Test Market Timing Models

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.

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

Trading Frequency

Signal Asset

Specify signal asset

Trade Execution

Compared Allocation

Benchmark

Benchmark Ticker

Timing Periods

Length

Unit

Weight

Time Period #1

Period 1 length

Period 1 time unit

Period 1 weight %

Time Period #2

Period 2 length

Period 2 time unit

Period 2 weight %

Time Period #3

Period 3 length

Period 3 time unit

Period 3 weight %

Time Period #4

Period 4 length

Period 4 time unit

Period 4 weight %

Time Period #5

Period 5 length

Period 5 time unit

Period 5 weight %

Volatility Period

Volatility period length

Volatility period time unit

Volatility period weight %

Asset 1

Select asset 1

Enter percentage allocation for asset 1 %

Asset 2

Select asset 2

Enter percentage allocation for asset 2 %

Asset 3

Select asset 3

Enter percentage allocation for asset 3 %

Asset 4

Select asset 4

Enter percentage allocation for asset 4 %

Asset 5

Select asset 5

Enter percentage allocation for asset 5 %

Asset 6

Select asset 6

Enter percentage allocation for asset 6 %

Asset 7

Select asset 7

Enter percentage allocation for asset 7 %

Asset 8

Select asset 8

Enter percentage allocation for asset 8 %

Asset 9

Select asset 9

Enter percentage allocation for asset 9 %

Asset 10

Select asset 10

Enter percentage allocation for asset 10 %

Total

Total allocation for portfolio %

Model Simulation Results (Jan 1997 - Dec 2018) Save

Tactical asset allocation model results from Jan 1997 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 1 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 - Mar 2021].

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	US Mkt Correlation
Dual Momentum Model	$10,000	$378,071	17.95%	14.45%	63.91%	-11.71%	-23.67%	1.08	1.87	0.44
Equal Weight Portfolio	$10,000	$57,678	8.29%	15.51%	52.57%	-41.80%	-55.28%	0.46	0.64	0.92
Vanguard 500 Index Investor	$10,000	$50,074	7.60%	14.96%	33.19%	-37.02%	-50.97%	0.43	0.61	0.99

Trailing Returns

Trailing Returns
Name	Annualized Return						Annualized Volatility
Name	3 Month	1 year	3 year	5 year	10 year	Full	3 year	5 year
Dual Momentum Model	-13.76%	-2.52%	5.35%	6.12%	14.28%	17.95%	12.25%	11.68%
Equal Weight Portfolio	-16.30%	-14.16%	5.41%	5.24%	11.30%	8.29%	11.73%	10.97%
Vanguard 500 Index Investor	-13.55%	-4.52%	9.11%	8.34%	12.97%	7.60%	10.96%	10.95%
Trailing annualized return and volatility are for full months ending in December 2018 excluding portfolio cashflows.

Notes on results:

Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
All portfolio returns presented are hypothetical and backtested. Hypothetical returns do not reflect trading costs, transaction fees, or taxes.
The backtested performance results are created by retroactively applying the specified investment strategy or methodology to historical data. Backtested models are developed with the benefit of hindsight but might not have foresight of the future.
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.
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.
The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
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
Additional trading costs and taxes for tactical asset allocation models are not reflected in the results
CAGR = Compound Annual Growth Rate
Stdev = Annualized standard deviation of monthly returns
Sharpe and Sortino ratios are calculated and annualized from monthly excess returns over the risk free rate (3-month treasury bill)
Stock market correlation is based on the correlation of monthly returns
Drawdowns are calculated based on monthly returns excluding cashflows
Refer to the FAQ section regarding the data sources and methodology descriptions

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)
1997	1.70%	16.03%	$11,603	7.55%	$10,755	33.19%	$13,319	33.19%	-14.13%	13.90%
1998	1.61%	33.56%	$15,497	27.76%	$13,741	28.62%	$17,131	28.62%	25.98%	13.05%
1999	2.68%	41.56%	$21,938	52.57%	$20,964	21.07%	$20,740	21.07%	90.29%	-8.66%
2000	3.39%	25.42%	$27,516	-4.75%	$19,969	-9.06%	$18,861	-9.06%	-2.68%	19.72%
2001	1.55%	5.26%	$28,962	-17.29%	$16,516	-12.02%	$16,594	-12.02%	-22.52%	4.31%
2002	2.38%	-11.71%	$25,570	-17.95%	$13,552	-22.15%	$12,919	-22.15%	-13.88%	16.67%
2003	1.88%	63.91%	$41,911	42.39%	$19,297	28.50%	$16,601	28.50%	57.37%	2.68%
2004	3.26%	34.19%	$56,240	20.89%	$23,328	10.74%	$18,384	10.74%	31.77%	7.12%
2005	3.42%	16.22%	$65,359	12.49%	$26,243	4.77%	$19,262	4.77%	20.49%	6.61%
2006	2.54%	37.76%	$90,042	22.89%	$32,250	15.64%	$22,275	15.64%	30.34%	1.74%
2007	4.08%	8.61%	$97,798	5.38%	$33,984	5.39%	$23,475	5.39%	5.15%	9.24%
2008	0.09%	1.77%	$99,524	-41.80%	$19,780	-37.02%	$14,784	-37.02%	-46.62%	22.52%
2009	2.72%	45.68%	$144,992	36.62%	$27,023	26.49%	$18,700	26.49%	47.12%	-12.05%
2010	1.50%	-5.35%	$137,232	18.82%	$32,107	14.91%	$21,489	14.91%	22.55%	8.93%
2011	2.96%	29.64%	$177,907	-9.42%	$29,084	1.97%	$21,911	1.97%	-19.74%	29.28%
2012	1.74%	32.54%	$235,796	17.00%	$34,027	15.82%	$25,379	15.82%	17.93%	3.47%
2013	1.50%	19.16%	$280,967	31.28%	$44,669	32.18%	$33,544	32.18%	30.24%	-13.03%
2014	0.76%	10.98%	$311,821	5.08%	$46,936	13.51%	$38,076	13.51%	-2.88%	25.28%
2015	0.73%	3.69%	$323,321	4.91%	$49,243	1.25%	$38,551	1.25%	8.60%	-1.54%
2016	2.07%	-7.42%	$299,333	4.93%	$51,671	11.82%	$43,107	11.82%	-1.77%	1.20%
2017	2.11%	29.57%	$387,855	30.04%	$67,195	21.67%	$52,447	21.67%	38.77%	8.58%
2018	1.91%	-2.52%	$378,071	-14.16%	$57,678	-4.52%	$50,074	-4.52%	-23.02%	-1.90%

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)
1997	1	-0.65%	$9,935	1.14%	$10,114	6.22%	$10,622	6.22%	-3.94%	-0.65%
1997	2	0.79%	$10,013	1.18%	$10,234	0.79%	$10,706	0.79%	1.58%	-0.11%
1997	3	-0.41%	$9,972	-2.27%	$10,001	-4.14%	$10,263	-4.14%	-0.41%	-2.29%
1997	4	2.35%	$10,206	1.52%	$10,153	5.96%	$10,874	5.96%	-2.91%	2.35%
1997	5	6.09%	$10,827	6.47%	$10,810	6.09%	$11,536	6.09%	6.84%	0.98%
1997	6	2.90%	$11,141	3.68%	$11,207	4.45%	$12,050	4.45%	2.90%	1.78%
1997	7	7.97%	$12,029	2.33%	$11,469	7.97%	$13,010	7.97%	-3.31%	5.34%
1997	8	-5.61%	$11,354	-5.17%	$10,876	-5.61%	$12,280	-5.61%	-4.73%	-2.57%
1997	9	2.63%	$11,653	3.21%	$11,225	5.47%	$12,951	5.47%	0.95%	2.63%
1997	10	-3.35%	$11,263	-3.45%	$10,837	-3.35%	$12,518	-3.35%	-3.56%	2.99%
1997	11	1.27%	$11,406	-0.25%	$10,810	4.60%	$13,093	4.60%	-5.10%	1.27%
1997	12	1.72%	$11,603	-0.51%	$10,755	1.72%	$13,319	1.72%	-2.74%	1.66%
1998	1	1.11%	$11,732	4.43%	$11,232	1.11%	$13,467	1.11%	7.75%	1.91%
1998	2	5.57%	$12,385	6.38%	$11,948	7.19%	$14,435	7.19%	5.57%	-0.75%
1998	3	5.10%	$13,017	5.41%	$12,595	5.10%	$15,172	5.10%	5.71%	0.14%
1998	4	5.09%	$13,680	3.05%	$12,979	1.01%	$15,325	1.01%	5.09%	0.40%
1998	5	5.04%	$14,370	1.65%	$13,193	-1.74%	$15,058	-1.74%	5.04%	1.83%
1998	6	-0.38%	$14,316	1.85%	$13,437	4.07%	$15,671	4.07%	-0.38%	2.35%
1998	7	-1.05%	$14,165	0.65%	$13,525	-1.05%	$15,506	-1.05%	2.36%	-0.51%
1998	8	-12.74%	$12,360	-13.61%	$11,684	-14.47%	$13,262	-14.47%	-12.74%	4.83%
1998	9	3.29%	$12,766	0.56%	$11,750	6.41%	$14,112	6.41%	-5.29%	3.29%
1998	10	8.16%	$13,809	6.32%	$12,492	8.16%	$15,264	8.16%	4.47%	-1.69%
1998	11	6.07%	$14,647	4.75%	$13,085	6.07%	$16,191	6.07%	3.42%	0.88%
1998	12	5.81%	$15,497	5.01%	$13,741	5.81%	$17,131	5.81%	4.22%	-0.16%
1999	1	4.20%	$16,149	3.01%	$14,155	4.20%	$17,851	4.20%	1.82%	0.98%
1999	2	-3.12%	$15,644	0.97%	$14,292	-3.12%	$17,293	-3.12%	5.06%	-4.76%
1999	3	5.22%	$16,460	4.61%	$14,950	4.00%	$17,984	4.00%	5.22%	-0.34%
1999	4	8.29%	$17,825	6.07%	$15,858	3.85%	$18,677	3.85%	8.29%	0.19%
1999	5	-0.88%	$17,668	-1.63%	$15,599	-2.39%	$18,231	-2.39%	-0.88%	-1.68%
1999	6	-1.05%	$17,482	8.99%	$17,002	5.56%	$19,243	5.56%	12.43%	-1.05%
1999	7	9.00%	$19,056	2.94%	$17,501	-3.13%	$18,641	-3.13%	9.00%	-0.58%
1999	8	3.19%	$19,664	1.35%	$17,737	-0.50%	$18,549	-0.50%	3.19%	-0.49%
1999	9	-1.40%	$19,388	-2.07%	$17,369	-2.74%	$18,041	-2.74%	-1.40%	0.91%
1999	10	0.12%	$19,411	4.09%	$18,080	6.33%	$19,182	6.33%	1.85%	0.12%
1999	11	2.02%	$19,804	6.99%	$19,344	2.02%	$19,570	2.02%	11.96%	-0.59%
1999	12	10.78%	$21,938	8.38%	$20,964	5.98%	$20,740	5.98%	10.78%	-1.60%
2000	1	11.64%	$24,492	3.30%	$21,657	-5.03%	$19,696	-5.03%	11.64%	1.25%
2000	2	17.38%	$28,748	7.74%	$23,332	-1.91%	$19,321	-1.91%	17.38%	2.96%
2000	3	-3.93%	$27,618	2.91%	$24,011	9.75%	$21,205	9.75%	-3.93%	3.14%
2000	4	-3.00%	$26,790	-7.23%	$22,274	-3.00%	$20,569	-3.00%	-11.47%	-0.66%
2000	5	-0.46%	$26,667	-4.36%	$21,303	-2.04%	$20,150	-2.04%	-6.68%	-0.46%
2000	6	2.30%	$27,280	4.24%	$22,207	2.49%	$20,652	2.49%	5.99%	2.30%
2000	7	-2.65%	$26,556	-2.08%	$21,746	-1.50%	$20,343	-1.50%	-2.65%	1.49%
2000	8	2.08%	$27,108	4.84%	$22,800	6.19%	$21,602	6.19%	3.50%	2.08%
2000	9	-5.29%	$25,674	-3.99%	$21,890	-5.29%	$20,459	-5.29%	-2.69%	-0.85%
2000	10	1.57%	$26,076	-4.60%	$20,883	-0.43%	$20,372	-0.43%	-8.77%	1.57%
2000	11	2.99%	$26,857	-6.10%	$19,608	-7.89%	$18,765	-7.89%	-4.32%	2.99%
2000	12	2.45%	$27,516	1.84%	$19,969	0.51%	$18,861	0.51%	3.16%	2.45%
2001	1	1.67%	$27,976	2.61%	$20,490	3.55%	$19,530	3.55%	1.67%	0.28%
2001	2	-9.14%	$25,420	-6.96%	$19,064	-9.14%	$17,746	-9.14%	-4.78%	1.80%
2001	3	-0.60%	$25,266	-7.33%	$17,665	-6.36%	$16,618	-6.36%	-8.31%	-0.60%
2001	4	-2.56%	$24,618	6.80%	$18,867	7.77%	$17,909	7.77%	5.83%	-2.56%
2001	5	0.65%	$24,778	-0.78%	$18,720	0.65%	$18,025	0.65%	-2.21%	0.21%
2001	6	-2.45%	$24,172	-3.39%	$18,086	-2.45%	$17,584	-2.45%	-4.34%	0.76%
2001	7	3.61%	$25,046	-2.81%	$17,577	-1.00%	$17,409	-1.00%	-4.62%	3.61%
2001	8	2.02%	$25,553	-4.09%	$16,859	-6.27%	$16,316	-6.27%	-1.90%	2.02%
2001	9	0.88%	$25,778	-11.46%	$14,927	-8.09%	$14,996	-8.09%	-14.83%	0.88%
2001	10	5.12%	$27,098	2.54%	$15,306	1.90%	$15,280	1.90%	3.19%	5.12%
2001	11	5.95%	$28,711	6.80%	$16,347	7.65%	$16,450	7.65%	5.95%	-4.98%
2001	12	0.87%	$28,962	1.03%	$16,516	0.87%	$16,594	0.87%	1.19%	-1.91%
2002	1	-1.57%	$28,509	-1.52%	$16,265	-1.47%	$16,349	-1.47%	-1.57%	1.20%
2002	2	1.24%	$28,863	-1.39%	$16,039	-1.94%	$16,033	-1.94%	-0.85%	1.24%
2002	3	-3.86%	$27,750	5.19%	$16,871	3.74%	$16,633	3.74%	6.63%	-3.86%
2002	4	2.91%	$28,557	-1.58%	$16,604	-6.07%	$15,622	-6.07%	2.91%	3.73%
2002	5	1.27%	$28,919	0.26%	$16,646	-0.75%	$15,505	-0.75%	1.27%	0.39%
2002	6	-4.52%	$27,610	-5.83%	$15,676	-7.13%	$14,398	-7.13%	-4.52%	1.76%
2002	7	2.93%	$28,419	-8.40%	$14,360	-7.72%	$13,287	-7.72%	-9.07%	2.93%
2002	8	4.28%	$29,635	-0.39%	$14,303	0.65%	$13,374	0.65%	-1.44%	4.28%
2002	9	-10.87%	$26,412	-10.78%	$12,761	-10.87%	$11,919	-10.87%	-10.69%	4.02%
2002	10	-2.84%	$25,663	5.46%	$13,458	8.78%	$12,966	8.78%	2.14%	-2.84%
2002	11	5.88%	$27,171	5.10%	$14,144	5.88%	$13,728	5.88%	4.32%	-0.98%
2002	12	-5.89%	$25,570	-4.18%	$13,552	-5.89%	$12,919	-5.89%	-2.47%	4.05%
2003	1	-0.45%	$25,456	-2.35%	$13,234	-2.62%	$12,580	-2.62%	-2.08%	-0.45%
2003	2	3.03%	$26,226	-2.07%	$12,960	-1.52%	$12,389	-1.52%	-2.62%	3.03%
2003	3	-1.13%	$25,929	-0.23%	$12,931	0.96%	$12,507	0.96%	-1.41%	-1.13%
2003	4	8.25%	$28,069	9.45%	$14,153	8.25%	$13,540	8.25%	10.65%	0.91%
2003	5	11.15%	$31,198	8.21%	$15,314	5.26%	$14,252	5.26%	11.15%	5.67%
2003	6	3.80%	$32,384	2.53%	$15,702	1.26%	$14,432	1.26%	3.80%	-1.48%
2003	7	4.78%	$33,933	3.26%	$16,214	1.74%	$14,684	1.74%	4.78%	-8.57%
2003	8	4.08%	$35,316	3.01%	$16,701	1.93%	$14,967	1.93%	4.08%	1.43%
2003	9	5.41%	$37,227	2.17%	$17,064	-1.07%	$14,807	-1.07%	5.41%	5.07%
2003	10	5.22%	$39,171	5.43%	$17,991	5.64%	$15,642	5.64%	5.22%	-2.58%
2003	11	0.86%	$39,510	1.53%	$18,265	0.86%	$15,778	0.86%	2.19%	0.31%
2003	12	6.08%	$41,911	5.65%	$19,297	5.22%	$16,601	5.22%	6.08%	1.23%
2004	1	4.21%	$43,677	3.02%	$19,879	1.82%	$16,904	1.82%	4.21%	1.74%
2004	2	3.52%	$45,213	2.45%	$20,366	1.38%	$17,136	1.38%	3.52%	1.96%
2004	3	2.31%	$46,259	0.40%	$20,447	-1.51%	$16,877	-1.51%	2.31%	1.45%
2004	4	-1.98%	$45,344	-1.78%	$20,084	-1.58%	$16,611	-1.58%	-1.98%	-5.52%
2004	5	-0.56%	$45,091	0.10%	$20,104	1.36%	$16,836	1.36%	-1.15%	-0.56%
2004	6	1.93%	$45,961	2.57%	$20,621	1.93%	$17,161	1.93%	3.21%	0.87%
2004	7	-2.76%	$44,695	-3.03%	$19,995	-3.31%	$16,593	-3.31%	-2.76%	1.52%
2004	8	3.39%	$46,208	0.63%	$20,121	0.38%	$16,657	0.38%	0.87%	3.39%
2004	9	2.38%	$47,307	1.72%	$20,467	1.07%	$16,834	1.07%	2.38%	0.94%
2004	10	3.03%	$48,738	2.27%	$20,932	1.51%	$17,089	1.51%	3.03%	1.46%
2004	11	7.72%	$52,500	5.88%	$22,163	4.05%	$17,781	4.05%	7.72%	-2.25%
2004	12	7.12%	$56,240	5.26%	$23,328	3.39%	$18,384	3.39%	7.12%	2.22%
2005	1	0.92%	$56,756	-0.77%	$23,149	-2.45%	$17,933	-2.45%	0.92%	2.59%
2005	2	4.31%	$59,200	3.20%	$23,890	2.09%	$18,308	2.09%	4.31%	-1.24%
2005	3	-2.21%	$57,892	-1.98%	$23,416	-1.76%	$17,986	-1.76%	-2.21%	-0.76%
2005	4	3.22%	$59,759	-1.97%	$22,955	-1.91%	$17,642	-1.91%	-2.02%	3.22%
2005	5	2.55%	$61,282	1.77%	$23,361	3.17%	$18,201	3.17%	0.36%	2.55%
2005	6	0.13%	$61,360	1.42%	$23,693	0.13%	$18,224	0.13%	2.72%	1.64%
2005	7	4.53%	$64,141	4.12%	$24,669	3.71%	$18,900	3.71%	4.53%	-2.58%
2005	8	2.03%	$65,441	0.56%	$24,807	-0.91%	$18,727	-0.91%	2.03%	2.87%
2005	9	3.53%	$67,753	2.16%	$25,343	0.79%	$18,876	0.79%	3.53%	-2.78%
2005	10	-4.10%	$64,972	-2.89%	$24,610	-1.68%	$18,559	-1.68%	-4.10%	-1.74%
2005	11	0.57%	$65,345	3.22%	$25,402	3.76%	$19,258	3.76%	2.67%	0.57%
2005	12	0.02%	$65,359	3.31%	$26,243	0.02%	$19,262	0.02%	6.60%	2.33%
2006	1	7.37%	$70,174	5.01%	$27,556	2.65%	$19,771	2.65%	7.37%	-0.90%
2006	2	0.62%	$70,612	0.44%	$27,679	0.26%	$19,823	0.26%	0.62%	0.81%
2006	3	5.27%	$74,332	3.25%	$28,578	1.23%	$20,067	1.23%	5.27%	-3.39%
2006	4	5.50%	$78,417	3.41%	$29,554	1.33%	$20,335	1.33%	5.50%	-1.96%
2006	5	-4.93%	$74,551	-3.91%	$28,397	-2.90%	$19,746	-2.90%	-4.93%	-0.03%
2006	6	0.71%	$75,077	-1.01%	$28,110	0.13%	$19,771	0.13%	-2.15%	0.71%
2006	7	1.84%	$76,458	0.05%	$28,125	0.61%	$19,891	0.61%	-0.50%	1.84%
2006	8	2.36%	$78,264	2.36%	$28,789	2.36%	$20,361	2.36%	2.36%	2.74%
2006	9	2.56%	$80,271	2.19%	$29,420	2.56%	$20,883	2.56%	1.82%	1.58%
2006	10	3.25%	$82,880	3.46%	$30,437	3.25%	$21,562	3.25%	3.66%	0.77%
2006	11	4.51%	$86,619	3.20%	$31,411	1.89%	$21,969	1.89%	4.51%	1.91%
2006	12	3.95%	$90,042	2.67%	$32,250	1.39%	$22,275	1.39%	3.95%	-2.14%
2007	1	2.94%	$92,688	2.22%	$32,964	1.49%	$22,607	1.49%	2.94%	-0.85%
2007	2	0.32%	$92,986	-0.82%	$32,693	-1.97%	$22,162	-1.97%	0.32%	2.93%
2007	3	-1.13%	$91,937	2.16%	$33,400	1.11%	$22,409	1.11%	3.21%	-1.13%
2007	4	3.87%	$95,494	4.14%	$34,784	4.42%	$23,399	4.42%	3.87%	0.86%
2007	5	3.48%	$98,814	2.96%	$35,813	3.48%	$24,212	3.48%	2.44%	-1.93%
2007	6	-1.68%	$97,158	-1.40%	$35,311	-1.68%	$23,806	-1.68%	-1.13%	-0.88%
2007	7	2.39%	$99,476	-1.77%	$34,684	-3.08%	$23,072	-3.08%	-0.46%	2.39%
2007	8	1.97%	$101,440	-0.74%	$34,428	1.50%	$23,418	1.50%	-2.97%	1.97%
2007	9	3.72%	$105,218	2.87%	$35,416	3.72%	$24,290	3.72%	2.01%	0.21%
2007	10	1.58%	$106,879	3.77%	$36,751	1.58%	$24,673	1.58%	5.96%	1.40%
2007	11	-8.06%	$98,268	-6.12%	$34,502	-4.19%	$23,640	-4.19%	-8.06%	4.59%
2007	12	-0.48%	$97,798	-1.50%	$33,984	-0.70%	$23,475	-0.70%	-2.30%	-0.48%
2008	1	2.64%	$100,381	-7.57%	$31,410	-6.02%	$22,063	-6.02%	-9.13%	2.64%
2008	2	0.35%	$100,733	-0.50%	$31,254	-3.25%	$21,345	-3.25%	2.26%	0.35%
2008	3	-1.34%	$99,386	-0.89%	$30,976	-0.44%	$21,251	-0.44%	-1.34%	1.02%
2008	4	-1.84%	$97,557	3.55%	$32,075	4.85%	$22,283	4.85%	2.24%	-1.84%
2008	5	1.29%	$98,818	1.68%	$32,615	1.29%	$22,571	1.29%	2.07%	-2.13%
2008	6	-7.91%	$91,006	-8.17%	$29,950	-8.44%	$20,666	-8.44%	-7.91%	1.80%
2008	7	0.30%	$91,275	-3.33%	$28,953	-0.83%	$20,494	-0.83%	-5.82%	0.30%
2008	8	1.80%	$92,922	-0.97%	$28,672	1.45%	$20,791	1.45%	-3.39%	1.80%
2008	9	-8.91%	$84,647	-12.17%	$25,183	-8.91%	$18,939	-8.91%	-15.43%	0.28%
2008	10	-3.63%	$81,576	-20.47%	$20,029	-16.79%	$15,759	-16.79%	-24.14%	-3.63%
2008	11	12.07%	$91,420	-6.06%	$18,816	-7.17%	$14,628	-7.17%	-4.94%	12.07%
2008	12	8.87%	$99,524	5.12%	$19,780	1.07%	$14,784	1.07%	9.18%	8.87%
2009	1	-9.15%	$90,420	-8.78%	$18,043	-8.41%	$13,540	-8.41%	-9.15%	-8.47%
2009	2	-1.01%	$89,508	-8.92%	$16,434	-10.66%	$12,097	-10.66%	-7.18%	-1.01%
2009	3	5.27%	$94,221	8.37%	$17,810	8.76%	$13,157	8.76%	7.98%	5.27%
2009	4	9.56%	$103,227	11.77%	$19,905	9.56%	$14,415	9.56%	13.97%	-4.99%
2009	5	13.98%	$117,660	9.80%	$21,856	5.62%	$15,225	5.62%	13.98%	-2.68%
2009	6	1.96%	$119,961	1.09%	$22,094	0.22%	$15,258	0.22%	1.96%	0.70%
2009	7	7.41%	$128,851	7.49%	$23,750	7.58%	$16,414	7.58%	7.41%	0.80%
2009	8	3.60%	$133,488	4.40%	$24,794	3.60%	$17,005	3.60%	5.19%	1.68%
2009	9	6.33%	$141,934	5.02%	$26,039	3.72%	$17,637	3.72%	6.33%	1.98%
2009	10	-1.67%	$139,565	-1.77%	$25,579	-1.87%	$17,308	-1.87%	-1.67%	-1.45%
2009	11	1.91%	$142,225	3.84%	$26,561	5.98%	$18,343	5.98%	1.70%	1.91%
2009	12	1.95%	$144,992	1.74%	$27,023	1.95%	$18,700	1.95%	1.53%	-5.66%
2010	1	-3.60%	$139,766	-2.78%	$26,271	-3.60%	$18,026	-3.60%	-1.96%	2.66%
2010	2	-0.21%	$139,475	1.10%	$26,561	3.09%	$18,583	3.09%	-0.89%	-0.21%
2010	3	6.01%	$147,862	6.59%	$28,311	6.01%	$19,701	6.01%	7.16%	-1.51%
2010	4	1.04%	$149,407	1.31%	$28,682	1.58%	$20,012	1.58%	1.04%	2.76%
2010	5	-8.01%	$137,447	-9.76%	$25,883	-8.01%	$18,410	-8.01%	-11.51%	4.23%
2010	6	4.67%	$143,860	-2.70%	$25,185	-5.24%	$17,445	-5.24%	-0.16%	4.67%
2010	7	-0.17%	$143,614	8.26%	$27,264	7.00%	$18,666	7.00%	9.52%	-0.17%
2010	8	-2.64%	$139,829	-3.58%	$26,288	-4.53%	$17,820	-4.53%	-2.64%	7.08%
2010	9	-1.82%	$137,281	10.24%	$28,979	8.92%	$19,410	8.92%	11.56%	-1.82%
2010	10	3.67%	$142,322	3.73%	$30,060	3.79%	$20,145	3.79%	3.67%	-3.29%
2010	11	0.00%	$142,322	-1.58%	$29,585	0.00%	$20,145	0.00%	-3.16%	-1.60%
2010	12	-3.58%	$137,232	8.53%	$32,107	6.67%	$21,489	6.67%	10.38%	-3.58%
2011	1	0.72%	$138,219	1.54%	$32,601	2.36%	$21,995	2.36%	0.72%	-2.38%
2011	2	3.42%	$142,941	2.33%	$33,362	3.42%	$22,747	3.42%	1.25%	1.24%
2011	3	0.03%	$142,978	0.25%	$33,445	0.03%	$22,753	0.03%	0.47%	0.02%
2011	4	4.92%	$150,010	3.93%	$34,760	2.95%	$23,423	2.95%	4.92%	2.04%
2011	5	-2.46%	$146,326	-1.80%	$34,134	-1.15%	$23,155	-1.15%	-2.46%	3.29%
2011	6	-2.00%	$143,405	-2.24%	$33,371	-1.67%	$22,768	-1.67%	-2.80%	-2.00%
2011	7	4.18%	$149,399	-1.82%	$32,764	-2.05%	$22,302	-2.05%	-1.59%	4.18%
2011	8	8.68%	$162,370	-7.57%	$30,284	-5.45%	$21,087	-5.45%	-9.69%	8.68%
2011	9	10.16%	$178,871	-9.42%	$27,433	-7.04%	$19,602	-7.04%	-11.79%	10.16%
2011	10	-3.34%	$172,905	9.55%	$30,052	10.91%	$21,741	10.91%	8.18%	-3.34%
2011	11	-0.23%	$172,501	-2.09%	$29,423	-0.23%	$21,691	-0.23%	-3.96%	1.82%
2011	12	3.13%	$177,907	-1.15%	$29,084	1.02%	$21,911	1.02%	-3.32%	3.13%
2012	1	4.46%	$185,850	6.64%	$31,015	4.46%	$22,889	4.46%	8.81%	0.08%
2012	2	5.59%	$196,242	4.95%	$32,549	4.31%	$23,875	4.31%	5.59%	-2.11%
2012	3	0.41%	$197,041	1.84%	$33,150	3.28%	$24,659	3.28%	0.41%	-3.77%
2012	4	-0.64%	$195,781	-0.66%	$32,932	-0.64%	$24,501	-0.64%	-0.68%	4.37%
2012	5	7.79%	$211,028	-8.90%	$30,002	-6.02%	$23,027	-6.02%	-11.78%	7.79%
2012	6	-1.44%	$207,980	3.98%	$31,197	4.11%	$23,973	4.11%	3.86%	-1.44%
2012	7	1.37%	$210,829	0.57%	$31,376	1.37%	$24,301	1.37%	-0.22%	3.32%
2012	8	2.24%	$215,550	2.57%	$32,183	2.24%	$24,845	2.24%	2.90%	-1.06%
2012	9	3.69%	$223,505	3.13%	$33,191	2.58%	$25,486	2.58%	3.69%	-2.10%
2012	10	1.19%	$226,156	-0.34%	$33,079	-1.86%	$25,012	-1.86%	1.19%	-0.43%
2012	11	0.62%	$227,560	0.59%	$33,275	0.56%	$25,152	0.56%	0.62%	1.35%
2012	12	3.62%	$235,796	2.26%	$34,027	0.90%	$25,379	0.90%	3.62%	-1.99%
2013	1	4.96%	$247,498	5.07%	$35,752	5.18%	$26,692	5.18%	4.96%	-3.27%
2013	2	1.34%	$250,811	0.77%	$36,026	1.34%	$27,050	1.34%	0.19%	1.26%
2013	3	3.74%	$260,188	2.52%	$36,932	3.74%	$28,061	3.74%	1.29%	0.03%
2013	4	1.91%	$265,154	2.80%	$37,968	1.91%	$28,597	1.91%	3.70%	3.87%
2013	5	-0.49%	$263,849	0.92%	$38,317	2.33%	$29,262	2.33%	-0.49%	-6.23%
2013	6	-1.35%	$260,285	-1.76%	$37,643	-1.35%	$28,867	-1.35%	-2.16%	-3.26%
2013	7	-1.93%	$255,265	5.29%	$39,633	5.07%	$30,331	5.07%	5.50%	-1.93%
2013	8	-0.66%	$253,582	-1.79%	$38,925	-2.91%	$29,448	-2.91%	-0.66%	-1.28%
2013	9	0.88%	$255,812	5.21%	$40,953	3.12%	$30,367	3.12%	7.30%	0.88%
2013	10	3.99%	$266,021	4.29%	$42,710	4.59%	$31,760	4.59%	3.99%	1.32%
2013	11	3.03%	$274,077	1.92%	$43,529	3.03%	$32,722	3.03%	0.81%	-2.49%
2013	12	2.51%	$280,967	2.62%	$44,669	2.51%	$33,544	2.51%	2.72%	-2.37%
2014	1	-2.23%	$274,713	-2.85%	$43,397	-3.47%	$32,381	-3.47%	-2.23%	6.26%
2014	2	0.60%	$276,356	5.25%	$45,676	4.56%	$33,857	4.56%	5.94%	0.60%
2014	3	0.73%	$278,384	0.78%	$46,031	0.82%	$34,136	0.82%	0.73%	0.63%
2014	4	0.72%	$280,400	0.05%	$46,054	0.72%	$34,383	0.72%	-0.62%	1.82%
2014	5	2.33%	$286,947	2.14%	$47,038	2.33%	$35,186	2.33%	1.94%	2.73%
2014	6	2.05%	$292,835	1.59%	$47,787	2.05%	$35,908	2.05%	1.13%	-0.16%
2014	7	-1.39%	$288,770	-1.74%	$46,957	-1.39%	$35,410	-1.39%	-2.08%	0.59%
2014	8	4.23%	$300,981	2.30%	$48,038	3.98%	$36,820	3.98%	0.62%	4.23%
2014	9	-1.41%	$296,729	-2.92%	$46,634	-1.41%	$36,300	-1.41%	-4.43%	-1.99%
2014	10	2.61%	$304,480	0.46%	$46,847	2.42%	$37,179	2.42%	-1.51%	2.61%
2014	11	2.68%	$312,647	0.63%	$47,142	2.68%	$38,177	2.68%	-1.42%	2.86%
2014	12	-0.26%	$311,821	-0.44%	$46,936	-0.26%	$38,076	-0.26%	-0.61%	2.82%
2015	1	8.97%	$339,778	-1.57%	$46,199	-3.02%	$36,927	-3.02%	-0.12%	8.97%
2015	2	-5.66%	$320,555	6.27%	$49,098	5.74%	$39,046	5.74%	6.81%	-5.66%
2015	3	0.57%	$322,380	-0.51%	$48,846	-1.59%	$38,424	-1.59%	0.57%	1.13%
2015	4	3.45%	$333,509	2.20%	$49,921	0.95%	$38,789	0.95%	3.45%	-3.07%
2015	5	0.88%	$336,428	1.07%	$50,457	1.27%	$39,282	1.27%	0.88%	-2.16%
2015	6	-1.93%	$329,925	-1.54%	$49,682	-1.93%	$38,523	-1.93%	-1.14%	-3.73%
2015	7	4.21%	$343,807	1.62%	$50,485	2.08%	$39,324	2.08%	1.15%	4.21%
2015	8	-6.05%	$323,018	-5.52%	$47,700	-6.05%	$36,946	-6.05%	-4.99%	-0.71%
2015	9	1.91%	$329,192	-2.78%	$46,372	-2.48%	$36,028	-2.48%	-3.08%	1.91%
2015	10	-0.48%	$327,616	6.51%	$49,390	8.42%	$39,063	8.42%	4.59%	-0.48%
2015	11	0.29%	$328,554	0.20%	$49,488	0.29%	$39,175	0.29%	0.11%	-0.81%
2015	12	-1.59%	$323,321	-0.50%	$49,243	-1.59%	$38,551	-1.59%	0.60%	-0.34%
2016	1	-6.67%	$301,766	-5.82%	$46,376	-4.98%	$36,632	-4.98%	-6.67%	5.24%
2016	2	2.86%	$310,395	-1.27%	$45,785	-0.15%	$36,579	-0.15%	-2.40%	2.86%
2016	3	0.05%	$310,558	7.18%	$49,071	6.78%	$39,058	6.78%	7.58%	0.05%
2016	4	0.66%	$312,614	0.52%	$49,325	0.37%	$39,204	0.37%	0.66%	-0.63%
2016	5	1.44%	$317,102	1.61%	$50,119	1.78%	$39,903	1.78%	1.44%	0.69%
2016	6	0.25%	$317,894	-2.65%	$48,793	0.25%	$40,002	0.25%	-5.54%	6.57%
2016	7	3.68%	$329,581	4.65%	$51,060	3.68%	$41,473	3.68%	5.62%	2.01%
2016	8	-0.18%	$328,997	-0.02%	$51,048	0.13%	$41,527	0.13%	-0.18%	-1.00%
2016	9	0.01%	$329,024	1.43%	$51,776	0.01%	$41,530	0.01%	2.84%	-1.32%
2016	10	-3.17%	$318,606	-2.50%	$50,481	-1.83%	$40,769	-1.83%	-3.17%	-4.23%
2016	11	-7.86%	$293,571	0.60%	$50,785	3.70%	$42,277	3.70%	-2.50%	-7.86%
2016	12	1.96%	$299,333	1.75%	$51,671	1.96%	$43,107	1.96%	1.53%	-0.35%
2017	1	1.88%	$304,970	3.15%	$53,297	1.88%	$43,918	1.88%	4.41%	0.65%
2017	2	1.82%	$310,515	2.89%	$54,838	3.96%	$45,659	3.96%	1.82%	1.57%
2017	3	0.10%	$310,825	1.92%	$55,892	0.10%	$45,704	0.10%	3.74%	-0.59%
2017	4	5.39%	$327,566	3.20%	$57,681	1.02%	$46,170	1.02%	5.39%	1.58%
2017	5	4.27%	$341,546	2.83%	$59,314	1.39%	$46,813	1.39%	4.27%	1.73%
2017	6	0.51%	$343,271	0.56%	$59,645	0.61%	$47,099	0.61%	0.51%	0.63%
2017	7	2.04%	$350,283	2.76%	$61,289	2.04%	$48,061	2.04%	3.47%	-0.59%
2017	8	0.39%	$351,644	0.34%	$61,498	0.29%	$48,202	0.29%	0.39%	3.27%
2017	9	3.97%	$365,601	3.01%	$63,352	2.06%	$49,195	2.06%	3.97%	-2.27%
2017	10	1.82%	$372,239	2.07%	$64,661	2.32%	$50,335	2.32%	1.82%	-0.02%
2017	11	3.06%	$383,627	1.76%	$65,798	3.06%	$51,875	3.06%	0.46%	0.63%
2017	12	1.10%	$387,855	2.12%	$67,195	1.10%	$52,447	1.10%	3.14%	1.78%
2018	1	5.12%	$407,712	5.42%	$70,834	5.71%	$55,443	5.71%	5.12%	-3.40%
2018	2	-3.69%	$392,649	-3.86%	$68,101	-3.69%	$53,394	-3.69%	-4.02%	-2.89%
2018	3	2.75%	$403,463	-1.44%	$67,120	-2.56%	$52,030	-2.56%	-0.33%	2.75%
2018	4	-2.04%	$395,245	0.33%	$67,339	0.37%	$52,224	0.37%	0.28%	-2.04%
2018	5	2.39%	$404,710	0.78%	$67,863	2.39%	$53,475	2.39%	-0.84%	1.79%
2018	6	0.61%	$407,158	-0.78%	$67,336	0.61%	$53,798	0.61%	-2.16%	0.66%
2018	7	3.71%	$422,261	1.90%	$68,617	3.71%	$55,794	3.71%	0.10%	-1.28%
2018	8	3.25%	$435,969	0.74%	$69,122	3.25%	$57,605	3.25%	-1.77%	1.18%
2018	9	0.55%	$438,386	-0.31%	$68,908	0.55%	$57,924	0.55%	-1.17%	-2.74%
2018	10	-6.85%	$408,361	-9.30%	$62,497	-6.85%	$53,957	-6.85%	-11.76%	-2.82%
2018	11	1.78%	$415,645	0.82%	$63,008	2.03%	$55,051	2.03%	-0.39%	1.78%
2018	12	-9.04%	$378,071	-8.46%	$57,678	-9.04%	$50,074	-9.04%	-7.88%	5.50%

Portfolio return and risk metrics
Metric	Dual Momentum Model	Equal Weight Portfolio	Vanguard 500 Index Investor
Arithmetic Mean (monthly)	1.47%	0.77%	0.71%
Arithmetic Mean (annualized)	19.16%	9.62%	8.81%
Geometric Mean (monthly)	1.39%	0.67%	0.61%
Geometric Mean (annualized)	17.95%	8.29%	7.60%
Volatility (monthly)	4.17%	4.48%	4.32%
Volatility (annualized)	14.45%	15.51%	14.96%
Downside Deviation (monthly)	2.33%	3.12%	2.95%
Max. Drawdown	-23.67%	-55.28%	-50.97%
US Market Correlation	0.44	0.92	0.99
Beta^(*)	0.40	0.93	1.00
Alpha (annualized)	14.24%	1.30%	0.00%
R²	17.38%	81.13%	100.00%
Sharpe Ratio	1.08	0.46	0.43
Sortino Ratio	1.87	0.64	0.61
Treynor Ratio (%)	38.72	7.65	6.41
Calmar Ratio	0.39	0.29	0.67
Active Return	10.36%	0.69%	N/A
Tracking Error	15.89%	6.81%	N/A
Information Ratio	0.65	0.10	N/A
Skewness	-0.10	-0.86	-0.65
Excess Kurtosis	1.54	2.08	1.11
Historical Value-at-Risk (5%)	-5.86%	-8.08%	-7.17%
Analytical Value-at-Risk (5%)	-5.39%	-6.60%	-6.40%
Conditional Value-at-Risk (5%)	-8.37%	-10.61%	-9.69%
Upside Capture Ratio (%)	77.74	97.24	100.00
Downside Capture Ratio (%)	17.14	92.79	100.00
Safe Withdrawal Rate	20.16%	9.16%	7.80%
Perpetual Withdrawal Rate	13.43%	5.70%	5.10%
Positive Periods	183 out of 264 (69.32%)	168 out of 264 (63.64%)	170 out of 264 (64.39%)
Gain/Loss Ratio	1.12	0.89	0.83
^* Vanguard 500 Index Investor is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.

Drawdowns for Historical Market Stress Periods

Drawdowns for Historical Market Stress Periods
Stress Period	Start	End	Dual Momentum Model	Equal Weight Portfolio	Vanguard 500 Index Investor
Asian Crisis	Jul 1997	Jan 1998	-6.37%	-6.22%	-5.61%
Russian Debt Default	Jul 1998	Oct 1998	-13.66%	-13.61%	-15.38%
Dotcom Crash	Mar 2000	Oct 2002	-15.92%	-46.85%	-44.82%
Subprime Crisis	Nov 2007	Mar 2009	-23.67%	-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	Nov 2007	Oct 2008	1 year	May 2009	7 months	1 year 7 months	-23.67%
2	Mar 2000	Jun 2001	1 year 4 months	Dec 2001	6 months	1 year 10 months	-15.92%
3	Aug 2015	Nov 2016	1 year 4 months	Jul 2017	8 months	2 years	-14.61%
4	Sep 2002	Jan 2003	5 months	May 2003	4 months	9 months	-14.10%
5	Jun 1998	Aug 1998	3 months	Nov 1998	3 months	6 months	-13.99%
6	Oct 2018	Dec 2018	3 months				-13.76%
7	May 2010	Dec 2010	8 months	Apr 2011	4 months	1 year	-8.15%
8	Aug 1997	Oct 1997	3 months	Feb 1998	4 months	7 months	-6.37%
9	Feb 2015	Feb 2015	1 month	Jul 2015	5 months	6 months	-5.66%
10	May 2006	May 2006	1 month	Sep 2006	4 months	5 months	-4.93%
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	Aug 1997	Dec 1997	5 months	Feb 1998	2 months	7 months	-6.22%
7	May 2006	Jun 2006	2 months	Oct 2006	4 months	6 months	-4.89%
8	Jun 2007	Aug 2007	3 months	Oct 2007	2 months	5 months	-3.87%
9	Sep 2014	Jan 2015	5 months	Feb 2015	1 month	6 months	-3.83%
10	Oct 2005	Oct 2005	1 month	Nov 2005	1 month	2 months	-2.89%
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	Aug 1997	Aug 1997	1 month	Nov 1997	3 months	4 months	-5.61%
10	Apr 2000	May 2000	2 months	Aug 2000	3 months	5 months	-4.98%
Worst 10 drawdowns included above

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	20.36%	83.76%	-23.67%	11.24%	63.25%	-47.42%	9.07%	53.61%	-43.32%
3 years	18.99%	42.13%	-3.01%	8.81%	33.90%	-18.64%	6.80%	27.53%	-16.14%
5 years	18.92%	33.02%	6.12%	7.84%	22.68%	-4.20%	6.09%	22.85%	-6.73%
7 years	19.62%	28.24%	10.91%	7.92%	15.76%	0.35%	6.08%	17.12%	-3.94%
10 years	19.38%	25.94%	12.65%	7.18%	13.10%	1.27%	5.31%	14.17%	-3.51%
15 years	19.57%	22.54%	15.79%	7.87%	11.83%	4.85%	5.98%	10.39%	3.64%

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
152	Jan 2019	Jan 2019	1	Please sign-in for forward signals	-	-	-	-
151	Dec 2018	Dec 2018	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -9.04%	-9.04%	-8.46%	-9.04%
150	Nov 2018	Nov 2018	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 1.78%	1.78%	0.82%	2.03%
149	May 2018	Oct 2018	6	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.32%	3.32%	-7.19%	3.32%
148	Mar 2018	Apr 2018	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 0.66%	0.66%	-1.12%	-2.19%
147	Feb 2018	Feb 2018	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -3.69%	-3.69%	-3.86%	-3.69%
146	Jan 2018	Jan 2018	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 5.12%	5.12%	5.42%	5.71%
145	Nov 2017	Dec 2017	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 4.20%	4.20%	3.92%	4.20%
144	Aug 2017	Oct 2017	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 6.27%	6.27%	5.50%	4.73%
143	Jul 2017	Jul 2017	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 2.04%	2.04%	2.76%	2.04%
142	Apr 2017	Jun 2017	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 10.44%	10.44%	6.72%	3.05%
141	Mar 2017	Mar 2017	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.10%	0.10%	1.92%	0.10%
140	Feb 2017	Feb 2017	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 1.82%	1.82%	2.89%	3.96%
139	Dec 2016	Jan 2017	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.88%	3.88%	4.95%	3.88%
138	Nov 2016	Nov 2016	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -7.86%	-7.86%	0.60%	3.70%
137	Oct 2016	Oct 2016	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -3.17%	-3.17%	-2.50%	-1.83%
136	Sep 2016	Sep 2016	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.01%	0.01%	1.43%	0.01%
135	Aug 2016	Aug 2016	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -0.18%	-0.18%	-0.02%	0.13%
134	Jun 2016	Jul 2016	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.94%	3.94%	1.88%	3.94%
133	Apr 2016	May 2016	2	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 2.11%	2.11%	2.14%	2.16%
132	Feb 2016	Mar 2016	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.91%	2.91%	5.81%	6.62%
131	Jan 2016	Jan 2016	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -6.67%	-6.67%	-5.82%	-4.98%
130	Nov 2015	Dec 2015	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -1.31%	-1.31%	-0.30%	-1.31%
129	Sep 2015	Oct 2015	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 1.42%	1.42%	3.54%	5.73%
128	Aug 2015	Aug 2015	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -6.05%	-6.05%	-5.52%	-6.05%
127	Jul 2015	Jul 2015	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 4.21%	4.21%	1.62%	2.08%
126	Jun 2015	Jun 2015	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -1.93%	-1.93%	-1.54%	-1.93%
125	Mar 2015	May 2015	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 4.95%	4.95%	2.77%	0.60%
124	Jan 2015	Feb 2015	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.80%	2.80%	4.61%	2.55%
123	Nov 2014	Dec 2014	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 2.41%	2.41%	0.19%	2.41%
122	Oct 2014	Oct 2014	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.61%	2.61%	0.46%	2.42%
121	Sep 2014	Sep 2014	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -1.41%	-1.41%	-2.92%	-1.41%
120	Aug 2014	Aug 2014	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 4.23%	4.23%	2.30%	3.98%
119	Apr 2014	Jul 2014	4	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.73%	3.73%	2.01%	3.73%
118	Mar 2014	Mar 2014	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 0.73%	0.73%	0.78%	0.82%
117	Feb 2014	Feb 2014	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 0.60%	0.60%	5.25%	4.56%
116	Jan 2014	Jan 2014	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -2.23%	-2.23%	-2.85%	-3.47%
115	Nov 2013	Dec 2013	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 5.62%	5.62%	4.59%	5.62%
114	Oct 2013	Oct 2013	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 3.99%	3.99%	4.29%	4.59%
113	Sep 2013	Sep 2013	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 0.88%	0.88%	5.21%	3.12%
112	Aug 2013	Aug 2013	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -0.66%	-0.66%	-1.79%	-2.91%
111	Jul 2013	Jul 2013	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -1.93%	-1.93%	5.29%	5.07%
110	Jun 2013	Jun 2013	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -1.35%	-1.35%	-1.76%	-1.35%
109	May 2013	May 2013	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -0.49%	-0.49%	0.92%	2.33%
108	Feb 2013	Apr 2013	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 7.13%	7.13%	6.20%	7.13%
107	Sep 2012	Jan 2013	5	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 14.82%	14.82%	11.09%	7.43%
106	Jul 2012	Aug 2012	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.64%	3.64%	3.16%	3.64%
105	May 2012	Jun 2012	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 6.23%	6.23%	-5.27%	-2.16%
104	Apr 2012	Apr 2012	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -0.64%	-0.64%	-0.66%	-0.64%
103	Feb 2012	Mar 2012	2	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 6.02%	6.02%	6.88%	7.73%
102	Jan 2012	Jan 2012	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 4.46%	4.46%	6.64%	4.46%
101	Dec 2011	Dec 2011	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 3.13%	3.13%	-1.15%	1.02%
100	Nov 2011	Nov 2011	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -0.23%	-0.23%	-2.09%	-0.23%
99	Jun 2011	Oct 2011	5	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 18.16%	18.16%	-11.96%	-6.11%
98	Apr 2011	May 2011	2	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 2.34%	2.34%	2.06%	1.77%
97	Feb 2011	Mar 2011	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.44%	3.44%	2.59%	3.44%
96	Jan 2011	Jan 2011	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 0.72%	0.72%	1.54%	2.36%
95	Dec 2010	Dec 2010	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -3.58%	-3.58%	8.53%	6.67%
94	Nov 2010	Nov 2010	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.00%	0.00%	-1.58%	0.00%
93	Oct 2010	Oct 2010	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 3.67%	3.67%	3.73%	3.79%
92	Sep 2010	Sep 2010	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -1.82%	-1.82%	10.24%	8.92%
91	Aug 2010	Aug 2010	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -2.64%	-2.64%	-3.58%	-4.53%
90	Jun 2010	Jul 2010	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 4.49%	4.49%	5.34%	1.39%
89	May 2010	May 2010	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -8.01%	-8.01%	-9.76%	-8.01%
88	Apr 2010	Apr 2010	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 1.04%	1.04%	1.31%	1.58%
87	Mar 2010	Mar 2010	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 6.01%	6.01%	6.59%	6.01%
86	Feb 2010	Feb 2010	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -0.21%	-0.21%	1.10%	3.09%
85	Dec 2009	Jan 2010	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -1.73%	-1.73%	-1.09%	-1.73%
84	Nov 2009	Nov 2009	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 1.91%	1.91%	3.84%	5.98%
83	Sep 2009	Oct 2009	2	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 4.55%	4.55%	3.16%	1.78%
82	Aug 2009	Aug 2009	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 3.60%	3.60%	4.40%	3.60%
81	May 2009	Jul 2009	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 24.82%	24.82%	19.31%	13.87%
80	Apr 2009	Apr 2009	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 9.56%	9.56%	11.77%	9.56%
79	Feb 2009	Mar 2009	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 4.20%	4.20%	-1.29%	-2.83%
78	Jan 2009	Jan 2009	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -9.15%	-9.15%	-8.78%	-8.41%
77	Oct 2008	Dec 2008	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 17.58%	17.58%	-21.46%	-21.94%
76	Sep 2008	Sep 2008	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -8.91%	-8.91%	-12.17%	-8.91%
75	Jul 2008	Aug 2008	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.11%	2.11%	-4.27%	0.60%
74	Jun 2008	Jun 2008	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -7.91%	-7.91%	-8.17%	-8.44%
73	May 2008	May 2008	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 1.29%	1.29%	1.68%	1.29%
72	Apr 2008	Apr 2008	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -1.84%	-1.84%	3.55%	4.85%
71	Mar 2008	Mar 2008	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -1.34%	-1.34%	-0.89%	-0.44%
70	Dec 2007	Feb 2008	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.51%	2.51%	-9.41%	-9.71%
69	Nov 2007	Nov 2007	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -8.06%	-8.06%	-6.12%	-4.19%
68	Sep 2007	Oct 2007	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 5.36%	5.36%	6.75%	5.36%
67	Jul 2007	Aug 2007	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 4.41%	4.41%	-2.50%	-1.63%
66	May 2007	Jun 2007	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 1.74%	1.74%	1.51%	1.74%
65	Apr 2007	Apr 2007	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 3.87%	3.87%	4.14%	4.42%
64	Mar 2007	Mar 2007	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -1.13%	-1.13%	2.16%	1.11%
63	Nov 2006	Feb 2007	4	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 12.19%	12.19%	7.41%	2.78%
62	Aug 2006	Oct 2006	3	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 8.40%	8.40%	8.22%	8.40%
61	Jun 2006	Jul 2006	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.56%	2.56%	-0.96%	0.74%
60	Jan 2006	May 2006	5	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 14.06%	14.06%	8.21%	2.51%
59	Dec 2005	Dec 2005	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.02%	0.02%	3.31%	0.02%
58	Nov 2005	Nov 2005	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 0.57%	0.57%	3.22%	3.76%
57	Jul 2005	Oct 2005	4	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 5.89%	5.89%	3.87%	1.84%
56	Jun 2005	Jun 2005	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.13%	0.13%	1.42%	0.13%
55	Apr 2005	May 2005	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 5.86%	5.86%	-0.24%	1.19%
54	Sep 2004	Mar 2005	7	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 25.29%	25.29%	16.38%	7.98%
53	Aug 2004	Aug 2004	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 3.39%	3.39%	0.63%	0.38%
52	Jul 2004	Jul 2004	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -2.76%	-2.76%	-3.03%	-3.31%
51	Jun 2004	Jun 2004	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 1.93%	1.93%	2.57%	1.93%
50	May 2004	May 2004	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -0.56%	-0.56%	0.10%	1.36%
49	Dec 2003	Apr 2004	5	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 14.77%	14.77%	9.96%	5.28%
48	Nov 2003	Nov 2003	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.86%	0.86%	1.53%	0.86%
47	May 2003	Oct 2003	6	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 39.55%	39.55%	27.12%	15.53%
46	Apr 2003	Apr 2003	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 8.25%	8.25%	9.45%	8.25%
45	Jan 2003	Mar 2003	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 1.40%	1.40%	-4.59%	-3.19%
44	Nov 2002	Dec 2002	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -0.36%	-0.36%	0.70%	-0.36%
43	Oct 2002	Oct 2002	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -2.84%	-2.84%	5.46%	8.78%
42	Sep 2002	Sep 2002	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -10.87%	-10.87%	-10.78%	-10.87%
41	Jul 2002	Aug 2002	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 7.33%	7.33%	-8.76%	-7.12%
40	Apr 2002	Jun 2002	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -0.50%	-0.50%	-7.08%	-13.43%
39	Feb 2002	Mar 2002	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -2.66%	-2.66%	3.72%	1.73%
38	Jan 2002	Jan 2002	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -1.57%	-1.57%	-1.52%	-1.47%
37	Dec 2001	Dec 2001	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.87%	0.87%	1.03%	0.87%
36	Nov 2001	Nov 2001	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 5.95%	5.95%	6.80%	7.65%
35	Jul 2001	Oct 2001	4	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 12.10%	12.10%	-15.37%	-13.10%
34	May 2001	Jun 2001	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -1.81%	-1.81%	-4.14%	-1.81%
33	Mar 2001	Apr 2001	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -3.15%	-3.15%	-1.03%	0.92%
32	Feb 2001	Feb 2001	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -9.14%	-9.14%	-6.96%	-9.14%
31	Jan 2001	Jan 2001	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 1.67%	1.67%	2.61%	3.55%
30	Oct 2000	Dec 2000	3	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 7.17%	7.17%	-8.78%	-7.81%
29	Sep 2000	Sep 2000	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -5.29%	-5.29%	-3.99%	-5.29%
28	Aug 2000	Aug 2000	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.08%	2.08%	4.84%	6.19%
27	Jul 2000	Jul 2000	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -2.65%	-2.65%	-2.08%	-1.50%
26	May 2000	Jun 2000	2	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 1.83%	1.83%	-0.30%	0.41%
25	Apr 2000	Apr 2000	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -3.00%	-3.00%	-7.23%	-3.00%
24	Dec 1999	Mar 2000	4	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 39.46%	39.46%	24.13%	8.35%
23	Nov 1999	Nov 1999	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 2.02%	2.02%	6.99%	2.02%
22	Oct 1999	Oct 1999	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 0.12%	0.12%	4.09%	6.33%
21	Jul 1999	Sep 1999	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 10.90%	10.90%	2.16%	-6.25%
20	Jun 1999	Jun 1999	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -1.05%	-1.05%	8.99%	5.56%
19	Mar 1999	May 1999	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 12.94%	12.94%	9.14%	5.42%
18	Oct 1998	Feb 1999	5	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 22.54%	22.54%	21.64%	22.54%
17	Sep 1998	Sep 1998	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 3.29%	3.29%	0.56%	6.41%
16	Aug 1998	Aug 1998	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -12.74%	-12.74%	-13.61%	-14.47%
15	Jul 1998	Jul 1998	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -1.05%	-1.05%	0.65%	-1.05%
14	Apr 1998	Jun 1998	3	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 9.98%	9.98%	6.69%	3.29%
13	Mar 1998	Mar 1998	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 5.10%	5.10%	5.41%	5.10%
12	Feb 1998	Feb 1998	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 5.57%	5.57%	6.38%	7.19%
11	Dec 1997	Jan 1998	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 2.85%	2.85%	3.90%	2.85%
10	Nov 1997	Nov 1997	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 1.27%	1.27%	-0.25%	4.60%
9	Oct 1997	Oct 1997	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: -3.35%	-3.35%	-3.45%	-3.35%
8	Sep 1997	Sep 1997	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.63%	2.63%	3.21%	5.47%
7	Jul 1997	Aug 1997	2	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 1.91%	1.91%	-2.96%	1.91%
6	Jun 1997	Jun 1997	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: 2.90%	2.90%	3.68%	4.45%
5	May 1997	May 1997	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 6.09%	6.09%	6.47%	6.09%
4	Apr 1997	Apr 1997	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: 2.35%	2.35%	1.52%	5.96%
3	Mar 1997	Mar 1997	1	100.00% Vanguard International Explorer Inv (VINEX)	VINEX: -0.41%	-0.41%	-2.27%	-4.14%
2	Feb 1997	Feb 1997	1	100.00% Vanguard 500 Index Investor (VFINX)	VFINX: 0.79%	0.79%	1.18%	0.79%
1	Jan 1997	Jan 1997	1	100.00% Vanguard Long-Term Treasury Inv (VUSTX)	VUSTX: -0.65%	-0.65%	1.14%	6.22%