Test Market Timing Models

Tactical Allocation Overview

This tool allows you to test different market timing and tactical asset allocation models based on moving averages, momentum, market valuation and target volatility. The supported models include:

Shiller PE Ratio Market Valuation
Seasonal Model
Moving Averages - Single Asset
Moving Averages - Portfolio Assets
Momentum - Relative Strength
Momentum - Dual Momentum
Momentum - Adaptive Allocation
Target Volatility

You can find a summary of the selected tactical asset allocation model below, and a more detailed description in the FAQ section.

Seasonal Model

Seasonal model moves the portfolio out of market based on specific calendar months. Sell in May and Go Away model is a well-known example that avoids historical underperformance of some stocks in the six-month period commencing in May and ending in October.

Shiller PE Ratio Market Valuation

Shiller PE Ratio (PE10) market valuation based timing model adjusts the allocation between stocks and bonds based on the start of year Shiller PE Ratio as follows:

PE10 >= 22 - 40% stocks, 60% bonds
14 <= PE10 < 22 - 60% stocks, 40% bonds
PE10 < 14 - 80% stocks, 20% bonds

The balanced 60% stock and 40% bond allocation is used as the benchmark portfolio.

Moving Averages - Single Asset

The moving average timing model is either invested in a specific stock, ETF or mutual fund, or is alternatively in cash or other risk-free asset based on the moving average signal. The model is invested in the asset when the adjusted close price is greater than the moving average and the model moves to cash when the adjusted close price is less than the moving average. The model also supports using moving average cross-over as the signal.

Moving Averages - Portfolio Assets

The moving average model applies the moving average signal to each portfolio asset. The model is invested in a portfolio asset when the adjusted close price is greater than the moving average and the allocation is moved to cash when the adjusted close price is less than the moving average. The model also supports using moving average cross-over as the signal.

Momentum - Relative Strength

The relative strength momentum model invests in the best performing assets in the model based on each asset's past return. The momentum can be based on a single timing period, or multiple weighted timing periods. Additionally the model supports using moving averages as a risk control to decide whether investments should be moved to cash.

Momentum - Dual Momentum

The dual momentum model uses relative momentum to select the best performing model assets and incorporates absolute momentum as a filter to invest in cash if the excess return of the selected asset over cash is negative.

Adaptive Allocation

The adaptive asset allocation model combines relative strength momentum model with different asset weighting. The relative strength model uses an equal weight allocation for the model selected assets, whereas the adaptive asset allocation uses either risk parity allocation or minimum variance allocation for the model assets to minimize the expected volatility.

Target Volatility

The target volatility model adjusts the market exposure of the portfolio based on the realized historic volatility and the given volatility target. The cash allocation in the portfolio is increased or decreased as required to meet the targeted volatility level in order to improve the risk adjusted performance.

Model Configuration

Timing Model

Time Period

Start Year

First Month

End Year

Last Month

Calendar Aligned

Include YTD

Initial Amount

$ .00

Cashflows

Contribution Amount

$ .00

Inflation Adjusted

Withdrawal Percentage

Frequency

Ticker

Tickers

Single absolute momentum

Absolute momentum asset

Target Volatility

Use Downside Volatility

Out Of Market Start Month

Out Of Market End Month

Out of Market Asset

Specify out of market asset

Buy Signal

Type of Moving Average

Performance Periods

Period Weighting

Timing Period

Timing period in trading days

Type of Moving Average #2

Timing Period #2

Timing period #2 in trading days

Exclude Previous Month

Normalize Returns

Volatility Period

Volatility window in trading days

Assets to hold

Allocation Weights

Risk Control

Risk Window Period

Risk window in trading days

Specify signal asset

Stop Loss

Stop Loss Threshold

Stop Loss Asset

Specify stop-loss asset

Trading Frequency

Signal Asset

Specify signal asset

Trade Execution

Leverage Type

Leverage Ratio

Debt Amount

$ .00

Debt Interest

Maintenance Margin

Leveraged Benchmark

Compared Allocation

Benchmark

Benchmark Ticker

Timing Periods

Length

Unit

Weight

Time Period #1

Time Period #2

Time Period #3

Time Period #4

Time Period #5

Volatility Period

Asset 1

Asset 2

Asset 3

Asset 4

Asset 5

Asset 6

Asset 7

Asset 8

Asset 9

Asset 10

Total

Model Simulation Results (Jan 2010 - Dec 2020) Save

Tactical asset allocation model results from Jan 2010 to Dec 2020 are based on dual momentum model holding the best performing asset. Absolute momentum based trend following filter is used to switch any selected assets that have a negative excess return over the risk free rate to iShares 1-3 Year Treasury Bond ETF (SHY). The model uses multiple weighted performance windows to rank the assets by weighted average of asset performance. Tactical asset allocation model trades are executed using the end of month close price each month based on the end of month signals.

Performance Summary

Performance statistics for the timing portfolio and benchmark portfolios
Portfolio	Initial Balance	Final Balance	CAGR	Stdev	Best Year	Worst Year	Max. Drawdown	Sharpe Ratio	Sortino Ratio	Market Correlation
Dual Momentum Model	$10,000	$28,086	9.84%	11.16%	25.12%	-8.10%	-15.76%	0.85	1.42	0.69
Equal Weight Portfolio	$10,000	$28,288	9.91%	14.94%	26.22%	-9.71%	-22.13%	0.67	1.04	0.96
SPDR S&P 500 ETF Trust	$10,000	$41,766	13.88%	14.02%	32.31%	-4.56%	-19.43%	0.96	1.57	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	10 year	Full	3 year	5 year
Dual Momentum Model	15.89%	20.79%	20.79%	10.30%	9.95%	9.43%	9.84%	13.51%	11.28%
Equal Weight Portfolio	15.67%	16.07%	16.07%	9.77%	12.35%	9.44%	9.91%	18.44%	15.11%
SPDR S&P 500 ETF Trust	12.12%	18.37%	18.37%	14.03%	15.11%	13.76%	13.88%	18.66%	15.15%
Trailing return and volatility are as of last full 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.
The simulated performance results are created by retroactively applying the specified investment strategy to historical data. Future results may vary.
The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
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.
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.
The selected portfolio allocation for comparison assumes monthly rebalancing.
An equal-weight allocation is used for the assets held by the momentum model.
The results for the tactical asset allocation model assume monthly rebalancing trades.
The relative strength signal is based on total return including dividends.

Annual Returns

Annual returns for the timing portfolio and various benchmark portfolios
Year	Inflation	Dual Momentum Model		Equal Weight Portfolio		SPDR S&P 500 ETF Trust		Vanguard Total Stock Market ETF (VTI)	Vanguard FTSE All-Wld ex-US ETF (VEU)	iShares 1-3 Year Treasury Bond ETF (SHY)
Year	Inflation	Return	Balance	Return	Balance	Return	Balance	Vanguard Total Stock Market ETF (VTI)	Vanguard FTSE All-Wld ex-US ETF (VEU)	iShares 1-3 Year Treasury Bond ETF (SHY)
2010	1.50%	14.05%	$11,405	14.72%	$11,472	15.06%	$11,506	17.42%	11.81%	2.28%
2011	2.96%	4.22%	$11,887	-6.74%	$10,699	1.89%	$11,723	0.97%	-14.02%	1.44%
2012	1.74%	17.15%	$13,925	17.79%	$12,602	15.99%	$13,598	16.45%	18.90%	0.28%
2013	1.50%	25.12%	$17,423	23.58%	$15,573	32.31%	$17,990	33.45%	14.18%	0.21%
2014	0.76%	9.15%	$19,017	3.73%	$16,154	13.46%	$20,412	12.54%	-4.54%	0.45%
2015	0.73%	-8.10%	$17,477	-2.19%	$15,800	1.25%	$20,668	0.36%	-4.78%	0.43%
2016	2.07%	-0.58%	$17,376	8.88%	$17,203	12.00%	$23,148	12.83%	4.91%	0.82%
2017	2.11%	20.44%	$20,928	24.32%	$21,386	21.70%	$28,172	21.21%	27.39%	0.26%
2018	1.91%	1.19%	$21,178	-9.71%	$19,309	-4.56%	$26,888	-5.21%	-14.19%	1.46%
2019	2.29%	9.79%	$23,252	26.22%	$24,372	31.22%	$35,283	30.67%	21.83%	3.38%
2020	1.36%	20.79%	$28,086	16.07%	$28,288	18.37%	$41,766	21.03%	11.12%	3.03%

Monthly Returns

Monthly returns for the timing portfolio and various benchmark portfolios
Year	Month	Dual Momentum Model		Equal Weight Portfolio		SPDR S&P 500 ETF Trust		Vanguard Total Stock Market ETF (VTI)	Vanguard FTSE All-Wld ex-US ETF (VEU)	iShares 1-3 Year Treasury Bond ETF (SHY)
Year	Month	Return	Balance	Return	Balance	Return	Balance	Vanguard Total Stock Market ETF (VTI)	Vanguard FTSE All-Wld ex-US ETF (VEU)	iShares 1-3 Year Treasury Bond ETF (SHY)
2010	1	-3.57%	$9,643	-4.66%	$9,534	-3.63%	$9,637	-3.57%	-5.76%	0.80%
2010	2	3.44%	$9,975	2.38%	$9,761	3.12%	$9,937	3.44%	1.31%	0.16%
2010	3	6.40%	$10,613	6.56%	$10,401	6.09%	$10,542	6.40%	6.72%	-0.27%
2010	4	2.18%	$10,845	0.21%	$10,423	1.55%	$10,705	2.18%	-1.76%	0.30%
2010	5	-7.88%	$9,990	-9.39%	$9,444	-7.95%	$9,855	-7.88%	-10.90%	0.45%
2010	6	0.42%	$10,032	-3.58%	$9,105	-5.17%	$9,345	-5.83%	-1.34%	0.42%
2010	7	0.19%	$10,051	8.89%	$9,915	6.83%	$9,983	7.02%	10.76%	0.19%
2010	8	-3.43%	$9,706	-4.07%	$9,511	-4.50%	$9,534	-4.71%	-3.43%	0.24%
2010	9	10.60%	$10,734	10.02%	$10,465	8.96%	$10,388	9.45%	10.60%	0.12%
2010	10	3.59%	$11,120	3.81%	$10,863	3.82%	$10,785	4.03%	3.59%	0.22%
2010	11	-4.10%	$10,664	-1.80%	$10,668	0.00%	$10,785	0.51%	-4.10%	-0.20%
2010	12	6.96%	$11,405	7.54%	$11,472	6.68%	$11,506	6.96%	8.12%	-0.16%
2011	1	2.05%	$11,639	1.42%	$11,635	2.33%	$11,774	2.05%	0.80%	0.13%
2011	2	3.70%	$12,069	3.22%	$12,010	3.47%	$12,183	3.70%	2.74%	-0.12%
2011	3	0.42%	$12,120	0.10%	$12,022	0.01%	$12,184	0.42%	-0.22%	-0.13%
2011	4	2.90%	$12,471	4.18%	$12,524	2.90%	$12,537	2.90%	5.45%	0.53%
2011	5	-1.06%	$12,338	-2.12%	$12,259	-1.12%	$12,396	-1.06%	-3.17%	0.36%
2011	6	-1.79%	$12,117	-1.44%	$12,082	-1.69%	$12,187	-1.79%	-1.09%	-0.00%
2011	7	-2.27%	$11,842	-2.32%	$11,802	-2.00%	$11,943	-2.27%	-2.37%	0.29%
2011	8	0.34%	$11,883	-7.28%	$10,942	-5.50%	$11,287	-6.09%	-8.47%	0.34%
2011	9	-0.10%	$11,871	-10.29%	$9,816	-6.94%	$10,503	-7.57%	-13.01%	-0.10%
2011	10	0.03%	$11,875	11.43%	$10,938	10.91%	$11,649	11.37%	11.49%	0.03%
2011	11	0.04%	$11,881	-1.47%	$10,777	-0.41%	$11,602	-0.37%	-2.57%	0.04%
2011	12	0.05%	$11,887	-0.73%	$10,699	1.04%	$11,723	0.98%	-2.43%	0.05%
2012	1	5.07%	$12,489	5.97%	$11,337	4.64%	$12,267	5.07%	6.86%	0.08%
2012	2	4.22%	$13,016	4.76%	$11,877	4.34%	$12,799	4.22%	5.31%	-0.14%
2012	3	3.06%	$13,415	1.08%	$12,006	3.22%	$13,211	3.06%	-0.90%	-0.08%
2012	4	-0.64%	$13,329	-1.22%	$11,859	-0.67%	$13,122	-0.64%	-1.81%	0.20%
2012	5	-6.23%	$12,500	-8.81%	$10,814	-6.01%	$12,334	-6.23%	-11.40%	0.06%
2012	6	-0.10%	$12,487	5.29%	$11,386	4.05%	$12,834	4.05%	6.52%	-0.10%
2012	7	0.88%	$12,597	0.68%	$11,463	1.18%	$12,986	0.88%	0.49%	0.22%
2012	8	2.70%	$12,937	2.67%	$11,770	2.51%	$13,311	2.70%	2.65%	0.01%
2012	9	2.49%	$13,260	2.99%	$12,122	2.54%	$13,649	2.49%	3.49%	0.02%
2012	10	-1.81%	$13,020	-0.52%	$12,059	-1.82%	$13,400	-1.81%	0.77%	-0.07%
2012	11	1.80%	$13,255	1.29%	$12,214	0.57%	$13,476	0.77%	1.80%	0.05%
2012	12	5.06%	$13,925	3.17%	$12,602	0.90%	$13,598	1.29%	5.06%	0.02%
2013	1	2.43%	$14,263	3.92%	$13,096	5.12%	$14,294	5.42%	2.43%	0.01%
2013	2	-1.39%	$14,065	-0.05%	$13,089	1.28%	$14,476	1.28%	-1.39%	0.06%
2013	3	3.95%	$14,620	2.28%	$13,388	3.80%	$15,026	3.95%	0.62%	0.03%
2013	4	1.61%	$14,855	2.68%	$13,747	1.92%	$15,314	1.61%	3.75%	0.07%
2013	5	2.44%	$15,218	-0.43%	$13,687	2.36%	$15,676	2.44%	-3.31%	-0.13%
2013	6	-1.43%	$15,000	-2.51%	$13,344	-1.34%	$15,467	-1.43%	-3.58%	-0.10%
2013	7	5.75%	$15,862	5.22%	$14,041	5.17%	$16,266	5.75%	4.70%	0.16%
2013	8	-3.03%	$15,381	-2.51%	$13,689	-3.00%	$15,778	-3.03%	-1.99%	-0.10%
2013	9	3.90%	$15,981	5.74%	$14,475	3.17%	$16,278	3.90%	7.58%	0.22%
2013	10	3.33%	$16,513	3.80%	$15,025	4.63%	$17,032	4.27%	3.33%	0.07%
2013	11	2.70%	$16,960	1.52%	$15,253	2.96%	$17,536	2.70%	0.34%	0.09%
2013	12	2.73%	$17,423	2.10%	$15,573	2.59%	$17,990	2.73%	1.47%	-0.18%
2014	1	-3.17%	$16,870	-4.48%	$14,875	-3.52%	$17,356	-3.17%	-5.80%	0.20%
2014	2	4.87%	$17,691	5.25%	$15,656	4.55%	$18,146	4.87%	5.63%	0.04%
2014	3	0.51%	$17,781	0.48%	$15,732	0.83%	$18,297	0.51%	0.46%	-0.11%
2014	4	0.06%	$17,792	0.77%	$15,852	0.70%	$18,424	0.06%	1.47%	0.11%
2014	5	2.10%	$18,166	2.01%	$16,171	2.32%	$18,852	2.10%	1.92%	0.18%
2014	6	2.62%	$18,643	2.15%	$16,519	2.06%	$19,241	2.62%	1.68%	-0.08%
2014	7	-1.99%	$18,271	-1.73%	$16,232	-1.34%	$18,982	-1.99%	-1.47%	-0.08%
2014	8	1.01%	$18,455	2.58%	$16,651	3.95%	$19,732	4.15%	1.01%	0.19%
2014	9	-2.10%	$18,068	-3.49%	$16,070	-1.38%	$19,459	-2.10%	-4.88%	-0.07%
2014	10	2.75%	$18,564	1.47%	$16,307	2.36%	$19,918	2.75%	0.20%	0.26%
2014	11	2.48%	$19,024	1.08%	$16,483	2.75%	$20,465	2.48%	-0.32%	0.11%
2014	12	-0.04%	$19,017	-2.00%	$16,154	-0.26%	$20,412	-0.04%	-3.96%	-0.29%
2015	1	-2.74%	$18,497	-1.38%	$15,931	-2.96%	$19,808	-2.74%	-0.02%	0.63%
2015	2	5.74%	$19,559	5.80%	$16,854	5.62%	$20,921	5.74%	5.85%	-0.29%
2015	3	-1.16%	$19,333	-1.28%	$16,638	-1.57%	$20,592	-1.16%	-1.41%	0.25%
2015	4	0.62%	$19,452	2.68%	$17,083	0.98%	$20,794	0.62%	4.74%	0.03%
2015	5	-1.04%	$19,250	0.13%	$17,105	1.29%	$21,061	1.30%	-1.04%	0.04%
2015	6	-1.67%	$18,927	-2.24%	$16,722	-2.03%	$20,634	-1.67%	-2.81%	0.03%
2015	7	-0.29%	$18,873	0.71%	$16,840	2.26%	$21,100	1.70%	-0.29%	0.04%
2015	8	-6.09%	$17,723	-6.92%	$15,675	-6.10%	$19,814	-6.09%	-7.75%	-0.05%
2015	9	0.30%	$17,775	-3.48%	$15,130	-2.54%	$19,310	-2.92%	-4.04%	0.30%
2015	10	-0.14%	$17,750	7.30%	$16,234	8.51%	$20,953	7.91%	6.69%	-0.14%
2015	11	0.60%	$17,857	-0.36%	$16,176	0.37%	$21,029	0.60%	-1.32%	-0.26%
2015	12	-2.13%	$17,477	-2.32%	$15,800	-1.72%	$20,668	-2.13%	-2.52%	-0.15%
2016	1	-5.72%	$16,476	-5.66%	$14,905	-4.98%	$19,639	-5.72%	-5.60%	0.65%
2016	2	0.11%	$16,495	-1.23%	$14,723	-0.08%	$19,623	-0.01%	-2.44%	0.11%
2016	3	0.14%	$16,518	7.71%	$15,858	6.72%	$20,942	7.11%	8.31%	0.14%
2016	4	0.66%	$16,626	1.38%	$16,077	0.39%	$21,025	0.66%	2.11%	0.04%
2016	5	1.73%	$16,915	0.47%	$16,153	1.70%	$21,383	1.73%	-0.79%	-0.12%
2016	6	0.27%	$16,961	-0.22%	$16,117	0.35%	$21,457	0.27%	-0.72%	0.60%
2016	7	3.98%	$17,635	4.11%	$16,779	3.65%	$22,240	3.98%	4.25%	-0.05%
2016	8	0.21%	$17,672	0.45%	$16,855	0.12%	$22,267	0.21%	0.69%	-0.23%
2016	9	0.21%	$17,708	0.89%	$17,006	0.01%	$22,268	0.21%	1.58%	0.13%
2016	10	-1.69%	$17,408	-1.94%	$16,675	-1.73%	$21,882	-2.19%	-1.69%	-0.05%
2016	11	-2.13%	$17,038	1.18%	$16,872	3.68%	$22,688	4.49%	-2.13%	-0.47%
2016	12	1.98%	$17,376	1.96%	$17,203	2.03%	$23,148	1.98%	1.93%	0.07%
2017	1	1.86%	$17,698	3.00%	$17,719	1.79%	$23,563	1.86%	4.14%	0.11%
2017	2	3.69%	$18,352	2.48%	$18,158	3.93%	$24,489	3.69%	1.26%	0.04%
2017	3	0.06%	$18,362	1.52%	$18,434	0.13%	$24,519	0.06%	2.99%	0.06%
2017	4	2.09%	$18,746	1.58%	$18,725	0.99%	$24,763	1.06%	2.09%	0.19%
2017	5	1.01%	$18,936	2.03%	$19,106	1.41%	$25,112	1.01%	3.05%	0.07%
2017	6	0.51%	$19,032	0.73%	$19,244	0.64%	$25,272	0.95%	0.51%	-0.08%
2017	7	3.38%	$19,675	2.63%	$19,750	2.06%	$25,792	1.88%	3.38%	0.19%
2017	8	0.64%	$19,800	0.39%	$19,828	0.29%	$25,867	0.15%	0.64%	0.20%
2017	9	1.84%	$20,164	2.14%	$20,252	2.01%	$26,388	2.44%	1.84%	-0.19%
2017	10	1.95%	$20,558	2.06%	$20,670	2.36%	$27,010	2.17%	1.95%	-0.09%
2017	11	0.63%	$20,688	1.83%	$21,048	3.06%	$27,835	3.03%	0.63%	-0.22%
2017	12	1.16%	$20,928	1.60%	$21,386	1.21%	$28,172	1.16%	2.05%	-0.02%
2018	1	5.23%	$22,023	5.47%	$22,555	5.64%	$29,759	5.23%	5.70%	-0.29%
2018	2	-3.76%	$21,195	-4.53%	$21,533	-3.64%	$28,677	-3.76%	-5.31%	-0.10%
2018	3	-1.95%	$20,781	-1.20%	$21,274	-2.74%	$27,891	-1.95%	-0.44%	0.25%
2018	4	0.57%	$20,900	0.51%	$21,383	0.52%	$28,035	0.45%	0.57%	-0.23%
2018	5	0.35%	$20,973	0.36%	$21,461	2.43%	$28,717	2.72%	-1.99%	0.35%
2018	6	0.70%	$21,121	-0.72%	$21,307	0.58%	$28,882	0.70%	-2.14%	0.04%
2018	7	3.32%	$21,822	3.11%	$21,969	3.70%	$29,952	3.32%	2.89%	-0.06%
2018	8	3.43%	$22,571	0.54%	$22,088	3.19%	$30,908	3.43%	-2.34%	0.35%
2018	9	0.20%	$22,615	0.32%	$22,159	0.59%	$31,092	0.20%	0.44%	-0.14%
2018	10	-7.41%	$20,939	-7.86%	$20,418	-6.91%	$28,944	-7.41%	-8.30%	0.15%
2018	11	0.38%	$21,019	1.74%	$20,774	1.85%	$29,480	2.01%	1.47%	0.38%
2018	12	0.76%	$21,178	-7.05%	$19,309	-8.79%	$26,888	-9.16%	-4.94%	0.76%
2019	1	0.25%	$21,232	8.05%	$20,865	8.01%	$29,041	8.54%	7.57%	0.25%
2019	2	3.56%	$21,987	2.60%	$21,406	3.24%	$29,982	3.56%	1.63%	0.09%
2019	3	1.00%	$22,208	1.21%	$21,665	1.81%	$30,524	1.42%	1.00%	0.63%
2019	4	3.93%	$23,080	3.39%	$22,399	4.09%	$31,771	3.93%	2.85%	0.18%
2019	5	-6.45%	$21,591	-6.00%	$21,056	-6.38%	$29,745	-6.45%	-5.54%	0.72%
2019	6	0.46%	$21,690	6.48%	$22,421	6.96%	$31,815	7.08%	5.89%	0.46%
2019	7	1.41%	$21,997	-0.20%	$22,377	1.51%	$32,296	1.41%	-1.80%	-0.06%
2019	8	-2.08%	$21,539	-2.26%	$21,871	-1.67%	$31,755	-2.08%	-2.44%	0.78%
2019	9	1.78%	$21,922	2.30%	$22,374	1.95%	$32,374	1.78%	2.82%	-0.13%
2019	10	2.11%	$22,384	2.78%	$22,995	2.21%	$33,090	2.11%	3.45%	0.31%
2019	11	1.05%	$22,618	2.42%	$23,551	3.62%	$34,287	3.79%	1.05%	-0.05%
2019	12	2.80%	$23,252	3.48%	$24,372	2.90%	$35,283	2.80%	4.17%	0.16%
2020	1	-0.06%	$23,238	-1.73%	$23,950	-0.04%	$35,269	-0.06%	-3.40%	0.58%
2020	2	-8.00%	$21,379	-7.30%	$22,201	-7.92%	$32,477	-8.00%	-6.61%	0.88%
2020	3	1.24%	$21,645	-14.52%	$18,977	-12.46%	$28,429	-13.91%	-15.13%	1.24%
2020	4	0.27%	$21,704	9.97%	$20,869	12.70%	$32,039	13.13%	6.80%	0.27%
2020	5	-0.08%	$21,687	5.04%	$21,920	4.76%	$33,565	5.40%	4.68%	-0.08%
2020	6	2.29%	$22,184	3.33%	$22,650	1.78%	$34,161	2.29%	4.36%	0.02%
2020	7	5.74%	$23,458	4.84%	$23,745	5.89%	$36,173	5.74%	3.93%	0.09%
2020	8	7.10%	$25,125	5.76%	$25,112	6.98%	$38,698	7.10%	4.41%	-0.02%
2020	9	-3.54%	$24,235	-2.61%	$24,456	-3.74%	$37,251	-3.54%	-1.68%	-0.00%
2020	10	-1.95%	$23,762	-2.01%	$23,965	-2.49%	$36,322	-1.95%	-2.06%	-0.05%
2020	11	11.80%	$26,567	12.21%	$26,891	10.88%	$40,273	11.80%	12.61%	0.02%
2020	12	5.72%	$28,086	5.20%	$28,288	3.71%	$41,766	4.68%	5.72%	0.04%

Risk and Return Metrics

Portfolio return and risk metrics
Metric	Dual Momentum Model	Equal Weight Portfolio	SPDR S&P 500 ETF Trust
Arithmetic Mean (monthly)	0.84%	0.88%	1.17%
Arithmetic Mean (annualized)	10.51%	11.13%	14.98%
Geometric Mean (monthly)	0.79%	0.79%	1.09%
Geometric Mean (annualized)	9.84%	9.91%	13.88%
Standard Deviation (monthly)	3.22%	4.31%	4.05%
Standard Deviation (annualized)	11.16%	14.94%	14.02%
Downside Deviation (monthly)	1.91%	2.77%	2.45%
Maximum Drawdown	-15.76%	-22.13%	-19.43%
Stock Market Correlation	0.69	0.96	1.00
Beta^(*)	0.56	1.03	1.00
Alpha (annualized)	2.21%	-3.80%	-0.00%
R²	49.11%	92.62%	100.00%
Sharpe Ratio	0.85	0.67	0.96
Sortino Ratio	1.42	1.04	1.57
Treynor Ratio (%)	17.01	9.80	13.49
Calmar Ratio	1.28	0.44	0.72
Active Return	-4.03%	-3.96%	N/A
Tracking Error	10.09%	4.07%	N/A
Information Ratio	-0.40	-0.97	N/A
Skewness	-0.03	-0.39	-0.32
Excess Kurtosis	1.51	1.26	1.07
Historical Value-at-Risk (5%)	4.83%	7.15%	6.22%
Analytical Value-at-Risk (5%)	4.46%	6.21%	5.49%
Conditional Value-at-Risk (5%)	6.83%	9.35%	8.19%
Upside Capture Ratio (%)	68.50	93.18	100.00
Downside Capture Ratio (%)	68.67	112.89	100.00
Safe Withdrawal Rate	14.22%	13.39%	16.22%
Perpetual Withdrawal Rate	7.39%	7.46%	10.68%
Positive Periods	92 out of 132 (69.70%)	85 out of 132 (64.39%)	92 out of 132 (69.70%)
Gain/Loss Ratio	0.89	0.95	0.90
^* SPDR S&P 500 ETF Trust 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	Dual Momentum Model	Equal Weight Portfolio	SPDR S&P 500 ETF Trust
COVID-19 Start	Jan 2020	Mar 2020	-8.06%	-22.13%	-19.43%

Drawdowns for Dual Momentum Model

Drawdowns for Dual Momentum Model (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Mar 2015	Jan 2016	11 months	Jul 2017	1 year 6 months	2 years 5 months	-15.76%
2	May 2010	Aug 2010	4 months	Oct 2010	2 months	6 months	-10.50%
3	Jan 2020	Feb 2020	2 months	Jul 2020	5 months	7 months	-8.06%
4	Oct 2018	Oct 2018	1 month	Apr 2019	6 months	7 months	-7.41%
5	Apr 2012	Jun 2012	3 months	Dec 2012	6 months	9 months	-6.91%
6	May 2019	Aug 2019	4 months	Dec 2019	4 months	8 months	-6.68%
7	Feb 2018	Mar 2018	2 months	Aug 2018	5 months	7 months	-5.64%
8	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-5.42%
9	May 2011	Jul 2011	3 months	Jan 2012	6 months	9 months	-5.04%
10	Nov 2010	Nov 2010	1 month	Dec 2010	1 month	2 months	-4.10%
Worst 10 drawdowns included above

Drawdowns for Equal Weight Portfolio

Drawdowns for Equal Weight Portfolio (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Jan 2020	Mar 2020	3 months	Aug 2020	5 months	8 months	-22.13%
2	May 2011	Sep 2011	5 months	Dec 2012	1 year 3 months	1 year 8 months	-21.62%
3	Feb 2018	Dec 2018	11 months	Oct 2019	10 months	1 year 9 months	-14.39%
4	Jun 2015	Feb 2016	9 months	Dec 2016	10 months	1 year 7 months	-13.93%
5	May 2010	Jun 2010	2 months	Sep 2010	3 months	5 months	-12.64%
6	Jan 2010	Jan 2010	1 month	Mar 2010	2 months	3 months	-4.66%
7	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-4.56%
8	Jan 2014	Jan 2014	1 month	Feb 2014	1 month	2 months	-4.48%
9	Sep 2014	Jan 2015	5 months	Feb 2015	1 month	6 months	-4.33%
10	May 2013	Jun 2013	2 months	Jul 2013	1 month	3 months	-2.93%
Worst 10 drawdowns included above

Drawdowns for SPDR S&P 500 ETF Trust

Drawdowns for SPDR S&P 500 ETF Trust (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	-19.43%
2	May 2011	Sep 2011	5 months	Feb 2012	5 months	10 months	-16.23%
3	Oct 2018	Dec 2018	3 months	Apr 2019	4 months	7 months	-13.52%
4	May 2010	Jun 2010	2 months	Oct 2010	4 months	6 months	-12.71%
5	Aug 2015	Sep 2015	2 months	May 2016	8 months	10 months	-8.48%
6	Apr 2012	May 2012	2 months	Aug 2012	3 months	5 months	-6.63%
7	May 2019	May 2019	1 month	Jun 2019	1 month	2 months	-6.38%
8	Feb 2018	Mar 2018	2 months	Jul 2018	4 months	6 months	-6.28%
9	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-6.14%
10	Jan 2010	Jan 2010	1 month	Mar 2010	2 months	3 months	-3.63%
Worst 10 drawdowns included above

Rolling Returns

Rolling returns summary
Roll Period	Dual Momentum Model			Equal Weight Portfolio			SPDR S&P 500 ETF Trust
Roll Period	Average	High	Low	Average	High	Low	Average	High	Low
1 year	9.01%	27.95%	-15.66%	9.35%	32.69%	-12.65%	13.54%	32.31%	-6.86%
3 years	8.51%	16.99%	-0.09%	9.19%	17.86%	0.97%	13.47%	22.82%	5.05%
5 years	7.34%	14.42%	1.80%	8.54%	12.93%	2.67%	12.91%	17.17%	6.66%
7 years	8.00%	10.72%	5.19%	9.06%	12.33%	5.11%	13.35%	16.77%	9.54%
10 years	8.54%	9.98%	7.18%	8.83%	10.20%	6.20%	13.22%	15.04%	10.43%

Annualized Rolling Return - 3 Years

Annualized Rolling Return - 5 Years

Timing Periods

Timing periods and related holdings for the timing portfolio
#	Start	End	Months	Assets	Asset Performance	Dual Momentum Model	Equal Weight Portfolio	SPDR S&P 500 ETF Trust
43	Jan 2021	Jan 2021	1	Please sign-in for forward signals	-	-	-	-
42	Dec 2020	Dec 2020	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 5.72%	5.72%	5.20%	3.71%
41	Jun 2020	Nov 2020	6	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 22.50%	22.50%	22.67%	19.98%
40	Mar 2020	May 2020	3	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: 1.44%	1.44%	-1.26%	3.35%
39	Dec 2019	Feb 2020	3	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: -5.48%	-5.48%	-5.73%	-5.28%
38	Nov 2019	Nov 2019	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 1.05%	1.05%	2.42%	3.62%
37	Jul 2019	Oct 2019	4	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 3.20%	3.20%	2.56%	4.01%
36	Jun 2019	Jun 2019	1	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: 0.46%	0.46%	6.48%	6.96%
35	Apr 2019	May 2019	2	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: -2.78%	-2.78%	-2.81%	-2.55%
34	Mar 2019	Mar 2019	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 1.00%	1.00%	1.21%	1.81%
33	Feb 2019	Feb 2019	1	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 3.56%	3.56%	2.60%	3.24%
32	Nov 2018	Jan 2019	3	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: 1.40%	1.40%	2.19%	0.34%
31	Jun 2018	Oct 2018	5	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: -0.16%	-0.16%	-4.86%	0.79%
30	May 2018	May 2018	1	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: 0.35%	0.35%	0.36%	2.43%
29	Apr 2018	Apr 2018	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 0.57%	0.57%	0.51%	0.52%
28	Dec 2017	Mar 2018	4	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 0.45%	0.45%	1.07%	0.20%
27	Jun 2017	Nov 2017	6	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 9.25%	9.25%	10.17%	10.84%
26	May 2017	May 2017	1	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 1.01%	1.01%	2.03%	1.41%
25	Apr 2017	Apr 2017	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 2.09%	2.09%	1.58%	0.99%
24	Dec 2016	Mar 2017	4	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 7.77%	7.77%	9.26%	8.07%
23	Oct 2016	Nov 2016	2	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: -3.79%	-3.79%	-0.78%	1.89%
22	Apr 2016	Sep 2016	6	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 7.21%	7.21%	7.24%	6.33%
21	Feb 2016	Mar 2016	2	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: 0.25%	0.25%	6.39%	6.64%
20	Nov 2015	Jan 2016	3	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: -7.18%	-7.18%	-8.18%	-6.27%
19	Sep 2015	Oct 2015	2	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: 0.15%	0.15%	3.57%	5.75%
18	Aug 2015	Aug 2015	1	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: -6.09%	-6.09%	-6.92%	-6.10%
17	Jul 2015	Jul 2015	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: -0.29%	-0.29%	0.71%	2.26%
16	Jun 2015	Jun 2015	1	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: -1.67%	-1.67%	-2.24%	-2.03%
15	May 2015	May 2015	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: -1.04%	-1.04%	0.13%	1.29%
14	Sep 2014	Apr 2015	8	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 5.40%	5.40%	2.60%	5.38%
13	Aug 2014	Aug 2014	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 1.01%	1.01%	2.58%	3.95%
12	Nov 2013	Jul 2014	9	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 10.64%	10.64%	8.04%	11.45%
11	Oct 2013	Oct 2013	1	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 3.33%	3.33%	3.80%	4.63%
10	Mar 2013	Sep 2013	7	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 13.62%	13.62%	10.59%	12.45%
9	Nov 2012	Feb 2013	4	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 8.02%	8.02%	8.54%	8.03%
8	Jul 2012	Oct 2012	4	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 4.27%	4.27%	5.91%	4.41%
7	Jun 2012	Jun 2012	1	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: -0.10%	-0.10%	5.29%	4.05%
6	Jan 2012	May 2012	5	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 5.16%	5.16%	1.07%	5.22%
5	Aug 2011	Dec 2011	5	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: 0.37%	0.37%	-9.35%	-1.84%
4	Dec 2010	Jul 2011	8	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: 11.06%	11.06%	10.63%	10.74%
3	Aug 2010	Nov 2010	4	100.00% Vanguard FTSE All-Wld ex-US ETF (VEU)	VEU: 6.09%	6.09%	7.59%	8.03%
2	Jun 2010	Jul 2010	2	100.00% iShares 1-3 Year Treasury Bond ETF (SHY)	SHY: 0.61%	0.61%	4.99%	1.30%
1	Jan 2010	May 2010	5	100.00% Vanguard Total Stock Market ETF (VTI)	VTI: -0.10%	-0.10%	-5.56%	-1.45%