Portfolio Optimization

This portfolio optimizer tool supports the following portfolio optimization strategies:

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.

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Asset Groups
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Portfolio Optimization Results (Jan 2006 - Dec 2019)

Portfolio optimization results with goal to maximize return subject to 10.00% targeted annual volatility. The possible range of expected annual portfolio returns for the given period is 6.97% to 10.69%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Return at 10.00% Volatility
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 64.29%
TLT iShares 20+ Year Treasury Bond ETF 15.25%
GLD SPDR Gold Shares 20.46%
Save portfolio »
Equal Weighted
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 12.50%
IJS iShares S&P Small-Cap 600 Value ETF 12.50%
EFA iShares MSCI EAFE ETF 12.50%
EEM iShares MSCI Emerging Markets ETF 12.50%
VNQ Vanguard Real Estate ETF 12.50%
TLT iShares 20+ Year Treasury Bond ETF 12.50%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 12.50%
GLD SPDR Gold Shares 12.50%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricMaximum Return at 10.00% VolatilityEqual Weighted
Start Balance$10,000$10,000
End Balance$34,293$28,195
CAGR9.20%7.68%
Expected Return 9.74% 8.40%
Stdev9.92%11.50%
Best Year25.99%23.38%
Worst Year-20.21%-21.23%
Max. Drawdown -31.20% -36.98%
Sharpe Ratio (ex-ante)0.860.63
Sharpe Ratio (ex-post)0.820.60
Sortino Ratio1.270.90
US Stock Market Correlation0.890.86
   

Trailing Returns

Trailing Returns
Name3 Month1 year3 year5 year10 yearFull
Maximum Return at 10.00% Volatility5.59%25.99%12.67%9.24%10.87%9.20%
Equal Weighted4.54%22.27%9.57%6.90%8.41%7.68%
Trailing returns are for full months ending in December 2019 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
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)9.34%10.52%14.60%0.6390.00%100.00%
2iShares S&P Small-Cap 600 Value ETF (IJS)8.46%10.44%19.08%0.4850.00%100.00%
3iShares MSCI EAFE ETF (EFA)4.10%5.66%17.16%0.2610.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)5.11%7.74%22.20%0.2950.00%100.00%
5Vanguard Real Estate ETF (VNQ)7.80%10.69%22.71%0.4190.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)6.27%7.20%13.36%0.4500.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.59%5.86%7.20%0.6500.00%100.00%
8SPDR Gold Shares (GLD)7.55%9.23%17.73%0.4540.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.18% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIIJSEFAEEMVNQTLTLQDGLD
Vanguard Total Stock Market ETFVTI1.000.910.890.790.72-0.330.270.04
iShares S&P Small-Cap 600 Value ETFIJS0.911.000.760.690.73-0.350.19-0.02
iShares MSCI EAFE ETFEFA0.890.761.000.880.67-0.240.370.15
iShares MSCI Emerging Markets ETFEEM0.790.690.881.000.60-0.230.350.29
Vanguard Real Estate ETFVNQ0.720.730.670.601.000.010.430.09
iShares 20+ Year Treasury Bond ETFTLT-0.33-0.35-0.24-0.230.011.000.520.21
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.270.190.370.350.430.521.000.26
SPDR Gold SharesGLD0.04-0.020.150.290.090.210.261.00
Based on provided custom correlation matrix
Efficient Frontier Assets
#VTIIJSEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
116.58%0.00%0.00%0.00%0.00%12.20%65.72%5.50%6.97%6.83%0.847
217.14%0.00%0.00%0.00%0.00%12.72%64.51%5.64%7.00%6.83%0.852
317.69%0.00%0.00%0.00%0.00%13.24%63.30%5.77%7.04%6.83%0.857
418.25%0.00%0.00%0.00%0.00%13.75%62.09%5.90%7.08%6.84%0.862
518.80%0.00%0.00%0.00%0.00%14.27%60.88%6.04%7.11%6.84%0.867
619.36%0.00%0.00%0.00%0.00%14.79%59.68%6.17%7.15%6.84%0.872
719.91%0.00%0.00%0.00%0.00%15.31%58.47%6.31%7.19%6.85%0.877
820.47%0.00%0.00%0.00%0.00%15.83%57.26%6.44%7.23%6.85%0.882
921.02%0.00%0.00%0.00%0.00%16.35%56.05%6.58%7.26%6.86%0.887
1021.58%0.00%0.00%0.00%0.00%16.87%54.84%6.71%7.30%6.87%0.891
1122.14%0.00%0.00%0.00%0.00%17.39%53.63%6.84%7.34%6.87%0.896
1222.69%0.00%0.00%0.00%0.00%17.91%52.43%6.98%7.37%6.88%0.900
1323.25%0.00%0.00%0.00%0.00%18.43%51.22%7.11%7.41%6.89%0.904
1423.80%0.00%0.00%0.00%0.00%18.94%50.01%7.25%7.45%6.90%0.908
1524.36%0.00%0.00%0.00%0.00%19.46%48.80%7.38%7.49%6.91%0.912
1624.91%0.00%0.00%0.00%0.00%19.98%47.59%7.51%7.52%6.92%0.916
1725.47%0.00%0.00%0.00%0.00%20.50%46.39%7.65%7.56%6.94%0.920
1826.02%0.00%0.00%0.00%0.00%21.02%45.18%7.78%7.60%6.95%0.923
1926.58%0.00%0.00%0.00%0.00%21.54%43.97%7.92%7.64%6.96%0.927
2027.13%0.00%0.00%0.00%0.00%22.06%42.76%8.05%7.67%6.98%0.930
2127.69%0.00%0.00%0.00%0.00%22.58%41.55%8.18%7.71%6.99%0.934
2228.24%0.00%0.00%0.00%0.00%23.10%40.34%8.32%7.75%7.01%0.937
2328.80%0.00%0.00%0.00%0.00%23.62%39.14%8.45%7.78%7.02%0.940
2429.35%0.00%0.00%0.00%0.00%24.13%37.93%8.59%7.82%7.04%0.943
2529.91%0.00%0.00%0.00%0.00%24.65%36.72%8.72%7.86%7.06%0.946
2630.46%0.00%0.00%0.00%0.00%25.17%35.51%8.85%7.90%7.08%0.948
2731.02%0.00%0.00%0.00%0.00%25.69%34.30%8.99%7.93%7.10%0.951
2831.57%0.00%0.00%0.00%0.00%26.21%33.10%9.12%7.97%7.12%0.954
2932.13%0.00%0.00%0.00%0.00%26.73%31.89%9.26%8.01%7.14%0.956
3032.68%0.00%0.00%0.00%0.00%27.25%30.68%9.39%8.05%7.16%0.958
3133.24%0.00%0.00%0.00%0.00%27.77%29.47%9.53%8.08%7.19%0.960
3233.79%0.00%0.00%0.00%0.00%28.29%28.26%9.66%8.12%7.21%0.962
3334.35%0.00%0.00%0.00%0.00%28.80%27.05%9.79%8.16%7.23%0.964
3434.90%0.00%0.00%0.00%0.00%29.32%25.85%9.93%8.20%7.26%0.966
3535.46%0.00%0.00%0.00%0.00%29.84%24.64%10.06%8.23%7.28%0.968
3636.01%0.00%0.00%0.00%0.00%30.36%23.43%10.20%8.27%7.31%0.970
3736.57%0.00%0.00%0.00%0.00%30.88%22.22%10.33%8.31%7.34%0.971
3837.12%0.00%0.00%0.00%0.00%31.40%21.01%10.46%8.35%7.36%0.973
3937.68%0.00%0.00%0.00%0.00%31.92%19.81%10.60%8.38%7.39%0.974
4038.23%0.00%0.00%0.00%0.00%32.44%18.60%10.73%8.42%7.42%0.976
4138.79%0.00%0.00%0.00%0.00%32.96%17.39%10.87%8.46%7.45%0.977
4239.34%0.00%0.00%0.00%0.00%33.48%16.18%11.00%8.50%7.48%0.978
4339.90%0.00%0.00%0.00%0.00%33.99%14.97%11.13%8.53%7.51%0.979
4440.45%0.00%0.00%0.00%0.00%34.51%13.76%11.27%8.57%7.54%0.980
4541.01%0.00%0.00%0.00%0.00%35.03%12.56%11.40%8.61%7.57%0.981
4641.56%0.00%0.00%0.00%0.00%35.55%11.35%11.54%8.65%7.60%0.982
4742.12%0.00%0.00%0.00%0.00%36.07%10.14%11.67%8.68%7.64%0.982
4842.67%0.00%0.00%0.00%0.00%36.59%8.93%11.80%8.72%7.67%0.983
4943.23%0.00%0.00%0.00%0.00%37.11%7.72%11.94%8.76%7.70%0.983
5043.78%0.00%0.00%0.00%0.00%37.63%6.51%12.07%8.80%7.74%0.984
5144.34%0.00%0.00%0.00%0.00%38.15%5.31%12.21%8.83%7.77%0.984
5244.89%0.00%0.00%0.00%0.00%38.67%4.10%12.34%8.87%7.81%0.985
5345.45%0.00%0.00%0.00%0.00%39.18%2.89%12.48%8.91%7.85%0.985
5446.00%0.00%0.00%0.00%0.00%39.70%1.68%12.61%8.95%7.88%0.985
5546.56%0.00%0.00%0.00%0.00%40.22%0.47%12.74%8.98%7.92%0.985
5647.32%0.00%0.00%0.00%0.00%39.65%0.00%13.03%9.02%7.96%0.985
5748.21%0.00%0.00%0.00%0.00%38.36%0.00%13.42%9.06%8.00%0.984
5849.11%0.00%0.00%0.00%0.00%37.08%0.00%13.82%9.10%8.06%0.982
5950.00%0.00%0.00%0.00%0.00%35.79%0.00%14.21%9.13%8.12%0.980
6050.89%0.00%0.00%0.00%0.00%34.51%0.00%14.60%9.17%8.19%0.976
6151.78%0.00%0.00%0.00%0.00%33.23%0.00%14.99%9.21%8.26%0.972
6252.68%0.00%0.00%0.00%0.00%31.94%0.00%15.38%9.25%8.34%0.967
6353.57%0.00%0.00%0.00%0.00%30.66%0.00%15.77%9.29%8.43%0.961
6454.46%0.00%0.00%0.00%0.00%29.37%0.00%16.16%9.32%8.52%0.955
6555.36%0.00%0.00%0.00%0.00%28.09%0.00%16.55%9.36%8.62%0.948
6656.25%0.00%0.00%0.00%0.00%26.81%0.00%16.94%9.40%8.73%0.941
6757.14%0.00%0.00%0.00%0.00%25.52%0.00%17.33%9.44%8.84%0.934
6858.04%0.00%0.00%0.00%0.00%24.24%0.00%17.73%9.47%8.96%0.926
6958.93%0.00%0.00%0.00%0.00%22.95%0.00%18.12%9.51%9.08%0.917
7059.82%0.00%0.00%0.00%0.00%21.67%0.00%18.51%9.55%9.21%0.909
7160.71%0.00%0.00%0.00%0.00%20.39%0.00%18.90%9.59%9.34%0.900
7261.61%0.00%0.00%0.00%0.00%19.10%0.00%19.29%9.63%9.48%0.891
7362.50%0.00%0.00%0.00%0.00%17.82%0.00%19.68%9.66%9.62%0.882
7463.39%0.00%0.00%0.00%0.00%16.54%0.00%20.07%9.70%9.77%0.872
7564.29%0.00%0.00%0.00%0.00%15.25%0.00%20.46%9.74%9.92%0.863
7665.18%0.00%0.00%0.00%0.00%13.97%0.00%20.85%9.78%10.07%0.853
7766.07%0.00%0.00%0.00%0.00%12.68%0.00%21.24%9.82%10.23%0.844
7866.97%0.00%0.00%0.00%0.00%11.40%0.00%21.64%9.85%10.39%0.835
7967.86%0.00%0.00%0.00%0.00%10.12%0.00%22.03%9.89%10.56%0.825
8068.75%0.00%0.00%0.00%0.00%8.83%0.00%22.42%9.93%10.72%0.816
8169.64%0.00%0.00%0.00%0.00%7.55%0.00%22.81%9.97%10.89%0.807
8270.54%0.00%0.00%0.00%0.00%6.26%0.00%23.20%10.01%11.07%0.797
8371.43%0.00%0.00%0.00%0.00%4.98%0.00%23.59%10.04%11.24%0.788
8472.32%0.00%0.00%0.00%0.00%3.70%0.00%23.98%10.08%11.42%0.779
8573.22%0.00%0.00%0.00%0.00%2.41%0.00%24.37%10.12%11.60%0.770
8674.11%0.00%0.00%0.00%0.00%1.13%0.00%24.76%10.16%11.79%0.761
8775.25%0.00%0.00%0.00%0.00%0.00%0.00%24.75%10.20%11.98%0.753
8878.19%0.00%0.00%0.00%0.00%0.00%0.00%21.81%10.23%12.18%0.743
8981.13%0.00%0.00%0.00%0.00%0.00%0.00%18.87%10.27%12.42%0.732
9084.07%0.00%0.00%0.00%0.00%0.00%0.00%15.93%10.31%12.69%0.719
9187.01%0.00%0.00%0.00%0.00%0.00%0.00%12.99%10.35%12.99%0.706
9289.95%0.00%0.00%0.00%0.00%0.00%0.00%10.05%10.39%13.32%0.691
9392.89%0.00%0.00%0.00%0.00%0.00%0.00%7.11%10.42%13.67%0.676
9495.83%0.00%0.00%0.00%0.00%0.00%0.00%4.17%10.46%14.04%0.661
9598.63%0.00%0.00%0.00%0.12%0.00%0.00%1.25%10.50%14.43%0.646
9687.33%0.00%0.00%0.00%12.67%0.00%0.00%0.00%10.54%14.96%0.625
9765.50%0.00%0.00%0.00%34.50%0.00%0.00%0.00%10.58%16.16%0.581
9843.67%0.00%0.00%0.00%56.33%0.00%0.00%0.00%10.62%17.95%0.526
9921.84%0.00%0.00%0.00%78.16%0.00%0.00%0.00%10.65%20.18%0.469
1000.01%0.00%0.00%0.00%99.99%0.00%0.00%0.00%10.69%22.71%0.419
*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 (1.18% annualized).
Annual returns for the configured portfolios
YearInflationReturnBalanceVanguard Total Stock Market ETF (VTI)iShares 20+ Year Treasury Bond ETF (TLT)SPDR Gold Shares (GLD)iShares S&P Small-Cap 600 Value ETF (IJS)iShares MSCI EAFE ETF (EFA)iShares MSCI Emerging Markets ETF (EEM)Vanguard Real Estate ETF (VNQ)iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)
Maximum Return at 10.00% VolatilityEqual WeightedMaximum Return at 10.00% VolatilityEqual Weighted
20062.54%14.99%19.39%$11,499$11,93915.69%0.71%22.55%19.37%25.81%31.19%35.30%4.22%
20074.08%11.18%8.39%$12,785$12,9415.37%10.29%30.45%-5.56%9.94%33.31%-16.50%3.73%
20080.09%-20.21%-21.23%$10,201$10,194-36.98%33.93%4.92%-29.39%-41.04%-48.88%-37.00%2.40%
20092.72%19.78%23.38%$12,219$12,57728.89%-21.80%24.03%22.36%26.95%68.93%30.08%8.46%
20101.50%19.46%18.79%$14,596$14,94117.42%9.05%29.27%24.69%8.15%16.51%28.37%9.33%
20112.96%8.41%4.04%$15,824$15,5450.97%33.96%9.57%-1.65%-12.25%-18.82%8.62%9.73%
20121.74%12.64%14.22%$17,825$17,75616.45%2.63%6.60%18.24%18.82%19.10%17.63%10.58%
20131.50%10.72%4.45%$19,736$18,54633.45%-13.37%-28.33%39.34%21.40%-3.69%2.31%-2.00%
20140.76%11.68%8.88%$22,041$20,19312.54%27.30%-2.19%7.56%-6.20%-3.93%30.36%8.21%
20150.73%-1.73%-3.92%$21,660$19,4010.36%-1.79%-10.67%-6.90%-1.00%-16.18%2.42%-1.25%
20162.07%10.71%10.46%$23,979$21,43112.83%1.18%8.03%31.25%1.37%10.87%8.60%6.21%
20172.11%17.66%15.92%$28,215$24,84221.21%9.18%12.81%11.35%25.10%37.28%4.91%7.06%
20181.91%-3.53%-7.18%$27,218$23,059-5.21%-1.61%-1.94%-12.84%-13.81%-15.31%-6.02%-3.79%
20192.29%25.99%22.27%$34,293$28,19530.67%14.12%17.86%24.12%22.03%18.20%28.87%17.37%
Monthly returns for the configured portfolios
YearMonthReturnBalanceVanguard Total Stock Market ETF (VTI)iShares 20+ Year Treasury Bond ETF (TLT)SPDR Gold Shares (GLD)iShares S&P Small-Cap 600 Value ETF (IJS)iShares MSCI EAFE ETF (EFA)iShares MSCI Emerging Markets ETF (EEM)Vanguard Real Estate ETF (VNQ)iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)
Maximum Return at 10.00% VolatilityEqual WeightedMaximum Return at 10.00% VolatilityEqual Weighted
200613.90%5.95%$10,390$10,5953.22%-1.34%9.93%8.75%5.77%14.20%7.54%-0.44%
200620.08%-0.19%$10,398$10,5750.22%1.11%-1.11%0.27%-0.70%-3.85%1.86%0.68%
200631.36%1.90%$10,540$10,7762.05%-4.57%3.62%4.86%4.01%2.17%4.73%-1.68%
200642.66%2.26%$10,820$11,0200.96%-2.75%12.03%0.18%4.79%6.52%-3.40%-0.20%
20065-2.37%-3.39%$10,563$10,646-3.22%-0.19%-1.32%-4.55%-3.82%-11.14%-2.70%-0.19%
20066-0.69%0.21%$10,490$10,6690.13%1.18%-4.67%0.04%-0.06%0.21%4.95%-0.09%
200670.90%1.33%$10,585$10,810-0.12%2.16%3.15%-3.10%0.81%2.34%3.89%1.46%
200681.66%2.07%$10,760$11,0332.30%3.06%-1.38%2.70%2.55%1.58%3.48%2.22%
200690.82%0.38%$10,848$11,0752.26%1.91%-4.53%1.19%0.22%-0.87%1.96%0.87%
2006102.66%3.63%$11,137$11,4773.53%0.85%1.29%5.52%3.75%7.06%6.03%1.00%
2006113.26%3.65%$11,500$11,8962.33%2.31%6.89%2.38%3.07%5.98%4.78%1.46%
200612-0.01%0.36%$11,499$11,9391.20%-2.69%-1.83%0.32%3.20%5.44%-1.83%-0.90%
200711.57%1.99%$11,679$12,1771.86%-1.00%2.56%2.14%1.39%0.11%8.78%0.09%
20072-0.01%-0.08%$11,679$12,167-1.62%3.39%2.55%-0.92%-0.12%-3.24%-2.70%2.00%
200730.23%0.59%$11,706$12,2381.12%-1.70%-1.11%0.91%2.90%5.33%-2.07%-0.68%
200743.14%2.13%$12,074$12,4994.02%0.90%2.05%1.84%3.75%3.73%-0.13%0.89%
200751.57%1.19%$12,263$12,6493.72%-2.31%-2.31%4.63%2.36%5.06%-0.38%-1.23%
20076-1.68%-1.67%$12,057$12,437-1.76%-1.01%-1.94%-2.24%-0.32%3.68%-8.99%-0.81%
20077-1.28%-1.85%$11,902$12,207-3.53%3.32%2.37%-6.26%-2.29%0.71%-8.26%-0.82%
200781.45%1.90%$12,074$12,4401.47%1.79%1.11%1.33%-0.63%1.04%6.74%2.38%
200794.66%4.55%$12,637$13,0063.85%0.23%10.51%0.31%5.32%11.57%3.90%0.73%
2007102.85%3.85%$12,997$13,5071.79%1.81%6.95%1.06%4.25%11.87%2.10%0.97%
200711-2.43%-3.46%$12,681$13,039-4.52%5.35%-1.65%-7.15%-3.62%-7.65%-9.47%1.02%
2007120.81%-0.75%$12,785$12,941-0.70%-0.64%6.65%-0.71%-2.99%-1.43%-5.41%-0.81%
20081-1.43%-1.53%$12,602$12,743-6.17%2.10%10.84%-4.00%-7.85%-8.92%-0.78%2.57%
20082-0.60%-0.50%$12,526$12,680-2.50%-0.46%5.23%-3.36%-1.02%1.99%-3.18%-0.71%
20083-1.48%-0.17%$12,341$12,658-0.90%2.14%-6.00%0.83%0.42%-3.75%6.48%-0.60%
200841.91%2.89%$12,577$13,0234.89%-2.48%-4.16%2.64%5.44%9.14%6.38%1.25%
200851.07%0.76%$12,712$13,1222.02%-2.69%0.92%3.92%1.19%3.16%-0.21%-2.21%
20086-3.89%-4.92%$12,218$12,477-8.12%2.65%4.52%-8.41%-8.80%-9.29%-10.62%-1.29%
20087-0.75%-0.61%$12,126$12,401-0.62%-0.37%-1.44%2.87%-3.32%-5.50%3.12%0.39%
20088-0.54%-1.05%$12,060$12,2711.46%2.74%-9.29%4.76%-4.25%-6.32%2.37%0.15%
20089-4.87%-5.68%$11,472$11,574-9.24%1.47%4.11%-4.82%-11.44%-14.68%-0.11%-10.73%
200810-14.82%-16.93%$9,771$9,615-17.48%-1.86%-16.14%-19.86%-20.83%-25.58%-31.73%-1.95%
200811-0.39%-3.55%$9,733$9,273-8.01%14.34%12.57%-11.80%-6.37%-9.75%-22.72%3.35%
2008124.80%9.93%$10,201$10,1941.78%13.64%7.73%6.57%8.88%10.35%16.67%13.80%
20091-6.03%-8.98%$9,585$9,278-8.05%-13.07%5.54%-13.94%-13.73%-9.29%-17.53%-1.80%
20092-6.70%-8.25%$8,943$8,512-10.53%-1.54%1.45%-13.03%-10.39%-6.27%-20.53%-5.20%
200935.41%5.84%$9,426$9,0098.26%4.04%-2.54%7.58%8.39%16.86%3.61%0.47%
200945.32%10.02%$9,928$9,91110.99%-6.95%-3.33%18.89%11.52%15.56%30.68%2.78%
200955.04%5.84%$10,429$10,4915.46%-3.69%10.23%0.67%13.19%15.94%2.62%2.32%
20096-0.72%-0.82%$10,354$10,4040.36%0.76%-5.22%1.52%-1.43%-2.25%-3.23%2.89%
200975.55%7.27%$10,928$11,1607.74%0.58%2.38%11.00%10.04%11.01%10.77%4.63%
200982.74%3.54%$11,228$11,5553.71%2.24%0.05%3.48%4.50%-1.31%14.32%1.31%
200994.23%4.88%$11,702$12,1194.14%2.46%5.84%4.21%3.80%10.20%6.63%1.76%
200910-1.33%-2.32%$11,547$11,838-2.63%-2.62%3.72%-6.07%-2.52%-3.44%-4.46%-0.49%
2009116.46%5.36%$12,293$12,4735.69%1.21%12.79%2.90%3.92%7.85%6.57%1.95%
200912-0.60%0.84%$12,219$12,5772.86%-6.34%-7.20%8.10%0.70%3.27%7.37%-2.07%
20101-2.14%-2.72%$11,957$12,235-3.57%2.69%-1.26%-2.54%-5.07%-7.76%-5.52%1.25%
201022.83%2.41%$12,296$12,5303.44%-0.34%3.27%4.76%0.27%1.78%5.58%0.51%
201033.71%4.63%$12,752$13,1106.40%-2.06%-0.44%7.80%6.39%8.11%10.18%0.65%
201043.11%3.01%$13,149$13,5052.18%3.32%5.88%6.63%-2.80%-0.17%7.15%1.91%
20105-3.66%-4.44%$12,667$12,906-7.88%5.11%3.05%-8.54%-11.19%-9.39%-5.33%-1.31%
20106-2.38%-1.42%$12,365$12,723-5.83%5.80%2.36%-8.27%-2.07%-1.40%-5.19%3.28%
201073.33%5.24%$12,776$13,3907.02%-0.95%-5.09%6.71%11.61%10.93%9.59%2.11%
20108-0.58%-0.50%$12,702$13,323-4.71%8.40%5.71%-7.91%-3.80%-3.24%-1.28%2.86%
201096.67%6.16%$13,550$14,1449.45%-2.51%4.78%10.93%9.97%11.76%4.45%0.46%
2010102.66%2.32%$13,910$14,4724.03%-4.47%3.68%4.04%3.81%3.02%4.74%-0.26%
2010110.50%-0.97%$13,980$14,3310.51%-1.69%2.11%2.47%-4.82%-2.91%-1.85%-1.62%
2010124.41%4.25%$14,596$14,9416.96%-3.68%2.44%8.97%8.30%7.27%4.54%-0.75%
20111-0.46%-0.76%$14,529$14,8272.05%-3.08%-6.38%-0.24%2.10%-3.84%3.25%0.04%
201123.86%3.11%$15,090$15,2873.70%1.65%6.00%4.21%3.55%-0.04%4.71%1.08%
201130.60%0.75%$15,180$15,4020.42%0.03%1.60%2.21%-2.39%6.29%-1.62%-0.54%
201144.05%3.98%$15,795$16,0152.90%2.34%8.94%1.06%5.63%2.73%5.75%2.50%
20115-0.53%-0.46%$15,712$15,941-1.06%3.42%-1.79%-1.77%-2.21%-2.94%1.37%1.27%
20116-2.01%-1.80%$15,396$15,655-1.79%-2.33%-2.43%-1.59%-1.19%-0.93%-3.30%-0.80%
201170.94%1.05%$15,541$15,819-2.27%4.42%8.42%-2.77%-2.38%-1.03%1.56%2.43%
201180.07%-1.93%$15,552$15,514-6.09%9.66%12.27%-7.98%-8.75%-9.25%-5.62%0.34%
20119-5.12%-6.90%$14,756$14,443-7.57%13.20%-11.06%-10.57%-10.81%-17.89%-10.85%0.35%
2011107.92%8.93%$15,925$15,73311.37%-3.84%5.87%15.34%9.63%16.27%14.29%2.51%
2011110.40%-0.90%$15,989$15,592-0.37%1.98%1.67%0.63%-2.18%-1.96%-3.80%-3.16%
201112-1.03%-0.30%$15,824$15,5450.98%3.44%-10.66%2.02%-2.21%-4.30%4.85%3.49%
201215.54%6.10%$16,701$16,4935.07%-0.33%11.40%7.90%5.27%10.99%6.38%2.14%
201221.71%1.37%$16,987$16,7194.22%-2.59%-2.96%1.71%4.83%5.27%-1.15%1.63%
201231.05%0.18%$17,166$16,7503.06%-4.23%-1.32%2.89%0.42%-3.11%5.19%-1.42%
201240.30%0.29%$17,217$16,798-0.64%4.83%-0.15%-1.91%-2.08%-1.70%2.86%1.08%
20125-3.92%-4.54%$16,541$16,036-6.23%9.03%-6.34%-7.18%-11.14%-10.71%-4.51%0.76%
201262.83%3.48%$17,010$16,5944.05%-1.68%2.35%4.54%7.11%5.08%5.52%0.87%
201271.32%1.30%$17,233$16,8090.88%3.82%0.84%-0.69%0.08%-0.03%2.00%3.48%
201282.55%1.74%$17,672$17,1022.70%-1.32%4.94%4.08%3.20%0.41%-0.01%-0.05%
201292.17%1.87%$18,056$17,4222.49%-2.53%4.67%3.14%2.71%5.22%-1.86%1.10%
201210-1.84%-0.76%$17,724$17,289-1.81%-0.48%-2.94%-1.96%1.09%-0.44%-0.91%1.35%
2012110.61%0.87%$17,833$17,4400.77%1.38%-0.47%1.65%2.78%1.56%-0.26%-0.42%
201212-0.05%1.81%$17,825$17,7561.29%-2.49%-2.43%3.55%4.37%6.80%3.72%-0.33%
201312.89%1.62%$18,340$18,0435.42%-3.19%-0.51%5.35%3.73%-0.29%3.74%-1.30%
20132-0.03%-0.28%$18,335$17,9931.28%1.24%-5.09%1.63%-1.29%-2.28%1.22%1.08%
201332.67%1.46%$18,824$18,2563.95%-0.42%0.95%4.11%1.31%-1.02%2.87%-0.05%
201340.20%1.75%$18,862$18,5751.61%4.68%-7.56%0.12%5.02%1.22%6.73%2.17%
20135-0.73%-2.91%$18,724$18,0352.44%-6.76%-6.20%4.29%-3.02%-4.83%-5.98%-3.22%
20136-3.68%-3.65%$18,035$17,377-1.43%-3.27%-11.06%-0.14%-2.70%-5.35%-1.98%-3.27%
201374.87%3.27%$18,913$17,9455.75%-2.26%7.43%6.56%5.32%1.32%0.90%1.11%
20138-1.09%-1.88%$18,707$17,607-3.03%-1.34%5.20%-3.41%-1.96%-2.54%-6.98%-1.00%
201391.63%3.20%$19,012$18,1713.90%0.66%-4.78%6.59%7.82%7.21%3.49%0.74%
2013102.89%2.82%$19,561$18,6844.27%1.43%-0.34%3.48%3.26%4.17%4.52%1.81%
2013110.20%-0.79%$19,600$18,5362.70%-2.70%-5.51%4.25%0.55%-0.26%-5.25%-0.14%
2013120.69%0.05%$19,736$18,5462.73%-1.87%-3.79%1.29%2.16%-0.42%0.10%0.22%
20141-0.38%-0.58%$19,662$18,438-3.17%6.30%3.42%-3.51%-5.20%-8.64%4.28%1.88%
201424.49%4.00%$20,545$19,1764.87%0.52%6.27%4.63%6.13%3.38%5.07%1.14%
20143-0.21%0.41%$20,503$19,2550.51%0.73%-3.14%1.34%-0.46%3.88%0.49%-0.03%
201440.46%0.93%$20,597$19,4340.06%2.10%0.49%-2.29%1.67%0.78%3.29%1.33%
201451.18%1.38%$20,839$19,7032.10%2.95%-3.05%0.62%1.60%2.95%2.40%1.51%
201462.94%2.13%$21,453$20,1222.62%-0.25%6.32%3.85%0.92%2.40%1.13%0.01%
20147-1.92%-1.44%$21,040$19,832-1.99%0.67%-3.63%-5.07%-2.60%1.36%0.08%-0.32%
201483.47%2.72%$21,769$20,3724.15%4.72%0.38%4.46%0.18%2.83%3.04%2.00%
20149-2.94%-4.46%$21,130$19,463-2.10%-2.11%-6.18%-5.94%-3.88%-7.77%-6.04%-1.68%
2014101.57%2.74%$21,462$19,9972.75%2.81%-3.05%7.13%-0.27%1.42%9.94%1.23%
2014111.95%0.86%$21,880$20,1692.48%2.97%-0.49%0.48%0.06%-1.54%2.00%0.91%
2014120.74%0.12%$22,041$20,193-0.04%3.25%1.31%2.56%-4.00%-3.99%1.88%-0.02%
201511.52%2.62%$22,375$20,723-2.74%9.82%8.69%-5.32%0.62%-0.69%6.85%3.75%
201521.55%0.65%$22,722$20,8585.74%-6.14%-5.91%5.86%6.34%4.41%-3.67%-1.42%
20153-1.02%-0.27%$22,491$20,801-1.16%1.10%-2.15%1.03%-1.43%-1.50%1.74%0.20%
20154-0.16%-0.17%$22,454$20,7660.62%-3.43%-0.17%-1.82%3.65%6.85%-5.85%-1.19%
201550.59%-0.64%$22,586$20,6341.30%-2.37%0.56%0.75%0.20%-4.10%-0.30%-1.12%
20156-2.01%-2.43%$22,133$20,133-1.67%-4.07%-1.52%0.42%-3.12%-2.93%-4.68%-1.88%
201570.43%-0.09%$22,228$20,1141.70%4.55%-6.62%-2.70%2.03%-6.31%5.77%0.83%
20158-3.26%-3.88%$21,503$19,333-6.09%-0.69%3.71%-4.62%-7.43%-8.84%-6.29%-0.83%
20159-1.95%-1.23%$21,084$19,095-2.92%1.97%-1.80%-3.77%-4.42%-3.13%3.05%1.19%
2015105.49%4.46%$22,242$19,9467.91%-0.41%2.28%6.57%6.61%6.38%5.76%0.57%
201511-1.13%-1.08%$21,991$19,7320.60%-0.87%-6.75%2.47%-0.75%-2.52%-0.63%-0.15%
201512-1.51%-1.67%$21,660$19,401-2.13%-0.30%-0.45%-5.08%-2.34%-3.83%1.82%-1.08%
20161-1.72%-1.81%$21,287$19,051-5.72%5.57%5.41%-5.85%-5.52%-5.03%-3.44%0.12%
201622.70%1.58%$21,862$19,351-0.01%3.09%10.93%2.08%-3.33%-0.82%-0.36%1.05%
201634.39%6.15%$22,820$20,5427.11%-0.09%-0.84%9.41%6.58%12.96%10.48%3.62%
201641.36%1.12%$23,130$20,7730.66%-0.74%5.11%2.13%2.22%0.41%-2.35%1.55%
20165-0.02%-0.65%$23,126$20,6381.73%0.81%-6.14%0.44%-0.09%-3.69%2.25%-0.51%
201663.07%3.65%$23,836$21,3910.27%6.93%8.97%0.83%-2.42%4.56%6.92%3.09%
201673.28%3.50%$24,618$22,1403.98%2.10%1.98%5.06%3.98%5.38%4.26%1.29%
20168-0.69%-0.64%$24,448$21,9990.21%-1.01%-3.26%1.13%0.53%0.88%-3.76%0.18%
201690.04%0.25%$24,459$22,0540.21%-1.51%0.69%0.87%1.34%2.52%-1.82%-0.32%
201610-2.68%-2.95%$23,804$21,404-2.19%-4.38%-2.94%-3.74%-2.22%-0.83%-5.74%-1.53%
201611-0.08%-1.22%$23,786$21,1424.49%-8.21%-8.36%13.34%-1.78%-4.42%-1.68%-3.17%
2016120.81%1.37%$23,979$21,4311.98%-0.46%-1.91%3.20%2.71%-0.25%4.82%0.84%
201712.43%2.10%$24,561$21,8811.86%0.81%5.42%-1.21%3.29%6.66%-0.19%0.15%
201723.27%2.20%$25,364$22,3613.69%1.59%3.18%1.35%1.19%1.74%3.51%1.32%
20173-0.15%0.32%$25,325$22,4320.06%-0.65%-0.43%-0.65%3.23%3.69%-2.42%-0.29%
201741.28%1.30%$25,649$22,7241.06%1.57%1.73%0.51%2.42%1.70%0.24%1.19%
201750.91%0.94%$25,883$22,9381.01%1.89%-0.12%-2.26%3.54%2.85%-0.72%1.33%
201760.29%0.81%$25,958$23,1240.95%0.79%-2.16%2.96%0.31%0.93%2.23%0.48%
201771.58%1.85%$26,368$23,5511.88%-0.66%2.31%0.75%2.65%5.82%1.24%0.77%
201781.48%0.97%$26,757$23,7790.15%3.41%4.20%-2.72%-0.04%2.35%-0.26%0.68%
201790.52%0.94%$26,898$24,0022.44%-2.32%-3.37%8.58%2.36%-0.04%-0.11%-0.05%
2017101.24%0.76%$27,230$24,1842.17%-0.04%-0.75%0.59%1.68%3.28%-1.07%0.19%
2017112.13%1.34%$27,811$24,5083.03%0.74%0.36%3.76%0.69%-0.39%2.66%-0.12%
2017121.45%1.36%$28,215$24,8421.16%1.81%2.11%-0.37%1.35%3.77%-0.14%1.22%
201813.53%1.80%$29,211$25,2895.23%-3.26%3.23%1.33%5.02%8.30%-4.25%-1.23%
20182-3.31%-4.20%$28,245$24,228-3.76%-3.04%-2.08%-4.04%-4.83%-5.90%-7.68%-2.24%
20183-0.69%0.88%$28,050$24,441-1.95%2.86%0.63%1.37%-0.84%0.54%3.88%0.56%
20184-0.22%-0.36%$27,987$24,3530.45%-2.09%-0.95%1.76%1.52%-2.82%0.82%-1.57%
201851.81%1.14%$28,494$24,6302.72%2.01%-1.20%5.87%-1.89%-2.62%3.68%0.52%
20186-0.19%-0.48%$28,440$24,5110.70%0.65%-3.61%0.80%-1.57%-4.54%4.20%-0.49%
201871.46%1.32%$28,854$24,8353.32%-1.44%-2.24%2.62%2.85%3.53%0.60%1.34%
201881.97%0.29%$29,422$24,9083.43%1.31%-2.14%3.14%-2.24%-3.77%2.58%0.02%
20189-0.45%-1.10%$29,291$24,6350.20%-2.86%-0.66%-3.05%0.97%-0.58%-2.64%-0.14%
201810-4.78%-5.00%$27,892$23,402-7.41%-2.93%2.12%-9.94%-8.13%-8.76%-2.93%-2.05%
2018111.64%1.80%$28,348$23,8242.01%1.79%0.34%0.57%0.50%4.90%4.67%-0.36%
201812-3.99%-3.21%$27,218$23,059-9.16%5.85%4.94%-12.38%-5.35%-3.50%-7.96%1.86%
201916.14%7.03%$28,889$24,6818.54%0.38%2.89%12.26%6.63%10.34%11.85%3.37%
201921.95%0.90%$29,453$24,9033.56%-1.38%-0.61%4.13%2.54%-1.53%0.70%-0.20%
201931.43%1.33%$29,876$25,2351.42%5.57%-1.60%-3.91%0.92%1.13%4.21%2.93%
201942.08%1.39%$30,498$25,5873.93%-1.99%-0.66%4.32%2.93%2.35%-0.16%0.44%
20195-2.74%-2.30%$29,661$24,998-6.45%6.84%1.76%-9.98%-5.03%-7.33%0.14%1.65%
201966.33%5.07%$31,540$26,2667.08%0.95%8.00%7.66%5.91%6.20%1.54%3.25%
201970.95%0.04%$31,839$26,2771.41%0.26%0.01%1.30%-1.95%-2.66%1.70%0.25%
201981.96%1.71%$32,464$26,726-2.08%11.04%7.91%-5.14%-1.92%-3.78%3.75%3.88%
201990.04%0.91%$32,478$26,9701.78%-2.68%-3.39%5.57%3.16%1.69%1.93%-0.76%
2019101.71%1.84%$33,033$27,4662.11%-1.11%2.56%2.00%3.39%4.18%1.13%0.44%
2019111.72%0.39%$33,600$27,5723.79%-0.41%-3.21%2.71%1.13%-0.09%-1.30%0.47%
2019122.06%2.26%$34,293$28,1952.80%-3.20%3.66%2.84%2.98%7.71%0.76%0.53%
Portfolio return and risk metrics
MetricMaximum Return at 10.00% VolatilityEqual Weighted
Arithmetic Mean (monthly)0.78%0.67%
Arithmetic Mean (annualized)9.74%8.40%
Geometric Mean (monthly)0.74%0.62%
Geometric Mean (annualized)9.20%7.68%
Volatility (monthly)2.86%3.32%
Volatility (annualized)9.92%11.50%
Downside Deviation (monthly)1.82%2.18%
Max. Drawdown-31.20%-36.98%
US Market Correlation0.890.86
Beta(*)0.610.68
Alpha (annualized)3.30%1.33%
R279.62%74.58%
Sharpe Ratio0.820.60
Sortino Ratio1.270.90
Treynor Ratio (%)13.4510.17
Calmar Ratio1.691.09
Active Return-0.03%-1.54%
Tracking Error7.28%7.44%
Information Ratio-0.00-0.21
Skewness-0.98-0.81
Excess Kurtosis4.684.89
Historical Value-at-Risk (5%)-3.91%-4.50%
Analytical Value-at-Risk (5%)-3.92%-4.77%
Conditional Value-at-Risk (5%)-6.28%-7.65%
Upside Capture Ratio (%)64.8065.66
Downside Capture Ratio (%)50.7961.05
Safe Withdrawal Rate10.73%10.32%
Perpetual Withdrawal Rate6.66%5.35%
Positive Periods106 out of 168 (63.10%)105 out of 168 (62.50%)
Gain/Loss Ratio1.221.06
* 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 PeriodStartEndMaximum Return at 10.00% VolatilityEqual Weighted
Subprime CrisisNov 2007Mar 2009-31.20%-36.98%

Drawdowns for Maximum Return at 10.00% Volatility

Drawdowns for Maximum Return at 10.00% Volatility (worst 10)
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Nov 2007Feb 20091 year 4 monthsApr 20101 year 2 months2 years 6 months-31.20%
2Sep 2018Dec 20184 monthsFeb 20192 months6 months-7.49%
3Mar 2015Sep 20157 monthsMar 20166 months1 year 1 month-7.21%
4May 2011Sep 20115 monthsOct 20111 month6 months-6.58%
5May 2010Jun 20102 monthsSep 20103 months5 months-5.96%
6May 2013Jun 20132 monthsJul 20131 month3 months-4.38%
7Feb 2018Apr 20183 monthsAug 20184 months7 months-4.19%
8May 2012May 20121 monthJul 20122 months3 months-3.92%
9Aug 2016Nov 20164 monthsFeb 20173 months7 months-3.38%
10May 2006Jun 20062 monthsSep 20063 months5 months-3.05%
Worst 10 drawdowns included above

Drawdowns for Equal Weighted

Drawdowns for Equal Weighted (worst 10)
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Nov 2007Feb 20091 year 4 monthsSep 20101 year 7 months2 years 11 months-36.98%
2May 2011Sep 20115 monthsJan 20124 months9 months-9.81%
3Feb 2018Dec 201811 monthsApr 20194 months1 year 3 months-8.82%
4Mar 2015Jan 201611 monthsJun 20165 months1 year 4 months-8.66%
5May 2013Jun 20132 monthsOct 20134 months6 months-6.45%
6May 2012May 20121 monthJul 20122 months3 months-4.54%
7Aug 2016Nov 20164 monthsFeb 20173 months7 months-4.51%
8Sep 2014Sep 20141 monthJan 20154 months5 months-4.46%
9Jun 2007Jul 20072 monthsSep 20072 months4 months-3.49%
10May 2006May 20061 monthAug 20063 months4 months-3.39%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
VTIVanguard Total Stock Market ETF9.34%14.60%33.45%-36.98%-50.84%0.610.871.00
TLTiShares 20+ Year Treasury Bond ETF6.27%13.36%33.96%-21.80%-21.80%0.430.76-0.33
GLDSPDR Gold Shares7.55%17.73%30.45%-28.33%-42.91%0.430.700.04
IJSiShares S&P Small-Cap 600 Value ETF8.46%19.08%39.34%-29.39%-54.13%0.460.680.91
EFAiShares MSCI EAFE ETF4.10%17.16%26.95%-41.04%-57.38%0.250.350.89
EEMiShares MSCI Emerging Markets ETF5.11%22.20%68.93%-48.88%-60.44%0.280.420.80
VNQVanguard Real Estate ETF7.80%22.71%35.30%-37.00%-68.30%0.400.570.72
LQDiShares iBoxx $ Invmt Grade Corp Bd ETF5.59%7.20%17.37%-3.79%-15.11%0.631.040.27

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTITLTGLDIJSEFAEEMVNQLQDMaximum Return at 10.00% VolatilityEqual Weighted
VTIVanguard Total Stock Market ETF1.00-0.330.040.910.890.790.720.270.890.86
TLTiShares 20+ Year Treasury Bond ETF-0.331.000.21-0.35-0.24-0.230.010.52-0.030.00
GLDSPDR Gold Shares0.040.211.00-0.020.150.290.090.260.440.37
IJSiShares S&P Small-Cap 600 Value ETF0.91-0.35-0.021.000.760.690.730.190.780.80
EFAiShares MSCI EAFE ETF0.89-0.240.150.761.000.880.670.370.840.89
EEMiShares MSCI Emerging Markets ETF0.79-0.230.290.690.881.000.600.350.810.87
VNQVanguard Real Estate ETF0.720.010.090.730.670.601.000.430.720.84
LQDiShares iBoxx $ Invmt Grade Corp Bd ETF0.270.520.260.190.370.350.431.000.460.55

Portfolio Risk Decomposition

Portfolio risk decomposition
TickerNameMaximum Return at 10.00% VolatilityEqual Weighted
VTIVanguard Total Stock Market ETF84.40%13.70%
TLTiShares 20+ Year Treasury Bond ETF-0.60%0.03%
GLDSPDR Gold Shares16.20%7.07%
IJSiShares S&P Small-Cap 600 Value ETF16.64%
EFAiShares MSCI EAFE ETF16.55%
EEMiShares MSCI Emerging Markets ETF21.07%
VNQVanguard Real Estate ETF20.67%
LQDiShares iBoxx $ Invmt Grade Corp Bd ETF4.27%

Annual Asset Returns

Rolling returns summary
Roll PeriodMaximum Return at 10.00% VolatilityEqual Weighted
AverageHighLowAverageHighLow
1 year9.84%25.99%-20.21%8.42%23.38%-21.23%
3 years8.44%15.76%0.66%6.81%15.10%0.64%
5 years9.03%14.11%6.59%7.33%12.71%4.45%
7 years9.24%11.36%8.02%7.41%9.63%5.79%
10 years9.02%10.87%7.63%7.31%8.50%6.02%
Result statistics are based on annualized rolling returns over full calendar year periods