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 - May 2019)

Portfolio optimization results with goal to minimize volatility subject to 8.00% targeted annual return. The possible range of expected annual portfolio returns for the given period is 4.92% to 10.40%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Minimum Volatility at 8.00% Return
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 38.97%
TLT iShares 20+ Year Treasury Bond ETF 36.14%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 13.96%
GLD SPDR Gold Shares 10.93%
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
MetricMinimum Volatility at 8.00% ReturnEqual Weighted
Start Balance$10,000$10,000
End Balance$27,047$24,998
CAGR7.70%7.07%
Expected Return 8.00% 7.80%
Stdev7.50%11.66%
Best Year15.57%23.38%
Worst Year-4.78%-21.23%
Max. Drawdown -16.53% -36.98%
Sharpe Ratio (ex-ante)0.920.57
Sharpe Ratio (ex-post)0.880.55
Sortino Ratio1.360.82
US Stock Market Correlation0.610.87
   
Notes on results:
  • Past performance is not a guarantee of future returns and data and other errors may exist. See Disclaimer and Terms of Use
  • The year range is automatically adjusted based on the selected year range and available return data for the specified assets
  • The annual results for 2019 are based on full calendar months from January to May
  • See methodology section of the FAQ for more information on portfolio optimization and its limitations.
  • 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 (1-month treasury bill)
  • Drawdowns are calculated based on monthly returns.
  • The backtested results include monthly rebalancing of portfolio assets to match the specified allocation.
  • The results use total return and assume that all dividends and distributions are reinvested. Taxes and transaction fees are not included.
Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)8.43%9.62%14.76%0.5760.00%100.00%
2iShares S&P Small-Cap 600 Value ETF (IJS)7.53%9.54%19.27%0.4370.00%100.00%
3iShares MSCI EAFE ETF (EFA)3.33%4.92%17.39%0.2190.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)4.36%7.03%22.47%0.2630.00%100.00%
5Vanguard Real Estate ETF (VNQ)7.40%10.40%23.18%0.4000.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)6.22%7.13%13.27%0.4530.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.22%5.49%7.25%0.6030.00%100.00%
8SPDR Gold Shares (GLD)6.71%8.39%17.80%0.4080.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (1.12% annualized).
Efficient Frontier Assets
#VTIIJSEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
10.00%0.00%100.00%0.00%0.00%0.00%0.00%0.00%4.92%17.39%0.219
20.00%0.00%90.38%0.00%0.00%0.00%9.62%0.00%4.98%16.00%0.241
30.00%0.00%80.76%0.00%0.00%0.00%19.24%0.00%5.03%14.63%0.267
40.00%0.00%71.15%0.00%0.00%0.00%28.85%0.00%5.09%13.31%0.298
50.00%0.00%61.53%0.00%0.00%0.00%38.47%0.00%5.14%12.04%0.334
60.00%0.00%51.91%0.00%0.00%0.00%48.09%0.00%5.19%10.84%0.376
70.00%0.00%42.29%0.00%0.00%0.00%57.71%0.00%5.25%9.75%0.424
80.00%0.00%32.68%0.00%0.00%0.00%67.32%0.00%5.30%8.78%0.476
90.00%0.00%23.06%0.00%0.00%0.00%76.94%0.00%5.36%8.01%0.529
100.00%0.00%13.44%0.00%0.00%0.00%86.56%0.00%5.41%7.48%0.574
110.00%0.00%3.82%0.00%0.00%0.00%96.18%0.00%5.47%7.25%0.599
120.00%0.00%2.87%0.00%0.00%0.00%95.42%1.71%5.52%7.20%0.611
130.00%0.57%2.09%0.00%0.00%0.00%94.68%2.66%5.57%7.16%0.622
140.00%1.52%1.14%0.00%0.00%0.00%94.29%3.05%5.63%7.13%0.632
150.98%1.60%0.25%0.00%0.00%0.00%93.91%3.27%5.68%7.10%0.643
162.49%1.12%0.00%0.00%0.00%0.09%92.71%3.58%5.74%7.07%0.653
173.64%0.85%0.00%0.00%0.00%0.93%90.83%3.75%5.79%7.04%0.664
184.78%0.59%0.00%0.00%0.00%1.78%88.94%3.91%5.85%7.01%0.674
195.93%0.32%0.00%0.00%0.00%2.62%87.06%4.07%5.90%6.99%0.684
207.07%0.06%0.00%0.00%0.00%3.46%85.18%4.24%5.96%6.97%0.694
217.99%0.00%0.00%0.00%0.00%4.33%83.27%4.42%6.01%6.95%0.704
228.84%0.00%0.00%0.00%0.00%5.21%81.35%4.60%6.06%6.93%0.714
239.70%0.00%0.00%0.00%0.00%6.09%79.43%4.78%6.12%6.91%0.724
2410.56%0.00%0.00%0.00%0.00%6.97%77.52%4.96%6.17%6.89%0.733
2511.41%0.00%0.00%0.00%0.00%7.85%75.60%5.14%6.23%6.88%0.742
2612.27%0.00%0.00%0.00%0.00%8.73%73.68%5.32%6.28%6.87%0.751
2713.13%0.00%0.00%0.00%0.00%9.61%71.77%5.50%6.34%6.86%0.760
2813.98%0.00%0.00%0.00%0.00%10.49%69.85%5.68%6.39%6.85%0.769
2914.84%0.00%0.00%0.00%0.00%11.37%67.93%5.86%6.45%6.85%0.778
3015.70%0.00%0.00%0.00%0.00%12.25%66.02%6.04%6.50%6.85%0.786
3116.55%0.00%0.00%0.00%0.00%13.13%64.10%6.22%6.56%6.85%0.794
3217.41%0.00%0.00%0.00%0.00%14.01%62.18%6.40%6.61%6.85%0.802
3318.27%0.00%0.00%0.00%0.00%14.89%60.27%6.58%6.67%6.85%0.810
3419.12%0.00%0.00%0.00%0.00%15.77%58.35%6.76%6.72%6.85%0.817
3519.98%0.00%0.00%0.00%0.00%16.65%56.43%6.94%6.78%6.86%0.824
3620.84%0.00%0.00%0.00%0.00%17.53%54.52%7.12%6.83%6.87%0.831
3721.69%0.00%0.00%0.00%0.00%18.41%52.60%7.30%6.89%6.88%0.838
3822.55%0.00%0.00%0.00%0.00%19.29%50.69%7.48%6.94%6.90%0.844
3923.41%0.00%0.00%0.00%0.00%20.17%48.77%7.66%7.00%6.91%0.850
4024.26%0.00%0.00%0.00%0.00%21.04%46.85%7.84%7.05%6.93%0.856
4125.12%0.00%0.00%0.00%0.00%21.92%44.94%8.02%7.11%6.95%0.862
4225.98%0.00%0.00%0.00%0.00%22.80%43.02%8.20%7.16%6.97%0.867
4326.83%0.00%0.00%0.00%0.00%23.68%41.10%8.38%7.22%6.99%0.872
4427.69%0.00%0.00%0.00%0.00%24.56%39.19%8.56%7.27%7.01%0.877
4528.55%0.00%0.00%0.00%0.00%25.44%37.27%8.74%7.33%7.04%0.882
4629.40%0.00%0.00%0.00%0.00%26.32%35.35%8.92%7.38%7.07%0.886
4730.26%0.00%0.00%0.00%0.00%27.20%33.44%9.10%7.44%7.10%0.890
4831.12%0.00%0.00%0.00%0.00%28.08%31.52%9.28%7.49%7.13%0.894
4931.97%0.00%0.00%0.00%0.00%28.96%29.60%9.46%7.55%7.17%0.897
5032.83%0.00%0.00%0.00%0.00%29.84%27.69%9.64%7.60%7.20%0.900
5133.69%0.00%0.00%0.00%0.00%30.72%25.77%9.82%7.66%7.24%0.903
5234.54%0.00%0.00%0.00%0.00%31.60%23.85%10.00%7.71%7.28%0.906
5335.40%0.00%0.00%0.00%0.00%32.48%21.94%10.18%7.77%7.32%0.909
5436.26%0.00%0.00%0.00%0.00%33.36%20.02%10.36%7.82%7.36%0.911
5537.11%0.00%0.00%0.00%0.00%34.24%18.10%10.54%7.88%7.40%0.913
5637.97%0.00%0.00%0.00%0.00%35.12%16.19%10.72%7.94%7.45%0.915
5738.83%0.00%0.00%0.00%0.00%36.00%14.27%10.90%7.99%7.50%0.917
5839.68%0.00%0.00%0.00%0.00%36.88%12.35%11.08%8.05%7.55%0.918
5940.54%0.00%0.00%0.00%0.00%37.76%10.44%11.26%8.10%7.60%0.919
6041.40%0.00%0.00%0.00%0.00%38.64%8.52%11.44%8.16%7.65%0.920
6142.25%0.00%0.00%0.00%0.00%39.52%6.60%11.62%8.21%7.70%0.921
6243.11%0.00%0.00%0.00%0.00%40.40%4.69%11.80%8.27%7.75%0.922
6343.97%0.00%0.00%0.00%0.00%41.28%2.77%11.99%8.32%7.81%0.922
6444.82%0.00%0.00%0.00%0.00%42.16%0.85%12.17%8.38%7.87%0.923
6546.33%0.00%0.00%0.00%0.00%41.19%0.00%12.48%8.44%7.93%0.922
6648.35%0.00%0.00%0.00%0.00%38.74%0.00%12.91%8.49%8.02%0.919
6750.37%0.00%0.00%0.00%0.00%36.29%0.00%13.34%8.55%8.14%0.912
6852.39%0.00%0.00%0.00%0.00%33.84%0.00%13.76%8.60%8.30%0.902
6954.41%0.00%0.00%0.00%0.00%31.39%0.00%14.19%8.66%8.47%0.890
7056.43%0.00%0.00%0.00%0.00%28.95%0.00%14.62%8.71%8.68%0.875
7158.46%0.00%0.00%0.00%0.00%26.50%0.00%15.05%8.77%8.91%0.859
7260.48%0.00%0.00%0.00%0.00%24.05%0.00%15.47%8.83%9.16%0.842
7362.50%0.00%0.00%0.00%0.00%21.60%0.00%15.90%8.88%9.43%0.823
7463.79%0.00%0.00%0.00%0.56%19.32%0.00%16.33%8.94%9.72%0.805
7564.04%0.00%0.00%0.00%1.91%17.29%0.00%16.77%8.99%10.02%0.786
7664.29%0.00%0.00%0.00%3.25%15.25%0.00%17.20%9.05%10.33%0.768
7764.54%0.00%0.00%0.00%4.60%13.22%0.00%17.64%9.11%10.65%0.750
7864.80%0.00%0.00%0.00%5.95%11.18%0.00%18.07%9.16%10.98%0.732
7965.05%0.00%0.00%0.00%7.30%9.15%0.00%18.51%9.22%11.32%0.716
8065.30%0.00%0.00%0.00%8.64%7.11%0.00%18.94%9.27%11.66%0.699
8165.56%0.00%0.00%0.00%9.99%5.08%0.00%19.37%9.33%12.01%0.683
8265.81%0.00%0.00%0.00%11.34%3.04%0.00%19.81%9.39%12.37%0.668
8366.06%0.00%0.00%0.00%12.69%1.01%0.00%20.24%9.44%12.73%0.654
8465.83%0.00%0.00%0.00%14.98%0.00%0.00%19.19%9.50%13.10%0.639
8565.11%0.00%0.00%0.00%18.21%0.00%0.00%16.68%9.56%13.50%0.625
8664.39%0.00%0.00%0.00%21.44%0.00%0.00%14.16%9.61%13.94%0.609
8763.68%0.00%0.00%0.00%24.67%0.00%0.00%11.65%9.67%14.40%0.594
8862.96%0.00%0.00%0.00%27.90%0.00%0.00%9.14%9.72%14.89%0.578
8962.24%0.00%0.00%0.00%31.13%0.00%0.00%6.62%9.78%15.40%0.562
9061.53%0.00%0.00%0.00%34.36%0.00%0.00%4.11%9.84%15.93%0.547
9160.81%0.00%0.00%0.00%37.60%0.00%0.00%1.59%9.89%16.48%0.532
9257.71%0.00%0.00%0.00%42.29%0.00%0.00%0.00%9.95%17.06%0.518
9350.50%0.00%0.00%0.00%49.50%0.00%0.00%0.00%10.01%17.68%0.503
9443.29%0.00%0.00%0.00%56.71%0.00%0.00%0.00%10.06%18.35%0.487
9536.07%0.00%0.00%0.00%63.93%0.00%0.00%0.00%10.12%19.07%0.472
9628.86%0.00%0.00%0.00%71.14%0.00%0.00%0.00%10.18%19.82%0.457
9721.64%0.00%0.00%0.00%78.36%0.00%0.00%0.00%10.23%20.62%0.442
9814.43%0.00%0.00%0.00%85.57%0.00%0.00%0.00%10.29%21.44%0.428
997.22%0.00%0.00%0.00%92.78%0.00%0.00%0.00%10.35%22.30%0.414
1000.00%0.00%0.00%0.00%100.00%0.00%0.00%0.00%10.40%23.18%0.400
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (1.12% annualized).
Annual returns for the configured portfolios
YearInflationReturnBalanceVanguard Total Stock Market ETF (VTI)iShares 20+ Year Treasury Bond ETF (TLT)iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)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)
Minimum Volatility at 8.00% ReturnEqual WeightedMinimum Volatility at 8.00% ReturnEqual Weighted
20062.54%9.45%19.39%$10,945$11,93915.69%0.71%4.22%22.55%19.37%25.81%31.19%35.30%
20074.08%9.76%8.39%$12,014$12,9415.37%10.29%3.73%30.45%-5.56%9.94%33.31%-16.50%
20080.09%-4.78%-21.23%$11,439$10,194-36.98%33.93%2.40%4.92%-29.39%-41.04%-48.88%-37.00%
20092.72%5.70%23.38%$12,091$12,57728.89%-21.80%8.46%24.03%22.36%26.95%68.93%30.08%
20101.50%15.55%18.79%$13,971$14,94117.42%9.05%9.33%29.27%24.69%8.15%16.51%28.37%
20112.96%15.57%4.04%$16,147$15,5450.97%33.96%9.73%9.57%-1.65%-12.25%-18.82%8.62%
20121.74%10.00%14.22%$17,762$17,75616.45%2.63%10.58%6.60%18.24%18.82%19.10%17.63%
20131.50%2.70%4.45%$18,242$18,54633.45%-13.37%-2.00%-28.33%39.34%21.40%-3.69%2.31%
20140.76%15.50%8.88%$21,068$20,19312.54%27.30%8.21%-2.19%7.56%-6.20%-3.93%30.36%
20150.73%-1.34%-3.92%$20,787$19,4010.36%-1.79%-1.25%-10.67%-6.90%-1.00%-16.18%2.42%
20162.07%7.63%10.46%$22,374$21,43112.83%1.18%6.21%8.03%31.25%1.37%10.87%8.60%
20172.11%13.91%15.92%$25,486$24,84221.21%9.18%7.06%12.81%11.35%25.10%37.28%4.91%
20181.91%-2.91%-7.18%$24,745$23,059-5.21%-1.61%-3.79%-1.94%-12.84%-13.81%-15.31%-6.02%
20191.72%9.30%8.41%$27,047$24,99810.83%9.44%8.41%1.72%5.48%7.86%4.22%17.35%
Annual returns for 2019 are based on partial year data
Monthly returns for the configured portfolios
YearMonthReturnBalanceVanguard Total Stock Market ETF (VTI)iShares 20+ Year Treasury Bond ETF (TLT)iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)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)
Minimum Volatility at 8.00% ReturnEqual WeightedMinimum Volatility at 8.00% ReturnEqual Weighted
200611.79%5.95%$10,179$10,5953.22%-1.34%-0.44%9.93%8.75%5.77%14.20%7.54%
200620.46%-0.19%$10,226$10,5750.22%1.11%0.68%-1.11%0.27%-0.70%-3.85%1.86%
20063-0.69%1.90%$10,156$10,7762.05%-4.57%-1.68%3.62%4.86%4.01%2.17%4.73%
200640.66%2.26%$10,223$11,0200.96%-2.75%-0.20%12.03%0.18%4.79%6.52%-3.40%
20065-1.49%-3.39%$10,070$10,646-3.22%-0.19%-0.19%-1.32%-4.55%-3.82%-11.14%-2.70%
20066-0.05%0.21%$10,066$10,6690.13%1.18%-0.09%-4.67%0.04%-0.06%0.21%4.95%
200671.28%1.33%$10,195$10,810-0.12%2.16%1.46%3.15%-3.10%0.81%2.34%3.89%
200682.16%2.07%$10,415$11,0332.30%3.06%2.22%-1.38%2.70%2.55%1.58%3.48%
200691.20%0.38%$10,540$11,0752.26%1.91%0.87%-4.53%1.19%0.22%-0.87%1.96%
2006101.96%3.63%$10,747$11,4773.53%0.85%1.00%1.29%5.52%3.75%7.06%6.03%
2006112.70%3.65%$11,037$11,8962.33%2.31%1.46%6.89%2.38%3.07%5.98%4.78%
200612-0.83%0.36%$10,945$11,9391.20%-2.69%-0.90%-1.83%0.32%3.20%5.44%-1.83%
200710.66%1.99%$11,017$12,1771.86%-1.00%0.09%2.56%2.14%1.39%0.11%8.78%
200721.15%-0.08%$11,144$12,167-1.62%3.39%2.00%2.55%-0.92%-0.12%-3.24%-2.70%
20073-0.39%0.59%$11,100$12,2381.12%-1.70%-0.68%-1.11%0.91%2.90%5.33%-2.07%
200742.24%2.13%$11,349$12,4994.02%0.90%0.89%2.05%1.84%3.75%3.73%-0.13%
200750.19%1.19%$11,371$12,6493.72%-2.31%-1.23%-2.31%4.63%2.36%5.06%-0.38%
20076-1.38%-1.67%$11,214$12,437-1.76%-1.01%-0.81%-1.94%-2.24%-0.32%3.68%-8.99%
20077-0.03%-1.85%$11,210$12,207-3.53%3.32%-0.82%2.37%-6.26%-2.29%0.71%-8.26%
200781.67%1.90%$11,398$12,4401.47%1.79%2.38%1.11%1.33%-0.63%1.04%6.74%
200792.83%4.55%$11,721$13,0063.85%0.23%0.73%10.51%0.31%5.32%11.57%3.90%
2007102.25%3.85%$11,985$13,5071.79%1.81%0.97%6.95%1.06%4.25%11.87%2.10%
2007110.13%-3.46%$12,000$13,039-4.52%5.35%1.02%-1.65%-7.15%-3.62%-7.65%-9.47%
2007120.11%-0.75%$12,014$12,941-0.70%-0.64%-0.81%6.65%-0.71%-2.99%-1.43%-5.41%
20081-0.10%-1.53%$12,002$12,743-6.17%2.10%2.57%10.84%-4.00%-7.85%-8.92%-0.78%
20082-0.67%-0.50%$11,922$12,680-2.50%-0.46%-0.71%5.23%-3.36%-1.02%1.99%-3.18%
20083-0.31%-0.17%$11,884$12,658-0.90%2.14%-0.60%-6.00%0.83%0.42%-3.75%6.48%
200840.73%2.89%$11,971$13,0234.89%-2.48%1.25%-4.16%2.64%5.44%9.14%6.38%
20085-0.39%0.76%$11,924$13,1222.02%-2.69%-2.21%0.92%3.92%1.19%3.16%-0.21%
20086-1.89%-4.92%$11,698$12,477-8.12%2.65%-1.29%4.52%-8.41%-8.80%-9.29%-10.62%
20087-0.48%-0.61%$11,642$12,401-0.62%-0.37%0.39%-1.44%2.87%-3.32%-5.50%3.12%
200880.56%-1.05%$11,708$12,2711.46%2.74%0.15%-9.29%4.76%-4.25%-6.32%2.37%
20089-4.12%-5.68%$11,226$11,574-9.24%1.47%-10.73%4.11%-4.82%-11.44%-14.68%-0.11%
200810-9.52%-16.93%$10,157$9,615-17.48%-1.86%-1.95%-16.14%-19.86%-20.83%-25.58%-31.73%
2008113.90%-3.55%$10,553$9,273-8.01%14.34%3.35%12.57%-11.80%-6.37%-9.75%-22.72%
2008128.39%9.93%$11,439$10,1941.78%13.64%13.80%7.73%6.57%8.88%10.35%16.67%
20091-7.51%-8.98%$10,580$9,278-8.05%-13.07%-1.80%5.54%-13.94%-13.73%-9.29%-17.53%
20092-5.22%-8.25%$10,028$8,512-10.53%-1.54%-5.20%1.45%-13.03%-10.39%-6.27%-20.53%
200934.47%5.84%$10,476$9,0098.26%4.04%0.47%-2.54%7.58%8.39%16.86%3.61%
200941.79%10.02%$10,664$9,91110.99%-6.95%2.78%-3.33%18.89%11.52%15.56%30.68%
200952.24%5.84%$10,902$10,4915.46%-3.69%2.32%10.23%0.67%13.19%15.94%2.62%
200960.25%-0.82%$10,929$10,4040.36%0.76%2.89%-5.22%1.52%-1.43%-2.25%-3.23%
200974.13%7.27%$11,381$11,1607.74%0.58%4.63%2.38%11.00%10.04%11.01%10.77%
200982.44%3.54%$11,659$11,5553.71%2.24%1.31%0.05%3.48%4.50%-1.31%14.32%
200993.39%4.88%$12,053$12,1194.14%2.46%1.76%5.84%4.21%3.80%10.20%6.63%
200910-1.63%-2.32%$11,857$11,838-2.63%-2.62%-0.49%3.72%-6.07%-2.52%-3.44%-4.46%
2009114.33%5.36%$12,370$12,4735.69%1.21%1.95%12.79%2.90%3.92%7.85%6.57%
200912-2.25%0.84%$12,091$12,5772.86%-6.34%-2.07%-7.20%8.10%0.70%3.27%7.37%
20101-0.38%-2.72%$12,045$12,235-3.57%2.69%1.25%-1.26%-2.54%-5.07%-7.76%-5.52%
201021.65%2.41%$12,243$12,5303.44%-0.34%0.51%3.27%4.76%0.27%1.78%5.58%
201031.79%4.63%$12,463$13,1106.40%-2.06%0.65%-0.44%7.80%6.39%8.11%10.18%
201042.96%3.01%$12,831$13,5052.18%3.32%1.91%5.88%6.63%-2.80%-0.17%7.15%
20105-1.07%-4.44%$12,694$12,906-7.88%5.11%-1.31%3.05%-8.54%-11.19%-9.39%-5.33%
201060.54%-1.42%$12,762$12,723-5.83%5.80%3.28%2.36%-8.27%-2.07%-1.40%-5.19%
201072.13%5.24%$13,034$13,3907.02%-0.95%2.11%-5.09%6.71%11.61%10.93%9.59%
201082.22%-0.50%$13,323$13,323-4.71%8.40%2.86%5.71%-7.91%-3.80%-3.24%-1.28%
201093.36%6.16%$13,771$14,1449.45%-2.51%0.46%4.78%10.93%9.97%11.76%4.45%
2010100.32%2.32%$13,815$14,4724.03%-4.47%-0.26%3.68%4.04%3.81%3.02%4.74%
201011-0.41%-0.97%$13,759$14,3310.51%-1.69%-1.62%2.11%2.47%-4.82%-2.91%-1.85%
2010121.54%4.25%$13,971$14,9416.96%-3.68%-0.75%2.44%8.97%8.30%7.27%4.54%
20111-1.01%-0.76%$13,830$14,8272.05%-3.08%0.04%-6.38%-0.24%2.10%-3.84%3.25%
201122.84%3.11%$14,224$15,2873.70%1.65%1.08%6.00%4.21%3.55%-0.04%4.71%
201130.27%0.75%$14,262$15,4020.42%0.03%-0.54%1.60%2.21%-2.39%6.29%-1.62%
201143.30%3.98%$14,733$16,0152.90%2.34%2.50%8.94%1.06%5.63%2.73%5.75%
201150.80%-0.46%$14,852$15,941-1.06%3.42%1.27%-1.79%-1.77%-2.21%-2.94%1.37%
20116-1.92%-1.80%$14,567$15,655-1.79%-2.33%-0.80%-2.43%-1.59%-1.19%-0.93%-3.30%
201171.97%1.05%$14,854$15,819-2.27%4.42%2.43%8.42%-2.77%-2.38%-1.03%1.56%
201182.51%-1.93%$15,227$15,514-6.09%9.66%0.34%12.27%-7.98%-8.75%-9.25%-5.62%
201190.66%-6.90%$15,327$14,443-7.57%13.20%0.35%-11.06%-10.57%-10.81%-17.89%-10.85%
2011104.03%8.93%$15,946$15,73311.37%-3.84%2.51%5.87%15.34%9.63%16.27%14.29%
2011110.31%-0.90%$15,995$15,592-0.37%1.98%-3.16%1.67%0.63%-2.18%-1.96%-3.80%
2011120.95%-0.30%$16,147$15,5450.98%3.44%3.49%-10.66%2.02%-2.21%-4.30%4.85%
201213.40%6.10%$16,696$16,4935.07%-0.33%2.14%11.40%7.90%5.27%10.99%6.38%
201220.61%1.37%$16,798$16,7194.22%-2.59%1.63%-2.96%1.71%4.83%5.27%-1.15%
20123-0.68%0.18%$16,683$16,7503.06%-4.23%-1.42%-1.32%2.89%0.42%-3.11%5.19%
201241.63%0.29%$16,956$16,798-0.64%4.83%1.08%-0.15%-1.91%-2.08%-1.70%2.86%
201250.25%-4.54%$16,998$16,036-6.23%9.03%0.76%-6.34%-7.18%-11.14%-10.71%-4.51%
201261.35%3.48%$17,228$16,5944.05%-1.68%0.87%2.35%4.54%7.11%5.08%5.52%
201272.30%1.30%$17,624$16,8090.88%3.82%3.48%0.84%-0.69%0.08%-0.03%2.00%
201281.11%1.74%$17,819$17,1022.70%-1.32%-0.05%4.94%4.08%3.20%0.41%-0.01%
201290.72%1.87%$17,947$17,4222.49%-2.53%1.10%4.67%3.14%2.71%5.22%-1.86%
201210-1.01%-0.76%$17,766$17,289-1.81%-0.48%1.35%-2.94%-1.96%1.09%-0.44%-0.91%
2012110.69%0.87%$17,889$17,4400.77%1.38%-0.42%-0.47%1.65%2.78%1.56%-0.26%
201212-0.71%1.81%$17,762$17,7561.29%-2.49%-0.33%-2.43%3.55%4.37%6.80%3.72%
201310.72%1.62%$17,890$18,0435.42%-3.19%-1.30%-0.51%5.35%3.73%-0.29%3.74%
201320.54%-0.28%$17,987$17,9931.28%1.24%1.08%-5.09%1.63%-1.29%-2.28%1.22%
201331.48%1.46%$18,254$18,2563.95%-0.42%-0.05%0.95%4.11%1.31%-1.02%2.87%
201341.79%1.75%$18,581$18,5751.61%4.68%2.17%-7.56%0.12%5.02%1.22%6.73%
20135-2.62%-2.91%$18,095$18,0352.44%-6.76%-3.22%-6.20%4.29%-3.02%-4.83%-5.98%
20136-3.41%-3.65%$17,479$17,377-1.43%-3.27%-3.27%-11.06%-0.14%-2.70%-5.35%-1.98%
201372.39%3.27%$17,896$17,9455.75%-2.26%1.11%7.43%6.56%5.32%1.32%0.90%
20138-1.23%-1.88%$17,675$17,607-3.03%-1.34%-1.00%5.20%-3.41%-1.96%-2.54%-6.98%
201391.34%3.20%$17,912$18,1713.90%0.66%0.74%-4.78%6.59%7.82%7.21%3.49%
2013102.39%2.82%$18,341$18,6844.27%1.43%1.81%-0.34%3.48%3.26%4.17%4.52%
201311-0.54%-0.79%$18,241$18,5362.70%-2.70%-0.14%-5.51%4.25%0.55%-0.26%-5.25%
2013120.00%0.05%$18,242$18,5462.73%-1.87%0.22%-3.79%1.29%2.16%-0.42%0.10%
201411.68%-0.58%$18,548$18,438-3.17%6.30%1.88%3.42%-3.51%-5.20%-8.64%4.28%
201422.93%4.00%$19,091$19,1764.87%0.52%1.14%6.27%4.63%6.13%3.38%5.07%
201430.11%0.41%$19,113$19,2550.51%0.73%-0.03%-3.14%1.34%-0.46%3.88%0.49%
201441.02%0.93%$19,308$19,4340.06%2.10%1.33%0.49%-2.29%1.67%0.78%3.29%
201451.76%1.38%$19,649$19,7032.10%2.95%1.51%-3.05%0.62%1.60%2.95%2.40%
201461.62%2.13%$19,968$20,1222.62%-0.25%0.01%6.32%3.85%0.92%2.40%1.13%
20147-0.98%-1.44%$19,773$19,832-1.99%0.67%-0.32%-3.63%-5.07%-2.60%1.36%0.08%
201483.65%2.72%$20,493$20,3724.15%4.72%2.00%0.38%4.46%0.18%2.83%3.04%
20149-2.49%-4.46%$19,983$19,463-2.10%-2.11%-1.68%-6.18%-5.94%-3.88%-7.77%-6.04%
2014101.92%2.74%$20,368$19,9972.75%2.81%1.23%-3.05%7.13%-0.27%1.42%9.94%
2014112.11%0.86%$20,798$20,1692.48%2.97%0.91%-0.49%0.48%0.06%-1.54%2.00%
2014121.30%0.12%$21,068$20,193-0.04%3.25%-0.02%1.31%2.56%-4.00%-3.99%1.88%
201513.96%2.62%$21,902$20,723-2.74%9.82%3.75%8.69%-5.32%0.62%-0.69%6.85%
20152-0.82%0.65%$21,721$20,8585.74%-6.14%-1.42%-5.91%5.86%6.34%4.41%-3.67%
20153-0.26%-0.27%$21,664$20,801-1.16%1.10%0.20%-2.15%1.03%-1.43%-1.50%1.74%
20154-1.18%-0.17%$21,408$20,7660.62%-3.43%-1.19%-0.17%-1.82%3.65%6.85%-5.85%
20155-0.45%-0.64%$21,312$20,6341.30%-2.37%-1.12%0.56%0.75%0.20%-4.10%-0.30%
20156-2.55%-2.43%$20,768$20,133-1.67%-4.07%-1.88%-1.52%0.42%-3.12%-2.93%-4.68%
201571.70%-0.09%$21,121$20,1141.70%4.55%0.83%-6.62%-2.70%2.03%-6.31%5.77%
20158-2.33%-3.88%$20,628$19,333-6.09%-0.69%-0.83%3.71%-4.62%-7.43%-8.84%-6.29%
20159-0.46%-1.23%$20,534$19,095-2.92%1.97%1.19%-1.80%-3.77%-4.42%-3.13%3.05%
2015103.26%4.46%$21,204$19,9467.91%-0.41%0.57%2.28%6.57%6.61%6.38%5.76%
201511-0.84%-1.08%$21,026$19,7320.60%-0.87%-0.15%-6.75%2.47%-0.75%-2.52%-0.63%
201512-1.14%-1.67%$20,787$19,401-2.13%-0.30%-1.08%-0.45%-5.08%-2.34%-3.83%1.82%
201610.39%-1.81%$20,868$19,051-5.72%5.57%0.12%5.41%-5.85%-5.52%-5.03%-3.44%
201622.45%1.58%$21,380$19,351-0.01%3.09%1.05%10.93%2.08%-3.33%-0.82%-0.36%
201633.15%6.15%$22,054$20,5427.11%-0.09%3.62%-0.84%9.41%6.58%12.96%10.48%
201640.77%1.12%$22,223$20,7730.66%-0.74%1.55%5.11%2.13%2.22%0.41%-2.35%
201650.23%-0.65%$22,273$20,6381.73%0.81%-0.51%-6.14%0.44%-0.09%-3.69%2.25%
201664.03%3.65%$23,169$21,3910.27%6.93%3.09%8.97%0.83%-2.42%4.56%6.92%
201672.71%3.50%$23,796$22,1403.98%2.10%1.29%1.98%5.06%3.98%5.38%4.26%
20168-0.62%-0.64%$23,650$21,9990.21%-1.01%0.18%-3.26%1.13%0.53%0.88%-3.76%
20169-0.43%0.25%$23,547$22,0540.21%-1.51%-0.32%0.69%0.87%1.34%2.52%-1.82%
201610-2.97%-2.95%$22,847$21,404-2.19%-4.38%-1.53%-2.94%-3.74%-2.22%-0.83%-5.74%
201611-2.57%-1.22%$22,259$21,1424.49%-8.21%-3.17%-8.36%13.34%-1.78%-4.42%-1.68%
2016120.51%1.37%$22,374$21,4311.98%-0.46%0.84%-1.91%3.20%2.71%-0.25%4.82%
201711.63%2.10%$22,738$21,8811.86%0.81%0.15%5.42%-1.21%3.29%6.66%-0.19%
201722.55%2.20%$23,317$22,3613.69%1.59%1.32%3.18%1.35%1.19%1.74%3.51%
20173-0.30%0.32%$23,247$22,4320.06%-0.65%-0.29%-0.43%-0.65%3.23%3.69%-2.42%
201741.34%1.30%$23,558$22,7241.06%1.57%1.19%1.73%0.51%2.42%1.70%0.24%
201751.25%0.94%$23,852$22,9381.01%1.89%1.33%-0.12%-2.26%3.54%2.85%-0.72%
201760.49%0.81%$23,968$23,1240.95%0.79%0.48%-2.16%2.96%0.31%0.93%2.23%
201770.85%1.85%$24,173$23,5511.88%-0.66%0.77%2.31%0.75%2.65%5.82%1.24%
201781.84%0.97%$24,619$23,7790.15%3.41%0.68%4.20%-2.72%-0.04%2.35%-0.26%
20179-0.26%0.94%$24,554$24,0022.44%-2.32%-0.05%-3.37%8.58%2.36%-0.04%-0.11%
2017100.78%0.76%$24,744$24,1842.17%-0.04%0.19%-0.75%0.59%1.68%3.28%-1.07%
2017111.47%1.34%$25,108$24,5083.03%0.74%-0.12%0.36%3.76%0.69%-0.39%2.66%
2017121.51%1.36%$25,486$24,8421.16%1.81%1.22%2.11%-0.37%1.35%3.77%-0.14%
201811.04%1.80%$25,753$25,2895.23%-3.26%-1.23%3.23%1.33%5.02%8.30%-4.25%
20182-3.10%-4.20%$24,954$24,228-3.76%-3.04%-2.24%-2.08%-4.04%-4.83%-5.90%-7.68%
201830.42%0.88%$25,058$24,441-1.95%2.86%0.56%0.63%1.37%-0.84%0.54%3.88%
20184-0.90%-0.36%$24,832$24,3530.45%-2.09%-1.57%-0.95%1.76%1.52%-2.82%0.82%
201851.73%1.14%$25,261$24,6302.72%2.01%0.52%-1.20%5.87%-1.89%-2.62%3.68%
201860.04%-0.48%$25,272$24,5110.70%0.65%-0.49%-3.61%0.80%-1.57%-4.54%4.20%
201870.72%1.32%$25,453$24,8353.32%-1.44%1.34%-2.24%2.62%2.85%3.53%0.60%
201881.58%0.29%$25,856$24,9083.43%1.31%0.02%-2.14%3.14%-2.24%-3.77%2.58%
20189-1.05%-1.10%$25,584$24,6350.20%-2.86%-0.14%-0.66%-3.05%0.97%-0.58%-2.64%
201810-4.00%-5.00%$24,561$23,402-7.41%-2.93%-2.05%2.12%-9.94%-8.13%-8.76%-2.93%
2018111.42%1.80%$24,909$23,8242.01%1.79%-0.36%0.34%0.57%0.50%4.90%4.67%
201812-0.66%-3.21%$24,745$23,059-9.16%5.85%1.86%4.94%-12.38%-5.35%-3.50%-7.96%
201914.25%7.03%$25,797$24,6818.54%0.38%3.37%2.89%12.26%6.63%10.34%11.85%
201920.79%0.90%$26,002$24,9033.56%-1.38%-0.20%-0.61%4.13%2.54%-1.53%0.70%
201932.80%1.33%$26,730$25,2351.42%5.57%2.93%-1.60%-3.91%0.92%1.13%4.21%
201940.80%1.39%$26,944$25,5873.93%-1.99%0.44%-0.66%4.32%2.93%2.35%-0.16%
201950.38%-2.30%$27,047$24,998-6.45%6.84%1.65%1.76%-9.98%-5.03%-7.33%0.14%
Portfolio return and risk metrics
MetricMinimum Volatility at 8.00% ReturnEqual Weighted
Arithmetic Mean (monthly)0.64%0.63%
Arithmetic Mean (annualized)8.00%7.80%
Geometric Mean (monthly)0.62%0.57%
Geometric Mean (annualized)7.70%7.07%
Volatility (monthly)2.17%3.37%
Volatility (annualized)7.50%11.66%
Downside Deviation (monthly)1.38%2.23%
Max. Drawdown-16.53%-36.98%
US Market Correlation0.610.87
Beta(*)0.310.69
Alpha (annualized)4.91%1.29%
R236.67%75.09%
Sharpe Ratio0.880.55
Sortino Ratio1.360.82
Treynor Ratio (%)21.459.37
Calmar Ratio1.040.75
Active Return-0.62%-1.25%
Tracking Error11.83%7.45%
Information Ratio-0.05-0.17
Skewness-0.86-0.79
Excess Kurtosis4.084.72
Historical Value-at-Risk (5%)-2.94%-4.53%
Analytical Value-at-Risk (5%)-2.91%-4.89%
Conditional Value-at-Risk (5%)-4.98%-7.65%
Upside Capture Ratio (%)40.0766.43
Downside Capture Ratio (%)19.1362.46
Safe Withdrawal Rate10.89%10.84%
Perpetual Withdrawal Rate5.49%4.92%
Positive Periods108 out of 161 (67.08%)98 out of 161 (60.87%)
Gain/Loss Ratio1.091.09
* 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 PeriodStartEndMinimum Volatility at 8.00% ReturnEqual Weighted
Subprime CrisisNov 2007Mar 2009-16.53%-36.98%

Drawdowns for Minimum Volatility at 8.00% Return

Drawdowns for Minimum Volatility at 8.00% Return (worst 10)
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Jan 2008Feb 20091 year 2 monthsSep 20097 months1 year 9 months-16.53%
2Aug 2016Nov 20164 monthsMay 20176 months10 months-6.46%
3Feb 2015Sep 20158 monthsMar 20166 months1 year 2 months-6.25%
4May 2013Jun 20132 monthsFeb 20148 months10 months-5.94%
5Sep 2018Oct 20182 monthsFeb 20194 months6 months-5.01%
6Feb 2018Apr 20183 monthsAug 20184 months7 months-3.57%
7Dec 2009Jan 20102 monthsMar 20102 months4 months-2.63%
8Sep 2014Sep 20141 monthNov 20142 months3 months-2.49%
9Jun 2011Jun 20111 monthJul 20111 month2 months-1.92%
10Oct 2009Oct 20091 monthNov 20091 month2 months-1.63%
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 ETF8.43%14.76%33.45%-36.98%-50.84%0.550.781.00
TLTiShares 20+ Year Treasury Bond ETF6.22%13.27%33.96%-21.80%-21.80%0.440.75-0.32
LQDiShares iBoxx $ Invmt Grade Corp Bd ETF5.22%7.25%10.58%-3.79%-15.11%0.580.950.27
GLDSPDR Gold Shares6.71%17.80%30.45%-28.33%-42.91%0.390.620.03
IJSiShares S&P Small-Cap 600 Value ETF7.53%19.27%39.34%-29.39%-54.13%0.420.610.91
EFAiShares MSCI EAFE ETF3.33%17.39%26.95%-41.04%-57.38%0.210.300.89
EEMiShares MSCI Emerging Markets ETF4.36%22.47%68.93%-48.88%-60.44%0.250.380.80
VNQVanguard Real Estate ETF7.40%23.18%35.30%-37.00%-68.30%0.380.540.73

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTITLTLQDGLDIJSEFAEEMVNQMinimum Volatility at 8.00% ReturnEqual Weighted
VTIVanguard Total Stock Market ETF--0.330.270.030.910.890.800.730.600.87
TLTiShares 20+ Year Treasury Bond ETF-0.33-0.510.20-0.34-0.24-0.220.010.510.00
LQDiShares iBoxx $ Invmt Grade Corp Bd ETF0.270.51-0.240.200.380.360.430.730.54
GLDSPDR Gold Shares0.030.200.24--0.020.150.290.090.440.36
IJSiShares S&P Small-Cap 600 Value ETF0.91-0.340.20-0.02-0.760.690.740.500.81
EFAiShares MSCI EAFE ETF0.89-0.240.380.150.76-0.880.680.620.89
EEMiShares MSCI Emerging Markets ETF0.80-0.220.360.290.690.88-0.600.590.88
VNQVanguard Real Estate ETF0.730.010.430.090.740.680.60-0.650.84

Portfolio Risk Decomposition

Portfolio risk decomposition
TickerNameMinimum Volatility at 8.00% ReturnEqual Weighted
VTIVanguard Total Stock Market ETF46.20%13.70%
TLTiShares 20+ Year Treasury Bond ETF32.51%0.00%
LQDiShares iBoxx $ Invmt Grade Corp Bd ETF9.86%4.22%
GLDSPDR Gold Shares11.42%6.84%
IJSiShares S&P Small-Cap 600 Value ETF16.67%
EFAiShares MSCI EAFE ETF16.57%
EEMiShares MSCI Emerging Markets ETF21.09%
VNQVanguard Real Estate ETF20.91%

Annual Asset Returns

Rolling returns summary
Roll PeriodMinimum Volatility at 8.00% ReturnEqual Weighted
AverageHighLowAverageHighLow
1 year7.44%15.57%-4.78%7.35%23.38%-21.23%
3 years7.50%13.68%3.37%6.56%15.10%0.64%
5 years8.16%11.75%6.29%7.37%12.71%4.45%
7 years8.26%9.19%6.29%7.50%9.63%5.79%
10 years7.71%8.02%7.41%7.03%8.50%6.02%
Result statistics are based on annualized rolling returns over full calendar year periods