dropna()

# Calculate cumulative returns
for etf in etfs:
    qqq_tqqq_aligned[f"{etf}_Return"] = qqq_tqqq_aligned[f"{etf}_Close"].pct_change()
    qqq_tqqq_aligned[f"{etf}_Cumulative_Return"] = (1 + qqq_tqqq_aligned[f"{etf}_Return"]).cumprod() - 1
    qqq_tqqq_aligned[f"{etf}_Cumulative_Return_Plus_One"] = 1 + qqq_tqqq_aligned[f"{etf}_Cumulative_Return"]
    qqq_tqqq_aligned[f"{etf}_Rolling_Max"] = qqq_tqqq_aligned[f"{etf}_Cumulative_Return_Plus_One"].cummax()
    qqq_tqqq_aligned[f"{etf}_Drawdown"] = qqq_tqqq_aligned[f"{etf}_Cumulative_Return_Plus_One"] / qqq_tqqq_aligned[f"{etf}_Rolling_Max"] - 1
    qqq_tqqq_aligned.drop(columns=[f"{etf}_Cumulative_Return_Plus_One", f"{etf}_Rolling_Max"], inplace=True)

# Define rolling windows in trading days
rolling_windows = {
    '1d': 1,      # 1 day
    '1w': 5,      # 1 week (5 trading days)
    '1m': 21,     # 1 month (~21 trading days)
    '3m': 63,     # 3 months (~63 trading days)
    '6m': 126,    # 6 months (~126 trading days)
    '1y': 252,    # 1 year (~252 trading days)
    '2y': 504,    # 2 years (~504 trading days)
    '3y': 756,    # 3 years (~756 trading days)
    '4y': 1008,   # 4 years (~1008 trading days)
    '5y': 1260,   # 5 years (~1260 trading days)
}

# Calculate rolling returns for each ETF and each window
for etf in etfs:
    for period_name, window in rolling_windows.items():
        qqq_tqqq_aligned[f"{etf}_Rolling_Return_{period_name}"] = (
            qqq_tqqq_aligned[f"{etf}_Close"].pct_change(periods=window)
        )
        
display(qqq_tqqq_aligned)

And now the plot for the cumulative returns:

plot_time_series(
    df=qqq_tqqq_aligned,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["QQQ_Cumulative_Return", "TQQQ_Cumulative_Return"],
    title="Cumulative Returns",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=1,
    x_tick_rotation=30,
    y_label="Cumulative Return",
    y_format="Decimal",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

And the drawdown plot:

plot_time_series(
    df=qqq_tqqq_aligned,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["QQQ_Drawdown", "TQQQ_Drawdown"],
    title="Drawdowns",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=1,
    x_tick_rotation=30,
    y_label="Drawdown",
    y_format="Percentage",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

Here is where we truly see the volatility of TQQQ relative to QQQ. In the past 5 years, TQQQ has had drawdowns of 50%, 60%, 70%, and 80%. While it has recovered to make new highs (with the exception of the current ~25% drawdown as of mid-March 2026), very few investors can endure those drawdowns and continue to hold their position. At the same time, we can see from the plot that a ~35% drawdown in QQQ equated to a ~80% drawdown in TQQQ, which is not in fact, 3x. So this tells us (which we already knew) that there is dispersion in the long-term returns relative to the short-term returns between the non-leveraged QQQ and 3x leveraged TQQQ. This idea is well documented in the financial literature as “volatility decay” or “volatility drag”. But, and this is the question we are trying to answer, how significant is this effect over various time horizons?

Summary Statistics (QQQ & TQQQ) #

Looking at the summary statistics further confirms our intuitions about the volatility and drawdowns.

qqq_sum_stats = summary_stats(
    fund_list=["QQQ"],
    df=qqq_tqqq_aligned[["QQQ_Return"]],
    period="Daily",
    use_calendar_days=False,
    excel_export=False,
    pickle_export=False,
    output_confirmation=False,
)

tqqq_sum_stats = summary_stats(
    fund_list=["TQQQ"],
    df=qqq_tqqq_aligned[["TQQQ_Return"]],
    period="Daily",
    use_calendar_days=False,
    excel_export=False,
    pickle_export=False,
    output_confirmation=False,
)

sum_stats = pd.concat([qqq_sum_stats, tqqq_sum_stats])

display(sum_stats)

Note that these statistics are being run on the partially-adjusted close prices, which are not the true returns (due to not accounting for dividends), but they do give us a picture of the relative volatility and drawdowns of the two ETFs. The mean return for TQQQ is much higher than that of QQQ, but the volatility is also much higher, which is consistent with the idea of leverage amplifying both the up-side and down-side. The maximum drawdown for TQQQ is also much higher than that of QQQ, which again confirms our observations from the drawdown plot.

Also note that the daily maximum return for both funds occured during “Liberation Day” and the daily minimum return for both funds occured early on during the COVID-19 pandemic.

Plot Returns & Verify Beta (QQQ & TQQQ) #

Before we look at the rolling returns, let us first verify that the daily returns for TQQQ are in fact ~3x those of QQQ. We can do that by plotting the daily returns for both funds against each other and running a linear regression to see if the beta is indeed ~3.

plot_scatter(
    df=qqq_tqqq_aligned,
    x_plot_column="QQQ_Return",
    y_plot_columns=["TQQQ_Return"],
    title="QQQ & TQQQ Returns",
    x_label="QQQ Return",
    x_format="Decimal",
    x_format_decimal_places=2,
    x_tick_spacing="Auto",
    x_tick_rotation=30,
    y_label="TQQQ Return",
    y_format="Decimal",
    y_format_decimal_places=2,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    plot_OLS_regression_line=True,
    OLS_column="TQQQ_Return",
    plot_Ridge_regression_line=False,
    Ridge_column=None,
    plot_RidgeCV_regression_line=True,
    RidgeCV_column="TQQQ_Return",
    regression_constant=True,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

model = run_linear_regression(
    df=qqq_tqqq_aligned,
    x_plot_column="QQQ_Return",
    y_plot_column="TQQQ_Return",
    regression_model="OLS-statsmodels",
    regression_constant=True,
)

print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:            TQQQ_Return   R-squared:                       0.997
Model:                            OLS   Adj. R-squared:                  0.997
Method:                 Least Squares   F-statistic:                 1.494e+06
Date:                Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                        21:59:08   Log-Likelihood:                 19431.
No. Observations:                4050   AIC:                        -3.886e+04
Df Residuals:                    4048   BIC:                        -3.884e+04
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const      -8.629e-05   3.14e-05     -2.746      0.006      -0.000   -2.47e-05
QQQ_Return     2.9553      0.002   1222.452      0.000       2.951       2.960
==============================================================================
Omnibus:                     5279.605   Durbin-Watson:                   2.567
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          9197656.554
Skew:                          -6.346   Prob(JB):                         0.00
Kurtosis:                     236.117   Cond. No.                         77.1
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Visually, this plot makes sense and we can see that there is a strong clustering of points, but we double check with the regression, regressing the TQQQ daily return (y) on the QQQ daily return (X).

Given the above result, with a coefficient of 2.96 and an R^2 of 0.997 (based on the statsmodels OLS regression), we can say that TQQQ does in fact return ~3x QQQ. We would also intuitively expect the coefficient to be 0, and it is nearly 0.

Interestingly, the coefficient varies between OLS and Ridge cross-validation, and both are less than 3.

Extrapolate Data (QQQ & TQQQ) #

With the above coefficient, we will now extrapolate the returns of QQQ to backfill the data from the inception of QQQ in 1999 to the inception of TQQQ in 2010 to expand our dataset of returns. For this, we’ll use the coefficient of 2.96 that we found in the regression results above.

# Set leverage multiplier based on regression coefficient
LEVERAGE_MULTIPLIER = model.params[1]

# Merge dataframes and extrapolate return values for QQQ back to 1999 using the leverage multiplier
qqq_tqqq_extrap = qqq[["QQQ_Close"]].merge(tqqq[["TQQQ_Close"]], left_index=True, right_index=True, how='left')

etfs = ["QQQ", "TQQQ"]

# Calculate cumulative returns
for etf in etfs:
    qqq_tqqq_extrap[f"{etf}_Return"] = qqq_tqqq_extrap[f"{etf}_Close"].pct_change()

# Extrapolate TQQQ returns for missing values
qqq_tqqq_extrap["TQQQ_Return"] = qqq_tqqq_extrap["TQQQ_Return"].fillna(LEVERAGE_MULTIPLIER * qqq_tqqq_extrap["QQQ_Return"])

# Find the first valid TQQQ_Close index and value
first_valid_idx = qqq_tqqq_extrap['TQQQ_Close'].first_valid_index()
print(first_valid_idx)
first_valid_price = qqq_tqqq_extrap.loc[first_valid_idx, 'TQQQ_Close']
print(first_valid_price)

2010-02-11 00:00:00
0.21627600491046906

Before we extrapolate, let’s first look at the data we have for QQQ and TQQQ around the inception of TQQQ in 2010:

# Check values around the first valid index
pandas_set_decimal_places(4)
display(qqq_tqqq_extrap.loc["2010-02-08":"2010-02-13"])

Now, backfill the data for the TQQQ close price:

# Iterate through the dataframe backwards
for i in range(qqq_tqqq_extrap.index.get_loc(first_valid_idx) - 1, -1, -1):
    
    # The return that led to the price the next day
    current_return = qqq_tqqq_extrap.iloc[i + 1]['TQQQ_Return']

    # Get the next day's price
    next_price = qqq_tqqq_extrap.iloc[i + 1]['TQQQ_Close']
    
    # Price_{t} = Price_{t+1} / (1 + Return_{t})
    qqq_tqqq_extrap.loc[qqq_tqqq_extrap.index[i], 'TQQQ_Close'] = next_price / (1 + current_return)

Finally, confirm the values are correct:

# Confirm values around the first valid index after extrapolation
display(qqq_tqqq_extrap.loc["2010-02-08":"2010-02-13"])

And the complete DataFrame with the extrapolated values:

pandas_set_decimal_places(2)
display(qqq_tqqq_extrap)

After the extrapolation, we now have the following plots for the prices, cumulative returns, and drawdowns:

etfs = ["QQQ", "TQQQ"]

# Calculate cumulative returns
for etf in etfs:
    qqq_tqqq_extrap[f"{etf}_Return"] = qqq_tqqq_extrap[f"{etf}_Close"].pct_change()
    qqq_tqqq_extrap[f"{etf}_Cumulative_Return"] = (1 + qqq_tqqq_extrap[f"{etf}_Return"]).cumprod() - 1
    qqq_tqqq_extrap[f"{etf}_Cumulative_Return_Plus_One"] = 1 + qqq_tqqq_extrap[f"{etf}_Cumulative_Return"]
    qqq_tqqq_extrap[f"{etf}_Rolling_Max"] = qqq_tqqq_extrap[f"{etf}_Cumulative_Return_Plus_One"].cummax()
    qqq_tqqq_extrap[f"{etf}_Drawdown"] = qqq_tqqq_extrap[f"{etf}_Cumulative_Return_Plus_One"] / qqq_tqqq_extrap[f"{etf}_Rolling_Max"] - 1
    qqq_tqqq_extrap.drop(columns=[f"{etf}_Cumulative_Return_Plus_One", f"{etf}_Rolling_Max"], inplace=True)

plot_time_series(
    df=qqq_tqqq_extrap,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["QQQ_Close"],
    title="QQQ Close Price",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=2,
    x_tick_rotation=30,
    y_label="Price ($)",
    y_format="Decimal",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=False,
    export_plot=False,
    plot_file_name=None,
)

plot_time_series(
    df=qqq_tqqq_extrap,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["TQQQ_Close"],
    title="TQQQ Close Price",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=2,
    x_tick_rotation=30,
    y_label="Price ($)",
    y_format="Decimal",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=False,
    export_plot=False,
    plot_file_name=None,
)

plot_time_series(
    df=qqq_tqqq_extrap,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["QQQ_Cumulative_Return", "TQQQ_Cumulative_Return"],
    title="Cumulative Returns",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=2,
    x_tick_rotation=30,
    y_label="Cumulative Return",
    y_format="Decimal",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

plot_time_series(
    df=qqq_tqqq_extrap,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["QQQ_Drawdown", "TQQQ_Drawdown"],
    title="Drawdowns",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=2,
    x_tick_rotation=30,
    y_label="Drawdown",
    y_format="Percentage",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

qqq_extrap_sum_stats = summary_stats(
    fund_list=["QQQ"],
    df=qqq_tqqq_extrap[["QQQ_Return"]],
    period="Daily",
    use_calendar_days=False,
    excel_export=False,
    pickle_export=False,
    output_confirmation=False,
)

tqqq_extrap_sum_stats = summary_stats(
    fund_list=["TQQQ"],
    df=qqq_tqqq_extrap[["TQQQ_Return"]],
    period="Daily",
    use_calendar_days=False,
    excel_export=False,
    pickle_export=False,
    output_confirmation=False,
)

sum_stats = pd.concat([qqq_sum_stats, tqqq_sum_stats, qqq_extrap_sum_stats, tqqq_extrap_sum_stats])
sum_stats.index = ["QQQ (2010 - Present)", "TQQQ (2010 - Present)", "QQQ (1999 - Present)", "TQQQ Extrapolated (1999 - Present)"]

display(sum_stats)

A few quick comments before we look at rolling returns:

• The cumulative return for TQQQ is less than that of QQQ - which is starkly different from the plot beginning in 2010 at the inception of TQQQ. So the return path really matters here.
• The drawdown for TQQQ is nearly 100%… which also represents nearly a total loss of capital for any allocation to the extrap-TQQQ. Furthermore, as we walk forward through time (2002, 2003, … etc.), there is really no reason to believe that the returns would ever recover (even partially). So while we can look at the rolling returns and see how they compare to the 3x return of QQQ, we should keep in mind that the drawdown post-1999 is so severe that it would be very difficult for any investor to hold through it.
• The recovery time for QQQ was more than 5,000 days, or ~14 years. Note that this is calendar days, not trading days. While returns have been great for QQQ since 2016, the 14 year dry spell is a reminder of just how large the tech bubble was.
• The extrapolated TQQQ data remains in a drawdown and has never recovered to make new highs (as of March 2026).

Plot Rolling Returns (QQQ & TQQQ) #

Next, we will consider the following:

• Histogram and scatter plots of the rolling returns of QQQ and TQQQ
• Regressions to establish a “leverage factor” for the rolling returns
• The deviation from a 3x return for each time period

For this set of regressions, we will also allow the constant. First, we need the rolling returns for various time periods:

# Define rolling windows in trading days
rolling_windows = {
    '1d': 1,      # 1 day
    '1w': 5,      # 1 week (5 trading days)
    '1m': 21,     # 1 month (~21 trading days)
    '3m': 63,     # 3 months (~63 trading days)
    '6m': 126,    # 6 months (~126 trading days)
    '1y': 252,    # 1 year (~252 trading days)
    '2y': 504,    # 2 years (~504 trading days)
    '3y': 756,    # 3 years (~756 trading days)
    '4y': 1008,   # 4 years (~1008 trading days)
    '5y': 1260,   # 5 years (~1260 trading days)
}

# Calculate rolling returns for each ETF and each window
for etf in etfs:
    for period_name, window in rolling_windows.items():
        qqq_tqqq_extrap[f"{etf}_Rolling_Return_{period_name}"] = (
            qqq_tqqq_extrap[f"{etf}_Close"].pct_change(periods=window)
        )

This gives us the following series of histograms, scatter plots, and regression model results:

# Create a dataframe to hold rolling returns stats
rolling_returns_stats = pd.DataFrame()

for period_name, window in rolling_windows.items():
    plot_histogram(
        df=qqq_tqqq_extrap,
        plot_columns=[f"QQQ_Rolling_Return_{period_name}", f"TQQQ_Rolling_Return_{period_name}"],
        title=f"QQQ & TQQQ {period_name} Rolling Returns",
        x_label="Rolling Return",
        x_tick_spacing="Auto",
        x_tick_rotation=30,
        y_label="# Of Datapoints",
        y_tick_spacing="Auto",
        y_tick_rotation=0,
        grid=True,
        legend=True,
        export_plot=False,
        plot_file_name=None,
    )

    plot_scatter(
        df=qqq_tqqq_extrap,
        x_plot_column=f"QQQ_Rolling_Return_{period_name}",
        y_plot_columns=[f"TQQQ_Rolling_Return_{period_name}"],
        title=f"QQQ & TQQQ {period_name} Rolling Returns",
        x_label="QQQ Rolling Return",
        x_format="Decimal",
        x_format_decimal_places=2,
        x_tick_spacing="Auto",
        x_tick_rotation=30,
        y_label="TQQQ Rolling Return",
        y_format="Decimal",
        y_format_decimal_places=2,
        y_tick_spacing="Auto",
        y_tick_rotation=0,
        plot_OLS_regression_line=True,
        OLS_column=f"TQQQ_Rolling_Return_{period_name}",
        plot_Ridge_regression_line=False,
        Ridge_column=None,
        plot_RidgeCV_regression_line=True,
        RidgeCV_column=f"TQQQ_Rolling_Return_{period_name}",
        regression_constant=True,
        grid=True,
        legend=True,
        export_plot=False,
        plot_file_name=None,
    )

    # Run OLS regression with statsmodels
    model = run_linear_regression(
        df=qqq_tqqq_extrap,
        x_plot_column=f"QQQ_Rolling_Return_{period_name}",
        y_plot_column=f"TQQQ_Rolling_Return_{period_name}",
        regression_model="OLS-statsmodels",
        regression_constant=True,
    )
    print(model.summary())

    # Add the regression results to the rolling returns stats dataframe
    intercept = model.params[0]
    intercept_pvalue = model.pvalues[0]   # p-value for Intercept
    slope = model.params[1]
    slope_pvalue = model.pvalues[1]       # p-value for QQQ_Return
    r_squared = model.rsquared

    # Calc skew
    return_ratio = qqq_tqqq_extrap[f'TQQQ_Rolling_Return_{period_name}'] / qqq_tqqq_extrap[f'QQQ_Rolling_Return_{period_name}']
    skew = return_ratio.skew()

    # Calc conditional symmetry
    up_markets = qqq_tqqq_extrap[qqq_tqqq_extrap[f'QQQ_Rolling_Return_{period_name}'] > 0]
    down_markets = qqq_tqqq_extrap[qqq_tqqq_extrap[f'QQQ_Rolling_Return_{period_name}'] <= 0]

    avg_beta_up = (up_markets[f'TQQQ_Rolling_Return_{period_name}'] / up_markets[f'QQQ_Rolling_Return_{period_name}']).mean()
    avg_beta_down = (down_markets[f'TQQQ_Rolling_Return_{period_name}'] / down_markets[f'QQQ_Rolling_Return_{period_name}']).mean()

    asymmetry = avg_beta_up - avg_beta_down

    rolling_returns_slope_int = pd.DataFrame({
        "Period": period_name,
        "Intercept": [intercept],
        # "Intercept_PValue": [intercept_pvalue],
        "Slope": [slope],
        # "Slope_PValue": [slope_pvalue],
        "R_Squared": [r_squared],
        "Return Skew": [skew],
        "Average Upside Beta": [avg_beta_up],
        "Average Downside Beta": [avg_beta_down],
        "Asymmetry": [asymmetry]
    })

    rolling_returns_stats = pd.concat([rolling_returns_stats, rolling_returns_slope_int])

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_1d   R-squared:                       0.999
Model:                                OLS   Adj. R-squared:                  0.999
Method:                     Least Squares   F-statistic:                 7.219e+06
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:12   Log-Likelihood:                 34378.
No. Observations:                    6799   AIC:                        -6.875e+04
Df Residuals:                        6797   BIC:                        -6.874e+04
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                 -5.138e-05   1.87e-05     -2.748      0.006    -8.8e-05   -1.47e-05
QQQ_Rolling_Return_1d     2.9552      0.001   2686.888      0.000       2.953       2.957
==============================================================================
Omnibus:                    10196.347   Durbin-Watson:                   2.565
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         43934832.029
Skew:                          -8.279   Prob(JB):                         0.00
Kurtosis:                     396.463   Cond. No.                         58.8
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_1w   R-squared:                       0.994
Model:                                OLS   Adj. R-squared:                  0.994
Method:                     Least Squares   F-statistic:                 1.117e+06
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:14   Log-Likelihood:                 23171.
No. Observations:                    6795   AIC:                        -4.634e+04
Df Residuals:                        6793   BIC:                        -4.632e+04
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                    -0.0008   9.72e-05     -8.359      0.000      -0.001      -0.001
QQQ_Rolling_Return_1w     2.9525      0.003   1056.784      0.000       2.947       2.958
==============================================================================
Omnibus:                     2840.677   Durbin-Watson:                   0.932
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           565062.032
Skew:                          -0.863   Prob(JB):                         0.00
Kurtosis:                      47.641   Cond. No.                         28.8
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_1m   R-squared:                       0.982
Model:                                OLS   Adj. R-squared:                  0.982
Method:                     Least Squares   F-statistic:                 3.698e+05
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:16   Log-Likelihood:                 14865.
No. Observations:                    6779   AIC:                        -2.973e+04
Df Residuals:                        6777   BIC:                        -2.971e+04
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                    -0.0037      0.000    -11.098      0.000      -0.004      -0.003
QQQ_Rolling_Return_1m     2.9306      0.005    608.073      0.000       2.921       2.940
==============================================================================
Omnibus:                     1630.144   Durbin-Watson:                   0.296
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            69176.713
Skew:                           0.358   Prob(JB):                         0.00
Kurtosis:                      18.633   Cond. No.                         14.7
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_3m   R-squared:                       0.958
Model:                                OLS   Adj. R-squared:                  0.958
Method:                     Least Squares   F-statistic:                 1.551e+05
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:18   Log-Likelihood:                 7953.7
No. Observations:                    6737   AIC:                        -1.590e+04
Df Residuals:                        6735   BIC:                        -1.589e+04
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                    -0.0083      0.001     -8.874      0.000      -0.010      -0.006
QQQ_Rolling_Return_3m     2.9849      0.008    393.789      0.000       2.970       3.000
==============================================================================
Omnibus:                     3466.652   Durbin-Watson:                   0.105
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            79721.487
Skew:                           1.963   Prob(JB):                         0.00
Kurtosis:                      19.389   Cond. No.                         8.38
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_6m   R-squared:                       0.916
Model:                                OLS   Adj. R-squared:                  0.916
Method:                     Least Squares   F-statistic:                 7.252e+04
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:19   Log-Likelihood:                 2613.7
No. Observations:                    6674   AIC:                            -5223.
Df Residuals:                        6672   BIC:                            -5210.
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                    -0.0097      0.002     -4.549      0.000      -0.014      -0.005
QQQ_Rolling_Return_6m     3.0397      0.011    269.293      0.000       3.018       3.062
==============================================================================
Omnibus:                     3659.091   Durbin-Watson:                   0.056
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            60225.360
Skew:                           2.263   Prob(JB):                         0.00
Kurtosis:                      17.003   Cond. No.                         5.66
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_1y   R-squared:                       0.880
Model:                                OLS   Adj. R-squared:                  0.880
Method:                     Least Squares   F-statistic:                 4.786e+04
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:21   Log-Likelihood:                -892.41
No. Observations:                    6548   AIC:                             1789.
Df Residuals:                        6546   BIC:                             1802.
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                     0.0189      0.004      5.003      0.000       0.012       0.026
QQQ_Rolling_Return_1y     2.8372      0.013    218.775      0.000       2.812       2.863
==============================================================================
Omnibus:                     3497.781   Durbin-Watson:                   0.037
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            68281.594
Skew:                           2.124   Prob(JB):                         0.00
Kurtosis:                      18.239   Cond. No.                         3.85
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_2y   R-squared:                       0.848
Model:                                OLS   Adj. R-squared:                  0.848
Method:                     Least Squares   F-statistic:                 3.521e+04
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:22   Log-Likelihood:                -4425.9
No. Observations:                    6296   AIC:                             8856.
Df Residuals:                        6294   BIC:                             8869.
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                     0.0092      0.007      1.243      0.214      -0.005       0.024
QQQ_Rolling_Return_2y     3.1310      0.017    187.631      0.000       3.098       3.164
==============================================================================
Omnibus:                     1596.134   Durbin-Watson:                   0.019
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4146.775
Skew:                           1.367   Prob(JB):                         0.00
Kurtosis:                       5.886   Cond. No.                         2.89
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_3y   R-squared:                       0.805
Model:                                OLS   Adj. R-squared:                  0.804
Method:                     Least Squares   F-statistic:                 2.487e+04
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:24   Log-Likelihood:                -6694.8
No. Observations:                    6044   AIC:                         1.339e+04
Df Residuals:                        6042   BIC:                         1.341e+04
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                    -0.0599      0.013     -4.764      0.000      -0.085      -0.035
QQQ_Rolling_Return_3y     3.3318      0.021    157.695      0.000       3.290       3.373
==============================================================================
Omnibus:                      858.024   Durbin-Watson:                   0.015
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1472.819
Skew:                           0.940   Prob(JB):                         0.00
Kurtosis:                       4.521   Cond. No.                         2.66
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_4y   R-squared:                       0.781
Model:                                OLS   Adj. R-squared:                  0.781
Method:                     Least Squares   F-statistic:                 2.064e+04
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:26   Log-Likelihood:                -8794.2
No. Observations:                    5792   AIC:                         1.759e+04
Df Residuals:                        5790   BIC:                         1.761e+04
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                    -0.2930      0.021    -13.695      0.000      -0.335      -0.251
QQQ_Rolling_Return_4y     3.9329      0.027    143.656      0.000       3.879       3.987
==============================================================================
Omnibus:                      200.096   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              104.261
Skew:                           0.140   Prob(JB):                     2.29e-23
Kurtosis:                       2.405   Cond. No.                         2.66
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                              OLS Regression Results                              
==================================================================================
Dep. Variable:     TQQQ_Rolling_Return_5y   R-squared:                       0.743
Model:                                OLS   Adj. R-squared:                  0.743
Method:                     Least Squares   F-statistic:                 1.598e+04
Date:                    Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                            21:59:28   Log-Likelihood:                -12084.
No. Observations:                    5540   AIC:                         2.417e+04
Df Residuals:                        5538   BIC:                         2.418e+04
Df Model:                               1                                         
Covariance Type:                nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                    -0.8875      0.044    -19.973      0.000      -0.975      -0.800
QQQ_Rolling_Return_5y     5.2051      0.041    126.424      0.000       5.124       5.286
==============================================================================
Omnibus:                      315.142   Durbin-Watson:                   0.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              460.565
Skew:                           0.499   Prob(JB):                    9.76e-101
Kurtosis:                       4.000   Cond. No.                         2.73
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

You’re welcome to digest each plot, but here’s my observations on the above results:

• 1d: TQQQ tracks QQQ as expected (it’s a 3x daily return leveraged ETF after all), with a regression coefficient of 2.96 and an R^2 of 0.997, and we extrapolated half the data with the same coefficient.
• 1w: Essentially the same as above. A few outliers, but the regression coefficient is still 2.95 with an R^2 of 0.994. We see a slight skew toward the positive in the rolling returns.
• 1m: The skew toward the positive is more pronounced, and we see more outliers. The regression coefficient has decreased to 2.93 and the R^2 has dropped to 0.98, which is still very high, but we are starting to see some dispersion in the returns.
• 3m: The skew toward the positive is even more pronounced, and we see even more outliers. The regression coefficient has increased, to 2.98 and the R^2 has dropped to 0.96.
• 6m: The skew toward the positive is very pronounced, and we see a significant number of outliers with pronounced curvanture in the plot. The regression coefficient has increased again, to 3.4 and the R^2 has dropped to 0.92.
• 1y: At this point, based on the plot and the regression results, we can start to see that the returns of TQQQ are no longer tracking 3x the returns of QQQ as closely as they did in the shorter time periods. The regression coefficient has is now 2.84 and the R^2 has dropped to 0.88.
• 4y and 5y: We can see that there are periods where the rolling returns of TQQQ are significantly higher and lower than 3x the returns of QQQ, which is consistent with the idea of volatility decay.

For 4y, based on the regression results, we see that if the rolling return of QQQ was 0, then we would expect a return of -0.30 for TQQQ.

$$ r_{TQQQ} = -0.30 + 3.93 \times r_{QQQ} = -0.30 + 3.93 \times 0 = -0.30 $$

On the other end of the spectrum, if the rolling return of QQQ was 1, then we would expect a return of:

$$ r_{TQQQ} = -0.30 + 3.93 \times r_{QQQ} = -0.30 + 3.93 \times 1 = 3.63 $$

In general, the positive skew of the rolling returns of TQQQ relative to QQQ is related to the general postive return performance of QQQ. With sustained positive returns, the leverage effect of TQQQ will amplify those returns, leading to a positive skew. However, during periods of negative returns for QQQ, the leverage effect will also amplify those losses, leading to a negative skew, and to the limit of a cumulative return of -1, or a 100% loss. The overall skewness of the rolling returns will depend on the balance of these positive and negative periods.

Rolling Returns Deviation (QQQ & TQQQ) #

Next, we will the rolling returns deviation from the expected 3x return for each time period. This will give us a better picture of the volatility decay effect and how it changes over different time horizons.

rolling_returns_stats["Return_Deviation_From_3x"] = rolling_returns_stats["Slope"] - 3.0
pandas_set_decimal_places(3)
display(rolling_returns_stats.set_index("Period"))

plot_scatter(
    df=rolling_returns_stats,
    x_plot_column="Period",
    y_plot_columns=["Return_Deviation_From_3x"],
    title="TQQQ Deviation from Perfect 3x Leverage by Time Period",
    x_label="Time Period",
    x_format="String",
    x_format_decimal_places=0,
    x_tick_spacing=1,
    x_tick_rotation=0,
    y_label="Deviation from 3x Leverage",
    y_format="Decimal",
    y_format_decimal_places=1,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    plot_OLS_regression_line=False,
    OLS_column=None,
    plot_Ridge_regression_line=False,
    Ridge_column=None,
    plot_RidgeCV_regression_line=False,
    RidgeCV_column=None,
    regression_constant=False,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

plot_scatter(
    df=rolling_returns_stats,
    x_plot_column="Period",
    y_plot_columns=["Slope"],
    title="TQQQ Slope by Time Period",
    x_label="Time Period",
    x_format="String",
    x_format_decimal_places=0,
    x_tick_spacing=1,
    x_tick_rotation=0,
    y_label="Slope",
    y_format="Decimal",
    y_format_decimal_places=1,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    plot_OLS_regression_line=False,
    OLS_column=None,
    plot_Ridge_regression_line=False,
    Ridge_column=None,
    plot_RidgeCV_regression_line=False,
    RidgeCV_column=None,
    regression_constant=False,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

plot_scatter(
    df=rolling_returns_stats,
    x_plot_column="Period",
    y_plot_columns=["Intercept"],
    title="Intercept by Time Period",
    x_label="Time Period",
    x_format="String",
    x_format_decimal_places=0,
    x_tick_spacing=1,
    x_tick_rotation=0,
    y_label="Intercept",
    y_format="Decimal",
    y_format_decimal_places=1,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    plot_OLS_regression_line=False,
    OLS_column=None,
    plot_Ridge_regression_line=False,
    Ridge_column=None,
    plot_RidgeCV_regression_line=False,
    RidgeCV_column=None,
    regression_constant=False,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

display(rolling_returns_stats.set_index("Period"))

This is very interesting. Up to 1 year, there is minimal difference between the mean TQQQ 1 year rolling return and the hypothetical 3x leverage, with an R^2 of greater than 0.9.

However, as we extend the time period, we see that

• The “leverage factor” increases significantly, resulting in a deviation from the perfect 3x leverage.
• The intercept also begins to deviate significantly from 0.

The above highlight the impact of volatility magnification over longer time horizons. This phenomenon is happening likely due to the positive returns that QQQ has achieved since 2010 - resulting in TQQQ compounding at a much higher rate than 3x - but it may and likely is not exhibited by other 3x leveraged ETFs that have not had the same positive return profile as QQQ.

With the above results, the next logical question is, when is the opportune time to buy a 3x leveraged ETF like TQQQ? To answer this, we will look a the drawdown levels of TQQQ and the subsequent returns over various time horizons.

Rolling Returns Following Drawdowns (QQQ & TQQQ) #

We will identify the drawdown levels of TQQQ and then look at the subsequent rolling returns over various time horizons.

# Copy DataFrame
qqq_tqqq_extrap_future = qqq_tqqq_extrap.copy()

# Create a list of drawdown levels to analyze
drawdown_levels = [-0.10, -0.20, -0.30, -0.40, -0.50, -0.60, -0.70, -0.80, -0.90]

# Shift the rolling return columns by the number of days in the rolling window to get the returns following the drawdown
for etf in etfs:
    for period_name, window in rolling_windows.items():
        qqq_tqqq_extrap_future[f"{etf}_Rolling_Future_Return_{period_name}"] = qqq_tqqq_extrap_future[f"{etf}_Rolling_Return_{period_name}"].shift(-window)

Now, we can analyze the future rolling returns following specific drawdown levels:

# Create a dataframe to hold rolling returns stats
rolling_returns_drawdown_stats = pd.DataFrame()

for drawdown in drawdown_levels:

    for period_name, window in rolling_windows.items():

        try:
            plot_histogram(
                df=qqq_tqqq_extrap_future[qqq_tqqq_extrap_future["TQQQ_Drawdown"] <= drawdown],
                plot_columns=[f"QQQ_Rolling_Future_Return_{period_name}", f"TQQQ_Rolling_Future_Return_{period_name}"],
                title=f"QQQ & TQQQ {period_name} Rolling Future Returns Post {drawdown} TQQQ Drawdown",
                x_label="Rolling Return",
                x_tick_spacing="Auto",
                x_tick_rotation=30,
                y_label="# Of Datapoints",
                y_tick_spacing="Auto",
                y_tick_rotation=0,
                grid=True,
                legend=True,
                export_plot=False,
                plot_file_name=None,
            )

            plot_scatter(
                df=qqq_tqqq_extrap_future[qqq_tqqq_extrap_future["TQQQ_Drawdown"] <= drawdown],
                x_plot_column=f"QQQ_Rolling_Future_Return_{period_name}",
                y_plot_columns=[f"TQQQ_Rolling_Future_Return_{period_name}"],
                title=f"QQQ & TQQQ {period_name} Rolling Future Returns Post {drawdown} TQQQ Drawdown",
                x_label="QQQ Rolling Return",
                x_format="Decimal",
                x_format_decimal_places=2,
                x_tick_spacing="Auto",
                x_tick_rotation=30,
                y_label="TQQQ Rolling Return",
                y_format="Decimal",
                y_format_decimal_places=2,
                y_tick_spacing="Auto",
                y_tick_rotation=0,
                plot_OLS_regression_line=True,
                OLS_column=f"TQQQ_Rolling_Future_Return_{period_name}",
                plot_Ridge_regression_line=False,
                Ridge_column=None,
                plot_RidgeCV_regression_line=True,
                RidgeCV_column=f"TQQQ_Rolling_Future_Return_{period_name}",
                regression_constant=True,
                grid=True,
                legend=True,
                export_plot=False,
                plot_file_name=None,
            )

            # Run OLS regression with statsmodels
            model = run_linear_regression(
                df=qqq_tqqq_extrap_future[qqq_tqqq_extrap_future["TQQQ_Drawdown"] <= drawdown],
                x_plot_column=f"QQQ_Rolling_Future_Return_{period_name}",
                y_plot_column=f"TQQQ_Rolling_Future_Return_{period_name}",
                regression_model="OLS-statsmodels",
                regression_constant=True,
            )
            print(model.summary())

            # Filter by drawdown
            drawdown_filter = qqq_tqqq_extrap_future[qqq_tqqq_extrap_future["TQQQ_Drawdown"] <= drawdown]

            # Filter by period, drop rows with missing values
            future_filter = drawdown_filter[[f"TQQQ_Rolling_Future_Return_{period_name}"]].dropna()

            # Find length of future dataframe
            future_length = len(future_filter)

            # Find length of future dataframe where return is positive
            positive_future_length = len(future_filter[future_filter[f"TQQQ_Rolling_Future_Return_{period_name}"] > 0])

            # Calculate percentage of future returns that are positive
            positive_future_percentage = (positive_future_length / future_length) if future_length > 0 else 0

            # Add the regression results to the rolling returns stats dataframe
            intercept = model.params[0]
            # intercept_pvalue = model.pvalues[0]   # p-value for Intercept
            slope = model.params[1]
            # slope_pvalue = model.pvalues[1]       # p-value for Slope
            r_squared = model.rsquared

            rolling_returns_slope_int = pd.DataFrame({
                "Drawdown": drawdown,
                "Period": period_name,
                "Intercept": [intercept],
                # "Intercept_PValue": [intercept_pvalue],
                "Slope": [slope],
                # "Slope_PValue": [slope_pvalue],
                "R_Squared": [r_squared],
                "Positive_Future_Percentage": [positive_future_percentage],
            })
            
            rolling_returns_drawdown_stats = pd.concat([rolling_returns_drawdown_stats, rolling_returns_slope_int])

        except:
            print(f"Not enough data points for drawdown level {drawdown} and period {period_name} to run regression.")

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 6.829e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:30   Log-Likelihood:                 33568.
No. Observations:                           6653   AIC:                        -6.713e+04
Df Residuals:                               6651   BIC:                        -6.712e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -5.251e-05   1.91e-05     -2.748      0.006      -9e-05    -1.5e-05
QQQ_Rolling_Future_Return_1d     2.9552      0.001   2613.230      0.000       2.953       2.957
==============================================================================
Omnibus:                     9921.143   Durbin-Watson:                   2.565
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         41149977.059
Skew:                          -8.188   Prob(JB):                         0.00
Kurtosis:                     387.936   Cond. No.                         59.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 1.089e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:32   Log-Likelihood:                 22728.
No. Observations:                           6649   AIC:                        -4.545e+04
Df Residuals:                               6647   BIC:                        -4.544e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0008   9.75e-05     -8.250      0.000      -0.001      -0.001
QQQ_Rolling_Future_Return_1w     2.9527      0.003   1043.680      0.000       2.947       2.958
==============================================================================
Omnibus:                     2702.988   Durbin-Watson:                   0.939
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           587592.935
Skew:                          -0.778   Prob(JB):                         0.00
Kurtosis:                      49.028   Cond. No.                         29.1
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.982
Model:                                       OLS   Adj. R-squared:                  0.982
Method:                            Least Squares   F-statistic:                 3.706e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:33   Log-Likelihood:                 14709.
No. Observations:                           6633   AIC:                        -2.941e+04
Df Residuals:                               6631   BIC:                        -2.940e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0035      0.000    -10.565      0.000      -0.004      -0.003
QQQ_Rolling_Future_Return_1m     2.9305      0.005    608.737      0.000       2.921       2.940
==============================================================================
Omnibus:                     1682.131   Durbin-Watson:                   0.312
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            81050.154
Skew:                           0.394   Prob(JB):                         0.00
Kurtosis:                      20.107   Cond. No.                         14.9
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.957
Model:                                       OLS   Adj. R-squared:                  0.957
Method:                            Least Squares   F-statistic:                 1.460e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:35   Log-Likelihood:                 7955.3
No. Observations:                           6591   AIC:                        -1.591e+04
Df Residuals:                               6589   BIC:                        -1.589e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0076      0.001     -8.295      0.000      -0.009      -0.006
QQQ_Rolling_Future_Return_3m     2.9584      0.008    382.045      0.000       2.943       2.974
==============================================================================
Omnibus:                     3406.252   Durbin-Watson:                   0.113
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            86494.126
Skew:                           1.943   Prob(JB):                         0.00
Kurtosis:                      20.316   Cond. No.                         8.69
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.921
Model:                                       OLS   Adj. R-squared:                  0.921
Method:                            Least Squares   F-statistic:                 7.570e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:37   Log-Likelihood:                 3158.3
No. Observations:                           6528   AIC:                            -6313.
Df Residuals:                               6526   BIC:                            -6299.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0042      0.002     -2.170      0.030      -0.008      -0.000
QQQ_Rolling_Future_Return_6m     2.9628      0.011    275.145      0.000       2.942       2.984
==============================================================================
Omnibus:                     4159.114   Durbin-Watson:                   0.065
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           100812.187
Skew:                           2.648   Prob(JB):                         0.00
Kurtosis:                      21.509   Cond. No.                         5.85
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.893
Model:                                       OLS   Adj. R-squared:                  0.893
Method:                            Least Squares   F-statistic:                 5.327e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:38   Log-Likelihood:                -135.02
No. Observations:                           6402   AIC:                             274.0
Df Residuals:                               6400   BIC:                             287.6
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                            0.0227      0.003      6.620      0.000       0.016       0.029
QQQ_Rolling_Future_Return_1y     2.8086      0.012    230.806      0.000       2.785       2.832
==============================================================================
Omnibus:                     2635.410   Durbin-Watson:                   0.052
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            29285.399
Skew:                           1.658   Prob(JB):                         0.00
Kurtosis:                      12.939   Cond. No.                         4.00
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.848
Model:                                       OLS   Adj. R-squared:                  0.848
Method:                            Least Squares   F-statistic:                 3.424e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:40   Log-Likelihood:                -4264.9
No. Observations:                           6150   AIC:                             8534.
Df Residuals:                               6148   BIC:                             8547.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0192      0.008     -2.513      0.012      -0.034      -0.004
QQQ_Rolling_Future_Return_2y     3.2011      0.017    185.033      0.000       3.167       3.235
==============================================================================
Omnibus:                     1671.115   Durbin-Watson:                   0.019
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4642.964
Skew:                           1.436   Prob(JB):                         0.00
Kurtosis:                       6.142   Cond. No.                         3.02
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.811
Model:                                       OLS   Adj. R-squared:                  0.811
Method:                            Least Squares   F-statistic:                 2.527e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:42   Log-Likelihood:                -6371.3
No. Observations:                           5898   AIC:                         1.275e+04
Df Residuals:                               5896   BIC:                         1.276e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.1589      0.013    -12.137      0.000      -0.185      -0.133
QQQ_Rolling_Future_Return_3y     3.5019      0.022    158.976      0.000       3.459       3.545
==============================================================================
Omnibus:                      871.703   Durbin-Watson:                   0.015
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1536.806
Skew:                           0.961   Prob(JB):                         0.00
Kurtosis:                       4.601   Cond. No.                         2.86
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.783
Model:                                       OLS   Adj. R-squared:                  0.783
Method:                            Least Squares   F-statistic:                 2.034e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:44   Log-Likelihood:                -8503.0
No. Observations:                           5646   AIC:                         1.701e+04
Df Residuals:                               5644   BIC:                         1.702e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.4276      0.023    -18.927      0.000      -0.472      -0.383
QQQ_Rolling_Future_Return_4y     4.0962      0.029    142.630      0.000       4.040       4.153
==============================================================================
Omnibus:                      127.164   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               79.194
Skew:                           0.148   Prob(JB):                     6.36e-18
Kurtosis:                       2.501   Cond. No.                         2.85
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.745
Model:                                       OLS   Adj. R-squared:                  0.745
Method:                            Least Squares   F-statistic:                 1.577e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:46   Log-Likelihood:                -11731.
No. Observations:                           5394   AIC:                         2.347e+04
Df Residuals:                               5392   BIC:                         2.348e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.1160      0.047    -23.806      0.000      -1.208      -1.024
QQQ_Rolling_Future_Return_5y     5.3968      0.043    125.578      0.000       5.313       5.481
==============================================================================
Omnibus:                      276.642   Durbin-Watson:                   0.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              406.454
Skew:                           0.460   Prob(JB):                     5.49e-89
Kurtosis:                       3.980   Cond. No.                         2.90
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 6.607e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:47   Log-Likelihood:                 33141.
No. Observations:                           6576   AIC:                        -6.628e+04
Df Residuals:                               6574   BIC:                        -6.626e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -5.312e-05   1.93e-05     -2.748      0.006    -9.1e-05   -1.52e-05
QQQ_Rolling_Future_Return_1d     2.9552      0.001   2570.336      0.000       2.953       2.957
==============================================================================
Omnibus:                     9776.502   Durbin-Watson:                   2.565
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         39728976.844
Skew:                          -8.139   Prob(JB):                         0.00
Kurtosis:                     383.436   Cond. No.                         59.5
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 1.070e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:49   Log-Likelihood:                 22472.
No. Observations:                           6572   AIC:                        -4.494e+04
Df Residuals:                               6570   BIC:                        -4.493e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0008   9.79e-05     -8.045      0.000      -0.001      -0.001
QQQ_Rolling_Future_Return_1w     2.9518      0.003   1034.395      0.000       2.946       2.957
==============================================================================
Omnibus:                     2706.760   Durbin-Watson:                   0.933
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           596172.137
Skew:                          -0.802   Prob(JB):                         0.00
Kurtosis:                      49.632   Cond. No.                         29.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.983
Model:                                       OLS   Adj. R-squared:                  0.983
Method:                            Least Squares   F-statistic:                 3.706e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:50   Log-Likelihood:                 14666.
No. Observations:                           6556   AIC:                        -2.933e+04
Df Residuals:                               6554   BIC:                        -2.931e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0035      0.000    -10.838      0.000      -0.004      -0.003
QQQ_Rolling_Future_Return_1m     2.9225      0.005    608.738      0.000       2.913       2.932
==============================================================================
Omnibus:                     1537.890   Durbin-Watson:                   0.317
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            81206.359
Skew:                           0.161   Prob(JB):                         0.00
Kurtosis:                      20.239   Cond. No.                         15.0
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.960
Model:                                       OLS   Adj. R-squared:                  0.960
Method:                            Least Squares   F-statistic:                 1.545e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:52   Log-Likelihood:                 8329.3
No. Observations:                           6514   AIC:                        -1.665e+04
Df Residuals:                               6512   BIC:                        -1.664e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0070      0.001     -8.214      0.000      -0.009      -0.005
QQQ_Rolling_Future_Return_3m     2.9105      0.007    393.118      0.000       2.896       2.925
==============================================================================
Omnibus:                     2149.722   Durbin-Watson:                   0.136
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            38861.452
Skew:                           1.110   Prob(JB):                         0.00
Kurtosis:                      14.758   Cond. No.                         8.88
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.926
Model:                                       OLS   Adj. R-squared:                  0.926
Method:                            Least Squares   F-statistic:                 8.107e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:54   Log-Likelihood:                 3783.3
No. Observations:                           6451   AIC:                            -7563.
Df Residuals:                               6449   BIC:                            -7549.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0016      0.002     -0.902      0.367      -0.005       0.002
QQQ_Rolling_Future_Return_6m     2.8745      0.010    284.728      0.000       2.855       2.894
==============================================================================
Omnibus:                     3187.487   Durbin-Watson:                   0.077
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            49858.855
Skew:                           1.979   Prob(JB):                         0.00
Kurtosis:                      16.032   Cond. No.                         6.04
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.898
Model:                                       OLS   Adj. R-squared:                  0.898
Method:                            Least Squares   F-statistic:                 5.552e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:55   Log-Likelihood:                 116.33
No. Observations:                           6325   AIC:                            -228.7
Df Residuals:                               6323   BIC:                            -215.2
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                            0.0225      0.003      6.800      0.000       0.016       0.029
QQQ_Rolling_Future_Return_1y     2.8341      0.012    235.629      0.000       2.811       2.858
==============================================================================
Omnibus:                     2426.355   Durbin-Watson:                   0.068
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            19481.948
Skew:                           1.622   Prob(JB):                         0.00
Kurtosis:                      10.963   Cond. No.                         4.09
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.847
Model:                                       OLS   Adj. R-squared:                  0.847
Method:                            Least Squares   F-statistic:                 3.363e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:57   Log-Likelihood:                -4185.9
No. Observations:                           6073   AIC:                             8376.
Df Residuals:                               6071   BIC:                             8389.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0292      0.008     -3.748      0.000      -0.044      -0.014
QQQ_Rolling_Future_Return_2y     3.2273      0.018    183.386      0.000       3.193       3.262
==============================================================================
Omnibus:                     1696.489   Durbin-Watson:                   0.019
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4868.815
Skew:                           1.463   Prob(JB):                         0.00
Kurtosis:                       6.269   Cond. No.                         3.08
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.814
Model:                                       OLS   Adj. R-squared:                  0.814
Method:                            Least Squares   F-statistic:                 2.553e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   21:59:59   Log-Likelihood:                -6195.0
No. Observations:                           5821   AIC:                         1.239e+04
Df Residuals:                               5819   BIC:                         1.241e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.2169      0.013    -16.188      0.000      -0.243      -0.191
QQQ_Rolling_Future_Return_3y     3.6000      0.023    159.772      0.000       3.556       3.644
==============================================================================
Omnibus:                      877.246   Durbin-Watson:                   0.015
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1578.522
Skew:                           0.967   Prob(JB):                         0.00
Kurtosis:                       4.663   Cond. No.                         2.98
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.784
Model:                                       OLS   Adj. R-squared:                  0.784
Method:                            Least Squares   F-statistic:                 2.020e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:00   Log-Likelihood:                -8345.7
No. Observations:                           5569   AIC:                         1.670e+04
Df Residuals:                               5567   BIC:                         1.671e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.5067      0.023    -21.753      0.000      -0.552      -0.461
QQQ_Rolling_Future_Return_4y     4.1913      0.029    142.118      0.000       4.134       4.249
==============================================================================
Omnibus:                       90.780   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               63.985
Skew:                           0.153   Prob(JB):                     1.28e-14
Kurtosis:                       2.573   Cond. No.                         2.96
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.746
Model:                                       OLS   Adj. R-squared:                  0.746
Method:                            Least Squares   F-statistic:                 1.565e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:02   Log-Likelihood:                -11544.
No. Observations:                           5317   AIC:                         2.309e+04
Df Residuals:                               5315   BIC:                         2.311e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.2461      0.048    -25.807      0.000      -1.341      -1.151
QQQ_Rolling_Future_Return_5y     5.5050      0.044    125.105      0.000       5.419       5.591
==============================================================================
Omnibus:                      257.259   Durbin-Watson:                   0.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              381.231
Skew:                           0.438   Prob(JB):                     1.65e-83
Kurtosis:                       3.976   Cond. No.                         3.00
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 6.438e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:04   Log-Likelihood:                 32920.
No. Observations:                           6536   AIC:                        -6.584e+04
Df Residuals:                               6534   BIC:                        -6.582e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -5.345e-05   1.95e-05     -2.748      0.006   -9.16e-05   -1.53e-05
QQQ_Rolling_Future_Return_1d     2.9552      0.001   2537.269      0.000       2.953       2.957
==============================================================================
Omnibus:                     9701.531   Durbin-Watson:                   2.565
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         39004118.756
Skew:                          -8.113   Prob(JB):                         0.00
Kurtosis:                     381.099   Cond. No.                         59.9
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 1.120e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:05   Log-Likelihood:                 22539.
No. Observations:                           6532   AIC:                        -4.507e+04
Df Residuals:                               6530   BIC:                        -4.506e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0008   9.52e-05     -8.363      0.000      -0.001      -0.001
QQQ_Rolling_Future_Return_1w     2.9553      0.003   1058.242      0.000       2.950       2.961
==============================================================================
Omnibus:                     3465.972   Durbin-Watson:                   0.902
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           389191.684
Skew:                          -1.579   Prob(JB):                         0.00
Kurtosis:                      40.683   Cond. No.                         29.4
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.983
Model:                                       OLS   Adj. R-squared:                  0.983
Method:                            Least Squares   F-statistic:                 3.677e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:07   Log-Likelihood:                 14636.
No. Observations:                           6516   AIC:                        -2.927e+04
Df Residuals:                               6514   BIC:                        -2.925e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0035      0.000    -11.070      0.000      -0.004      -0.003
QQQ_Rolling_Future_Return_1m     2.9177      0.005    606.418      0.000       2.908       2.927
==============================================================================
Omnibus:                     1513.769   Durbin-Watson:                   0.308
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            82043.239
Skew:                           0.084   Prob(JB):                         0.00
Kurtosis:                      20.383   Cond. No.                         15.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.961
Model:                                       OLS   Adj. R-squared:                  0.961
Method:                            Least Squares   F-statistic:                 1.586e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:09   Log-Likelihood:                 8465.8
No. Observations:                           6474   AIC:                        -1.693e+04
Df Residuals:                               6472   BIC:                        -1.691e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0067      0.001     -8.081      0.000      -0.008      -0.005
QQQ_Rolling_Future_Return_3m     2.8944      0.007    398.234      0.000       2.880       2.909
==============================================================================
Omnibus:                     1349.017   Durbin-Watson:                   0.103
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            15307.847
Skew:                           0.668   Prob(JB):                         0.00
Kurtosis:                      10.414   Cond. No.                         8.94
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.929
Model:                                       OLS   Adj. R-squared:                  0.929
Method:                            Least Squares   F-statistic:                 8.383e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:11   Log-Likelihood:                 4132.8
No. Observations:                           6411   AIC:                            -8262.
Df Residuals:                               6409   BIC:                            -8248.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0006      0.002     -0.381      0.703      -0.004       0.003
QQQ_Rolling_Future_Return_6m     2.8224      0.010    289.527      0.000       2.803       2.842
==============================================================================
Omnibus:                     2686.399   Durbin-Watson:                   0.109
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            36557.241
Skew:                           1.631   Prob(JB):                         0.00
Kurtosis:                      14.235   Cond. No.                         6.16
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.902
Model:                                       OLS   Adj. R-squared:                  0.902
Method:                            Least Squares   F-statistic:                 5.755e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:13   Log-Likelihood:                 292.28
No. Observations:                           6285   AIC:                            -580.6
Df Residuals:                               6283   BIC:                            -567.1
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                            0.0222      0.003      6.880      0.000       0.016       0.029
QQQ_Rolling_Future_Return_1y     2.8512      0.012    239.888      0.000       2.828       2.875
==============================================================================
Omnibus:                     1989.506   Durbin-Watson:                   0.043
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8599.570
Skew:                           1.494   Prob(JB):                         0.00
Kurtosis:                       7.890   Cond. No.                         4.14
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.847
Model:                                       OLS   Adj. R-squared:                  0.847
Method:                            Least Squares   F-statistic:                 3.330e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:15   Log-Likelihood:                -4146.1
No. Observations:                           6033   AIC:                             8296.
Df Residuals:                               6031   BIC:                             8310.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0321      0.008     -4.090      0.000      -0.048      -0.017
QQQ_Rolling_Future_Return_2y     3.2363      0.018    182.474      0.000       3.202       3.271
==============================================================================
Omnibus:                     1703.989   Durbin-Watson:                   0.019
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4959.915
Skew:                           1.473   Prob(JB):                         0.00
Kurtosis:                       6.325   Cond. No.                         3.10
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.817
Model:                                       OLS   Adj. R-squared:                  0.816
Method:                            Least Squares   F-statistic:                 2.571e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:16   Log-Likelihood:                -6097.7
No. Observations:                           5781   AIC:                         1.220e+04
Df Residuals:                               5779   BIC:                         1.221e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.2501      0.014    -18.444      0.000      -0.277      -0.224
QQQ_Rolling_Future_Return_3y     3.6560      0.023    160.357      0.000       3.611       3.701
==============================================================================
Omnibus:                      879.259   Durbin-Watson:                   0.015
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1604.922
Skew:                           0.969   Prob(JB):                         0.00
Kurtosis:                       4.706   Cond. No.                         3.05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.785
Model:                                       OLS   Adj. R-squared:                  0.785
Method:                            Least Squares   F-statistic:                 2.013e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:18   Log-Likelihood:                -8262.7
No. Observations:                           5529   AIC:                         1.653e+04
Df Residuals:                               5527   BIC:                         1.654e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.5505      0.024    -23.246      0.000      -0.597      -0.504
QQQ_Rolling_Future_Return_4y     4.2437      0.030    141.872      0.000       4.185       4.302
==============================================================================
Omnibus:                       73.818   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               55.847
Skew:                           0.155   Prob(JB):                     7.46e-13
Kurtosis:                       2.617   Cond. No.                         3.02
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.747
Model:                                       OLS   Adj. R-squared:                  0.747
Method:                            Least Squares   F-statistic:                 1.560e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:20   Log-Likelihood:                -11446.
No. Observations:                           5277   AIC:                         2.290e+04
Df Residuals:                               5275   BIC:                         2.291e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.3180      0.049    -26.870      0.000      -1.414      -1.222
QQQ_Rolling_Future_Return_5y     5.5645      0.045    124.886      0.000       5.477       5.652
==============================================================================
Omnibus:                      246.937   Durbin-Watson:                   0.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              368.613
Skew:                           0.425   Prob(JB):                     9.05e-81
Kurtosis:                       3.977   Cond. No.                         3.05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 6.390e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:22   Log-Likelihood:                 32859.
No. Observations:                           6525   AIC:                        -6.571e+04
Df Residuals:                               6523   BIC:                        -6.570e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -5.353e-05   1.95e-05     -2.748      0.006   -9.17e-05   -1.53e-05
QQQ_Rolling_Future_Return_1d     2.9552      0.001   2527.781      0.000       2.953       2.957
==============================================================================
Omnibus:                     9680.797   Durbin-Watson:                   2.565
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         38804068.521
Skew:                          -8.106   Prob(JB):                         0.00
Kurtosis:                     380.445   Cond. No.                         60.0
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 1.119e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:24   Log-Likelihood:                 22546.
No. Observations:                           6521   AIC:                        -4.509e+04
Df Residuals:                               6519   BIC:                        -4.508e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0008   9.46e-05     -8.597      0.000      -0.001      -0.001
QQQ_Rolling_Future_Return_1w     2.9536      0.003   1057.873      0.000       2.948       2.959
==============================================================================
Omnibus:                     3596.565   Durbin-Watson:                   0.881
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           404696.936
Skew:                          -1.687   Prob(JB):                         0.00
Kurtosis:                      41.446   Cond. No.                         29.6
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.983
Model:                                       OLS   Adj. R-squared:                  0.983
Method:                            Least Squares   F-statistic:                 3.664e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:26   Log-Likelihood:                 14632.
No. Observations:                           6505   AIC:                        -2.926e+04
Df Residuals:                               6503   BIC:                        -2.925e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0035      0.000    -11.058      0.000      -0.004      -0.003
QQQ_Rolling_Future_Return_1m     2.9151      0.005    605.320      0.000       2.906       2.925
==============================================================================
Omnibus:                     1512.367   Durbin-Watson:                   0.297
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            83017.003
Skew:                           0.063   Prob(JB):                         0.00
Kurtosis:                      20.501   Cond. No.                         15.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.961
Model:                                       OLS   Adj. R-squared:                  0.961
Method:                            Least Squares   F-statistic:                 1.592e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:28   Log-Likelihood:                 8479.8
No. Observations:                           6463   AIC:                        -1.696e+04
Df Residuals:                               6461   BIC:                        -1.694e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0066      0.001     -7.911      0.000      -0.008      -0.005
QQQ_Rolling_Future_Return_3m     2.8926      0.007    399.038      0.000       2.878       2.907
==============================================================================
Omnibus:                     1379.365   Durbin-Watson:                   0.101
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            15633.345
Skew:                           0.693   Prob(JB):                         0.00
Kurtosis:                      10.492   Cond. No.                         8.95
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.931
Model:                                       OLS   Adj. R-squared:                  0.931
Method:                            Least Squares   F-statistic:                 8.660e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:29   Log-Likelihood:                 4309.6
No. Observations:                           6400   AIC:                            -8615.
Df Residuals:                               6398   BIC:                            -8602.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -7.935e-05      0.002     -0.049      0.961      -0.003       0.003
QQQ_Rolling_Future_Return_6m     2.8038      0.010    294.287      0.000       2.785       2.822
==============================================================================
Omnibus:                     1641.226   Durbin-Watson:                   0.057
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8159.048
Skew:                           1.148   Prob(JB):                         0.00
Kurtosis:                       8.033   Cond. No.                         6.19
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.902
Model:                                       OLS   Adj. R-squared:                  0.902
Method:                            Least Squares   F-statistic:                 5.795e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:31   Log-Likelihood:                 326.52
No. Observations:                           6274   AIC:                            -649.0
Df Residuals:                               6272   BIC:                            -635.5
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                            0.0209      0.003      6.496      0.000       0.015       0.027
QQQ_Rolling_Future_Return_1y     2.8615      0.012    240.734      0.000       2.838       2.885
==============================================================================
Omnibus:                     1986.979   Durbin-Watson:                   0.039
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8588.911
Skew:                           1.495   Prob(JB):                         0.00
Kurtosis:                       7.890   Cond. No.                         4.16
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.847
Model:                                       OLS   Adj. R-squared:                  0.847
Method:                            Least Squares   F-statistic:                 3.332e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:33   Log-Likelihood:                -4126.3
No. Observations:                           6022   AIC:                             8257.
Df Residuals:                               6020   BIC:                             8270.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0349      0.008     -4.437      0.000      -0.050      -0.019
QQQ_Rolling_Future_Return_2y     3.2436      0.018    182.525      0.000       3.209       3.278
==============================================================================
Omnibus:                     1713.005   Durbin-Watson:                   0.018
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5037.679
Skew:                           1.479   Prob(JB):                         0.00
Kurtosis:                       6.365   Cond. No.                         3.11
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.818
Model:                                       OLS   Adj. R-squared:                  0.818
Method:                            Least Squares   F-statistic:                 2.586e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:34   Log-Likelihood:                -6062.3
No. Observations:                           5770   AIC:                         1.213e+04
Df Residuals:                               5768   BIC:                         1.214e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.2617      0.014    -19.250      0.000      -0.288      -0.235
QQQ_Rolling_Future_Return_3y     3.6758      0.023    160.808      0.000       3.631       3.721
==============================================================================
Omnibus:                      872.524   Durbin-Watson:                   0.015
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1594.376
Skew:                           0.963   Prob(JB):                         0.00
Kurtosis:                       4.709   Cond. No.                         3.07
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.785
Model:                                       OLS   Adj. R-squared:                  0.785
Method:                            Least Squares   F-statistic:                 2.015e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:37   Log-Likelihood:                -8235.5
No. Observations:                           5518   AIC:                         1.647e+04
Df Residuals:                               5516   BIC:                         1.649e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.5654      0.024    -23.773      0.000      -0.612      -0.519
QQQ_Rolling_Future_Return_4y     4.2617      0.030    141.942      0.000       4.203       4.321
==============================================================================
Omnibus:                       68.572   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               52.789
Skew:                           0.153   Prob(JB):                     3.44e-12
Kurtosis:                       2.631   Cond. No.                         3.04
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.748
Model:                                       OLS   Adj. R-squared:                  0.748
Method:                            Least Squares   F-statistic:                 1.561e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:38   Log-Likelihood:                -11415.
No. Observations:                           5266   AIC:                         2.283e+04
Df Residuals:                               5264   BIC:                         2.285e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.3430      0.049    -27.264      0.000      -1.440      -1.246
QQQ_Rolling_Future_Return_5y     5.5855      0.045    124.935      0.000       5.498       5.673
==============================================================================
Omnibus:                      242.424   Durbin-Watson:                   0.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              363.603
Skew:                           0.418   Prob(JB):                     1.11e-79
Kurtosis:                       3.979   Cond. No.                         3.07
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 6.259e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:40   Log-Likelihood:                 32521.
No. Observations:                           6462   AIC:                        -6.504e+04
Df Residuals:                               6460   BIC:                        -6.502e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -4.963e-05   1.96e-05     -2.527      0.012   -8.81e-05   -1.11e-05
QQQ_Rolling_Future_Return_1d     2.9550      0.001   2501.868      0.000       2.953       2.957
==============================================================================
Omnibus:                     9587.532   Durbin-Watson:                   2.567
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         38153267.854
Skew:                          -8.108   Prob(JB):                         0.00
Kurtosis:                     379.084   Cond. No.                         60.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 1.110e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:42   Log-Likelihood:                 22331.
No. Observations:                           6458   AIC:                        -4.466e+04
Df Residuals:                               6456   BIC:                        -4.464e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0008    9.5e-05     -8.200      0.000      -0.001      -0.001
QQQ_Rolling_Future_Return_1w     2.9530      0.003   1053.776      0.000       2.947       2.958
==============================================================================
Omnibus:                     3543.021   Durbin-Watson:                   0.887
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           403213.894
Skew:                          -1.668   Prob(JB):                         0.00
Kurtosis:                      41.566   Cond. No.                         29.5
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.983
Model:                                       OLS   Adj. R-squared:                  0.983
Method:                            Least Squares   F-statistic:                 3.617e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:44   Log-Likelihood:                 14468.
No. Observations:                           6442   AIC:                        -2.893e+04
Df Residuals:                               6440   BIC:                        -2.892e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0034      0.000    -10.631      0.000      -0.004      -0.003
QQQ_Rolling_Future_Return_1m     2.9145      0.005    601.447      0.000       2.905       2.924
==============================================================================
Omnibus:                     1492.448   Durbin-Watson:                   0.295
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            81230.387
Skew:                           0.050   Prob(JB):                         0.00
Kurtosis:                      20.396   Cond. No.                         15.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.961
Model:                                       OLS   Adj. R-squared:                  0.961
Method:                            Least Squares   F-statistic:                 1.589e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:46   Log-Likelihood:                 8433.0
No. Observations:                           6427   AIC:                        -1.686e+04
Df Residuals:                               6425   BIC:                        -1.685e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0063      0.001     -7.555      0.000      -0.008      -0.005
QQQ_Rolling_Future_Return_3m     2.8921      0.007    398.661      0.000       2.878       2.906
==============================================================================
Omnibus:                     1377.477   Durbin-Watson:                   0.101
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            15521.588
Skew:                           0.699   Prob(JB):                         0.00
Kurtosis:                      10.484   Cond. No.                         8.93
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.931
Model:                                       OLS   Adj. R-squared:                  0.931
Method:                            Least Squares   F-statistic:                 8.678e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:48   Log-Likelihood:                 4316.3
No. Observations:                           6397   AIC:                            -8629.
Df Residuals:                               6395   BIC:                            -8615.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                         3.496e-05      0.002      0.022      0.983      -0.003       0.003
QQQ_Rolling_Future_Return_6m     2.8039      0.010    294.583      0.000       2.785       2.823
==============================================================================
Omnibus:                     1657.019   Durbin-Watson:                   0.055
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8164.864
Skew:                           1.163   Prob(JB):                         0.00
Kurtosis:                       8.022   Cond. No.                         6.19
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.902
Model:                                       OLS   Adj. R-squared:                  0.902
Method:                            Least Squares   F-statistic:                 5.802e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:49   Log-Likelihood:                 334.10
No. Observations:                           6271   AIC:                            -664.2
Df Residuals:                               6269   BIC:                            -650.7
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                            0.0204      0.003      6.337      0.000       0.014       0.027
QQQ_Rolling_Future_Return_1y     2.8641      0.012    240.870      0.000       2.841       2.887
==============================================================================
Omnibus:                     1985.718   Durbin-Watson:                   0.038
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8605.916
Skew:                           1.494   Prob(JB):                         0.00
Kurtosis:                       7.900   Cond. No.                         4.16
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.847
Model:                                       OLS   Adj. R-squared:                  0.847
Method:                            Least Squares   F-statistic:                 3.334e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:51   Log-Likelihood:                -4119.1
No. Observations:                           6019   AIC:                             8242.
Df Residuals:                               6017   BIC:                             8256.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0364      0.008     -4.622      0.000      -0.052      -0.021
QQQ_Rolling_Future_Return_2y     3.2472      0.018    182.598      0.000       3.212       3.282
==============================================================================
Omnibus:                     1718.217   Durbin-Watson:                   0.018
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5077.476
Skew:                           1.483   Prob(JB):                         0.00
Kurtosis:                       6.384   Cond. No.                         3.12
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.818
Model:                                       OLS   Adj. R-squared:                  0.818
Method:                            Least Squares   F-statistic:                 2.593e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:53   Log-Likelihood:                -6049.6
No. Observations:                           5767   AIC:                         1.210e+04
Df Residuals:                               5765   BIC:                         1.212e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.2658      0.014    -19.545      0.000      -0.292      -0.239
QQQ_Rolling_Future_Return_3y     3.6829      0.023    161.036      0.000       3.638       3.728
==============================================================================
Omnibus:                      869.247   Durbin-Watson:                   0.015
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1588.727
Skew:                           0.960   Prob(JB):                         0.00
Kurtosis:                       4.709   Cond. No.                         3.08
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.785
Model:                                       OLS   Adj. R-squared:                  0.785
Method:                            Least Squares   F-statistic:                 2.017e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:55   Log-Likelihood:                -8226.6
No. Observations:                           5515   AIC:                         1.646e+04
Df Residuals:                               5513   BIC:                         1.647e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.5704      0.024    -23.957      0.000      -0.617      -0.524
QQQ_Rolling_Future_Return_4y     4.2678      0.030    142.009      0.000       4.209       4.327
==============================================================================
Omnibus:                       66.838   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               51.664
Skew:                           0.151   Prob(JB):                     6.04e-12
Kurtosis:                       2.635   Cond. No.                         3.05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.748
Model:                                       OLS   Adj. R-squared:                  0.748
Method:                            Least Squares   F-statistic:                 1.562e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:57   Log-Likelihood:                -11405.
No. Observations:                           5263   AIC:                         2.281e+04
Df Residuals:                               5261   BIC:                         2.283e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.3518      0.049    -27.413      0.000      -1.448      -1.255
QQQ_Rolling_Future_Return_5y     5.5930      0.045    124.992      0.000       5.505       5.681
==============================================================================
Omnibus:                      240.577   Durbin-Watson:                   0.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              361.692
Skew:                           0.415   Prob(JB):                     2.88e-79
Kurtosis:                       3.980   Cond. No.                         3.08
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 6.000e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:00:59   Log-Likelihood:                 31538.
No. Observations:                           6281   AIC:                        -6.307e+04
Df Residuals:                               6279   BIC:                        -6.306e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -4.239e-05   2.02e-05     -2.103      0.035   -8.19e-05   -2.88e-06
QQQ_Rolling_Future_Return_1d     2.9548      0.001   2449.504      0.000       2.952       2.957
==============================================================================
Omnibus:                     9289.579   Durbin-Watson:                   2.569
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         35733225.202
Skew:                          -8.060   Prob(JB):                         0.00
Kurtosis:                     372.159   Cond. No.                         59.9
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 1.076e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:00   Log-Likelihood:                 21679.
No. Observations:                           6281   AIC:                        -4.335e+04
Df Residuals:                               6279   BIC:                        -4.334e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0007    9.7e-05     -7.559      0.000      -0.001      -0.001
QQQ_Rolling_Future_Return_1w     2.9525      0.003   1037.518      0.000       2.947       2.958
==============================================================================
Omnibus:                     3409.174   Durbin-Watson:                   0.895
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           384856.284
Skew:                          -1.639   Prob(JB):                         0.00
Kurtosis:                      41.207   Cond. No.                         29.4
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.982
Model:                                       OLS   Adj. R-squared:                  0.982
Method:                            Least Squares   F-statistic:                 3.507e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:02   Log-Likelihood:                 14071.
No. Observations:                           6281   AIC:                        -2.814e+04
Df Residuals:                               6279   BIC:                        -2.812e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0032      0.000     -9.799      0.000      -0.004      -0.003
QQQ_Rolling_Future_Return_1m     2.9141      0.005    592.215      0.000       2.904       2.924
==============================================================================
Omnibus:                     1452.768   Durbin-Watson:                   0.296
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            78418.997
Skew:                           0.053   Prob(JB):                         0.00
Kurtosis:                      20.310   Cond. No.                         15.1
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.961
Model:                                       OLS   Adj. R-squared:                  0.961
Method:                            Least Squares   F-statistic:                 1.567e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:03   Log-Likelihood:                 8265.9
No. Observations:                           6281   AIC:                        -1.653e+04
Df Residuals:                               6279   BIC:                        -1.651e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0059      0.001     -7.039      0.000      -0.008      -0.004
QQQ_Rolling_Future_Return_3m     2.8978      0.007    395.792      0.000       2.883       2.912
==============================================================================
Omnibus:                     1352.373   Durbin-Watson:                   0.102
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            15607.922
Skew:                           0.696   Prob(JB):                         0.00
Kurtosis:                      10.596   Cond. No.                         8.95
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.932
Model:                                       OLS   Adj. R-squared:                  0.932
Method:                            Least Squares   F-statistic:                 8.618e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:05   Log-Likelihood:                 4282.8
No. Observations:                           6281   AIC:                            -8562.
Df Residuals:                               6279   BIC:                            -8548.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0002      0.002     -0.115      0.909      -0.003       0.003
QQQ_Rolling_Future_Return_6m     2.8190      0.010    293.571      0.000       2.800       2.838
==============================================================================
Omnibus:                     1637.301   Durbin-Watson:                   0.057
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8392.287
Skew:                           1.158   Prob(JB):                         0.00
Kurtosis:                       8.167   Cond. No.                         6.24
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.904
Model:                                       OLS   Adj. R-squared:                  0.904
Method:                            Least Squares   F-statistic:                 5.855e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:07   Log-Likelihood:                 405.83
No. Observations:                           6205   AIC:                            -807.7
Df Residuals:                               6203   BIC:                            -794.2
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                            0.0161      0.003      4.999      0.000       0.010       0.022
QQQ_Rolling_Future_Return_1y     2.8916      0.012    241.975      0.000       2.868       2.915
==============================================================================
Omnibus:                     1969.830   Durbin-Watson:                   0.038
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8759.005
Skew:                           1.488   Prob(JB):                         0.00
Kurtosis:                       8.002   Cond. No.                         4.22
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.850
Model:                                       OLS   Adj. R-squared:                  0.850
Method:                            Least Squares   F-statistic:                 3.400e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:09   Log-Likelihood:                -4015.6
No. Observations:                           5983   AIC:                             8035.
Df Residuals:                               5981   BIC:                             8049.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0508      0.008     -6.452      0.000      -0.066      -0.035
QQQ_Rolling_Future_Return_2y     3.2856      0.018    184.379      0.000       3.251       3.321
==============================================================================
Omnibus:                     1729.276   Durbin-Watson:                   0.019
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5279.242
Skew:                           1.487   Prob(JB):                         0.00
Kurtosis:                       6.511   Cond. No.                         3.16
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.822
Model:                                       OLS   Adj. R-squared:                  0.821
Method:                            Least Squares   F-statistic:                 2.637e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:11   Log-Likelihood:                -5948.5
No. Observations:                           5731   AIC:                         1.190e+04
Df Residuals:                               5729   BIC:                         1.191e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.2891      0.014    -21.177      0.000      -0.316      -0.262
QQQ_Rolling_Future_Return_3y     3.7262      0.023    162.382      0.000       3.681       3.771
==============================================================================
Omnibus:                      849.429   Durbin-Watson:                   0.015
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1564.767
Skew:                           0.943   Prob(JB):                         0.00
Kurtosis:                       4.731   Cond. No.                         3.12
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.788
Model:                                       OLS   Adj. R-squared:                  0.788
Method:                            Least Squares   F-statistic:                 2.040e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:12   Log-Likelihood:                -8128.7
No. Observations:                           5479   AIC:                         1.626e+04
Df Residuals:                               5477   BIC:                         1.627e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.6029      0.024    -25.170      0.000      -0.650      -0.556
QQQ_Rolling_Future_Return_4y     4.3128      0.030    142.830      0.000       4.254       4.372
==============================================================================
Omnibus:                       52.539   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               41.303
Skew:                           0.131   Prob(JB):                     1.07e-09
Kurtosis:                       2.665   Cond. No.                         3.09
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.750
Model:                                       OLS   Adj. R-squared:                  0.750
Method:                            Least Squares   F-statistic:                 1.573e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:14   Log-Likelihood:                -11339.
No. Observations:                           5243   AIC:                         2.268e+04
Df Residuals:                               5241   BIC:                         2.270e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.4128      0.050    -28.446      0.000      -1.510      -1.315
QQQ_Rolling_Future_Return_5y     5.6452      0.045    125.418      0.000       5.557       5.733
==============================================================================
Omnibus:                      227.541   Durbin-Watson:                   0.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              348.386
Skew:                           0.394   Prob(JB):                     2.23e-76
Kurtosis:                       3.988   Cond. No.                         3.11
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 5.380e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:16   Log-Likelihood:                 29443.
No. Observations:                           5890   AIC:                        -5.888e+04
Df Residuals:                               5888   BIC:                        -5.887e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -3.037e-05   2.13e-05     -1.427      0.154   -7.21e-05    1.14e-05
QQQ_Rolling_Future_Return_1d     2.9544      0.001   2319.390      0.000       2.952       2.957
==============================================================================
Omnibus:                     8698.998   Durbin-Watson:                   2.576
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         31790538.925
Skew:                          -8.045   Prob(JB):                         0.00
Kurtosis:                     362.553   Cond. No.                         59.9
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 1.008e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:18   Log-Likelihood:                 20303.
No. Observations:                           5890   AIC:                        -4.060e+04
Df Residuals:                               5888   BIC:                        -4.059e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0006      0.000     -6.363      0.000      -0.001      -0.000
QQQ_Rolling_Future_Return_1w     2.9526      0.003   1003.859      0.000       2.947       2.958
==============================================================================
Omnibus:                     3288.219   Durbin-Watson:                   0.897
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           369148.693
Skew:                          -1.720   Prob(JB):                         0.00
Kurtosis:                      41.631   Cond. No.                         29.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.983
Model:                                       OLS   Adj. R-squared:                  0.983
Method:                            Least Squares   F-statistic:                 3.372e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:20   Log-Likelihood:                 13210.
No. Observations:                           5890   AIC:                        -2.642e+04
Df Residuals:                               5888   BIC:                        -2.640e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0025      0.000     -7.379      0.000      -0.003      -0.002
QQQ_Rolling_Future_Return_1m     2.9140      0.005    580.676      0.000       2.904       2.924
==============================================================================
Omnibus:                     1415.341   Durbin-Watson:                   0.310
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            78303.043
Skew:                           0.193   Prob(JB):                         0.00
Kurtosis:                      20.858   Cond. No.                         15.0
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.962
Model:                                       OLS   Adj. R-squared:                  0.962
Method:                            Least Squares   F-statistic:                 1.509e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:21   Log-Likelihood:                 7799.8
No. Observations:                           5890   AIC:                        -1.560e+04
Df Residuals:                               5888   BIC:                        -1.558e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0040      0.001     -4.619      0.000      -0.006      -0.002
QQQ_Rolling_Future_Return_3m     2.9068      0.007    388.462      0.000       2.892       2.921
==============================================================================
Omnibus:                     1368.479   Durbin-Watson:                   0.107
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            16451.791
Skew:                           0.766   Prob(JB):                         0.00
Kurtosis:                      11.043   Cond. No.                         8.93
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.934
Model:                                       OLS   Adj. R-squared:                  0.934
Method:                            Least Squares   F-statistic:                 8.379e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:23   Log-Likelihood:                 4198.8
No. Observations:                           5890   AIC:                            -8394.
Df Residuals:                               5888   BIC:                            -8380.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0018      0.002     -1.052      0.293      -0.005       0.002
QQQ_Rolling_Future_Return_6m     2.8731      0.010    289.460      0.000       2.854       2.893
==============================================================================
Omnibus:                     1462.376   Durbin-Watson:                   0.063
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8112.635
Skew:                           1.074   Prob(JB):                         0.00
Kurtosis:                       8.333   Cond. No.                         6.45
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.912
Model:                                       OLS   Adj. R-squared:                  0.912
Method:                            Least Squares   F-statistic:                 6.072e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:25   Log-Likelihood:                 715.42
No. Observations:                           5857   AIC:                            -1427.
Df Residuals:                               5855   BIC:                            -1413.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0011      0.003     -0.327      0.744      -0.007       0.005
QQQ_Rolling_Future_Return_1y     3.0129      0.012    246.405      0.000       2.989       3.037
==============================================================================
Omnibus:                     1765.613   Durbin-Watson:                   0.043
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             8325.388
Skew:                           1.385   Prob(JB):                         0.00
Kurtosis:                       8.142   Cond. No.                         4.45
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.865
Model:                                       OLS   Adj. R-squared:                  0.865
Method:                            Least Squares   F-statistic:                 3.711e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:27   Log-Likelihood:                -3522.7
No. Observations:                           5789   AIC:                             7049.
Df Residuals:                               5787   BIC:                             7063.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.1121      0.008    -14.185      0.000      -0.128      -0.097
QQQ_Rolling_Future_Return_2y     3.4520      0.018    192.643      0.000       3.417       3.487
==============================================================================
Omnibus:                     1654.985   Durbin-Watson:                   0.020
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5614.089
Skew:                           1.426   Prob(JB):                         0.00
Kurtosis:                       6.891   Cond. No.                         3.36
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.838
Model:                                       OLS   Adj. R-squared:                  0.838
Method:                            Least Squares   F-statistic:                 2.860e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:28   Log-Likelihood:                -5448.4
No. Observations:                           5537   AIC:                         1.090e+04
Df Residuals:                               5535   BIC:                         1.091e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.3842      0.014    -27.758      0.000      -0.411      -0.357
QQQ_Rolling_Future_Return_3y     3.9118      0.023    169.113      0.000       3.866       3.957
==============================================================================
Omnibus:                      674.134   Durbin-Watson:                   0.016
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1252.709
Skew:                           0.794   Prob(JB):                    9.50e-273
Kurtosis:                       4.706   Cond. No.                         3.31
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.805
Model:                                       OLS   Adj. R-squared:                  0.805
Method:                            Least Squares   F-statistic:                 2.185e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:30   Log-Likelihood:                -7609.7
No. Observations:                           5285   AIC:                         1.522e+04
Df Residuals:                               5283   BIC:                         1.524e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.7332      0.024    -30.056      0.000      -0.781      -0.685
QQQ_Rolling_Future_Return_4y     4.5096      0.031    147.803      0.000       4.450       4.569
==============================================================================
Omnibus:                       12.958   Durbin-Watson:                   0.011
Prob(Omnibus):                  0.002   Jarque-Bera (JB):               10.506
Skew:                          -0.007   Prob(JB):                      0.00523
Kurtosis:                       2.782   Cond. No.                         3.25
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.759
Model:                                       OLS   Adj. R-squared:                  0.759
Method:                            Least Squares   F-statistic:                 1.625e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:32   Log-Likelihood:                -11064.
No. Observations:                           5163   AIC:                         2.213e+04
Df Residuals:                               5161   BIC:                         2.215e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.6771      0.051    -32.821      0.000      -1.777      -1.577
QQQ_Rolling_Future_Return_5y     5.8699      0.046    127.459      0.000       5.780       5.960
==============================================================================
Omnibus:                      168.793   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              286.855
Skew:                           0.283   Prob(JB):                     5.13e-63
Kurtosis:                       4.007   Cond. No.                         3.27
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 4.767e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:33   Log-Likelihood:                 27167.
No. Observations:                           5450   AIC:                        -5.433e+04
Df Residuals:                               5448   BIC:                        -5.432e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                        -1.602e-05   2.24e-05     -0.714      0.475      -6e-05     2.8e-05
QQQ_Rolling_Future_Return_1d     2.9532      0.001   2183.311      0.000       2.951       2.956
==============================================================================
Omnibus:                     8184.121   Durbin-Watson:                   2.578
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         30349901.921
Skew:                          -8.326   Prob(JB):                         0.00
Kurtosis:                     368.204   Cond. No.                         60.3
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 9.352e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:35   Log-Likelihood:                 18855.
No. Observations:                           5450   AIC:                        -3.771e+04
Df Residuals:                               5448   BIC:                        -3.769e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0006      0.000     -5.512      0.000      -0.001      -0.000
QQQ_Rolling_Future_Return_1w     2.9495      0.003    967.071      0.000       2.944       2.956
==============================================================================
Omnibus:                     3225.262   Durbin-Watson:                   0.872
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           383451.023
Skew:                          -1.880   Prob(JB):                         0.00
Kurtosis:                      43.920   Cond. No.                         29.6
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.982
Model:                                       OLS   Adj. R-squared:                  0.982
Method:                            Least Squares   F-statistic:                 3.035e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:37   Log-Likelihood:                 12190.
No. Observations:                           5450   AIC:                        -2.438e+04
Df Residuals:                               5448   BIC:                        -2.436e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0021      0.000     -5.911      0.000      -0.003      -0.001
QQQ_Rolling_Future_Return_1m     2.9063      0.005    550.932      0.000       2.896       2.917
==============================================================================
Omnibus:                     1331.250   Durbin-Watson:                   0.299
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            76809.720
Skew:                           0.205   Prob(JB):                         0.00
Kurtosis:                      21.387   Cond. No.                         15.1
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.961
Model:                                       OLS   Adj. R-squared:                  0.961
Method:                            Least Squares   F-statistic:                 1.352e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:38   Log-Likelihood:                 7159.6
No. Observations:                           5450   AIC:                        -1.432e+04
Df Residuals:                               5448   BIC:                        -1.430e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0036      0.001     -3.910      0.000      -0.005      -0.002
QQQ_Rolling_Future_Return_3m     2.9142      0.008    367.681      0.000       2.899       2.930
==============================================================================
Omnibus:                     1265.130   Durbin-Watson:                   0.097
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            15817.100
Skew:                           0.752   Prob(JB):                         0.00
Kurtosis:                      11.209   Cond. No.                         9.00
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.937
Model:                                       OLS   Adj. R-squared:                  0.937
Method:                            Least Squares   F-statistic:                 8.117e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:40   Log-Likelihood:                 4027.1
No. Observations:                           5450   AIC:                            -8050.
Df Residuals:                               5448   BIC:                            -8037.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0043      0.002     -2.531      0.011      -0.008      -0.001
QQQ_Rolling_Future_Return_6m     2.9104      0.010    284.899      0.000       2.890       2.930
==============================================================================
Omnibus:                      970.645   Durbin-Watson:                   0.061
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4546.797
Skew:                           0.789   Prob(JB):                         0.00
Kurtosis:                       7.187   Cond. No.                         6.55
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.917
Model:                                       OLS   Adj. R-squared:                  0.917
Method:                            Least Squares   F-statistic:                 5.979e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:42   Log-Likelihood:                 790.67
No. Observations:                           5446   AIC:                            -1577.
Df Residuals:                               5444   BIC:                            -1564.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0019      0.003     -0.560      0.575      -0.008       0.005
QQQ_Rolling_Future_Return_1y     3.0627      0.013    244.513      0.000       3.038       3.087
==============================================================================
Omnibus:                     1401.338   Durbin-Watson:                   0.045
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             6208.882
Skew:                           1.187   Prob(JB):                         0.00
Kurtosis:                       7.661   Cond. No.                         4.51
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.876
Model:                                       OLS   Adj. R-squared:                  0.876
Method:                            Least Squares   F-statistic:                 3.834e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:43   Log-Likelihood:                -3105.2
No. Observations:                           5446   AIC:                             6214.
Df Residuals:                               5444   BIC:                             6228.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.1258      0.008    -15.614      0.000      -0.142      -0.110
QQQ_Rolling_Future_Return_2y     3.5394      0.018    195.794      0.000       3.504       3.575
==============================================================================
Omnibus:                     1479.606   Durbin-Watson:                   0.022
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5093.275
Skew:                           1.346   Prob(JB):                         0.00
Kurtosis:                       6.899   Cond. No.                         3.45
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.850
Model:                                       OLS   Adj. R-squared:                  0.850
Method:                            Least Squares   F-statistic:                 2.993e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:45   Log-Likelihood:                -5026.2
No. Observations:                           5295   AIC:                         1.006e+04
Df Residuals:                               5293   BIC:                         1.007e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.3931      0.014    -28.257      0.000      -0.420      -0.366
QQQ_Rolling_Future_Return_3y     3.9740      0.023    172.992      0.000       3.929       4.019
==============================================================================
Omnibus:                      582.216   Durbin-Watson:                   0.018
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1156.163
Skew:                           0.707   Prob(JB):                    8.76e-252
Kurtosis:                       4.801   Cond. No.                         3.36
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.819
Model:                                       OLS   Adj. R-squared:                  0.819
Method:                            Least Squares   F-statistic:                 2.300e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:47   Log-Likelihood:                -7134.0
No. Observations:                           5071   AIC:                         1.427e+04
Df Residuals:                               5069   BIC:                         1.429e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.7493      0.024    -30.704      0.000      -0.797      -0.701
QQQ_Rolling_Future_Return_4y     4.5868      0.030    151.643      0.000       4.528       4.646
==============================================================================
Omnibus:                       13.206   Durbin-Watson:                   0.011
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               13.284
Skew:                          -0.121   Prob(JB):                      0.00130
Kurtosis:                       2.931   Cond. No.                         3.30
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.766
Model:                                       OLS   Adj. R-squared:                  0.766
Method:                            Least Squares   F-statistic:                 1.658e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:48   Log-Likelihood:                -10802.
No. Observations:                           5069   AIC:                         2.161e+04
Df Residuals:                               5067   BIC:                         2.162e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.7617      0.052    -34.121      0.000      -1.863      -1.660
QQQ_Rolling_Future_Return_5y     5.9669      0.046    128.779      0.000       5.876       6.058
==============================================================================
Omnibus:                      145.271   Durbin-Watson:                   0.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              276.687
Skew:                           0.211   Prob(JB):                     8.28e-61
Kurtosis:                       4.064   Cond. No.                         3.33
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1d   R-squared:                       0.999
Model:                                       OLS   Adj. R-squared:                  0.999
Method:                            Least Squares   F-statistic:                 3.965e+06
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:50   Log-Likelihood:                 24386.
No. Observations:                           4909   AIC:                        -4.877e+04
Df Residuals:                               4907   BIC:                        -4.875e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                         7.129e-06   2.41e-05      0.296      0.767      -4e-05    5.43e-05
QQQ_Rolling_Future_Return_1d     2.9508      0.001   1991.332      0.000       2.948       2.954
==============================================================================
Omnibus:                     7546.968   Durbin-Watson:                   2.588
Prob(Omnibus):                  0.000   Jarque-Bera (JB):         28785736.106
Skew:                          -8.740   Prob(JB):                         0.00
Kurtosis:                     377.736   Cond. No.                         61.6
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1w   R-squared:                       0.994
Model:                                       OLS   Adj. R-squared:                  0.994
Method:                            Least Squares   F-statistic:                 8.425e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:52   Log-Likelihood:                 17077.
No. Observations:                           4909   AIC:                        -3.415e+04
Df Residuals:                               4907   BIC:                        -3.414e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0005      0.000     -4.398      0.000      -0.001      -0.000
QQQ_Rolling_Future_Return_1w     2.9537      0.003    917.898      0.000       2.947       2.960
==============================================================================
Omnibus:                     3458.331   Durbin-Watson:                   0.891
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           430375.683
Skew:                          -2.502   Prob(JB):                         0.00
Kurtosis:                      48.597   Cond. No.                         30.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1m   R-squared:                       0.982
Model:                                       OLS   Adj. R-squared:                  0.982
Method:                            Least Squares   F-statistic:                 2.620e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:53   Log-Likelihood:                 11004.
No. Observations:                           4909   AIC:                        -2.200e+04
Df Residuals:                               4907   BIC:                        -2.199e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0014      0.000     -3.884      0.000      -0.002      -0.001
QQQ_Rolling_Future_Return_1m     2.8966      0.006    511.823      0.000       2.886       2.908
==============================================================================
Omnibus:                     1234.759   Durbin-Watson:                   0.289
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            81518.307
Skew:                           0.182   Prob(JB):                         0.00
Kurtosis:                      22.960   Cond. No.                         15.4
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3m   R-squared:                       0.964
Model:                                       OLS   Adj. R-squared:                  0.964
Method:                            Least Squares   F-statistic:                 1.297e+05
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:55   Log-Likelihood:                 6687.8
No. Observations:                           4909   AIC:                        -1.337e+04
Df Residuals:                               4907   BIC:                        -1.336e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                            0.0002      0.001      0.215      0.829      -0.002       0.002
QQQ_Rolling_Future_Return_3m     2.8959      0.008    360.175      0.000       2.880       2.912
==============================================================================
Omnibus:                     1438.612   Durbin-Watson:                   0.111
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            18131.281
Skew:                           1.037   Prob(JB):                         0.00
Kurtosis:                      12.184   Cond. No.                         9.10
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_6m   R-squared:                       0.940
Model:                                       OLS   Adj. R-squared:                  0.940
Method:                            Least Squares   F-statistic:                 7.744e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:56   Log-Likelihood:                 3783.0
No. Observations:                           4909   AIC:                            -7562.
Df Residuals:                               4907   BIC:                            -7549.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0006      0.002     -0.378      0.705      -0.004       0.003
QQQ_Rolling_Future_Return_6m     2.9398      0.011    278.286      0.000       2.919       2.960
==============================================================================
Omnibus:                     1092.173   Durbin-Watson:                   0.063
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5026.717
Skew:                           1.005   Prob(JB):                         0.00
Kurtosis:                       7.531   Cond. No.                         6.63
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_1y   R-squared:                       0.921
Model:                                       OLS   Adj. R-squared:                  0.921
Method:                            Least Squares   F-statistic:                 5.687e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:01:58   Log-Likelihood:                 835.19
No. Observations:                           4909   AIC:                            -1666.
Df Residuals:                               4907   BIC:                            -1653.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.0041      0.003     -1.223      0.222      -0.011       0.002
QQQ_Rolling_Future_Return_1y     3.1266      0.013    238.485      0.000       3.101       3.152
==============================================================================
Omnibus:                     1289.761   Durbin-Watson:                   0.048
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5901.804
Skew:                           1.201   Prob(JB):                         0.00
Kurtosis:                       7.804   Cond. No.                         4.58
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_2y   R-squared:                       0.890
Model:                                       OLS   Adj. R-squared:                  0.890
Method:                            Least Squares   F-statistic:                 3.983e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:02:00   Log-Likelihood:                -2555.1
No. Observations:                           4909   AIC:                             5114.
Df Residuals:                               4907   BIC:                             5127.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.1417      0.008    -17.612      0.000      -0.157      -0.126
QQQ_Rolling_Future_Return_2y     3.6958      0.019    199.587      0.000       3.660       3.732
==============================================================================
Omnibus:                     1260.114   Durbin-Watson:                   0.024
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4504.068
Skew:                           1.255   Prob(JB):                         0.00
Kurtosis:                       6.965   Cond. No.                         3.50
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_3y   R-squared:                       0.867
Model:                                       OLS   Adj. R-squared:                  0.867
Method:                            Least Squares   F-statistic:                 3.200e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:02:02   Log-Likelihood:                -4386.9
No. Observations:                           4909   AIC:                             8778.
Df Residuals:                               4907   BIC:                             8791.
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.4053      0.014    -29.517      0.000      -0.432      -0.378
QQQ_Rolling_Future_Return_3y     4.1031      0.023    178.879      0.000       4.058       4.148
==============================================================================
Omnibus:                      498.122   Durbin-Watson:                   0.020
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1119.080
Skew:                           0.622   Prob(JB):                    9.88e-244
Kurtosis:                       4.981   Cond. No.                         3.40
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_4y   R-squared:                       0.841
Model:                                       OLS   Adj. R-squared:                  0.841
Method:                            Least Squares   F-statistic:                 2.561e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:02:03   Log-Likelihood:                -6578.4
No. Observations:                           4854   AIC:                         1.316e+04
Df Residuals:                               4852   BIC:                         1.317e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -0.7780      0.024    -32.745      0.000      -0.825      -0.731
QQQ_Rolling_Future_Return_4y     4.7051      0.029    160.037      0.000       4.647       4.763
==============================================================================
Omnibus:                       37.797   Durbin-Watson:                   0.012
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               38.924
Skew:                          -0.203   Prob(JB):                     3.53e-09
Kurtosis:                       3.167   Cond. No.                         3.31
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

                                  OLS Regression Results                                 
=========================================================================================
Dep. Variable:     TQQQ_Rolling_Future_Return_5y   R-squared:                       0.790
Model:                                       OLS   Adj. R-squared:                  0.790
Method:                            Least Squares   F-statistic:                 1.825e+04
Date:                           Mon, 23 Mar 2026   Prob (F-statistic):               0.00
Time:                                   22:02:05   Log-Likelihood:                -10152.
No. Observations:                           4854   AIC:                         2.031e+04
Df Residuals:                               4852   BIC:                         2.032e+04
Df Model:                                      1                                         
Covariance Type:                       nonrobust                                         
================================================================================================
                                   coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------------------
const                           -1.8225      0.051    -35.999      0.000      -1.922      -1.723
QQQ_Rolling_Future_Return_5y     6.1390      0.045    135.095      0.000       6.050       6.228
==============================================================================
Omnibus:                      154.299   Durbin-Watson:                   0.011
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              381.366
Skew:                           0.121   Prob(JB):                     1.54e-83
Kurtosis:                       4.352   Cond. No.                         3.32
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Rolling Returns Following Drawdowns Deviation (QQQ & TQQQ) #

rolling_returns_positive_future_returns = pd.DataFrame(index=rolling_windows.keys(), data=rolling_windows.values())
rolling_returns_positive_future_returns.reset_index(inplace=True)
rolling_returns_positive_future_returns.rename(columns={"index":"Period", 0:"Days"}, inplace=True)

for drawdown in drawdown_levels:
    temp = rolling_returns_drawdown_stats.loc[rolling_returns_drawdown_stats["Drawdown"] == drawdown]
    temp = temp[["Period", "Positive_Future_Percentage"]]
    temp.rename(columns={"Positive_Future_Percentage" : f"Positive_Future_Percentage_Post_{drawdown}_Drawdown"}, inplace=True)
    rolling_returns_positive_future_returns = pd.merge(rolling_returns_positive_future_returns, temp, left_on="Period", right_on="Period", how="outer")
    rolling_returns_positive_future_returns.sort_values(by="Days", ascending=True, inplace=True)

rolling_returns_positive_future_returns.drop(columns={"Days"}, inplace=True)
rolling_returns_positive_future_returns.reset_index(drop=True, inplace=True)
pandas_set_decimal_places(2)
display(rolling_returns_positive_future_returns.set_index("Period"))

plot_scatter(
    df=rolling_returns_positive_future_returns,
    x_plot_column="Period",
    y_plot_columns=[col for col in rolling_returns_positive_future_returns.columns if col != "Period"],
    title="TQQQ Future Return by Time Period Post Drawdown",
    x_label="Rolling Return Time Period",
    x_format="String",
    x_format_decimal_places=0,
    x_tick_spacing=1,
    x_tick_rotation=0,
    y_label="Positive Future Return Percentage",
    y_format="Decimal",
    y_format_decimal_places=2,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    plot_OLS_regression_line=False,
    OLS_column=None,
    plot_Ridge_regression_line=False,
    Ridge_column=None,
    plot_RidgeCV_regression_line=False,
    RidgeCV_column=None,
    regression_constant=False,
    grid=True,
    legend=True,
    export_plot=False,
    plot_file_name=None,
)

This plot summarizes the future rolling returns well. For rolling returns up to ~3 months following all drawdown levels, we see the rolling returns of TQQQ are positive ~65% of the time.

As we extend the time horizon, the percentage of positive rolling returns increases, which is consistent with the idea that the longer you hold through and post drawdown, the more likely you are to recover and achieve positive returns.

From a timing standpoint, this analysis suggests that the optimal time to buy TQQQ would be following a drawdown of 70% or more, and holding for at least 3 years. The data tells us that having a positive rolling return over time is ~75%.

One might consider the idea of allocating to TQQQ via a ladder, starting at a drawdown of 50%, and continuing to add to the position as the drawdown deepens, with the idea that the more severe the drawdown, the higher the expected future returns. However, this strategy could require enduring significant volatility, as one would be adding to the position during periods of paper losses.

SPY & UPRO #

Next, we will repeat the same analysis for SPY and UPRO, and see how the results compare to those of QQQ and TQQQ.

Acquire & Plot Data (SPY) #

First, let’s get the data for SPY. If we already have the desired data, we can load it from a local pickle file. Otherwise, we can download it from Yahoo Finance using the yf_pull_data function.

pandas_set_decimal_places(2)

yf_pull_data(
    base_directory=DATA_DIR,
    ticker="SPY",
    adjusted=False,
    source="Yahoo_Finance",
    asset_class="Exchange_Traded_Funds",
    excel_export=True,
    pickle_export=True,
    output_confirmation=False,
)

spy = load_data(
    base_directory=DATA_DIR,
    ticker="SPY",
    source="Yahoo_Finance",
    asset_class="Exchange_Traded_Funds",
    timeframe="Daily",
    file_format="pickle",
)

# Rename columns to "SPY_Close", etc.
spy = spy.rename(columns={
    "Adj Close": "SPY_Adj_Close",
    "Close": "SPY_Close",
    "High": "SPY_High",
    "Low": "SPY_Low",
    "Open": "SPY_Open",
    "Volume": "SPY_Volume"
})

display(spy)

And the plot of the time series of partially adjusted close prices:

plot_time_series(
    df=spy,
    plot_start_date=None,
    plot_end_date=None,
    plot_columns=["SPY_Close"],
    title="SPY Close Price",
    x_label="Date",
    x_format="Year",
    x_tick_spacing=2,
    x_tick_rotation=30,
    y_label="Price ($)",
    y_format="Decimal",
    y_format_decimal_places=0,
    y_tick_spacing="Auto",
    y_tick_rotation=0,
    grid=True,
    legend=False,
    export_plot=False,
    plot_file_name=None,
)

Acquire & Plot Data (UPRO) #

Next, UPRO:

yf_pull_data(
    base_directory=DATA_DIR,
    ticker="UPRO",
    adjusted=False,
    source="Yahoo_Finance", 
    asset_class="Exchange_Traded_Funds", 
    excel_export=True,
    pickle_export=True,
    output_confirmation=False,
)
    
upro = load_data(
    base_directory=DATA_DIR,
    ticker="UPRO",
    source="Yahoo_Finance", 
    asset_class="Exchange_Traded_Funds",
    timeframe="Daily",
    file_format="pickle",
)

# Rename columns to "UPRO_Close", etc.
upro = upro.rename(columns={
    "Adj Close": "UPRO_Adj_Close",
    "Close": "UPRO_Close", 
    "High": "UPRO_High", 
    "Low": "UPRO_Low", 
    "Open": "UPRO_Open", 
    "Volume": "UPRO_Volume"
})

display(upro)