Portfolio Optimization

This portfolio optimizer tool supports the following portfolio optimization strategies:

Mean Variance Optimization – Find the optimal risk adjusted portfolio that lies on the efficient frontier
Conditional Value-at-Risk – Optimize the portfolio to minimize the expected tail loss
Risk Parity – Find the portfolio that equalizes the risk contribution of portfolio assets
Tracking Error – Find the portfolio that minimizes the tracking error against the selected benchmark
Information Ratio – Find the portfolio that maximizes the information ratio against the selected benchmark
Kelly Criterion – Finds the portfolio with the maximum expected geometric growth rate
Sortino Ratio – Find the portfolio that maximizes the Sortino ratio for the given minimum acceptable return
Omega Ratio – Find the portfolio that maximizes the Omega ratio for the given minimum acceptable return
Maximum Drawdown – Find the portfolio with the minimum worst case drawdown with optional minimum acceptable return

The optimization is based on the monthly return statistics of the selected portfolio assets for the given time period. The optimization result does not predict what allocation would perform best outside the given time period, and the actual performance of portfolios constructed using the optimized asset weights may vary from the given performance goal.

The required inputs for the optimization include the time range and the portfolio assets. Portfolio asset weights and constraints are optional. You can also use the Black-Litterman model based portfolio optimization, which allows the benchmark portfolio asset weights to be optimized based on investor's views.

Portfolio Type

Time Period

Start Year

First Month

End Year

Last Month

Optimization Goal

Targeted Annual Return

Targeted Annual Volatility

Targeted Tracking Error

Targeted Monthly CVaR

Robust Optimization

Use Historical Returns

Use Historical Volatility

Use Historical Correlations

Correlation Matrix

Browse…

Asset Constraints

Group Constraints

Compared Allocation

Benchmark

Benchmark Ticker

Asset Allocation

Allocation

Expected Return

Volatility

Min. Weight

Max. Weight

Group

Select asset 1

Enter percentage allocation for asset 1 %

Expected return for asset 1 %

Expected volatility for asset 1 %

Minimum allocation for asset 1 %

Maximum allocation for asset 1 %

Group assignment for asset 1

Select asset 2

Enter percentage allocation for asset 2 %

Expected return for asset 2 %

Expected volatility for asset 2 %

Minimum allocation for asset 2 %

Maximum allocation for asset 2 %

Group assignment for asset 2

Select asset 3

Enter percentage allocation for asset 3 %

Expected return for asset 3 %

Expected volatility for asset 3 %

Minimum allocation for asset 3 %

Maximum allocation for asset 3 %

Group assignment for asset 3

Select asset 4

Enter percentage allocation for asset 4 %

Expected return for asset 4 %

Expected volatility for asset 4 %

Minimum allocation for asset 4 %

Maximum allocation for asset 4 %

Group assignment for asset 4

Select asset 5

Enter percentage allocation for asset 5 %

Expected return for asset 5 %

Expected volatility for asset 5 %

Minimum allocation for asset 5 %

Maximum allocation for asset 5 %

Group assignment for asset 5

Select asset 6

Enter percentage allocation for asset 6 %

Expected return for asset 6 %

Expected volatility for asset 6 %

Minimum allocation for asset 6 %

Maximum allocation for asset 6 %

Group assignment for asset 6

Select asset 7

Enter percentage allocation for asset 7 %

Expected return for asset 7 %

Expected volatility for asset 7 %

Minimum allocation for asset 7 %

Maximum allocation for asset 7 %

Group assignment for asset 7

Select asset 8

Enter percentage allocation for asset 8 %

Expected return for asset 8 %

Expected volatility for asset 8 %

Minimum allocation for asset 8 %

Maximum allocation for asset 8 %

Group assignment for asset 8

Select asset 9

Enter percentage allocation for asset 9 %

Expected return for asset 9 %

Expected volatility for asset 9 %

Minimum allocation for asset 9 %

Maximum allocation for asset 9 %

Group assignment for asset 9

Select asset 10

Enter percentage allocation for asset 10 %

Expected return for asset 10 %

Expected volatility for asset 10 %

Minimum allocation for asset 10 %

Maximum allocation for asset 10 %

Group assignment for asset 10

Total

Total allocation for portfolio %

Asset Groups

Min. Weight

Max. Weight

Full name for group A at index 1

Minimum allocation for group A at index 1 %

Maximum allocation for group A at index 1 %

Full name for group B at index 2

Minimum allocation for group B at index 2 %

Maximum allocation for group B at index 2 %

Full name for group C at index 3

Minimum allocation for group C at index 3 %

Maximum allocation for group C at index 3 %

Full name for group D at index 4

Minimum allocation for group D at index 4 %

Maximum allocation for group D at index 4 %

Full name for group E at index 5

Minimum allocation for group E at index 5 %

Maximum allocation for group E at index 5 %

Full name for group F at index 6

Minimum allocation for group F at index 6 %

Maximum allocation for group F at index 6 %

Portfolio Optimization Results (Jan 1986 - Dec 2008) Save

Note: The time period was constrained by the available data for Global ex-US Stock Market [Jan 1986 - Aug 2021].

Portfolio optimization results with goal to maximize Sharpe ratio. The possible range of expected annual portfolio returns for the given period is 9.49% to 9.86%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Sharpe Ratio
Asset Class	Allocation
US Stock Market	99.14%
Global ex-US Stock Market	0.86%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
Metric	Maximum Sharpe Ratio
Start Balance	$10,000
End Balance	$65,670
CAGR	8.53%
Expected Return	9.85%
Stdev	15.43%
Best Year	35.49%
Worst Year	-37.10%
Max. Drawdown	-44.09%
Sharpe Ratio (ex-ante)	0.32
Sharpe Ratio (ex-post)	0.32
Sortino Ratio	0.43
US Stock Market Correlation	1.00
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return.

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
Maximum Sharpe Ratio	-22.71%	-37.10%	-8.43%	-1.72%	-0.63%	8.53%	15.98%	13.57%
Trailing annualized return and volatility are for full months ending in December 2008 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.
Portfolio optimization determines target weights for portfolio assets based on mathematical models that can use either historical or forecasted data as inputs. Optimization results are not guarantees of future performance.
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.
CAGR = Compound Annual Growth Rate
Stdev = Annualized standard deviation of monthly returns
Sharpe ratio is calculated and annualized from monthly excess returns over the risk free rate (3-month treasury bill)
Drawdowns are calculated based on monthly returns.
The backtested results assume monthly rebalancing of portfolio assets to match the specified allocation.

Efficient Frontier Assets
#	Asset	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	US Stock Market	9.86%	15.46%	0.321	0.00%	100.00%
2	Global ex-US Stock Market	8.55%	18.21%	0.206	0.00%	100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

Efficient Frontier Asset Correlations
Asset	US Stock Market	Global ex-US Stock Market
US Stock Market	1.00	0.63
Global ex-US Stock Market	0.63	1.00
Based on monthly returns from Jan 1986 to Dec 2008

Note: You can hover over any of the data points on the chart for more information.

Efficient Frontier Assets
#	US Stock Market	Global ex-US Stock Market	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	71.67%	28.33%	9.49%	14.90%	0.310
2	71.96%	28.04%	9.49%	14.90%	0.310
3	72.25%	27.75%	9.50%	14.90%	0.310
4	72.53%	27.47%	9.50%	14.90%	0.311
5	72.82%	27.18%	9.50%	14.90%	0.311
6	73.10%	26.90%	9.51%	14.90%	0.311
7	73.39%	26.61%	9.51%	14.90%	0.311
8	73.68%	26.32%	9.52%	14.90%	0.311
9	73.96%	26.04%	9.52%	14.90%	0.312
10	74.25%	25.75%	9.52%	14.90%	0.312
11	74.54%	25.46%	9.53%	14.90%	0.312
12	74.82%	25.18%	9.53%	14.91%	0.312
13	75.11%	24.89%	9.53%	14.91%	0.312
14	75.39%	24.61%	9.54%	14.91%	0.313
15	75.68%	24.32%	9.54%	14.91%	0.313
16	75.97%	24.03%	9.55%	14.91%	0.313
17	76.25%	23.75%	9.55%	14.91%	0.313
18	76.54%	23.46%	9.55%	14.92%	0.313
19	76.82%	23.18%	9.56%	14.92%	0.314
20	77.11%	22.89%	9.56%	14.92%	0.314
21	77.40%	22.60%	9.56%	14.92%	0.314
22	77.68%	22.32%	9.57%	14.92%	0.314
23	77.97%	22.03%	9.57%	14.93%	0.314
24	78.25%	21.75%	9.58%	14.93%	0.315
25	78.54%	21.46%	9.58%	14.93%	0.315
26	78.83%	21.17%	9.58%	14.93%	0.315
27	79.11%	20.89%	9.59%	14.94%	0.315
28	79.40%	20.60%	9.59%	14.94%	0.315
29	79.69%	20.31%	9.59%	14.94%	0.315
30	79.97%	20.03%	9.60%	14.95%	0.316
31	80.26%	19.74%	9.60%	14.95%	0.316
32	80.54%	19.46%	9.61%	14.95%	0.316
33	80.83%	19.17%	9.61%	14.96%	0.316
34	81.12%	18.88%	9.61%	14.96%	0.316
35	81.40%	18.60%	9.62%	14.97%	0.316
36	81.69%	18.31%	9.62%	14.97%	0.317
37	81.97%	18.03%	9.62%	14.97%	0.317
38	82.26%	17.74%	9.63%	14.98%	0.317
39	82.55%	17.45%	9.63%	14.98%	0.317
40	82.83%	17.17%	9.64%	14.99%	0.317
41	83.12%	16.88%	9.64%	14.99%	0.317
42	83.40%	16.60%	9.64%	15.00%	0.317
43	83.69%	16.31%	9.65%	15.00%	0.317
44	83.98%	16.02%	9.65%	15.01%	0.318
45	84.26%	15.74%	9.65%	15.01%	0.318
46	84.55%	15.45%	9.66%	15.02%	0.318
47	84.84%	15.16%	9.66%	15.02%	0.318
48	85.12%	14.88%	9.67%	15.03%	0.318
49	85.41%	14.59%	9.67%	15.03%	0.318
50	85.69%	14.31%	9.67%	15.04%	0.318
51	85.98%	14.02%	9.68%	15.04%	0.318
52	86.27%	13.73%	9.68%	15.05%	0.319
53	86.55%	13.45%	9.69%	15.06%	0.319
54	86.84%	13.16%	9.69%	15.06%	0.319
55	87.12%	12.88%	9.69%	15.07%	0.319
56	87.41%	12.59%	9.70%	15.07%	0.319
57	87.70%	12.30%	9.70%	15.08%	0.319
58	87.98%	12.02%	9.70%	15.09%	0.319
59	88.27%	11.73%	9.71%	15.09%	0.319
60	88.55%	11.45%	9.71%	15.10%	0.319
61	88.84%	11.16%	9.72%	15.11%	0.319
62	89.13%	10.87%	9.72%	15.11%	0.319
63	89.41%	10.59%	9.72%	15.12%	0.320
64	89.70%	10.30%	9.73%	15.13%	0.320
65	89.99%	10.01%	9.73%	15.14%	0.320
66	90.27%	9.73%	9.73%	15.14%	0.320
67	90.56%	9.44%	9.74%	15.15%	0.320
68	90.84%	9.16%	9.74%	15.16%	0.320
69	91.13%	8.87%	9.75%	15.17%	0.320
70	91.42%	8.58%	9.75%	15.17%	0.320
71	91.70%	8.30%	9.75%	15.18%	0.320
72	91.99%	8.01%	9.76%	15.19%	0.320
73	92.27%	7.73%	9.76%	15.20%	0.320
74	92.56%	7.44%	9.76%	15.21%	0.320
75	92.85%	7.15%	9.77%	15.22%	0.320
76	93.13%	6.87%	9.77%	15.22%	0.320
77	93.42%	6.58%	9.78%	15.23%	0.320
78	93.70%	6.30%	9.78%	15.24%	0.320
79	93.99%	6.01%	9.78%	15.25%	0.320
80	94.28%	5.72%	9.79%	15.26%	0.321
81	94.56%	5.44%	9.79%	15.27%	0.321
82	94.85%	5.15%	9.79%	15.28%	0.321
83	95.14%	4.86%	9.80%	15.29%	0.321
84	95.42%	4.58%	9.80%	15.30%	0.321
85	95.71%	4.29%	9.81%	15.31%	0.321
86	95.99%	4.01%	9.81%	15.32%	0.321
87	96.28%	3.72%	9.81%	15.33%	0.321
88	96.57%	3.43%	9.82%	15.34%	0.321
89	96.85%	3.15%	9.82%	15.35%	0.321
90	97.14%	2.86%	9.83%	15.36%	0.321
91	97.42%	2.58%	9.83%	15.37%	0.321
92	97.71%	2.29%	9.83%	15.38%	0.321
93	98.00%	2.00%	9.84%	15.39%	0.321
94	98.28%	1.72%	9.84%	15.40%	0.321
95	98.57%	1.43%	9.84%	15.41%	0.321
96	98.85%	1.15%	9.85%	15.42%	0.321
97	99.14%	0.86%	9.85%	15.43%	0.321
98	99.43%	0.57%	9.86%	15.44%	0.321
99	99.71%	0.29%	9.86%	15.45%	0.321
100	100.00%	0.00%	9.86%	15.46%	0.321
^*Ex-ante values shown for portfolio return and volatility. Ex-ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate.

Annual returns for the configured portfolios
Year	Inflation	Maximum Sharpe Ratio Return	Maximum Sharpe Ratio Balance	US Stock Market	Global ex-US Stock Market
1986	1.10%	14.95%	$11,495	14.57%	63.38%
1987	4.43%	2.85%	$11,823	2.61%	30.48%
1988	4.42%	17.40%	$13,880	17.32%	25.66%
1989	4.65%	27.99%	$17,765	28.12%	12.85%
1990	6.11%	-6.22%	$16,660	-6.08%	-24.79%
1991	3.06%	32.19%	$22,023	32.39%	9.48%
1992	2.90%	8.89%	$23,981	9.11%	-14.79%
1993	2.75%	10.79%	$26,569	10.62%	29.92%
1994	2.67%	-0.08%	$26,547	-0.17%	9.76%
1995	2.54%	35.49%	$35,968	35.79%	3.98%
1996	3.32%	20.82%	$43,454	20.96%	4.68%
1997	1.70%	30.69%	$56,792	30.99%	-0.77%
1998	1.61%	23.20%	$69,970	23.26%	15.60%
1999	2.68%	23.87%	$86,671	23.81%	29.92%
2000	3.39%	-10.62%	$77,470	-10.57%	-15.61%
2001	1.55%	-11.05%	$68,913	-10.97%	-20.15%
2002	2.38%	-20.91%	$54,504	-20.96%	-15.08%
2003	1.88%	31.43%	$71,634	31.35%	40.34%
2004	3.26%	12.59%	$80,650	12.52%	20.84%
2005	3.42%	6.06%	$85,540	5.98%	15.57%
2006	2.54%	15.60%	$98,888	15.51%	26.64%
2007	4.08%	5.57%	$104,400	5.49%	15.52%
2008	0.09%	-37.10%	$65,670	-37.04%	-44.10%

Monthly returns for the configured portfolios
Year	Month	Maximum Sharpe Ratio Return	Maximum Sharpe Ratio Balance	US Stock Market	Global ex-US Stock Market
1986	1	0.84%	$10,084	0.83%	2.34%
1986	2	7.13%	$10,803	7.10%	10.41%
1986	3	5.86%	$11,437	5.81%	12.66%
1986	4	-0.77%	$11,349	-0.84%	7.25%
1986	5	4.83%	$11,896	4.90%	-3.22%
1986	6	1.38%	$12,061	1.33%	7.37%
1986	7	-5.78%	$11,364	-5.88%	6.08%
1986	8	6.42%	$12,093	6.41%	7.22%
1986	9	-7.86%	$11,142	-7.92%	-1.88%
1986	10	4.65%	$11,660	4.75%	-6.95%
1986	11	1.45%	$11,829	1.42%	5.61%
1986	12	-2.82%	$11,495	-2.89%	5.01%
1987	1	12.84%	$12,972	12.85%	11.67%
1987	2	4.77%	$13,590	4.79%	2.32%
1987	3	2.34%	$13,908	2.26%	11.16%
1987	4	-1.38%	$13,716	-1.48%	10.54%
1987	5	0.47%	$13,781	0.47%	0.50%
1987	6	4.13%	$14,350	4.19%	-3.10%
1987	7	4.53%	$15,000	4.57%	-0.52%
1987	8	3.81%	$15,571	3.77%	8.40%
1987	9	-2.07%	$15,249	-2.08%	-1.19%
1987	10	-22.19%	$11,866	-22.27%	-12.42%
1987	11	-7.10%	$11,024	-7.16%	0.47%
1987	12	7.25%	$11,823	7.30%	1.78%
1988	1	4.37%	$12,340	4.38%	3.66%
1988	2	5.23%	$12,984	5.21%	6.56%
1988	3	-1.36%	$12,808	-1.42%	6.14%
1988	4	1.12%	$12,951	1.11%	1.88%
1988	5	-0.08%	$12,941	-0.06%	-2.42%
1988	6	4.85%	$13,569	4.92%	-3.00%
1988	7	-0.62%	$13,484	-0.64%	1.69%
1988	8	-2.82%	$13,104	-2.80%	-5.91%
1988	9	3.70%	$13,589	3.71%	2.88%
1988	10	1.69%	$13,818	1.65%	6.31%
1988	11	-1.50%	$13,611	-1.57%	6.75%
1988	12	1.98%	$13,880	2.00%	-0.51%
1989	1	6.57%	$14,792	6.61%	2.30%
1989	2	-1.80%	$14,526	-1.82%	0.56%
1989	3	2.07%	$14,827	2.11%	-2.27%
1989	4	4.78%	$15,536	4.81%	1.33%
1989	5	3.80%	$16,126	3.87%	-4.80%
1989	6	-0.23%	$16,088	-0.22%	-2.36%
1989	7	7.66%	$17,321	7.63%	12.20%
1989	8	2.20%	$17,702	2.25%	-3.98%
1989	9	-0.18%	$17,670	-0.23%	5.55%
1989	10	-2.83%	$17,170	-2.83%	-3.67%
1989	11	1.59%	$17,443	1.56%	4.78%
1989	12	1.85%	$17,765	1.83%	3.83%
1990	1	-6.99%	$16,524	-7.01%	-3.64%
1990	2	1.53%	$16,778	1.60%	-6.54%
1990	3	2.36%	$17,174	2.47%	-10.36%
1990	4	-2.84%	$16,687	-2.84%	-2.75%
1990	5	8.79%	$18,154	8.77%	11.68%
1990	6	-0.53%	$18,057	-0.53%	-0.30%
1990	7	-1.07%	$17,863	-1.10%	2.33%
1990	8	-9.03%	$16,249	-9.02%	-10.37%
1990	9	-5.26%	$15,395	-5.18%	-14.18%
1990	10	-1.08%	$15,228	-1.24%	17.08%
1990	11	6.28%	$16,184	6.40%	-7.85%
1990	12	2.94%	$16,660	2.95%	1.34%
1991	1	4.93%	$17,481	4.96%	1.66%
1991	2	6.96%	$18,697	6.92%	11.05%
1991	3	2.82%	$19,225	2.89%	-4.78%
1991	4	0.40%	$19,302	0.39%	1.60%
1991	5	3.94%	$20,062	3.98%	-0.38%
1991	6	-4.49%	$19,161	-4.47%	-6.58%
1991	7	4.82%	$20,085	4.83%	4.04%
1991	8	2.60%	$20,608	2.65%	-3.14%
1991	9	-1.13%	$20,376	-1.19%	6.35%
1991	10	1.72%	$20,726	1.72%	2.02%
1991	11	-3.84%	$19,930	-3.83%	-5.27%
1991	12	10.50%	$22,023	10.56%	4.01%
1992	1	-0.03%	$22,017	-0.01%	-2.42%
1992	2	1.24%	$22,290	1.28%	-3.69%
1992	3	-2.44%	$21,747	-2.40%	-7.18%
1992	4	1.40%	$22,050	1.41%	-0.77%
1992	5	0.58%	$22,178	0.52%	7.08%
1992	6	-1.87%	$21,763	-1.85%	-4.63%
1992	7	3.79%	$22,588	3.85%	-3.35%
1992	8	-2.00%	$22,137	-2.07%	6.95%
1992	9	1.03%	$22,366	1.07%	-2.73%
1992	10	1.11%	$22,615	1.17%	-5.33%
1992	11	4.17%	$23,558	4.20%	0.81%
1992	12	1.79%	$23,981	1.81%	0.45%
1993	1	1.01%	$24,222	1.01%	-0.01%
1993	2	0.48%	$24,339	0.46%	3.51%
1993	3	2.53%	$24,954	2.46%	10.13%
1993	4	-2.66%	$24,291	-2.77%	9.98%
1993	5	3.04%	$25,028	3.03%	3.58%
1993	6	0.52%	$25,157	0.55%	-2.98%
1993	7	-0.23%	$25,100	-0.27%	4.21%
1993	8	3.94%	$26,088	3.93%	4.76%
1993	9	-0.02%	$26,083	0.01%	-3.03%
1993	10	1.64%	$26,511	1.64%	1.34%
1993	11	-1.68%	$26,065	-1.62%	-9.37%
1993	12	1.93%	$26,569	1.90%	6.07%
1994	1	3.14%	$27,403	3.08%	9.92%
1994	2	-2.22%	$26,795	-2.24%	0.42%
1994	3	-4.43%	$25,608	-4.44%	-3.02%
1994	4	0.91%	$25,842	0.89%	3.28%
1994	5	0.96%	$26,091	0.97%	-0.09%
1994	6	-2.69%	$25,390	-2.73%	1.97%
1994	7	3.06%	$26,167	3.08%	0.48%
1994	8	4.37%	$27,310	4.39%	1.74%
1994	9	-1.86%	$26,803	-1.85%	-2.85%
1994	10	1.56%	$27,222	1.55%	2.77%
1994	11	-3.67%	$26,224	-3.65%	-5.40%
1994	12	1.23%	$26,547	1.23%	0.93%
1995	1	2.15%	$27,117	2.20%	-3.94%
1995	2	3.97%	$28,192	4.04%	-5.16%
1995	3	2.69%	$28,949	2.65%	6.46%
1995	4	2.52%	$29,678	2.51%	3.51%
1995	5	3.43%	$30,696	3.48%	-1.88%
1995	6	2.94%	$31,598	2.98%	-1.80%
1995	7	4.04%	$32,873	4.02%	5.72%
1995	8	1.04%	$33,213	1.07%	-3.35%
1995	9	3.60%	$34,408	3.61%	1.58%
1995	10	-1.18%	$34,002	-1.17%	-2.59%
1995	11	4.15%	$35,414	4.17%	2.55%
1995	12	1.56%	$35,968	1.54%	3.68%
1996	1	2.64%	$36,917	2.66%	0.49%
1996	2	1.61%	$37,511	1.62%	0.34%
1996	3	1.15%	$37,943	1.14%	1.98%
1996	4	2.42%	$38,862	2.41%	3.98%
1996	5	2.63%	$39,883	2.66%	-1.33%
1996	6	-0.83%	$39,551	-0.84%	0.41%
1996	7	-5.35%	$37,435	-5.37%	-3.24%
1996	8	3.07%	$38,583	3.09%	0.01%
1996	9	5.35%	$40,648	5.38%	2.13%
1996	10	1.41%	$41,220	1.43%	-1.20%
1996	11	6.78%	$44,015	6.81%	3.13%
1996	12	-1.27%	$43,454	-1.27%	-1.86%
1997	1	5.39%	$45,797	5.46%	-2.37%
1997	2	-0.09%	$45,756	-0.11%	1.82%
1997	3	-4.42%	$43,735	-4.45%	-0.10%
1997	4	4.46%	$45,685	4.50%	0.20%
1997	5	7.10%	$48,927	7.10%	6.54%
1997	6	4.38%	$51,069	4.37%	5.40%
1997	7	7.72%	$55,010	7.77%	1.59%
1997	8	-3.76%	$52,943	-3.72%	-8.60%
1997	9	5.77%	$55,995	5.77%	5.51%
1997	10	-3.44%	$54,067	-3.40%	-9.10%
1997	11	3.29%	$55,847	3.33%	-1.19%
1997	12	1.69%	$56,792	1.70%	0.92%
1998	1	0.46%	$57,056	0.44%	3.04%
1998	2	7.34%	$61,244	7.34%	6.88%
1998	3	5.05%	$64,334	5.06%	3.22%
1998	4	1.09%	$65,036	1.10%	0.53%
1998	5	-2.70%	$63,280	-2.71%	-1.51%
1998	6	3.51%	$65,502	3.54%	-0.27%
1998	7	-2.24%	$64,031	-2.27%	1.08%
1998	8	-15.64%	$54,019	-15.65%	-13.66%
1998	9	6.60%	$57,586	6.68%	-2.07%
1998	10	7.54%	$61,928	7.51%	10.77%
1998	11	6.16%	$65,746	6.17%	5.34%
1998	12	6.43%	$69,970	6.45%	3.26%
1999	1	3.61%	$72,496	3.65%	-0.63%
1999	2	-3.72%	$69,802	-3.73%	-2.16%
1999	3	3.94%	$72,554	3.93%	4.97%
1999	4	4.68%	$75,950	4.68%	5.08%
1999	5	-2.02%	$74,413	-2.00%	-5.00%
1999	6	5.15%	$78,248	5.16%	4.39%
1999	7	-3.15%	$75,784	-3.20%	2.27%
1999	8	-0.91%	$75,096	-0.92%	0.33%
1999	9	-2.41%	$73,286	-2.44%	0.82%
1999	10	6.26%	$77,876	6.29%	3.74%
1999	11	3.43%	$80,546	3.42%	4.08%
1999	12	7.60%	$86,671	7.59%	9.37%
2000	1	-4.20%	$83,029	-4.18%	-6.22%
2000	2	2.55%	$85,144	2.54%	2.83%
2000	3	5.67%	$89,970	5.69%	3.48%
2000	4	-5.21%	$85,283	-5.21%	-5.41%
2000	5	-3.40%	$82,382	-3.41%	-2.67%
2000	6	4.42%	$86,022	4.42%	4.27%
2000	7	-1.97%	$84,324	-1.95%	-4.46%
2000	8	7.23%	$90,418	7.28%	1.00%
2000	9	-4.67%	$86,193	-4.67%	-5.00%
2000	10	-2.05%	$84,424	-2.04%	-3.03%
2000	11	-9.86%	$76,102	-9.90%	-4.44%
2000	12	1.80%	$77,470	1.78%	3.72%
2001	1	3.80%	$80,418	3.83%	1.10%
2001	2	-9.40%	$72,859	-9.41%	-7.61%
2001	3	-6.72%	$67,960	-6.72%	-7.15%
2001	4	8.16%	$73,507	8.16%	7.89%
2001	5	0.97%	$74,222	1.01%	-3.52%
2001	6	-1.65%	$72,994	-1.64%	-3.84%
2001	7	-1.72%	$71,740	-1.71%	-2.43%
2001	8	-5.97%	$67,455	-6.00%	-2.30%
2001	9	-9.01%	$61,376	-9.00%	-10.73%
2001	10	2.53%	$62,926	2.52%	2.97%
2001	11	7.60%	$67,708	7.63%	3.56%
2001	12	1.78%	$68,913	1.78%	1.35%
2002	1	-1.27%	$68,036	-1.24%	-4.63%
2002	2	-2.02%	$66,661	-2.05%	0.90%
2002	3	4.39%	$69,587	4.38%	5.71%
2002	4	-4.85%	$66,209	-4.90%	0.42%
2002	5	-1.20%	$65,417	-1.22%	1.16%
2002	6	-7.04%	$60,812	-7.06%	-4.28%
2002	7	-8.03%	$55,926	-8.02%	-9.80%
2002	8	0.52%	$56,219	0.53%	-0.12%
2002	9	-10.07%	$50,556	-10.07%	-10.88%
2002	10	7.63%	$54,413	7.65%	5.70%
2002	11	6.05%	$57,705	6.06%	4.75%
2002	12	-5.55%	$54,504	-5.57%	-3.43%
2003	1	-2.55%	$53,113	-2.54%	-3.76%
2003	2	-1.69%	$52,213	-1.69%	-2.42%
2003	3	1.06%	$52,767	1.09%	-1.93%
2003	4	8.22%	$57,105	8.21%	9.70%
2003	5	6.11%	$60,593	6.11%	6.15%
2003	6	1.44%	$61,468	1.43%	2.66%
2003	7	2.36%	$62,921	2.36%	3.18%
2003	8	2.39%	$64,424	2.39%	2.51%
2003	9	-1.11%	$63,708	-1.15%	2.78%
2003	10	6.12%	$67,606	6.12%	6.49%
2003	11	1.39%	$68,544	1.38%	2.13%
2003	12	4.51%	$71,634	4.48%	7.80%
2004	1	2.23%	$73,229	2.23%	1.60%
2004	2	1.44%	$74,283	1.43%	2.50%
2004	3	-1.06%	$73,498	-1.07%	0.45%
2004	4	-2.12%	$71,943	-2.11%	-3.14%
2004	5	1.34%	$72,905	1.35%	0.46%
2004	6	2.09%	$74,429	2.09%	2.40%
2004	7	-3.80%	$71,602	-3.80%	-3.34%
2004	8	0.31%	$71,827	0.31%	0.75%
2004	9	1.75%	$73,084	1.74%	2.96%
2004	10	1.69%	$74,319	1.68%	3.24%
2004	11	4.71%	$77,816	4.68%	7.23%
2004	12	3.64%	$80,650	3.63%	4.44%
2005	1	-2.67%	$78,499	-2.68%	-1.67%
2005	2	2.09%	$80,142	2.07%	4.68%
2005	3	-1.76%	$78,734	-1.75%	-2.93%
2005	4	-2.32%	$76,907	-2.32%	-2.07%
2005	5	3.74%	$79,781	3.77%	0.08%
2005	6	0.82%	$80,432	0.81%	1.30%
2005	7	4.10%	$83,731	4.11%	3.68%
2005	8	-0.91%	$82,968	-0.94%	2.85%
2005	9	0.89%	$83,706	0.86%	4.73%
2005	10	-1.88%	$82,135	-1.86%	-3.37%
2005	11	3.96%	$85,388	3.97%	2.67%
2005	12	0.18%	$85,540	0.14%	5.14%
2006	1	3.53%	$88,558	3.50%	6.87%
2006	2	-0.01%	$88,553	0.00%	-0.72%
2006	3	1.81%	$90,160	1.80%	3.17%
2006	4	1.15%	$91,193	1.11%	5.12%
2006	5	-3.25%	$88,233	-3.23%	-4.45%
2006	6	0.17%	$88,381	0.17%	-0.38%
2006	7	-0.12%	$88,275	-0.13%	1.15%
2006	8	2.31%	$90,319	2.31%	2.53%
2006	9	2.25%	$92,350	2.27%	0.25%
2006	10	3.54%	$95,615	3.53%	4.00%
2006	11	2.25%	$97,763	2.23%	3.73%
2006	12	1.15%	$98,888	1.13%	3.09%
2007	1	1.87%	$100,737	1.88%	0.96%
2007	2	-1.60%	$99,127	-1.61%	0.06%
2007	3	1.12%	$100,240	1.11%	2.80%
2007	4	4.01%	$104,259	4.01%	3.92%
2007	5	3.68%	$108,099	3.69%	3.09%
2007	6	-1.65%	$106,314	-1.67%	0.61%
2007	7	-3.39%	$102,710	-3.41%	-1.06%
2007	8	1.43%	$104,183	1.45%	-0.72%
2007	9	3.62%	$107,951	3.59%	6.38%
2007	10	1.88%	$109,985	1.85%	5.90%
2007	11	-4.49%	$105,049	-4.49%	-4.57%
2007	12	-0.62%	$104,400	-0.60%	-2.28%
2008	1	-6.10%	$98,030	-6.08%	-8.55%
2008	2	-3.04%	$95,048	-3.07%	0.33%
2008	3	-0.58%	$94,493	-0.58%	-0.71%
2008	4	5.03%	$99,245	5.02%	5.85%
2008	5	2.09%	$101,316	2.09%	1.51%
2008	6	-8.20%	$93,009	-8.19%	-8.99%
2008	7	-0.79%	$92,271	-0.77%	-3.67%
2008	8	1.52%	$93,678	1.58%	-5.10%
2008	9	-9.30%	$84,969	-9.26%	-13.09%
2008	10	-17.67%	$69,958	-17.63%	-22.09%
2008	11	-7.89%	$64,439	-7.90%	-6.29%
2008	12	1.91%	$65,670	1.86%	8.16%

Portfolio return and risk metrics
Metric	Maximum Sharpe Ratio
Arithmetic Mean (monthly)	0.79%
Arithmetic Mean (annualized)	9.85%
Geometric Mean (monthly)	0.68%
Geometric Mean (annualized)	8.53%
Volatility (monthly)	4.45%
Volatility (annualized)	15.43%
Downside Deviation (monthly)	3.14%
Max. Drawdown	-44.09%
US Market Correlation	1.00
Beta^(*)	1.00
Alpha (annualized)	0.01%
R²	99.99%
Sharpe Ratio	0.32
Sortino Ratio	0.43
Treynor Ratio (%)	4.96
Calmar Ratio	-0.20
Active Return	-0.01%
Tracking Error	0.13%
Information Ratio	-0.04
Skewness	-1.10
Excess Kurtosis	3.39
Historical Value-at-Risk (5%)	-7.05%
Analytical Value-at-Risk (5%)	-6.54%
Conditional Value-at-Risk (5%)	-10.80%
Upside Capture Ratio (%)	99.73
Downside Capture Ratio (%)	99.71
Safe Withdrawal Rate	10.49%
Perpetual Withdrawal Rate	5.20%
Positive Periods	172 out of 276 (62.32%)
Gain/Loss Ratio	0.96
^* US stock market 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	Maximum Sharpe Ratio
Black Monday Period	Sep 1987	Nov 1987	-29.21%
Asian Crisis	Jul 1997	Jan 1998	-3.76%
Russian Debt Default	Jul 1998	Oct 1998	-17.53%
Dotcom Crash	Mar 2000	Oct 2002	-44.09%

Drawdowns for Maximum Sharpe Ratio

Drawdowns for Maximum Sharpe Ratio (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Sep 2000	Sep 2002	2 years 1 month	Apr 2006	3 years 7 months	5 years 8 months	-44.09%
2	Nov 2007	Nov 2008	1 year 1 month				-41.41%
3	Sep 1987	Nov 1987	3 months	May 1989	1 year 6 months	1 year 9 months	-29.21%
4	Jul 1998	Aug 1998	2 months	Nov 1998	3 months	5 months	-17.53%
5	Jun 1990	Oct 1990	5 months	Feb 1991	4 months	9 months	-16.12%
6	Apr 2000	May 2000	2 months	Aug 2000	3 months	5 months	-8.43%
7	Sep 1986	Sep 1986	1 month	Jan 1987	4 months	5 months	-7.86%
8	Feb 1994	Jun 1994	5 months	Feb 1995	8 months	1 year 1 month	-7.34%
9	Jan 1990	Jan 1990	1 month	May 1990	4 months	5 months	-6.99%
10	Jul 1999	Sep 1999	3 months	Nov 1999	2 months	5 months	-6.34%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
Name	CAGR	Stdev	Best Year	Worst Year	Max. Drawdown	Sharpe Ratio	Sortino Ratio	US Mkt Correlation
US Stock Market	8.53%	15.46%	35.79%	-37.04%	-44.11%	0.32	0.43	1.00
Global ex-US Stock Market	6.76%	18.21%	63.38%	-44.10%	-51.80%	0.21	0.29	0.63

Monthly Correlations

Correlations for the portfolio assets
Name	US Stock Market	Global ex-US Stock Market	Maximum Sharpe Ratio
US Stock Market	1.00	0.63	1.00
Global ex-US Stock Market	0.63	1.00	0.64

Portfolio Risk Decomposition

Portfolio risk decomposition
Name	Maximum Sharpe Ratio
US Stock Market	99.35%
Global ex-US Stock Market	0.65%

Annual Asset Returns

Rolling returns summary
Roll Period	Average	High	Low
1 year	10.94%	47.10%	-38.66%
3 years	10.98%	30.50%	-16.29%
5 years	10.89%	26.70%	-3.89%
7 years	10.70%	20.26%	-0.70%
10 years	11.68%	18.80%	-0.63%
15 years	10.77%	14.85%	6.22%