Backtest Portfolio Asset Allocation

Portfolio Backtesting Overview

This portfolio backtesting tool allows you to construct one or more portfolios based on the selected mutual funds, ETFs, and stocks. You can analyze and backtest portfolio returns, risk characteristics, style exposures, and drawdowns. The results cover both returns and fund fundamentals based portfolio style analysis along with risk and return decomposition by each portfolio asset. You can compare up to three different portfolios against the selected benchmark, and you can also specify any periodic contribution or withdrawal cashflows and the preferred portfolio rebalancing strategy.

The related asset class level portfolio modeling tool allows you to analyze and compare asset class level portfolios with a longer time horizon starting from 1972.

Portfolio Model Configuration

Time Period

Start Year

First Month

End Year

Last Month

Calendar Aligned

Include YTD

Start Date

End Date

Initial Amount

$ .00

Cashflows

Contribution Amount

$ .00

Inflation Adjusted

Withdrawal Percentage

Frequency

Rebalancing

Absolute Deviation

Relative Deviation

Leverage Type

Leverage Ratio

Debt Amount

$ .00

Debt Interest

Maintenance Margin

Leveraged Benchmark

Reinvest Dividends

Display Income

Factor Regression

Equity Factor Model

Benchmark

Benchmark Ticker

Portfolio Names

Portfolio #1

Portfolio #2

Portfolio #3

Asset Allocation

Portfolio Assets

Portfolio #1

Portfolio #2

Portfolio #3

Asset 1

Asset 2

Asset 3

Asset 4

Asset 5

Asset 6

Asset 7

Asset 8

Asset 9

Asset 10

Total

Portfolio Analysis Results (Jan 2012 - Dec 2020)

Note: The time period was constrained by the available data for ProShares VIX Mid-Term Futures (VIXM) [Feb 2011 - Aug 2023].

Portfolio 1

Ticker	Name	Allocation
SSO	ProShares Ultra S&P500	65.00%
VIXM	ProShares VIX Mid-Term Futures	35.00%
Save portfolio »

Portfolio 2

Ticker	Name	Allocation
SPY	SPDR S&P 500 ETF Trust	35.00%
SHY	iShares 1-3 Year Treasury Bond ETF	65.00%
Save portfolio »

Performance Summary

Portfolio performance statistics
Portfolio	Initial Balance	Final Balance	CAGR	Stdev	Best Year	Worst Year	Max. Drawdown	Sharpe Ratio	Sortino Ratio	Market Correlation
Portfolio 1	$10,000	$27,062	11.70%	12.55%	57.11%	-4.89%	-13.17%	0.89	1.76	0.76
Portfolio 2	$10,000	$17,276	6.26%	4.70%	13.17%	-0.74%	-6.61%	1.18	1.96	0.99
Vanguard 500 Index Investor	$10,000	$35,489	15.11%	13.29%	32.18%	-4.52%	-19.63%	1.08	1.75	1.00

Portfolio Growth

Annual Returns

Trailing Returns

Trailing Returns
Name	Total Return			Annualized Return			Annualized Standard Deviation
Name	3 Month	Year To Date	1 year	3 year	5 year	Full	3 year	5 year
Portfolio 1	13.22%	57.11%	57.11%	26.39%	17.14%	11.70%	17.58%	14.78%
Portfolio 2	4.15%	8.68%	8.68%	6.88%	6.69%	6.26%	6.61%	5.33%
Vanguard 500 Index Investor	12.12%	18.25%	18.25%	14.03%	15.07%	15.11%	18.80%	15.26%
Trailing return and volatility are as of last calendar month ending December 2020

Notes and Disclosures

IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
Portfolio model information represents a blended portfolio consisting of the model's underlying positions and assigned weights provided by the user and rebalanced at the specified schedule. The results were constructed using net of fee mutual fund performance. Portfolio Visualizer does not provide preferential treatment to any specific security or investment.
The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
Market capitalization refers to the total value of all a company's shares of stock. It is calculated by multiplying the price of a stock by its total number of outstanding shares. Large cap refers to a company with a market capitalization value of more than $10 billion, mid cap refers to a company with a market capitalization value between $2 and $10 billion, and small cap refers to a company with a market capitalization value below $2 billion. For funds and portfolios the equity market capitalization is calculated based on the long position of the equity holdings.
Credit quality measures the ability of a bond issuer to repay a bond's interest and principal in a timely manner. Ratings agencies research the financial health of each bond issuer and assign ratings to the bonds being offered. Lower-rated bonds generally offer higher yields to compensate investors for the additional risk. AAA is the highest possible rating that may be assigned to an issuer's bonds by any of the major credit rating agencies. Bonds rated AAA to AA are known as high-grade bonds, bonds rated A to BBB are known as medium-grade bonds, and bonds rated BB to C are known as non-investment grade bonds. An issuer will receive a rating of D if it is already in default on some of its debt. For funds and portfolios the fixed income credit quality break-down is calculated based on the long position of the fixed income holdings.
A fixed income maturity date refers to the specific date on which the investor's principal will be repaid. Duration measures a bond's or fixed income portfolio's price sensitivity to interest rate changes. If a bond has a duration of 5 years, and interest rates increase by 1%, the bond's price will decline by approximately 5%. Conversely, if a bond has a duration of 5 years and interest rates fall by 1%, the bond's price will increase by approximately 5%. A fixed income portfolio's duration is computed as the weighted average of individual bond durations held in the portfolio.
Compound annualized growth rate (CAGR) is the annualized geometric mean return of the portfolio. It is calculated from the portfolio start and end balance and is thus impacted by any cashflows.
The time-weighted rate of return (TWRR) is a measure of the compound rate of growth in a portfolio. This is calculated from the holding period returns (e.g. monthly returns), and TWRR will thus not be impacted by cashflows. If there are no external cashflows, TWRR will equal CAGR.
The money-weighted rate of return (MWRR) is the internal rate of return (IRR) taking into account cashflows. This is the discount rate at which the present value of cash inflows equals the present value of cash outflows.
Total return is the combined return in income and capital appreciation from investment in an asset. Yield measures the current cash income received from investment in an asset. Bonds provide yield in the form of interest payments and stocks through dividends.
Standard deviation (Stdev) is used to measure the dispersion of returns around the mean and is often used as a measure of risk. A higher standard deviation implies greater the dispersion of data points around the mean.
Sharpe Ratio is a measure of risk-adjusted performance of the portfolio, and it is calculated by dividing the mean monthly excess return of the portfolio over the risk-free rate by the standard deviation of excess return, and the displayed value is annualized.
Sortino Ratio is a measure of risk-adjusted return which is a modification of the Sharpe Ratio. While the latter is the ratio of average returns in excess of a risk-free rate divided by the standard deviation of those excess returns, the Sortino Ratio has the same denominator divided by the standard deviation of returns below the risk-free rate.
Treynor Ratio is a measure of risk-adjusted performance of the portfolio. It is similar to the Sharpe Ratio, but it uses portfolio beta (systematic risk) as the risk metric in the denominator.
Calmar Ratio is a measure of risk-adjusted performance of the portfolio. It is calculated as the annualized return over the past 36 months divided by the maximum drawdown over the past 36 months based on monthly returns.
Risk-free returns are calculated based on the Federal Reserve 3-Month Treasury Bill (secondary market) rates.
Downside deviation measures the downside volatility of the portfolio returns unlike standard deviation, which includes both upside and downside deviations. Downside deviation is calculated based on negative returns that hurt the portfolio performance.
Correlation measures to what degree the returns of the two assets move in relation to each other. Correlation coefficient is a numerical value between -1 and +1. If one variable goes up by a certain amount, the correlation coefficient indicates which way the other variable moves and by how much. Asset correlations are calculated based on monthly returns.
Skewness is a measure of the asymmetry of the probability distribution or returns from a normal Gaussian distribution shape about its mean. Negative skewness is associated with the left (typically negative returns) tail of the distribution extending further than the right tail; and positive skewness is associated with the right (typically positive returns) tail of the distribution extending further than the left tail.
Excess kurtosis is a measure of whether a data distribution is peaked or flat relative to a normal distribution. Distributions with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy or fat tails.
A drawdown refers to the decline in value of a single investment or an investment portfolio from a relative peak value to a relative trough. A maximum drawdown (Max Drawdown) is the maximum observed loss from a peak to a trough of a portfolio before a new peak is attained. Drawdown values are calculated based on monthly returns.
Value at Risk (VaR) measures the scale of loss at a given confidence level. For example, if the 95% confidence one-month VaR is 3%, there is 95% confidence that over the next month the portfolio will not lose more than 3%. Value at Risk can be calculated directly based on historical returns based on a given percentile or analytically based on the mean and standard deviation of the returns.
Conditional Value at Risk (CVaR) measures the scale of the expected loss once the specific Value at Risk (VaR) breakpoint has been breached, i.e., it calculates the average tail loss by taking a weighted average between the value at risk and losses exceeding the value at risk.
Beta is a measure of systematic risk and measures the volatility of a particular investment relative to the market or its benchmark. Alpha measures the active return of the investment compared to the market benchmark return. R-squared is the percentage of a portfolio's movements that can be explained by movements in the selected benchmark index.
Active return is the investment return minus the return of its benchmark. For periods longer than 12 months this is displayed as annualized value, i.e., annualized investment return minus annualized benchmark return.
Tracking error, also known as active risk, is the standard deviation of active return. This is displayed as annualized value based on the standard deviation of monthly active returns.
Information ratio is the active return divided by the tracking error. It measures whether the investment outperformed its benchmark consistently.
Gain/Loss ratio is a measure of downside risk, and it is calculated as the average positive return in up periods divided by the average negative return in down periods.
Upside Capture Ratio measures how well the fund performed relative to the benchmark when the market was up, and Downside Capture Ratio measures how well the fund performed relative to the benchmark when the market was down. An upside capture ratio greater than 100 would indicate that the fund outperformed its benchmark when the market was up, and a downside capture ratio below 100 would indicate that the fund lost less than its benchmark when the market was down. To calculate upside capture ratio a new series from the portfolio returns is constructed by dropping all time periods where the benchmark return is less than equal to zero. The up capture is then the quotient of the annualized return of the resulting manager series, divided by the annualized return of the resulting benchmark series. The downside capture ratio is calculated analogously.
All risk measures for the portfolio and portfolio assets are calculated based on monthly returns.
Gross expense ratio reflects the total annual operating expenses paid by each fund. Net expense ratio reflects what investors were charged after waivers, reductions, and reimbursements.
Price to earnings (P/E) ratio of a stock is calculated by dividing the current price of the stock by its trailing 12 months' earnings per share. For funds the price to earnings ratio is computed as the weighted average of fund holdings.
The results assume bands based (6.00% corridor) rebalancing of portfolio assets to match the specified allocation.

Annualized Active Return

Active Return Contribution

Rolling Active Return

Up vs. Down Market Performance

Portfolio 1 vs. Vanguard 500 Index Investor

Up vs. Down Market Performance - Portfolio 1 vs. Vanguard 500 Index Investor
Market Type	Occurrences				Average Active Return
Market Type	Above Benchmark	Below Benchmark	Total	% Above Benchmark	Above Benchmark	Below Benchmark	Total
Up Market	23	56	79	29%	1.17%	-1.65%	-0.83%
Down Market	18	11	29	62%	2.72%	-1.10%	1.27%
Total	41	67	108	38%	1.85%	-1.56%	-0.26%

Portfolio 2 vs. Vanguard 500 Index Investor

Up vs. Down Market Performance - Portfolio 2 vs. Vanguard 500 Index Investor
Market Type	Occurrences				Average Active Return
Market Type	Above Benchmark	Below Benchmark	Total	% Above Benchmark	Above Benchmark	Below Benchmark	Total
Up Market	2	77	79	3%	0.17%	-1.90%	-1.85%
Down Market	28	1	29	97%	2.38%	-0.02%	2.30%
Total	30	78	108	28%	2.24%	-1.88%	-0.74%

Annual Returns

Annual returns for the configured portfolios
Year	Inflation	Portfolio 1		Portfolio 2		Vanguard 500 Index Investor		ProShares Ultra S&P500 (SSO)	ProShares VIX Mid-Term Futures (VIXM)	SPDR S&P 500 ETF Trust (SPY)	iShares 1-3 Year Treasury Bond ETF (SHY)
Year	Inflation	Return	Balance	Return	Balance	Return	Balance	ProShares Ultra S&P500 (SSO)	ProShares VIX Mid-Term Futures (VIXM)	SPDR S&P 500 ETF Trust (SPY)	iShares 1-3 Year Treasury Bond ETF (SHY)
2012	1.74%	-4.89%	$9,511	5.78%	$10,578	15.82%	$11,582	31.04%	-53.84%	15.99%	0.28%
2013	1.50%	22.48%	$11,649	11.40%	$11,784	32.18%	$15,309	70.46%	-43.63%	32.31%	0.21%
2014	0.76%	9.99%	$12,813	5.32%	$12,410	13.51%	$17,377	25.53%	-17.20%	13.46%	0.45%
2015	0.73%	-4.23%	$12,270	0.72%	$12,500	1.25%	$17,594	-1.19%	-15.50%	1.25%	0.43%
2016	2.07%	5.91%	$12,996	4.82%	$13,103	11.82%	$19,673	21.55%	-21.58%	12.00%	0.82%
2017	2.11%	3.15%	$13,405	7.99%	$14,150	21.67%	$23,936	44.35%	-50.05%	21.70%	0.26%
2018	1.91%	0.36%	$13,453	-0.74%	$14,046	-4.52%	$22,853	-14.62%	26.43%	-4.56%	1.46%
2019	2.29%	28.04%	$17,225	13.17%	$15,896	31.33%	$30,012	63.45%	-20.38%	31.22%	3.38%
2020	1.36%	57.11%	$27,062	8.68%	$17,276	18.25%	$35,489	21.53%	72.38%	18.37%	3.03%

Monthly Returns

Monthly returns for the configured portfolios
Year	Month	Portfolio 1		Portfolio 2		Vanguard 500 Index Investor		ProShares Ultra S&P500 (SSO)	ProShares VIX Mid-Term Futures (VIXM)	SPDR S&P 500 ETF Trust (SPY)	iShares 1-3 Year Treasury Bond ETF (SHY)
Year	Month	Return	Balance	Return	Balance	Return	Balance	ProShares Ultra S&P500 (SSO)	ProShares VIX Mid-Term Futures (VIXM)	SPDR S&P 500 ETF Trust (SPY)	iShares 1-3 Year Treasury Bond ETF (SHY)
2012	1	2.43%	$10,243	1.68%	$10,168	4.46%	$10,446	8.97%	-9.71%	4.64%	0.08%
2012	2	5.91%	$10,848	1.47%	$10,318	4.31%	$10,896	8.45%	0.21%	4.34%	-0.14%
2012	3	0.25%	$10,875	1.14%	$10,435	3.28%	$11,254	6.71%	-15.40%	3.22%	-0.08%
2012	4	-1.69%	$10,691	-0.13%	$10,422	-0.64%	$11,182	-1.61%	-1.84%	-0.67%	0.20%
2012	5	-3.57%	$10,309	-2.22%	$10,191	-6.02%	$10,509	-11.37%	10.94%	-6.01%	0.06%
2012	6	-0.02%	$10,307	1.40%	$10,333	4.11%	$10,941	7.27%	-10.86%	4.05%	-0.10%
2012	7	-0.50%	$10,255	0.58%	$10,393	1.37%	$11,091	2.53%	-5.94%	1.18%	0.22%
2012	8	2.02%	$10,463	0.94%	$10,491	2.24%	$11,339	4.61%	-3.03%	2.51%	0.01%
2012	9	-2.20%	$10,232	0.97%	$10,593	2.58%	$11,631	4.87%	-17.08%	2.54%	0.02%
2012	10	-5.15%	$9,705	-0.74%	$10,514	-1.86%	$11,415	-4.15%	-7.01%	-1.82%	-0.07%
2012	11	-2.71%	$9,443	0.25%	$10,540	0.56%	$11,479	0.94%	-9.68%	0.57%	0.05%
2012	12	0.72%	$9,511	0.36%	$10,578	0.90%	$11,582	2.08%	-2.20%	0.90%	0.02%
2013	1	1.52%	$9,655	1.97%	$10,786	5.18%	$12,182	10.27%	-18.03%	5.12%	0.01%
2013	2	0.61%	$9,714	0.54%	$10,845	1.34%	$12,345	2.16%	-2.28%	1.28%	0.06%
2013	3	3.66%	$10,069	1.53%	$11,011	3.74%	$12,807	7.39%	-3.58%	3.80%	0.03%
2013	4	0.39%	$10,109	0.82%	$11,102	1.91%	$13,051	3.86%	-7.11%	1.92%	0.07%
2013	5	4.83%	$10,597	0.74%	$11,184	2.33%	$13,355	4.55%	5.50%	2.36%	-0.13%
2013	6	0.48%	$10,647	-0.54%	$11,123	-1.35%	$13,174	-3.11%	9.07%	-1.34%	-0.10%
2013	7	1.94%	$10,854	1.93%	$11,338	5.07%	$13,843	10.41%	-16.11%	5.17%	0.16%
2013	8	-1.90%	$10,648	-1.15%	$11,207	-2.91%	$13,440	-6.08%	5.86%	-3.00%	-0.10%
2013	9	0.92%	$10,745	1.28%	$11,350	3.12%	$13,859	6.48%	-8.25%	3.17%	0.22%
2013	10	4.63%	$11,243	1.73%	$11,546	4.59%	$14,495	9.07%	-3.87%	4.63%	0.07%
2013	11	2.27%	$11,498	1.17%	$11,681	3.03%	$14,934	5.77%	-5.33%	2.96%	0.09%
2013	12	1.31%	$11,649	0.88%	$11,784	2.51%	$15,309	5.13%	-7.92%	2.59%	-0.18%
2014	1	-3.38%	$11,255	-1.24%	$11,637	-3.47%	$14,778	-7.23%	3.78%	-3.52%	0.20%
2014	2	4.19%	$11,727	1.75%	$11,840	4.56%	$15,452	9.06%	-3.90%	4.55%	0.04%
2014	3	-0.34%	$11,687	0.26%	$11,871	0.82%	$15,579	1.52%	-3.85%	0.83%	-0.11%
2014	4	-0.32%	$11,650	0.34%	$11,911	0.72%	$15,692	1.23%	-3.41%	0.70%	0.11%
2014	5	1.64%	$11,841	1.02%	$12,032	2.33%	$16,059	4.41%	-4.14%	2.32%	0.18%
2014	6	-0.12%	$11,827	0.77%	$12,125	2.05%	$16,388	4.10%	-9.69%	2.06%	-0.08%
2014	7	-1.73%	$11,622	-0.59%	$12,054	-1.39%	$16,161	-2.88%	0.39%	-1.34%	-0.08%
2014	8	3.88%	$12,073	1.69%	$12,258	3.98%	$16,804	7.87%	-3.28%	3.95%	0.19%
2014	9	0.15%	$12,091	-0.61%	$12,183	-1.41%	$16,567	-2.93%	6.32%	-1.38%	-0.07%
2014	10	2.01%	$12,334	1.11%	$12,318	2.42%	$16,968	4.38%	-2.32%	2.36%	0.26%
2014	11	2.65%	$12,661	1.03%	$12,445	2.68%	$17,423	5.54%	-2.98%	2.75%	0.11%
2014	12	1.20%	$12,813	-0.28%	$12,410	-0.26%	$17,377	-0.84%	5.53%	-0.26%	-0.29%
2015	1	-1.56%	$12,613	-0.65%	$12,330	-3.02%	$16,853	-6.15%	7.62%	-2.96%	0.63%
2015	2	3.07%	$13,001	1.76%	$12,547	5.74%	$17,820	11.40%	-11.45%	5.62%	-0.29%
2015	3	-2.25%	$12,708	-0.41%	$12,496	-1.59%	$17,536	-3.43%	0.33%	-1.57%	0.25%
2015	4	-0.31%	$12,668	0.37%	$12,542	0.95%	$17,703	1.84%	-4.85%	0.98%	0.03%
2015	5	-0.26%	$12,635	0.49%	$12,604	1.27%	$17,928	2.31%	-6.07%	1.29%	0.04%
2015	6	-2.84%	$12,276	-0.71%	$12,514	-1.93%	$17,581	-4.09%	-0.53%	-2.03%	0.03%
2015	7	0.23%	$12,304	0.84%	$12,618	2.08%	$17,947	4.22%	-6.90%	2.26%	0.04%
2015	8	0.16%	$12,323	-2.24%	$12,336	-6.05%	$16,862	-12.48%	25.47%	-6.10%	-0.05%
2015	9	-3.60%	$11,879	-0.69%	$12,250	-2.48%	$16,443	-5.54%	0.00%	-2.54%	0.30%
2015	10	5.63%	$12,548	2.81%	$12,595	8.42%	$17,828	17.45%	-15.10%	8.51%	-0.14%
2015	11	0.42%	$12,601	-0.03%	$12,590	0.29%	$17,879	0.60%	0.00%	0.37%	-0.26%
2015	12	-2.62%	$12,270	-0.72%	$12,500	-1.59%	$17,594	-3.80%	0.24%	-1.72%	-0.15%
2016	1	-4.60%	$11,705	-1.36%	$12,330	-4.98%	$16,719	-10.37%	8.89%	-4.98%	0.65%
2016	2	1.35%	$11,863	0.04%	$12,335	-0.15%	$16,694	-0.62%	5.15%	-0.08%	0.11%
2016	3	3.90%	$12,326	2.41%	$12,632	6.78%	$17,825	13.98%	-14.48%	6.72%	0.14%
2016	4	1.49%	$12,510	0.16%	$12,653	0.37%	$17,892	0.60%	3.67%	0.39%	0.04%
2016	5	0.38%	$12,557	0.54%	$12,721	1.78%	$18,211	3.18%	-6.22%	1.70%	-0.12%
2016	6	0.88%	$12,667	0.51%	$12,786	0.25%	$18,257	0.16%	2.20%	0.35%	0.60%
2016	7	1.53%	$12,860	1.30%	$12,951	3.68%	$18,928	7.40%	-9.16%	3.65%	-0.05%
2016	8	-0.16%	$12,840	-0.10%	$12,938	0.13%	$18,952	0.10%	-0.71%	0.12%	-0.23%
2016	9	-1.32%	$12,671	0.08%	$12,949	0.01%	$18,954	-0.28%	-3.57%	0.01%	0.13%
2016	10	-3.10%	$12,278	-0.68%	$12,861	-1.83%	$18,606	-3.68%	-1.82%	-1.73%	-0.05%
2016	11	3.46%	$12,702	1.06%	$12,998	3.70%	$19,295	7.23%	-4.84%	3.68%	-0.47%
2016	12	2.31%	$12,996	0.81%	$13,103	1.96%	$19,673	4.00%	-0.82%	2.03%	0.07%
2017	1	-1.94%	$12,744	0.75%	$13,201	1.88%	$20,044	3.47%	-12.47%	1.79%	0.11%
2017	2	4.21%	$13,280	1.54%	$13,405	3.96%	$20,838	7.83%	-4.13%	3.93%	0.04%
2017	3	-3.54%	$12,810	0.09%	$13,417	0.10%	$20,859	-0.02%	-10.08%	0.13%	0.06%
2017	4	-0.72%	$12,717	0.51%	$13,484	1.02%	$21,071	1.85%	-6.04%	0.99%	0.19%
2017	5	1.13%	$12,861	0.61%	$13,566	1.39%	$21,365	2.55%	-2.03%	1.41%	0.07%
2017	6	-1.29%	$12,696	0.21%	$13,594	0.61%	$21,496	1.04%	-6.73%	0.64%	-0.08%
2017	7	-0.11%	$12,681	0.94%	$13,722	2.04%	$21,935	3.95%	-7.66%	2.06%	0.19%
2017	8	1.44%	$12,864	0.24%	$13,755	0.29%	$21,999	0.31%	3.79%	0.29%	0.20%
2017	9	1.14%	$13,011	0.71%	$13,852	2.06%	$22,452	3.82%	-4.26%	2.01%	-0.19%
2017	10	0.56%	$13,083	0.77%	$13,958	2.32%	$22,972	4.53%	-8.14%	2.36%	-0.09%
2017	11	4.26%	$13,641	0.95%	$14,090	3.06%	$23,675	5.87%	1.27%	3.06%	-0.22%
2017	12	-1.73%	$13,405	0.43%	$14,150	1.10%	$23,936	2.36%	-9.67%	1.21%	-0.02%
2018	1	8.06%	$14,486	1.88%	$14,417	5.71%	$25,303	11.17%	1.23%	5.64%	-0.29%
2018	2	-1.07%	$14,330	-1.44%	$14,209	-3.69%	$24,369	-8.07%	15.83%	-3.64%	-0.10%
2018	3	-1.36%	$14,135	-0.86%	$14,086	-2.56%	$23,746	-5.54%	6.65%	-2.74%	0.25%
2018	4	-2.31%	$13,808	0.04%	$14,092	0.37%	$23,834	0.20%	-6.58%	0.52%	-0.23%
2018	5	0.47%	$13,872	1.11%	$14,249	2.39%	$24,405	4.41%	-6.72%	2.43%	0.35%
2018	6	0.64%	$13,961	0.24%	$14,283	0.61%	$24,553	1.02%	-0.13%	0.58%	0.04%
2018	7	2.90%	$14,366	1.34%	$14,474	3.71%	$25,464	7.09%	-5.73%	3.70%	-0.06%
2018	8	3.76%	$14,906	1.43%	$14,681	3.25%	$26,290	6.15%	-1.84%	3.19%	0.35%
2018	9	-0.44%	$14,841	0.14%	$14,702	0.55%	$26,436	0.89%	-2.91%	0.59%	-0.14%
2018	10	-2.27%	$14,505	-2.59%	$14,321	-6.85%	$24,625	-14.01%	20.40%	-6.91%	0.15%
2018	11	0.50%	$14,577	0.93%	$14,454	2.03%	$25,124	3.15%	-4.42%	1.85%	0.38%
2018	12	-7.71%	$13,453	-2.82%	$14,046	-9.04%	$22,853	-17.72%	12.35%	-8.79%	0.76%
2019	1	4.40%	$14,045	2.98%	$14,464	8.00%	$24,682	15.73%	-12.23%	8.01%	0.25%
2019	2	1.23%	$14,218	1.25%	$14,645	3.20%	$25,472	6.21%	-8.39%	3.24%	0.09%
2019	3	2.51%	$14,575	1.07%	$14,802	1.94%	$25,965	3.45%	0.42%	1.81%	0.63%
2019	4	4.81%	$15,277	1.66%	$15,048	4.04%	$27,014	7.72%	-1.90%	4.09%	0.18%
2019	5	-5.49%	$14,438	-2.03%	$14,742	-6.36%	$25,295	-12.77%	8.03%	-6.38%	0.72%
2019	6	6.27%	$15,343	2.87%	$15,165	7.03%	$27,074	14.09%	-5.46%	6.96%	0.46%
2019	7	1.72%	$15,607	0.54%	$15,248	1.43%	$27,460	2.52%	0.28%	1.51%	-0.06%
2019	8	0.47%	$15,679	-0.17%	$15,221	-1.59%	$27,023	-4.04%	8.81%	-1.67%	0.78%
2019	9	2.36%	$16,049	0.66%	$15,322	1.86%	$27,525	3.62%	0.30%	1.95%	-0.13%
2019	10	1.19%	$16,240	1.05%	$15,483	2.15%	$28,119	4.00%	-3.55%	2.21%	0.31%
2019	11	3.44%	$16,799	1.39%	$15,699	3.62%	$29,137	7.07%	-3.15%	3.62%	-0.05%
2019	12	2.54%	$17,225	1.26%	$15,896	3.01%	$30,012	5.65%	-3.71%	2.90%	0.16%
2020	1	-0.51%	$17,138	0.33%	$15,948	-0.05%	$29,997	-0.44%	-0.66%	-0.04%	0.58%
2020	2	-7.04%	$15,932	-2.70%	$15,518	-8.24%	$27,525	-15.46%	11.58%	-7.92%	0.88%
2020	3	4.86%	$16,707	-4.03%	$14,893	-12.37%	$24,120	-29.80%	62.89%	-12.46%	1.24%
2020	4	16.84%	$19,520	4.63%	$15,583	12.81%	$27,210	25.18%	1.35%	12.70%	0.27%
2020	5	6.84%	$20,856	1.75%	$15,856	4.76%	$28,504	9.16%	1.54%	4.76%	-0.08%
2020	6	2.52%	$21,382	0.70%	$15,967	1.98%	$29,068	2.95%	1.72%	1.78%	0.02%
2020	7	7.15%	$22,910	2.37%	$16,346	5.63%	$30,704	11.69%	-1.39%	5.89%	0.09%
2020	8	10.06%	$25,215	2.82%	$16,808	7.18%	$32,907	14.29%	1.06%	6.98%	-0.02%
2020	9	-5.20%	$23,903	-1.31%	$16,588	-3.81%	$31,653	-7.97%	1.45%	-3.74%	-0.00%
2020	10	-3.28%	$23,119	-0.88%	$16,441	-2.67%	$30,808	-5.38%	1.30%	-2.49%	-0.05%
2020	11	10.81%	$25,617	3.67%	$17,044	10.94%	$34,177	22.51%	-13.08%	10.88%	0.02%
2020	12	5.64%	$27,062	1.36%	$17,276	3.84%	$35,489	7.36%	2.46%	3.71%	0.04%

Returns Based Style Analysis

Returns Based Style Analysis
Style Category	Portfolio 2	Vanguard 500 Index Investor
Large-cap Value	15.91%	44.97%
Large-cap Growth	19.13%	54.95%
Mid-cap Value	0.00%	0.00%
Mid-cap Growth	0.00%	0.00%
Small-cap Value	0.00%	0.08%
Small-cap Growth	0.00%	0.00%
Global ex-US Developed Markets	0.00%	0.00%
Emerging Markets	0.00%	0.00%
Corporate Bonds	0.00%	0.00%
Long-Term Treasuries	0.00%	0.00%
Intermediate-Term Treasuries	0.00%	0.00%
Short-Term Treasuries	64.96%	0.00%
R Squared	99.94%	99.93%
Style analysis is based on monthly returns from January 2012 to December 2020 and uses total portfolio return with monthly rebalancing. Returns based style analysis aims to explain the portfolio returns based on asset class exposures, it does not identify the actual portfolio holdings.

Holdings Based Style Analysis for Portfolio 1

Holdings Based Style Analysis for Portfolio 1
Ticker	Name	Category	Weight	TTM Yield	Expense Ratio		P/E	Contribution
Ticker	Name	Category	Weight	TTM Yield	Net	Gross	P/E	Return	Risk
SSO	ProShares Ultra S&P500	Leveraged Equity	65.00%	0.31%	0.89%	0.89%	22.40	$22,120	108.74%
VIXM	ProShares VIX Mid-Term Futures	Miscellaneous	35.00%		0.93%	0.93%		-$5,058	-8.74%
			100.00%	0.20%	0.90%	0.90%	22.40	$17,062	100.00%

Asset Allocation

Equity Market Capitalization

Equity Sectors

Holdings Based Style Analysis for Portfolio 2

Holdings Based Style Analysis for Portfolio 2
Ticker	Name	Category	Weight	Yield		Expense Ratio		P/E	Duration	Contribution
Ticker	Name	Category	Weight	SEC	TTM	Net	Gross	P/E	Duration	Return	Risk
SPY	SPDR S&P 500 ETF Trust	Large Blend	35.00%	1.40%	1.45%	0.09%	0.09%	22.40		$6,369	104.08%
SHY	iShares 1-3 Year Treasury Bond ETF	Short Government	65.00%	4.89%	2.46%	0.15%	0.15%		1.87	$907	-4.08%
			100.00%	3.67%	2.11%	0.13%	0.13%	22.40	1.87	$7,276	100.00%

Asset Allocation

Equity Market Capitalization

Equity Sectors

Fixed Income Credit Quality

Fixed Income Maturity

Fund fundamentals data as of 09/27/2023. (c) 2023 Morningstar. All Rights Reserved. The fund fundamentals information contained herein: (1) is proprietary to Morningstar and/or its content providers; (2) may not be copied or distributed; and (3) is not warranted to be accurate, complete or timely. Neither Morningstar nor its content providers are responsible for any damages or losses arising from any use of this information.

Risk and Return Metrics

Portfolio return and risk metrics
Metric	Portfolio 1	Portfolio 2	Vanguard 500 Index Investor
Arithmetic Mean (monthly)	0.99%	0.52%	1.25%
Arithmetic Mean (annualized)	12.54%	6.38%	16.11%
Geometric Mean (monthly)	0.93%	0.51%	1.18%
Geometric Mean (annualized)	11.70%	6.26%	15.11%
Standard Deviation (monthly)	3.62%	1.36%	3.84%
Standard Deviation (annualized)	12.55%	4.70%	13.29%
Downside Deviation (monthly)	1.81%	0.78%	2.34%
Maximum Drawdown	-13.17%	-6.61%	-19.63%
Stock Market Correlation	0.76	0.99	1.00
Beta^(*)	0.73	0.35	1.00
Alpha (annualized)	0.96%	0.92%	-0.00%
R²	59.14%	98.65%	100.00%
Sharpe Ratio	0.89	1.18	1.08
Sortino Ratio	1.76	1.96	1.75
Treynor Ratio (%)	15.46	15.82	14.39
Calmar Ratio	2.71	1.04	0.71
Active Return	-3.42%	-8.85%	N/A
Tracking Error	8.81%	8.64%	N/A
Information Ratio	-0.39	-1.02	N/A
Skewness	0.87	-0.41	-0.49
Excess Kurtosis	3.09	1.47	1.92
Historical Value-at-Risk (5%)	4.25%	2.16%	6.04%
Analytical Value-at-Risk (5%)	4.83%	1.59%	5.06%
Conditional Value-at-Risk (5%)	5.87%	2.77%	8.15%
Upside Capture Ratio (%)	68.93	35.47	100.00
Downside Capture Ratio (%)	64.30	33.95	100.00
Safe Withdrawal Rate	13.94%	13.74%	20.24%
Perpetual Withdrawal Rate	9.04%	4.38%	11.73%
Positive Periods	67 out of 108 (62.04%)	79 out of 108 (73.15%)	79 out of 108 (73.15%)
Gain/Loss Ratio	1.32	0.97	0.86
^* Vanguard 500 Index Investor is used as the benchmark for calculations. Value-at-risk metrics are monthly values.

Drawdowns

Historical Market Stress Periods

Drawdowns for Historical Market Stress Periods
Stress Period	Start	End	Portfolio 1	Portfolio 2	Vanguard 500 Index Investor
COVID-19 Start	Jan 2020	Mar 2020	-7.51%	-6.61%	-19.63%

Drawdowns for Portfolio 1

Drawdowns for Portfolio 1 (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Apr 2012	Nov 2012	8 months	Oct 2013	11 months	1 year 7 months	-13.17%
2	Mar 2015	Jan 2016	11 months	Feb 2017	1 year 1 month	2 years	-9.96%
3	Sep 2018	Dec 2018	4 months	Apr 2019	4 months	8 months	-9.75%
4	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-8.31%
5	Jan 2020	Feb 2020	2 months	Apr 2020	2 months	4 months	-7.51%
6	May 2019	May 2019	1 month	Jun 2019	1 month	2 months	-5.49%
7	Feb 2018	Apr 2018	3 months	Aug 2018	4 months	7 months	-4.68%
8	Mar 2017	Jul 2017	5 months	Nov 2017	4 months	9 months	-4.51%
9	Jan 2014	Jan 2014	1 month	Feb 2014	1 month	2 months	-3.38%
10	Jun 2014	Jul 2014	2 months	Aug 2014	1 month	3 months	-1.85%
Worst 10 drawdowns included above

Drawdowns for Portfolio 2

Drawdowns for Portfolio 2 (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Feb 2020	Mar 2020	2 months	Jun 2020	3 months	5 months	-6.61%
2	Oct 2018	Dec 2018	3 months	Mar 2019	3 months	6 months	-4.46%
3	Aug 2015	Sep 2015	2 months	Mar 2016	6 months	8 months	-2.91%
4	Apr 2012	May 2012	2 months	Aug 2012	3 months	5 months	-2.35%
5	Feb 2018	Mar 2018	2 months	Jul 2018	4 months	6 months	-2.29%
6	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-2.18%
7	May 2019	May 2019	1 month	Jun 2019	1 month	2 months	-2.03%
8	Jan 2014	Jan 2014	1 month	Feb 2014	1 month	2 months	-1.24%
9	Aug 2013	Aug 2013	1 month	Sep 2013	1 month	2 months	-1.15%
10	Dec 2014	Jan 2015	2 months	Feb 2015	1 month	3 months	-0.93%
Worst 10 drawdowns included above

Drawdowns for Vanguard 500 Index Investor

Drawdowns for Vanguard 500 Index Investor (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Jan 2020	Mar 2020	3 months	Jul 2020	4 months	7 months	-19.63%
2	Oct 2018	Dec 2018	3 months	Apr 2019	4 months	7 months	-13.55%
3	Aug 2015	Sep 2015	2 months	May 2016	8 months	10 months	-8.38%
4	Apr 2012	May 2012	2 months	Aug 2012	3 months	5 months	-6.62%
5	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-6.38%
6	May 2019	May 2019	1 month	Jun 2019	1 month	2 months	-6.36%
7	Feb 2018	Mar 2018	2 months	Jul 2018	4 months	6 months	-6.16%
8	Jan 2014	Jan 2014	1 month	Feb 2014	1 month	2 months	-3.47%
9	Dec 2014	Jan 2015	2 months	Feb 2015	1 month	3 months	-3.27%
10	Aug 2013	Aug 2013	1 month	Sep 2013	1 month	2 months	-2.91%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
Ticker	Name	CAGR	Stdev	Best Year	Worst Year	Max Drawdown	Sharpe Ratio	Sortino Ratio	Market Correlation
SSO	ProShares Ultra S&P500	26.41%	27.29%	70.46%	-14.62%	-40.91%	0.98	1.55	1.00
VIXM	ProShares VIX Mid-Term Futures	-20.72%	33.60%	72.38%	-53.84%	-93.03%	-0.56	-0.88	-0.71
SPY	SPDR S&P 500 ETF Trust	15.16%	13.24%	32.31%	-4.56%	-19.43%	1.09	1.77	1.00
SHY	iShares 1-3 Year Treasury Bond ETF	1.14%	0.93%	3.38%	0.21%	-0.90%	0.56	1.12	-0.40

Portfolio Asset Performance

Performance of portfolio assets
Name	Total Return			Annualized Return		Expense Ratio
Name	3 Month	Year To Date	1 year	3 year	5 year	Net	Gross
ProShares Ultra S&P500	24.45%	21.53%	21.53%	19.25%	24.37%	0.89%	0.89%
ProShares VIX Mid-Term Futures	-9.78%	72.38%	72.38%	20.17%	-7.43%	0.93%	0.93%
SPDR S&P 500 ETF Trust	12.12%	18.37%	18.37%	14.03%	15.11%	0.09%	0.09%
iShares 1-3 Year Treasury Bond ETF	0.02%	3.03%	3.03%	2.62%	1.79%	0.15%	0.15%
Trailing returns as of last calendar month ending December 2020

Monthly Correlations

Correlations for the portfolio assets
Ticker	Name	SSO	VIXM	SPY	SHY	Portfolio 1	Portfolio 2	Vanguard 500 Index Investor
SSO	ProShares Ultra S&P500	1.00	-0.73	1.00	-0.41	0.74	0.99	1.00
VIXM	ProShares VIX Mid-Term Futures	-0.73	1.00	-0.70	0.44	-0.09	-0.69	-0.70
SPY	SPDR S&P 500 ETF Trust	1.00	-0.70	1.00	-0.39	0.77	0.99	1.00
SHY	iShares 1-3 Year Treasury Bond ETF	-0.41	0.44	-0.39	1.00	-0.16	-0.30	-0.39

Portfolio Return Decomposition

Portfolio return decomposition
Ticker	Name	Portfolio 1	Portfolio 2
SSO	ProShares Ultra S&P500	$22,120
VIXM	ProShares VIX Mid-Term Futures	-$5,058
SPY	SPDR S&P 500 ETF Trust		$6,369
SHY	iShares 1-3 Year Treasury Bond ETF		$907
Return attribution decomposes portfolio gains into its constituent parts and identifies the contribution to returns by each of the assets.

Portfolio Risk Decomposition

Portfolio risk decomposition
Ticker	Name	Portfolio 1	Portfolio 2
SSO	ProShares Ultra S&P500	108.74%
VIXM	ProShares VIX Mid-Term Futures	-8.74%
SPY	SPDR S&P 500 ETF Trust		104.08%
SHY	iShares 1-3 Year Treasury Bond ETF		-4.08%
Risk attribution decomposes portfolio risk into its constituent parts and identifies the contribution to overall volatility by each of the assets.

Annual Asset Returns

Rolling Returns

Rolling returns summary
Roll Period	Portfolio 1			Portfolio 2			Vanguard 500 Index Investor
Roll Period	Average	High	Low	Average	High	Low	Average	High	Low
1 year	10.23%	60.82%	-10.45%	5.70%	13.17%	-1.69%	13.55%	32.18%	-7.11%
3 years	7.56%	26.39%	1.52%	5.21%	7.46%	3.54%	12.53%	20.22%	4.96%
5 years	6.87%	17.14%	2.92%	5.13%	6.69%	3.57%	12.39%	15.74%	6.58%
7 years	8.12%	13.11%	3.94%	5.40%	5.99%	4.41%	12.77%	14.57%	9.47%

Annualized Rolling Return - 3 Years

Annualized Rolling Return - 5 Years

Portfolio 1 Rebalancing Events

Rebalancing dates for portfolio 1
#	Date	Allocation
1	03/31/2012	ProShares Ultra S&P500 (SSO): 75.37% ProShares VIX Mid-Term Futures (VIXM): 24.63%
2	09/30/2012	ProShares Ultra S&P500 (SSO): 72.69% ProShares VIX Mid-Term Futures (VIXM): 27.31%
3	01/31/2013	ProShares Ultra S&P500 (SSO): 75.03% ProShares VIX Mid-Term Futures (VIXM): 24.97%
4	07/31/2013	ProShares Ultra S&P500 (SSO): 73.69% ProShares VIX Mid-Term Futures (VIXM): 26.31%
5	12/31/2013	ProShares Ultra S&P500 (SSO): 73.46% ProShares VIX Mid-Term Futures (VIXM): 26.54%
6	06/30/2014	ProShares Ultra S&P500 (SSO): 72.35% ProShares VIX Mid-Term Futures (VIXM): 27.65%
7	05/31/2015	ProShares Ultra S&P500 (SSO): 71.09% ProShares VIX Mid-Term Futures (VIXM): 28.91%
8	08/31/2015	ProShares Ultra S&P500 (SSO): 58.30% ProShares VIX Mid-Term Futures (VIXM): 41.70%
9	05/31/2016	ProShares Ultra S&P500 (SSO): 72.17% ProShares VIX Mid-Term Futures (VIXM): 27.83%
10	11/30/2016	ProShares Ultra S&P500 (SSO): 71.26% ProShares VIX Mid-Term Futures (VIXM): 28.74%
11	02/28/2017	ProShares Ultra S&P500 (SSO): 72.14% ProShares VIX Mid-Term Futures (VIXM): 27.86%
12	06/30/2017	ProShares Ultra S&P500 (SSO): 71.74% ProShares VIX Mid-Term Futures (VIXM): 28.26%
13	10/31/2017	ProShares Ultra S&P500 (SSO): 71.37% ProShares VIX Mid-Term Futures (VIXM): 28.63%
14	08/31/2018	ProShares Ultra S&P500 (SSO): 71.70% ProShares VIX Mid-Term Futures (VIXM): 28.30%
15	10/31/2018	ProShares Ultra S&P500 (SSO): 57.95% ProShares VIX Mid-Term Futures (VIXM): 42.05%
16	04/30/2019	ProShares Ultra S&P500 (SSO): 71.73% ProShares VIX Mid-Term Futures (VIXM): 28.27%
17	03/31/2020	ProShares Ultra S&P500 (SSO): 41.91% ProShares VIX Mid-Term Futures (VIXM): 58.09%
18	05/31/2020	ProShares Ultra S&P500 (SSO): 71.15% ProShares VIX Mid-Term Futures (VIXM): 28.85%
19	11/30/2020	ProShares Ultra S&P500 (SSO): 74.20% ProShares VIX Mid-Term Futures (VIXM): 25.80%

Portfolio 2 Rebalancing Events

Rebalancing dates for portfolio 2
#	Date	Allocation
1	04/30/2013	SPDR S&P 500 ETF Trust (SPY): 41.19% iShares 1-3 Year Treasury Bond ETF (SHY): 58.81%
2	10/31/2014	SPDR S&P 500 ETF Trust (SPY): 41.02% iShares 1-3 Year Treasury Bond ETF (SHY): 58.98%
3	09/30/2017	SPDR S&P 500 ETF Trust (SPY): 41.24% iShares 1-3 Year Treasury Bond ETF (SHY): 58.76%
4	08/31/2020	SPDR S&P 500 ETF Trust (SPY): 42.30% iShares 1-3 Year Treasury Bond ETF (SHY): 57.70%