Test Tactical Allocation Models

Tactical Allocation Overview

This tool allows you to test different 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 documentation 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 tactical asset allocation 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 tactical asset allocation 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 lookback period, or multiple weighted lookback 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.

Risk Managed Allocation

The risk managed portfolio allocation model adjusts the risky asset exposure in the portfolio based the defined signal in order to protect against large drawdowns.

Model Configuration

Tactical 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

Risk Management Strategy

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

Lookback Period

Lookback period in trading days

Type of Moving Average #2

Lookback Period #2

Lookback 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

Max Derisk Percentage

Derisk Increment

Rerisk Increment

Risk Adjustment Levels

Trade	Rule	Z-Score	Change
			%
			%
			%
			%

Trading Frequency

Signal Asset

Specify signal asset

Rebalancing

Trade Execution

Leverage Type

Leverage Ratio

Debt Amount

$ .00

Debt Interest

Maintenance Margin

Leveraged Benchmark

Compared Allocation

Benchmark

Benchmark Ticker

Lookback Periods

Length

Unit

Weight

Lookback Period #1

Lookback Period #2

Lookback Period #3

Lookback Period #4

Lookback 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 1998 - Dec 2018) Save

Tactical asset allocation model results from Jan 1998 to Dec 2018 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 Vanguard Long-Term Treasury Inv (VUSTX). The model uses a single performance window of 3 calendar month(s). Tactical asset allocation model trades are executed using the end of month close price each month based on the end of month signals. The time period was constrained by the available data for Vanguard International Explorer Inv (VINEX) [Dec 1996 - Aug 2023].

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	$312,650	17.81%	14.36%	79.57%	-10.87%	-22.13%	1.09	1.97	0.34
Equal Weight Portfolio	$10,000	$53,628	8.33%	15.71%	52.57%	-41.80%	-55.28%	0.47	0.66	0.93
Vanguard 500 Index Investor	$10,000	$37,596	6.51%	14.88%	32.18%	-37.02%	-50.97%	0.37	0.52	0.99

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	0.03%	12.30%	12.30%	9.39%	5.52%	14.24%	17.81%	11.52%	10.79%
Equal Weight Portfolio	-16.30%	-14.16%	-14.16%	5.41%	5.24%	11.30%	8.33%	11.73%	10.97%
Vanguard 500 Index Investor	-13.55%	-4.52%	-4.52%	9.11%	8.34%	12.97%	6.51%	10.96%	10.95%
Trailing return and volatility are as of last calendar month ending December 2018

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.

Active Returns Chart

Annualized Active Return

Rolling Active Return

Up vs. Down Market Performance

Up vs. Down Market Performance - Model 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	103	59	162	64%	1.40%	-4.18%	-0.63%
Down Market	73	17	90	81%	4.54%	-1.04%	3.48%
Total	176	76	252	70%	2.70%	-3.48%	0.84%

Active Return Confidence

Annual Returns

Annual returns for the timing portfolio and various benchmark portfolios
Year	Inflation	Dual Momentum Model		Equal Weight Portfolio		Vanguard 500 Index Investor		Vanguard 500 Index Investor (VFINX)	Vanguard International Explorer Inv (VINEX)	Vanguard Long-Term Treasury Inv (VUSTX)
Year	Inflation	Return	Balance	Return	Balance	Return	Balance	Vanguard 500 Index Investor (VFINX)	Vanguard International Explorer Inv (VINEX)	Vanguard Long-Term Treasury Inv (VUSTX)
1998	1.61%	21.98%	$12,198	27.76%	$12,776	28.62%	$12,862	28.62%	25.98%	13.05%
1999	2.68%	79.57%	$21,905	52.57%	$19,492	21.07%	$15,571	21.07%	90.29%	-8.66%
2000	3.39%	17.67%	$25,775	-4.75%	$18,566	-9.06%	$14,161	-9.06%	-2.68%	19.72%
2001	1.55%	-0.77%	$25,576	-17.29%	$15,356	-12.02%	$12,459	-12.02%	-22.52%	4.31%
2002	2.38%	-6.57%	$23,897	-17.95%	$12,601	-22.15%	$9,700	-22.15%	-13.88%	16.67%
2003	1.88%	43.38%	$34,264	42.39%	$17,942	28.50%	$12,464	28.50%	57.37%	2.68%
2004	3.26%	31.24%	$44,970	20.89%	$21,690	10.74%	$13,803	10.74%	31.77%	7.12%
2005	3.42%	13.41%	$50,999	12.49%	$24,400	4.77%	$14,462	4.77%	20.49%	6.61%
2006	2.54%	30.97%	$66,794	22.89%	$29,985	15.64%	$16,724	15.64%	30.34%	1.74%
2007	4.08%	7.57%	$71,849	5.38%	$31,597	5.39%	$17,625	5.39%	5.15%	9.24%
2008	0.09%	14.93%	$82,573	-41.80%	$18,391	-37.02%	$11,100	-37.02%	-46.62%	22.52%
2009	2.72%	28.98%	$106,503	36.62%	$25,125	26.49%	$14,040	26.49%	47.12%	-12.05%
2010	1.50%	31.59%	$140,149	18.82%	$29,853	14.91%	$16,134	14.91%	22.55%	8.93%
2011	2.96%	18.57%	$166,177	-9.42%	$27,041	1.97%	$16,451	1.97%	-19.74%	29.28%
2012	1.74%	11.35%	$185,034	17.00%	$31,638	15.82%	$19,054	15.82%	17.93%	3.47%
2013	1.50%	29.17%	$239,011	31.28%	$41,532	32.18%	$25,185	32.18%	30.24%	-13.03%
2014	0.76%	11.89%	$267,426	5.08%	$43,640	13.51%	$28,587	13.51%	-2.88%	25.28%
2015	0.73%	-10.68%	$238,865	4.91%	$45,785	1.25%	$28,944	1.25%	8.60%	-1.54%
2016	2.07%	-10.87%	$212,907	4.93%	$48,043	11.82%	$32,365	11.82%	-1.77%	1.20%
2017	2.11%	30.76%	$278,407	30.04%	$62,476	21.67%	$39,377	21.67%	38.77%	8.58%
2018	1.91%	12.30%	$312,650	-14.16%	$53,628	-4.52%	$37,596	-4.52%	-23.02%	-1.90%

Monthly Returns

Monthly returns for the timing portfolio and various benchmark portfolios
Year	Month	Dual Momentum Model		Equal Weight Portfolio		Vanguard 500 Index Investor		Vanguard 500 Index Investor (VFINX)	Vanguard International Explorer Inv (VINEX)	Vanguard Long-Term Treasury Inv (VUSTX)
Year	Month	Return	Balance	Return	Balance	Return	Balance	Vanguard 500 Index Investor (VFINX)	Vanguard International Explorer Inv (VINEX)	Vanguard Long-Term Treasury Inv (VUSTX)
1998	1	1.11%	$10,111	4.43%	$10,443	1.11%	$10,111	1.11%	7.75%	1.91%
1998	2	7.19%	$10,838	6.38%	$11,109	7.19%	$10,838	7.19%	5.57%	-0.75%
1998	3	5.71%	$11,458	5.41%	$11,710	5.10%	$11,391	5.10%	5.71%	0.14%
1998	4	5.09%	$12,041	3.05%	$12,067	1.01%	$11,506	1.01%	5.09%	0.40%
1998	5	5.04%	$12,649	1.65%	$12,267	-1.74%	$11,306	-1.74%	5.04%	1.83%
1998	6	-0.38%	$12,601	1.85%	$12,493	4.07%	$11,766	4.07%	-0.38%	2.35%
1998	7	2.36%	$12,899	0.65%	$12,575	-1.05%	$11,642	-1.05%	2.36%	-0.51%
1998	8	-12.74%	$11,255	-13.61%	$10,864	-14.47%	$9,957	-14.47%	-12.74%	4.83%
1998	9	3.29%	$11,625	0.56%	$10,925	6.41%	$10,595	6.41%	-5.29%	3.29%
1998	10	-1.69%	$11,428	6.32%	$11,615	8.16%	$11,460	8.16%	4.47%	-1.69%
1998	11	0.88%	$11,529	4.75%	$12,166	6.07%	$12,156	6.07%	3.42%	0.88%
1998	12	5.81%	$12,198	5.01%	$12,776	5.81%	$12,862	5.81%	4.22%	-0.16%
1999	1	4.20%	$12,711	3.01%	$13,161	4.20%	$13,402	4.20%	1.82%	0.98%
1999	2	-3.12%	$12,314	0.97%	$13,288	-3.12%	$12,984	-3.12%	5.06%	-4.76%
1999	3	5.22%	$12,956	4.61%	$13,900	4.00%	$13,502	4.00%	5.22%	-0.34%
1999	4	8.29%	$14,031	6.07%	$14,745	3.85%	$14,023	3.85%	8.29%	0.19%
1999	5	-0.88%	$13,907	-1.63%	$14,504	-2.39%	$13,688	-2.39%	-0.88%	-1.68%
1999	6	12.43%	$15,636	8.99%	$15,808	5.56%	$14,448	5.56%	12.43%	-1.05%
1999	7	9.00%	$17,044	2.94%	$16,272	-3.13%	$13,996	-3.13%	9.00%	-0.58%
1999	8	3.19%	$17,588	1.35%	$16,491	-0.50%	$13,926	-0.50%	3.19%	-0.49%
1999	9	-1.40%	$17,341	-2.07%	$16,150	-2.74%	$13,545	-2.74%	-1.40%	0.91%
1999	10	1.85%	$17,662	4.09%	$16,810	6.33%	$14,402	6.33%	1.85%	0.12%
1999	11	11.96%	$19,774	6.99%	$17,985	2.02%	$14,693	2.02%	11.96%	-0.59%
1999	12	10.78%	$21,905	8.38%	$19,492	5.98%	$15,571	5.98%	10.78%	-1.60%
2000	1	11.64%	$24,455	3.30%	$20,136	-5.03%	$14,788	-5.03%	11.64%	1.25%
2000	2	17.38%	$28,705	7.74%	$21,694	-1.91%	$14,506	-1.91%	17.38%	2.96%
2000	3	-3.93%	$27,576	2.91%	$22,325	9.75%	$15,921	9.75%	-3.93%	3.14%
2000	4	-11.47%	$24,413	-7.23%	$20,710	-3.00%	$15,443	-3.00%	-11.47%	-0.66%
2000	5	-2.04%	$23,915	-4.36%	$19,807	-2.04%	$15,128	-2.04%	-6.68%	-0.46%
2000	6	2.49%	$24,512	4.24%	$20,648	2.49%	$15,506	2.49%	5.99%	2.30%
2000	7	1.49%	$24,876	-2.08%	$20,219	-1.50%	$15,274	-1.50%	-2.65%	1.49%
2000	8	2.08%	$25,393	4.84%	$21,199	6.19%	$16,219	6.19%	3.50%	2.08%
2000	9	-5.29%	$24,050	-3.99%	$20,353	-5.29%	$15,361	-5.29%	-2.69%	-0.85%
2000	10	1.57%	$24,427	-4.60%	$19,417	-0.43%	$15,295	-0.43%	-8.77%	1.57%
2000	11	2.99%	$25,158	-6.10%	$18,231	-7.89%	$14,089	-7.89%	-4.32%	2.99%
2000	12	2.45%	$25,775	1.84%	$18,566	0.51%	$14,161	0.51%	3.16%	2.45%
2001	1	0.28%	$25,848	2.61%	$19,051	3.55%	$14,663	3.55%	1.67%	0.28%
2001	2	1.80%	$26,314	-6.96%	$17,725	-9.14%	$13,323	-9.14%	-4.78%	1.80%
2001	3	-0.60%	$26,155	-7.33%	$16,425	-6.36%	$12,477	-6.36%	-8.31%	-0.60%
2001	4	-2.56%	$25,484	6.80%	$17,542	7.77%	$13,446	7.77%	5.83%	-2.56%
2001	5	0.21%	$25,537	-0.78%	$17,406	0.65%	$13,533	0.65%	-2.21%	0.21%
2001	6	-2.45%	$24,912	-3.39%	$16,816	-2.45%	$13,202	-2.45%	-4.34%	0.76%
2001	7	-1.00%	$24,663	-2.81%	$16,343	-1.00%	$13,070	-1.00%	-4.62%	3.61%
2001	8	2.02%	$25,162	-4.09%	$15,675	-6.27%	$12,250	-6.27%	-1.90%	2.02%
2001	9	0.88%	$25,384	-11.46%	$13,879	-8.09%	$11,259	-8.09%	-14.83%	0.88%
2001	10	5.12%	$26,684	2.54%	$14,231	1.90%	$11,473	1.90%	3.19%	5.12%
2001	11	-4.98%	$25,355	6.80%	$15,200	7.65%	$12,351	7.65%	5.95%	-4.98%
2001	12	0.87%	$25,576	1.03%	$15,356	0.87%	$12,459	0.87%	1.19%	-1.91%
2002	1	-1.47%	$25,200	-1.52%	$15,123	-1.47%	$12,275	-1.47%	-1.57%	1.20%
2002	2	-1.94%	$24,712	-1.39%	$14,912	-1.94%	$12,037	-1.94%	-0.85%	1.24%
2002	3	-3.86%	$23,759	5.19%	$15,686	3.74%	$12,488	3.74%	6.63%	-3.86%
2002	4	2.91%	$24,450	-1.58%	$15,438	-6.07%	$11,729	-6.07%	2.91%	3.73%
2002	5	1.27%	$24,760	0.26%	$15,477	-0.75%	$11,641	-0.75%	1.27%	0.39%
2002	6	-4.52%	$23,640	-5.83%	$14,575	-7.13%	$10,810	-7.13%	-4.52%	1.76%
2002	7	2.93%	$24,332	-8.40%	$13,351	-7.72%	$9,976	-7.72%	-9.07%	2.93%
2002	8	4.28%	$25,373	-0.39%	$13,299	0.65%	$10,041	0.65%	-1.44%	4.28%
2002	9	4.02%	$26,392	-10.78%	$11,865	-10.87%	$8,949	-10.87%	-10.69%	4.02%
2002	10	-2.84%	$25,643	5.46%	$12,513	8.78%	$9,735	8.78%	2.14%	-2.84%
2002	11	-0.98%	$25,393	5.10%	$13,151	5.88%	$10,307	5.88%	4.32%	-0.98%
2002	12	-5.89%	$23,897	-4.18%	$12,601	-5.89%	$9,700	-5.89%	-2.47%	4.05%
2003	1	-2.62%	$23,270	-2.35%	$12,304	-2.62%	$9,445	-2.62%	-2.08%	-0.45%
2003	2	3.03%	$23,974	-2.07%	$12,050	-1.52%	$9,302	-1.52%	-2.62%	3.03%
2003	3	-1.13%	$23,702	-0.23%	$12,023	0.96%	$9,391	0.96%	-1.41%	-1.13%
2003	4	0.91%	$23,917	9.45%	$13,159	8.25%	$10,166	8.25%	10.65%	0.91%
2003	5	5.26%	$25,176	8.21%	$14,239	5.26%	$10,701	5.26%	11.15%	5.67%
2003	6	3.80%	$26,133	2.53%	$14,599	1.26%	$10,836	1.26%	3.80%	-1.48%
2003	7	4.78%	$27,383	3.26%	$15,076	1.74%	$11,025	1.74%	4.78%	-8.57%
2003	8	4.08%	$28,499	3.01%	$15,529	1.93%	$11,238	1.93%	4.08%	1.43%
2003	9	5.41%	$30,041	2.17%	$15,866	-1.07%	$11,117	-1.07%	5.41%	5.07%
2003	10	5.22%	$31,610	5.43%	$16,727	5.64%	$11,744	5.64%	5.22%	-2.58%
2003	11	2.19%	$32,301	1.53%	$16,982	0.86%	$11,846	0.86%	2.19%	0.31%
2003	12	6.08%	$34,264	5.65%	$17,942	5.22%	$12,464	5.22%	6.08%	1.23%
2004	1	4.21%	$35,708	3.02%	$18,483	1.82%	$12,691	1.82%	4.21%	1.74%
2004	2	3.52%	$36,964	2.45%	$18,935	1.38%	$12,866	1.38%	3.52%	1.96%
2004	3	2.31%	$37,819	0.40%	$19,011	-1.51%	$12,671	-1.51%	2.31%	1.45%
2004	4	-1.98%	$37,071	-1.78%	$18,673	-1.58%	$12,472	-1.58%	-1.98%	-5.52%
2004	5	-1.15%	$36,643	0.10%	$18,692	1.36%	$12,641	1.36%	-1.15%	-0.56%
2004	6	0.87%	$36,962	2.57%	$19,173	1.93%	$12,885	1.93%	3.21%	0.87%
2004	7	-3.31%	$35,738	-3.03%	$18,591	-3.31%	$12,458	-3.31%	-2.76%	1.52%
2004	8	3.39%	$36,948	0.63%	$18,708	0.38%	$12,506	0.38%	0.87%	3.39%
2004	9	2.38%	$37,827	1.72%	$19,030	1.07%	$12,639	1.07%	2.38%	0.94%
2004	10	3.03%	$38,972	2.27%	$19,462	1.51%	$12,831	1.51%	3.03%	1.46%
2004	11	7.72%	$41,980	5.88%	$20,607	4.05%	$13,350	4.05%	7.72%	-2.25%
2004	12	7.12%	$44,970	5.26%	$21,690	3.39%	$13,803	3.39%	7.12%	2.22%
2005	1	0.92%	$45,383	-0.77%	$21,524	-2.45%	$13,464	-2.45%	0.92%	2.59%
2005	2	4.31%	$47,337	3.20%	$22,212	2.09%	$13,746	2.09%	4.31%	-1.24%
2005	3	-2.21%	$46,291	-1.98%	$21,772	-1.76%	$13,504	-1.76%	-2.21%	-0.76%
2005	4	-2.02%	$45,355	-1.97%	$21,343	-1.91%	$13,246	-1.91%	-2.02%	3.22%
2005	5	2.55%	$46,511	1.77%	$21,720	3.17%	$13,666	3.17%	0.36%	2.55%
2005	6	1.64%	$47,275	1.42%	$22,030	0.13%	$13,683	0.13%	2.72%	1.64%
2005	7	3.71%	$49,028	4.12%	$22,937	3.71%	$14,190	3.71%	4.53%	-2.58%
2005	8	2.03%	$50,021	0.56%	$23,065	-0.91%	$14,060	-0.91%	2.03%	2.87%
2005	9	3.53%	$51,788	2.16%	$23,564	0.79%	$14,172	0.79%	3.53%	-2.78%
2005	10	-4.10%	$49,662	-2.89%	$22,882	-1.68%	$13,934	-1.68%	-4.10%	-1.74%
2005	11	2.67%	$50,988	3.22%	$23,618	3.76%	$14,459	3.76%	2.67%	0.57%
2005	12	0.02%	$50,999	3.31%	$24,400	0.02%	$14,462	0.02%	6.60%	2.33%
2006	1	7.37%	$54,755	5.01%	$25,621	2.65%	$14,845	2.65%	7.37%	-0.90%
2006	2	0.62%	$55,097	0.44%	$25,735	0.26%	$14,884	0.26%	0.62%	0.81%
2006	3	5.27%	$58,000	3.25%	$26,571	1.23%	$15,067	1.23%	5.27%	-3.39%
2006	4	5.50%	$61,187	3.41%	$27,479	1.33%	$15,268	1.33%	5.50%	-1.96%
2006	5	-4.93%	$58,170	-3.91%	$26,403	-2.90%	$14,825	-2.90%	-4.93%	-0.03%
2006	6	-2.15%	$56,918	-1.01%	$26,136	0.13%	$14,844	0.13%	-2.15%	0.71%
2006	7	1.84%	$57,965	0.05%	$26,150	0.61%	$14,934	0.61%	-0.50%	1.84%
2006	8	2.74%	$59,552	2.36%	$26,768	2.36%	$15,287	2.36%	2.36%	2.74%
2006	9	2.56%	$61,079	2.19%	$27,354	2.56%	$15,679	2.56%	1.82%	1.58%
2006	10	3.25%	$63,064	3.46%	$28,300	3.25%	$16,189	3.25%	3.66%	0.77%
2006	11	1.89%	$64,256	3.20%	$29,205	1.89%	$16,495	1.89%	4.51%	1.91%
2006	12	3.95%	$66,794	2.67%	$29,985	1.39%	$16,724	1.39%	3.95%	-2.14%
2007	1	2.94%	$68,757	2.22%	$30,650	1.49%	$16,974	1.49%	2.94%	-0.85%
2007	2	0.32%	$68,979	-0.82%	$30,397	-1.97%	$16,640	-1.97%	0.32%	2.93%
2007	3	3.21%	$71,195	2.16%	$31,055	1.11%	$16,825	1.11%	3.21%	-1.13%
2007	4	3.87%	$73,949	4.14%	$32,341	4.42%	$17,568	4.42%	3.87%	0.86%
2007	5	2.44%	$75,753	2.96%	$33,298	3.48%	$18,179	3.48%	2.44%	-1.93%
2007	6	-1.13%	$74,898	-1.40%	$32,831	-1.68%	$17,874	-1.68%	-1.13%	-0.88%
2007	7	-3.08%	$72,588	-1.77%	$32,248	-3.08%	$17,323	-3.08%	-0.46%	2.39%
2007	8	1.97%	$74,021	-0.74%	$32,011	1.50%	$17,582	1.50%	-2.97%	1.97%
2007	9	0.21%	$74,178	2.87%	$32,929	3.72%	$18,237	3.72%	2.01%	0.21%
2007	10	1.58%	$75,349	3.77%	$34,171	1.58%	$18,525	1.58%	5.96%	1.40%
2007	11	-4.19%	$72,194	-6.12%	$32,079	-4.19%	$17,749	-4.19%	-8.06%	4.59%
2007	12	-0.48%	$71,849	-1.50%	$31,597	-0.70%	$17,625	-0.70%	-2.30%	-0.48%
2008	1	2.64%	$73,747	-7.57%	$29,204	-6.02%	$16,565	-6.02%	-9.13%	2.64%
2008	2	0.35%	$74,005	-0.50%	$29,060	-3.25%	$16,026	-3.25%	2.26%	0.35%
2008	3	1.02%	$74,761	-0.89%	$28,801	-0.44%	$15,956	-0.44%	-1.34%	1.02%
2008	4	-1.84%	$73,385	3.55%	$29,823	4.85%	$16,730	4.85%	2.24%	-1.84%
2008	5	2.07%	$74,908	1.68%	$30,325	1.29%	$16,946	1.29%	2.07%	-2.13%
2008	6	-8.44%	$68,587	-8.17%	$27,847	-8.44%	$15,516	-8.44%	-7.91%	1.80%
2008	7	0.30%	$68,790	-3.33%	$26,920	-0.83%	$15,387	-0.83%	-5.82%	0.30%
2008	8	1.80%	$70,031	-0.97%	$26,659	1.45%	$15,610	1.45%	-3.39%	1.80%
2008	9	0.28%	$70,230	-12.17%	$23,415	-8.91%	$14,220	-8.91%	-15.43%	0.28%
2008	10	-3.63%	$67,682	-20.47%	$18,622	-16.79%	$11,832	-16.79%	-24.14%	-3.63%
2008	11	12.07%	$75,849	-6.06%	$17,495	-7.17%	$10,983	-7.17%	-4.94%	12.07%
2008	12	8.87%	$82,573	5.12%	$18,391	1.07%	$11,100	1.07%	9.18%	8.87%
2009	1	-8.47%	$75,579	-8.78%	$16,776	-8.41%	$10,166	-8.41%	-9.15%	-8.47%
2009	2	-1.01%	$74,817	-8.92%	$15,280	-10.66%	$9,083	-10.66%	-7.18%	-1.01%
2009	3	5.27%	$78,756	8.37%	$16,559	8.76%	$9,879	8.76%	7.98%	5.27%
2009	4	-4.99%	$74,827	11.77%	$18,508	9.56%	$10,823	9.56%	13.97%	-4.99%
2009	5	13.98%	$85,290	9.80%	$20,321	5.62%	$11,431	5.62%	13.98%	-2.68%
2009	6	1.96%	$86,958	1.09%	$20,542	0.22%	$11,456	0.22%	1.96%	0.70%
2009	7	7.41%	$93,402	7.49%	$22,082	7.58%	$12,324	7.58%	7.41%	0.80%
2009	8	5.19%	$98,254	4.40%	$23,053	3.60%	$12,768	3.60%	5.19%	1.68%
2009	9	6.33%	$104,470	5.02%	$24,211	3.72%	$13,242	3.72%	6.33%	1.98%
2009	10	-1.67%	$102,727	-1.77%	$23,782	-1.87%	$12,995	-1.87%	-1.67%	-1.45%
2009	11	1.70%	$104,470	3.84%	$24,696	5.98%	$13,772	5.98%	1.70%	1.91%
2009	12	1.95%	$106,503	1.74%	$25,125	1.95%	$14,040	1.95%	1.53%	-5.66%
2010	1	-3.60%	$102,665	-2.78%	$24,426	-3.60%	$13,534	-3.60%	-1.96%	2.66%
2010	2	3.09%	$105,839	1.10%	$24,696	3.09%	$13,952	3.09%	-0.89%	-0.21%
2010	3	6.01%	$112,204	6.59%	$26,323	6.01%	$14,791	6.01%	7.16%	-1.51%
2010	4	1.58%	$113,974	1.31%	$26,668	1.58%	$15,025	1.58%	1.04%	2.76%
2010	5	-8.01%	$104,850	-9.76%	$24,066	-8.01%	$13,822	-8.01%	-11.51%	4.23%
2010	6	4.67%	$109,743	-2.70%	$23,417	-5.24%	$13,098	-5.24%	-0.16%	4.67%
2010	7	-0.17%	$109,555	8.26%	$25,350	7.00%	$14,014	7.00%	9.52%	-0.17%
2010	8	7.08%	$117,310	-3.58%	$24,442	-4.53%	$13,379	-4.53%	-2.64%	7.08%
2010	9	11.56%	$130,869	10.24%	$26,944	8.92%	$14,573	8.92%	11.56%	-1.82%
2010	10	3.67%	$135,675	3.73%	$27,949	3.79%	$15,125	3.79%	3.67%	-3.29%
2010	11	-3.16%	$131,384	-1.58%	$27,507	0.00%	$15,125	0.00%	-3.16%	-1.60%
2010	12	6.67%	$140,149	8.53%	$29,853	6.67%	$16,134	6.67%	10.38%	-3.58%
2011	1	0.72%	$141,158	1.54%	$30,312	2.36%	$16,514	2.36%	0.72%	-2.38%
2011	2	3.42%	$145,981	2.33%	$31,019	3.42%	$17,078	3.42%	1.25%	1.24%
2011	3	0.03%	$146,018	0.25%	$31,096	0.03%	$17,083	0.03%	0.47%	0.02%
2011	4	2.95%	$150,323	3.93%	$32,319	2.95%	$17,586	2.95%	4.92%	2.04%
2011	5	-2.46%	$146,632	-1.80%	$31,738	-1.15%	$17,385	-1.15%	-2.46%	3.29%
2011	6	-2.80%	$142,521	-2.24%	$31,027	-1.67%	$17,094	-1.67%	-2.80%	-2.00%
2011	7	-2.05%	$139,604	-1.82%	$30,463	-2.05%	$16,744	-2.05%	-1.59%	4.18%
2011	8	8.68%	$151,724	-7.57%	$28,158	-5.45%	$15,832	-5.45%	-9.69%	8.68%
2011	9	10.16%	$167,143	-9.42%	$25,507	-7.04%	$14,717	-7.04%	-11.79%	10.16%
2011	10	-3.34%	$161,569	9.55%	$27,942	10.91%	$16,323	10.91%	8.18%	-3.34%
2011	11	1.82%	$164,503	-2.09%	$27,357	-0.23%	$16,285	-0.23%	-3.96%	1.82%
2011	12	1.02%	$166,177	-1.15%	$27,041	1.02%	$16,451	1.02%	-3.32%	3.13%
2012	1	4.46%	$173,596	6.64%	$28,837	4.46%	$17,186	4.46%	8.81%	0.08%
2012	2	4.31%	$181,073	4.95%	$30,264	4.31%	$17,926	4.31%	5.59%	-2.11%
2012	3	0.41%	$181,811	1.84%	$30,822	3.28%	$18,514	3.28%	0.41%	-3.77%
2012	4	-0.68%	$180,581	-0.66%	$30,619	-0.64%	$18,396	-0.64%	-0.68%	4.37%
2012	5	-6.02%	$169,714	-8.90%	$27,895	-6.02%	$17,288	-6.02%	-11.78%	7.79%
2012	6	-1.44%	$167,263	3.98%	$29,006	4.11%	$17,999	4.11%	3.86%	-1.44%
2012	7	3.32%	$172,820	0.57%	$29,173	1.37%	$18,245	1.37%	-0.22%	3.32%
2012	8	-1.06%	$170,983	2.57%	$29,923	2.24%	$18,654	2.24%	2.90%	-1.06%
2012	9	2.58%	$175,389	3.13%	$30,860	2.58%	$19,135	2.58%	3.69%	-2.10%
2012	10	1.19%	$177,470	-0.34%	$30,757	-1.86%	$18,779	-1.86%	1.19%	-0.43%
2012	11	0.62%	$178,571	0.59%	$30,938	0.56%	$18,884	0.56%	0.62%	1.35%
2012	12	3.62%	$185,034	2.26%	$31,638	0.90%	$19,054	0.90%	3.62%	-1.99%
2013	1	4.96%	$194,217	5.07%	$33,241	5.18%	$20,041	5.18%	4.96%	-3.27%
2013	2	0.19%	$194,594	0.77%	$33,496	1.34%	$20,309	1.34%	0.19%	1.26%
2013	3	1.29%	$197,110	2.52%	$34,339	3.74%	$21,068	3.74%	1.29%	0.03%
2013	4	1.91%	$200,872	2.80%	$35,302	1.91%	$21,470	1.91%	3.70%	3.87%
2013	5	2.33%	$205,547	0.92%	$35,626	2.33%	$21,970	2.33%	-0.49%	-6.23%
2013	6	-1.35%	$202,771	-1.76%	$35,000	-1.35%	$21,673	-1.35%	-2.16%	-3.26%
2013	7	5.07%	$213,056	5.29%	$36,850	5.07%	$22,773	5.07%	5.50%	-1.93%
2013	8	-2.91%	$206,852	-1.79%	$36,192	-2.91%	$22,110	-2.91%	-0.66%	-1.28%
2013	9	7.30%	$221,948	5.21%	$38,078	3.12%	$22,800	3.12%	7.30%	0.88%
2013	10	3.99%	$230,806	4.29%	$39,711	4.59%	$23,846	4.59%	3.99%	1.32%
2013	11	0.81%	$232,677	1.92%	$40,473	3.03%	$24,568	3.03%	0.81%	-2.49%
2013	12	2.72%	$239,011	2.62%	$41,532	2.51%	$25,185	2.51%	2.72%	-2.37%
2014	1	-3.47%	$230,719	-2.85%	$40,350	-3.47%	$24,312	-3.47%	-2.23%	6.26%
2014	2	4.56%	$241,241	5.25%	$42,468	4.56%	$25,420	4.56%	5.94%	0.60%
2014	3	0.73%	$243,011	0.78%	$42,799	0.82%	$25,630	0.82%	0.73%	0.63%
2014	4	-0.62%	$241,494	0.05%	$42,821	0.72%	$25,815	0.72%	-0.62%	1.82%
2014	5	2.33%	$247,133	2.14%	$43,735	2.33%	$26,418	2.33%	1.94%	2.73%
2014	6	2.05%	$252,204	1.59%	$44,431	2.05%	$26,960	2.05%	1.13%	-0.16%
2014	7	-1.39%	$248,703	-1.74%	$43,660	-1.39%	$26,586	-1.39%	-2.08%	0.59%
2014	8	3.98%	$258,606	2.30%	$44,665	3.98%	$27,644	3.98%	0.62%	4.23%
2014	9	-1.41%	$254,953	-2.92%	$43,360	-1.41%	$27,254	-1.41%	-4.43%	-1.99%
2014	10	2.42%	$261,131	0.46%	$43,558	2.42%	$27,914	2.42%	-1.51%	2.61%
2014	11	2.68%	$268,135	0.63%	$43,832	2.68%	$28,663	2.68%	-1.42%	2.86%
2014	12	-0.26%	$267,426	-0.44%	$43,640	-0.26%	$28,587	-0.26%	-0.61%	2.82%
2015	1	-3.02%	$259,357	-1.57%	$42,955	-3.02%	$27,725	-3.02%	-0.12%	8.97%
2015	2	-5.66%	$244,684	6.27%	$45,650	5.74%	$29,316	5.74%	6.81%	-5.66%
2015	3	0.57%	$246,076	-0.51%	$45,416	-1.59%	$28,849	-1.59%	0.57%	1.13%
2015	4	3.45%	$254,571	2.20%	$46,416	0.95%	$29,123	0.95%	3.45%	-3.07%
2015	5	0.88%	$256,799	1.07%	$46,914	1.27%	$29,493	1.27%	0.88%	-2.16%
2015	6	-1.14%	$253,875	-1.54%	$46,194	-1.93%	$28,923	-1.93%	-1.14%	-3.73%
2015	7	1.15%	$256,799	1.62%	$46,940	2.08%	$29,525	2.08%	1.15%	4.21%
2015	8	-6.05%	$241,271	-5.52%	$44,350	-6.05%	$27,740	-6.05%	-4.99%	-0.71%
2015	9	1.91%	$245,882	-2.78%	$43,116	-2.48%	$27,050	-2.48%	-3.08%	1.91%
2015	10	-0.48%	$244,705	6.51%	$45,922	8.42%	$29,329	8.42%	4.59%	-0.48%
2015	11	-0.81%	$242,730	0.20%	$46,013	0.29%	$29,413	0.29%	0.11%	-0.81%
2015	12	-1.59%	$238,865	-0.50%	$45,785	-1.59%	$28,944	-1.59%	0.60%	-0.34%
2016	1	-4.98%	$226,977	-5.82%	$43,120	-4.98%	$27,504	-4.98%	-6.67%	5.24%
2016	2	2.86%	$233,468	-1.27%	$42,570	-0.15%	$27,464	-0.15%	-2.40%	2.86%
2016	3	0.05%	$233,590	7.18%	$45,626	6.78%	$29,325	6.78%	7.58%	0.05%
2016	4	0.37%	$234,463	0.52%	$45,862	0.37%	$29,434	0.37%	0.66%	-0.63%
2016	5	1.78%	$238,643	1.61%	$46,600	1.78%	$29,959	1.78%	1.44%	0.69%
2016	6	-5.54%	$225,416	-2.65%	$45,367	0.25%	$30,034	0.25%	-5.54%	6.57%
2016	7	3.68%	$233,703	4.65%	$47,475	3.68%	$31,138	3.68%	5.62%	2.01%
2016	8	0.13%	$234,006	-0.02%	$47,464	0.13%	$31,178	0.13%	-0.18%	-1.00%
2016	9	0.01%	$234,025	1.43%	$48,140	0.01%	$31,181	0.01%	2.84%	-1.32%
2016	10	-3.17%	$226,615	-2.50%	$46,937	-1.83%	$30,609	-1.83%	-3.17%	-4.23%
2016	11	-7.86%	$208,809	0.60%	$47,219	3.70%	$31,742	3.70%	-2.50%	-7.86%
2016	12	1.96%	$212,907	1.75%	$48,043	1.96%	$32,365	1.96%	1.53%	-0.35%
2017	1	1.88%	$216,916	3.15%	$49,555	1.88%	$32,974	1.88%	4.41%	0.65%
2017	2	3.96%	$225,512	2.89%	$50,987	3.96%	$34,281	3.96%	1.82%	1.57%
2017	3	0.10%	$225,738	1.92%	$51,967	0.10%	$34,315	0.10%	3.74%	-0.59%
2017	4	5.39%	$237,896	3.20%	$53,631	1.02%	$34,664	1.02%	5.39%	1.58%
2017	5	4.27%	$248,048	2.83%	$55,149	1.39%	$35,148	1.39%	4.27%	1.73%
2017	6	0.51%	$249,302	0.56%	$55,457	0.61%	$35,362	0.61%	0.51%	0.63%
2017	7	3.47%	$257,950	2.76%	$56,985	2.04%	$36,085	2.04%	3.47%	-0.59%
2017	8	0.39%	$258,953	0.34%	$57,180	0.29%	$36,191	0.29%	0.39%	3.27%
2017	9	3.97%	$269,231	3.01%	$58,903	2.06%	$36,936	2.06%	3.97%	-2.27%
2017	10	1.82%	$274,119	2.07%	$60,120	2.32%	$37,792	2.32%	1.82%	-0.02%
2017	11	0.46%	$275,372	1.76%	$61,178	3.06%	$38,948	3.06%	0.46%	0.63%
2017	12	1.10%	$278,407	2.12%	$62,476	1.10%	$39,377	1.10%	3.14%	1.78%
2018	1	5.71%	$294,311	5.42%	$65,860	5.71%	$41,627	5.71%	5.12%	-3.40%
2018	2	-3.69%	$283,438	-3.86%	$63,319	-3.69%	$40,089	-3.69%	-4.02%	-2.89%
2018	3	-0.33%	$282,514	-1.44%	$62,407	-2.56%	$39,064	-2.56%	-0.33%	2.75%
2018	4	0.28%	$283,306	0.33%	$62,611	0.37%	$39,210	0.37%	0.28%	-2.04%
2018	5	1.79%	$288,390	0.78%	$63,098	2.39%	$40,149	2.39%	-0.84%	1.79%
2018	6	0.66%	$290,291	-0.78%	$62,607	0.61%	$40,392	0.61%	-2.16%	0.66%
2018	7	3.71%	$301,059	1.90%	$63,799	3.71%	$41,890	3.71%	0.10%	-1.28%
2018	8	3.25%	$310,832	0.74%	$64,268	3.25%	$43,250	3.25%	-1.77%	1.18%
2018	9	0.55%	$312,555	-0.31%	$64,070	0.55%	$43,490	0.55%	-1.17%	-2.74%
2018	10	-6.85%	$291,148	-9.30%	$58,109	-6.85%	$40,511	-6.85%	-11.76%	-2.82%
2018	11	1.78%	$296,342	0.82%	$58,584	2.03%	$41,332	2.03%	-0.39%	1.78%
2018	12	5.50%	$312,650	-8.46%	$53,628	-9.04%	$37,596	-9.04%	-7.88%	5.50%

Risk and Return Metrics

Portfolio return and risk metrics
Metric	Dual Momentum Model	Equal Weight Portfolio	Vanguard 500 Index Investor
Arithmetic Mean (monthly)	1.46%	0.77%	0.62%
Arithmetic Mean (annualized)	19.00%	9.69%	7.70%
Geometric Mean (monthly)	1.38%	0.67%	0.53%
Geometric Mean (annualized)	17.81%	8.33%	6.51%
Standard Deviation (monthly)	4.15%	4.53%	4.30%
Standard Deviation (annualized)	14.36%	15.71%	14.88%
Downside Deviation (monthly)	2.21%	3.16%	2.98%
Maximum Drawdown	-22.13%	-55.28%	-50.97%
Stock Market Correlation	0.34	0.93	0.99
Beta^(*)	0.30	0.96	1.00
Alpha (annualized)	15.31%	2.13%	-0.00%
R²	9.47%	82.77%	100.00%
Sharpe Ratio	1.09	0.47	0.37
Sortino Ratio	1.97	0.66	0.52
Treynor Ratio (%)	52.50	7.66	5.52
Calmar Ratio	0.75	0.29	0.67
Active Return	11.30%	1.82%	N/A
Tracking Error	17.21%	6.55%	N/A
Information Ratio	0.66	0.28	N/A
Skewness	0.13	-0.87	-0.67
Excess Kurtosis	1.61	2.05	1.25
Historical Value-at-Risk (5%)	5.12%	8.27%	7.42%
Analytical Value-at-Risk (5%)	5.36%	6.68%	6.45%
Conditional Value-at-Risk (5%)	7.56%	10.80%	9.88%
Upside Capture Ratio (%)	77.56	102.45	100.00
Downside Capture Ratio (%)	12.14	93.12	100.00
Safe Withdrawal Rate	21.18%	9.49%	6.34%
Perpetual Withdrawal Rate	13.31%	5.72%	4.11%
Positive Periods	176 out of 252 (69.84%)	161 out of 252 (63.89%)	161 out of 252 (63.89%)
Gain/Loss Ratio	1.10	0.88	0.81
^* 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	Dual Momentum Model	Equal Weight Portfolio	Vanguard 500 Index Investor
Russian Debt Default	Jul 1998	Oct 1998	-12.74%	-13.61%	-15.38%
Dotcom Crash	Mar 2000	Oct 2002	-17.65%	-46.85%	-44.82%
Subprime Crisis	Nov 2007	Mar 2009	-10.18%	-55.28%	-50.97%

Drawdowns for Dual Momentum Model

Drawdowns for Dual Momentum Model (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Dec 2014	Nov 2016	2 years	Sep 2017	10 months	2 years 10 months	-22.13%
2	Mar 2000	Jan 2003	2 years 11 months	Sep 2003	8 months	3 years 7 months	-18.94%
3	Aug 1998	Aug 1998	1 month	Mar 1999	7 months	8 months	-12.74%
4	Jun 2007	Oct 2008	1 year 5 months	Nov 2008	1 month	1 year 6 months	-10.65%
5	Jan 2009	Feb 2009	2 months	May 2009	3 months	5 months	-9.39%
6	May 2010	May 2010	1 month	Aug 2010	3 months	4 months	-8.01%
7	Apr 2012	Jun 2012	3 months	Dec 2012	6 months	9 months	-8.00%
8	May 2011	Jul 2011	3 months	Aug 2011	1 month	4 months	-7.13%
9	May 2006	Jun 2006	2 months	Oct 2006	4 months	6 months	-6.98%
10	Oct 2018	Oct 2018	1 month	Dec 2018	2 months	3 months	-6.85%
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	Nov 2007	Feb 2009	1 year 4 months	Mar 2013	4 years 1 month	5 years 5 months	-55.28%
2	Apr 2000	Sep 2002	2 years 6 months	Jul 2005	2 years 10 months	5 years 4 months	-46.85%
3	Feb 2018	Dec 2018	11 months				-18.57%
4	Aug 1998	Aug 1998	1 month	Dec 1998	4 months	5 months	-13.61%
5	Aug 2015	Feb 2016	7 months	Jul 2016	5 months	1 year	-9.31%
6	May 2006	Jun 2006	2 months	Oct 2006	4 months	6 months	-4.89%
7	Jun 2007	Aug 2007	3 months	Oct 2007	2 months	5 months	-3.87%
8	Sep 2014	Jan 2015	5 months	Feb 2015	1 month	6 months	-3.83%
9	Oct 2005	Oct 2005	1 month	Nov 2005	1 month	2 months	-2.89%
10	Jan 2014	Jan 2014	1 month	Feb 2014	1 month	2 months	-2.85%
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	Nov 2007	Feb 2009	1 year 4 months	Aug 2012	3 years 6 months	4 years 10 months	-50.97%
2	Sep 2000	Sep 2002	2 years 1 month	Nov 2006	4 years 2 months	6 years 3 months	-44.82%
3	Jul 1998	Aug 1998	2 months	Nov 1998	3 months	5 months	-15.38%
4	Oct 2018	Dec 2018	3 months				-13.55%
5	Aug 2015	Sep 2015	2 months	May 2016	8 months	10 months	-8.38%
6	Jan 2000	Feb 2000	2 months	Mar 2000	1 month	3 months	-6.84%
7	Jul 1999	Sep 1999	3 months	Nov 1999	2 months	5 months	-6.25%
8	Feb 2018	Mar 2018	2 months	Jul 2018	4 months	6 months	-6.16%
9	Apr 2000	May 2000	2 months	Aug 2000	3 months	5 months	-4.98%
10	Jun 2007	Jul 2007	2 months	Sep 2007	2 months	4 months	-4.71%
Worst 10 drawdowns included above

Rolling Returns

Rolling returns summary
Roll Period	Dual Momentum Model			Equal Weight Portfolio			Vanguard 500 Index Investor
Roll Period	Average	High	Low	Average	High	Low	Average	High	Low
1 year	19.15%	133.11%	-13.98%	10.98%	63.25%	-47.42%	8.17%	53.61%	-43.32%
3 years	16.90%	37.11%	-5.83%	7.80%	30.26%	-18.64%	6.04%	25.43%	-16.14%
5 years	17.48%	27.81%	4.42%	7.86%	22.68%	-4.20%	6.17%	22.85%	-6.73%
7 years	18.28%	24.99%	8.77%	7.79%	15.76%	0.35%	6.12%	17.12%	-3.94%
10 years	18.26%	23.71%	12.18%	6.71%	12.85%	1.27%	5.14%	14.17%	-3.51%
15 years	17.98%	22.19%	15.09%	7.92%	11.83%	4.85%	6.14%	10.39%	3.64%

Annualized Rolling Return - 3 Years

Annualized Rolling Return - 5 Years

Allocation Changes

Model Selections

Timing periods and related holdings for the timing portfolio
#	Start	End	Months	Assets	Asset Performance	Dual Momentum Model	Equal Weight Portfolio	Vanguard 500 Index Investor
78	Jan 2019	Jan 2019	1	Please sign-in for forward signals	-	-	-	-
77	Nov 2018	Dec 2018	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 7.39%	7.39%	-7.71%	-7.20%
76	Jul 2018	Oct 2018	4	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.30%	0.30%	-7.19%	0.30%
75	May 2018	Jun 2018	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.47%	2.47%	-0.01%	3.01%
74	Mar 2018	Apr 2018	2	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -0.05%	-0.05%	-1.12%	-2.19%
73	Dec 2017	Feb 2018	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 2.93%	2.93%	3.50%	2.93%
72	Apr 2017	Nov 2017	8	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 21.99%	21.99%	17.72%	13.50%
71	Dec 2016	Mar 2017	4	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 8.11%	8.11%	10.06%	8.11%
70	Nov 2016	Nov 2016	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -7.86%	-7.86%	0.60%	3.70%
69	Oct 2016	Oct 2016	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -3.17%	-3.17%	-2.50%	-1.83%
68	Jul 2016	Sep 2016	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.82%	3.82%	6.11%	3.82%
67	Jun 2016	Jun 2016	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -5.54%	-5.54%	-2.65%	0.25%
66	Apr 2016	May 2016	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 2.16%	2.16%	2.14%	2.16%
65	Feb 2016	Mar 2016	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.91%	2.91%	5.81%	6.62%
64	Dec 2015	Jan 2016	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -6.49%	-6.49%	-6.29%	-6.49%
63	Sep 2015	Nov 2015	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 0.60%	0.60%	3.75%	6.03%
62	Aug 2015	Aug 2015	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -6.05%	-6.05%	-5.52%	-6.05%
61	Mar 2015	Jul 2015	5	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 4.95%	4.95%	2.83%	0.71%
60	Feb 2015	Feb 2015	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -5.66%	-5.66%	6.27%	5.74%
59	May 2014	Jan 2015	9	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 7.40%	7.40%	0.31%	7.40%
58	Mar 2014	Apr 2014	2	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 0.10%	0.10%	0.83%	1.55%
57	Jan 2014	Feb 2014	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.93%	0.93%	2.25%	0.93%
56	Sep 2013	Dec 2013	4	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 15.55%	15.55%	14.76%	13.91%
55	Apr 2013	Aug 2013	5	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 4.94%	4.94%	5.40%	4.94%
54	Oct 2012	Mar 2013	6	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 12.38%	12.38%	11.27%	10.11%
53	Sep 2012	Sep 2012	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 2.58%	2.58%	3.13%	2.58%
52	Jun 2012	Aug 2012	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 0.75%	0.75%	7.27%	7.90%
51	May 2012	May 2012	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -6.02%	-6.02%	-8.90%	-6.02%
50	Mar 2012	Apr 2012	2	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -0.27%	-0.27%	1.17%	2.62%
49	Dec 2011	Feb 2012	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 10.07%	10.07%	10.63%	10.07%
48	Aug 2011	Nov 2011	4	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 17.84%	17.84%	-10.20%	-2.74%
47	Jul 2011	Jul 2011	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -2.05%	-2.05%	-1.82%	-2.05%
46	May 2011	Jun 2011	2	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -5.19%	-5.19%	-4.00%	-2.80%
45	Feb 2011	Apr 2011	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 6.49%	6.49%	6.62%	6.49%
44	Jan 2011	Jan 2011	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 0.72%	0.72%	1.54%	2.36%
43	Dec 2010	Dec 2010	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 6.67%	6.67%	8.53%	6.67%
42	Sep 2010	Nov 2010	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 12.00%	12.00%	12.54%	13.05%
41	Jun 2010	Aug 2010	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 11.88%	11.88%	1.56%	-3.20%
40	Dec 2009	May 2010	6	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.36%	0.36%	-2.55%	0.36%
39	May 2009	Nov 2009	7	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 39.61%	39.61%	33.43%	27.25%
38	Jul 2008	Apr 2009	10	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 9.10%	9.10%	-33.54%	-30.25%
37	Jun 2008	Jun 2008	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -8.44%	-8.44%	-8.17%	-8.44%
36	May 2008	May 2008	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 2.07%	2.07%	1.68%	1.29%
35	Dec 2007	Apr 2008	5	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 1.65%	1.65%	-7.03%	-5.74%
34	Oct 2007	Nov 2007	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -2.67%	-2.67%	-2.58%	-2.67%
33	Aug 2007	Sep 2007	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.19%	2.19%	2.11%	5.28%
32	Jul 2007	Jul 2007	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -3.08%	-3.08%	-1.77%	-3.08%
31	Dec 2006	Jun 2007	7	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 16.56%	16.56%	12.42%	8.36%
30	Sep 2006	Nov 2006	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 7.90%	7.90%	9.11%	7.90%
29	Jul 2006	Aug 2006	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 4.63%	4.63%	2.42%	2.98%
28	Jan 2006	Jun 2006	6	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 11.61%	11.61%	7.11%	2.64%
27	Dec 2005	Dec 2005	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.02%	0.02%	3.31%	0.02%
26	Aug 2005	Nov 2005	4	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 4.00%	4.00%	2.97%	1.89%
25	Jul 2005	Jul 2005	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.71%	3.71%	4.12%	3.71%
24	May 2005	Jun 2005	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 4.23%	4.23%	3.21%	3.30%
23	Sep 2004	Apr 2005	8	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 22.75%	22.75%	14.09%	5.92%
22	Aug 2004	Aug 2004	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 3.39%	3.39%	0.63%	0.38%
21	Jul 2004	Jul 2004	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -3.31%	-3.31%	-3.03%	-3.31%
20	Jun 2004	Jun 2004	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 0.87%	0.87%	2.57%	1.93%
19	Jun 2003	May 2004	12	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 45.55%	45.55%	31.28%	18.13%
18	May 2003	May 2003	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 5.26%	5.26%	8.21%	5.26%
17	Feb 2003	Apr 2003	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.78%	2.78%	6.95%	7.63%
16	Dec 2002	Jan 2003	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -8.36%	-8.36%	-6.44%	-8.36%
15	Jul 2002	Nov 2002	5	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 7.42%	7.42%	-9.77%	-4.66%
14	Apr 2002	Jun 2002	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -0.50%	-0.50%	-7.08%	-13.43%
13	Mar 2002	Mar 2002	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -3.86%	-3.86%	5.19%	3.74%
12	Dec 2001	Feb 2002	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -2.54%	-2.54%	-1.89%	-2.54%
11	Aug 2001	Nov 2001	4	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.80%	2.80%	-7.00%	-5.51%
10	Jun 2001	Jul 2001	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -3.42%	-3.42%	-6.11%	-3.42%
9	Oct 2000	May 2001	8	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 6.18%	6.18%	-14.48%	-11.90%
8	Sep 2000	Sep 2000	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -5.29%	-5.29%	-3.99%	-5.29%
7	Jul 2000	Aug 2000	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 3.59%	3.59%	2.67%	4.60%
6	May 2000	Jun 2000	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.41%	0.41%	-0.30%	0.41%
5	Mar 1999	Apr 2000	14	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 98.26%	98.26%	55.85%	18.94%
4	Dec 1998	Feb 1999	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 6.81%	6.81%	9.22%	6.81%
3	Sep 1998	Nov 1998	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.43%	2.43%	11.99%	22.09%
2	Mar 1998	Aug 1998	6	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 3.85%	3.85%	-2.21%	-8.13%
1	Jan 1998	Feb 1998	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 8.38%	8.38%	11.09%	8.38%