Portfolio Optimization

This online portfolio optimizer tool performs Markowitz mean variance optimization on the provided portfolio to find the optimal risk adjusted portfolio that lies on the efficient frontier. Supported optimization goals include:

Mean variance 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, constraints and goal parameters are optional, and will be determined automatically based on the highest Sharpe Ratio if not specified. You can also use the Black-Litterman model based portfolio optimization, which allows the benchmark portfolio weights to be optimized based on investor's views.

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Portfolio Optimization Results (Jan 2006 - Dec 2016)

Portfolio optimization results for minimized standard deviation subject to 10.00% expected annual return. The possible range of expected annual portfolio returns for the given period taking into account the specified constraints is 4.44% to 11.13%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Equal Weight
Ticker Name Allocation
Save portfolio »
VTI Vanguard Total Stock Market ETF 12.50%
IJS iShares S&P SmallCap 600 Value ETF 12.50%
EFA iShares MSCI EAFE ETF 12.50%
EEM iShares MSCI Emerging Index Fund 12.50%
VNQ Vanguard REIT ETF 12.50%
TLT iShares 20+ Year Treasury Bond ETF 12.50%
LQD iShares iBoxx $ Investment Grade Corporate Bond ETF 12.50%
GLD SPDR Gold Trust 12.50%
Inverse Volatility Weight
Ticker Name Allocation
Save portfolio »
VTI Vanguard Total Stock Market ETF 13.02%
IJS iShares S&P SmallCap 600 Value ETF 10.10%
EFA iShares MSCI EAFE ETF 10.70%
EEM iShares MSCI Emerging Index Fund 8.33%
VNQ Vanguard REIT ETF 7.96%
TLT iShares 20+ Year Treasury Bond ETF 14.11%
LQD iShares iBoxx $ Investment Grade Corporate Bond ETF 25.53%
GLD SPDR Gold Trust 10.26%
Optimized Portfolio
Ticker Name Allocation
Save portfolio »
IJS iShares S&P SmallCap 600 Value ETF 60.40%
TLT iShares 20+ Year Treasury Bond ETF 14.97%
GLD SPDR Gold Trust 24.63%

Portfolio Returns

Portfolio performance statistics
PortfolioInitial BalanceFinal BalanceCAGRExpected ReturnStd.Dev.Best YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
Equal Weight$10,000$21,417 7.17% 8.00% 12.35%23.38%-21.23%-36.98% 0.540.800.87
Inverse Volatility Weight$10,000$21,014 6.98% 7.57% 10.39%18.27%-15.60%-30.00% 0.600.910.83
Optimized Portfolio$10,000$26,205 9.15% 10.00% 12.40%24.75%-12.69%-28.81% 0.681.060.84
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
  • Mean variance optimization is based on the monthly return statistics of the selected assets, and the portfolio return statistics above use the same methodology.
  • See methodology section of the FAQ for more information on mean variance optimization and its limitations.
  • Expected annual return is based on annualized monthly returns
  • CAGR = Compound Annual Growth Rate
  • StdDev = Standard Deviation based on annualized standard deviation of monthly arithmetic returns (population standard deviation)
  • Sharpe and Sortino ratios are calculated and annualized from monthly excess returns over risk free rate (1-month t-bills)
  • Drawdowns are calculated based on monthly returns.
  • Inverse volatility weighted portfolio is based on a simple risk-parity technique that uses inverse volatility weighting for portfolio assets
  • 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
#AssetExpected ReturnStandard DeviationSharpe Ratio
1Vanguard Total Stock Market ETF (VTI)9.23%15.19%0.608
2iShares S&P SmallCap 600 Value ETF (IJS)11.12%19.59%0.568
3iShares MSCI EAFE ETF (EFA)4.45%18.49%0.241
4iShares MSCI Emerging Index Fund (EEM)6.48%23.76%0.273
5Vanguard REIT ETF (VNQ)11.13%24.86%0.448
6iShares 20+ Year Treasury Bond ETF (TLT)7.06%14.02%0.504
7iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD)5.62%7.75%0.725
8SPDR Gold Trust (GLD)9.07%19.28%0.470
Efficient Frontier Assets
#VTIIJSEFAEEMVNQTLTLQDGLDExpected ReturnStandard DeviationSharpe Ratio*
*Ex ante Sharpe Ratio calculated directly from the expected return and standard deviation
10.00%0.00%100.00%0.00%0.00%0.00%0.00%0.00%4.45%18.49%0.241
20.00%0.00%94.36%0.00%0.00%0.00%5.64%0.00%4.51%17.62%0.256
30.00%0.00%88.71%0.00%0.00%0.00%11.29%0.00%4.58%16.76%0.273
40.00%0.00%83.07%0.00%0.00%0.00%16.93%0.00%4.64%15.91%0.292
50.00%0.00%77.43%0.00%0.00%0.00%22.57%0.00%4.71%15.07%0.312
60.00%0.00%71.79%0.00%0.00%0.00%28.21%0.00%4.78%14.26%0.335
70.00%0.00%66.15%0.00%0.00%0.00%33.85%0.00%4.84%13.46%0.360
80.00%0.00%60.50%0.00%0.00%0.00%39.50%0.00%4.91%12.68%0.387
90.00%0.00%54.86%0.00%0.00%0.00%45.14%0.00%4.97%11.93%0.417
100.00%0.00%49.22%0.00%0.00%0.00%50.78%0.00%5.04%11.22%0.449
110.00%0.00%43.58%0.00%0.00%0.00%56.42%0.00%5.11%10.54%0.484
120.00%0.00%37.94%0.00%0.00%0.00%62.06%0.00%5.17%9.91%0.522
130.00%0.00%32.30%0.00%0.00%0.00%67.70%0.00%5.24%9.34%0.561
140.00%0.00%26.65%0.00%0.00%0.00%73.35%0.00%5.30%8.84%0.600
150.00%0.00%21.01%0.00%0.00%0.00%78.99%0.00%5.37%8.42%0.638
160.00%0.00%15.37%0.00%0.00%0.00%84.63%0.00%5.44%8.09%0.672
170.00%0.00%9.73%0.00%0.00%0.00%90.27%0.00%5.50%7.86%0.700
180.00%0.00%4.78%0.00%0.00%0.57%94.64%0.00%5.57%7.75%0.718
190.00%0.00%4.45%0.00%0.00%1.92%92.37%1.27%5.63%7.70%0.732
201.21%0.00%3.51%0.00%0.00%2.20%91.57%1.51%5.70%7.65%0.745
212.50%0.00%2.54%0.00%0.00%2.43%90.86%1.67%5.77%7.61%0.758
223.79%0.00%1.56%0.00%0.00%2.66%90.14%1.84%5.83%7.57%0.771
235.09%0.00%0.59%0.00%0.00%2.90%89.43%2.00%5.90%7.52%0.784
246.31%0.00%0.00%0.00%0.00%3.47%88.00%2.22%5.97%7.48%0.797
257.44%0.00%0.00%0.00%0.00%4.56%85.47%2.53%6.03%7.45%0.810
268.56%0.00%0.00%0.00%0.00%5.65%82.94%2.84%6.10%7.41%0.823
279.69%0.00%0.00%0.00%0.00%6.75%80.41%3.15%6.17%7.38%0.836
2810.82%0.00%0.00%0.00%0.00%7.84%77.88%3.47%6.23%7.35%0.848
2911.94%0.00%0.00%0.00%0.00%8.94%75.35%3.78%6.30%7.33%0.860
3013.07%0.00%0.00%0.00%0.00%10.03%72.81%4.09%6.37%7.31%0.871
3114.20%0.00%0.00%0.00%0.00%11.12%70.28%4.40%6.43%7.29%0.882
3215.32%0.00%0.00%0.00%0.00%12.22%67.75%4.71%6.50%7.28%0.893
3316.45%0.00%0.00%0.00%0.00%13.31%65.22%5.02%6.57%7.27%0.903
3417.58%0.00%0.00%0.00%0.00%14.41%62.69%5.33%6.63%7.27%0.913
3518.70%0.00%0.00%0.00%0.00%15.50%60.16%5.64%6.70%7.27%0.922
3619.83%0.00%0.00%0.00%0.00%16.59%57.63%5.95%6.77%7.27%0.931
3720.95%0.00%0.00%0.00%0.00%17.69%55.10%6.26%6.83%7.28%0.939
3822.08%0.00%0.00%0.00%0.00%18.78%52.57%6.57%6.90%7.29%0.947
3923.21%0.00%0.00%0.00%0.00%19.88%50.04%6.88%6.97%7.30%0.955
4024.33%0.00%0.00%0.00%0.00%20.97%47.51%7.19%7.04%7.32%0.962
4124.48%0.70%0.00%0.00%0.00%21.93%45.41%7.47%7.10%7.34%0.968
4224.52%1.47%0.00%0.00%0.00%22.88%43.37%7.76%7.17%7.36%0.974
4324.56%2.24%0.00%0.00%0.00%23.83%41.32%8.04%7.24%7.39%0.979
4424.60%3.02%0.00%0.00%0.00%24.78%39.27%8.32%7.31%7.42%0.984
4524.64%3.79%0.00%0.00%0.00%25.73%37.23%8.61%7.37%7.46%0.989
4624.68%4.56%0.00%0.00%0.00%26.68%35.18%8.89%7.44%7.49%0.993
4724.72%5.34%0.00%0.00%0.00%27.63%33.13%9.18%7.51%7.53%0.997
4824.76%6.11%0.00%0.00%0.00%28.58%31.09%9.46%7.57%7.57%1.000
4924.80%6.89%0.00%0.00%0.00%29.53%29.04%9.74%7.64%7.62%1.003
5024.84%7.66%0.00%0.00%0.00%30.48%26.99%10.03%7.71%7.67%1.005
5124.88%8.43%0.00%0.00%0.00%31.43%24.95%10.31%7.78%7.72%1.008
5224.92%9.21%0.00%0.00%0.00%32.38%22.90%10.59%7.84%7.77%1.009
5324.96%9.98%0.00%0.00%0.00%33.33%20.85%10.88%7.91%7.83%1.011
5425.00%10.75%0.00%0.00%0.00%34.28%18.81%11.16%7.98%7.89%1.012
5525.04%11.53%0.00%0.00%0.00%35.23%16.76%11.44%8.05%7.95%1.013
5625.08%12.30%0.00%0.00%0.00%36.18%14.71%11.73%8.12%8.01%1.013
5725.12%13.07%0.00%0.00%0.00%37.13%12.66%12.01%8.18%8.08%1.013
5825.16%13.85%0.00%0.00%0.00%38.08%10.62%12.29%8.25%8.15%1.013
5925.20%14.62%0.00%0.00%0.00%39.03%8.57%12.58%8.32%8.22%1.012
6025.24%15.39%0.00%0.00%0.00%39.98%6.52%12.86%8.39%8.29%1.012
6125.28%16.17%0.00%0.00%0.00%40.93%4.48%13.15%8.45%8.37%1.011
6225.32%16.94%0.00%0.00%0.00%41.88%2.43%13.43%8.52%8.44%1.009
6325.36%17.72%0.00%0.00%0.00%42.82%0.38%13.71%8.59%8.52%1.008
6422.61%20.52%0.00%0.00%0.00%42.72%0.00%14.15%8.66%8.61%1.006
6519.22%23.79%0.00%0.00%0.00%42.37%0.00%14.63%8.73%8.70%1.003
6615.83%27.06%0.00%0.00%0.00%42.02%0.00%15.10%8.79%8.80%1.000
6712.43%30.33%0.00%0.00%0.00%41.67%0.00%15.57%8.86%8.91%0.995
689.04%33.60%0.00%0.00%0.00%41.32%0.00%16.05%8.93%9.02%0.990
695.64%36.87%0.00%0.00%0.00%40.97%0.00%16.52%9.00%9.14%0.984
702.25%40.14%0.00%0.00%0.00%40.62%0.00%17.00%9.07%9.27%0.978
710.00%42.78%0.00%0.00%0.00%39.72%0.00%17.50%9.14%9.41%0.971
720.00%44.18%0.00%0.00%0.00%37.76%0.00%18.07%9.20%9.56%0.962
730.00%45.58%0.00%0.00%0.00%35.79%0.00%18.63%9.27%9.74%0.952
740.00%46.97%0.00%0.00%0.00%33.83%0.00%19.20%9.34%9.93%0.941
750.00%48.37%0.00%0.00%0.00%31.86%0.00%19.76%9.41%10.13%0.929
760.00%49.77%0.00%0.00%0.00%29.90%0.00%20.33%9.48%10.35%0.915
770.00%51.17%0.00%0.00%0.00%27.93%0.00%20.90%9.55%10.59%0.901
780.00%52.57%0.00%0.00%0.00%25.97%0.00%21.46%9.62%10.84%0.887
790.00%53.97%0.00%0.00%0.00%24.00%0.00%22.03%9.68%11.10%0.872
800.00%55.37%0.00%0.00%0.00%22.04%0.00%22.59%9.75%11.38%0.857
810.00%56.77%0.00%0.00%0.00%20.07%0.00%23.16%9.82%11.66%0.842
820.00%58.17%0.00%0.00%0.00%18.11%0.00%23.72%9.89%11.96%0.827
830.00%59.57%0.00%0.00%0.00%16.14%0.00%24.29%9.96%12.26%0.812
840.00%60.97%0.00%0.00%0.00%14.18%0.00%24.85%10.03%12.58%0.797
850.00%62.36%0.00%0.00%0.00%12.22%0.00%25.42%10.10%12.90%0.783
860.00%63.76%0.00%0.00%0.00%10.25%0.00%25.99%10.17%13.23%0.768
870.00%65.16%0.00%0.00%0.00%8.29%0.00%26.55%10.23%13.57%0.754
880.00%66.56%0.00%0.00%0.00%6.32%0.00%27.12%10.30%13.91%0.741
890.00%67.96%0.00%0.00%0.00%4.36%0.00%27.68%10.37%14.26%0.727
900.00%69.36%0.00%0.00%0.00%2.39%0.00%28.25%10.44%14.61%0.714
910.00%70.76%0.00%0.00%0.00%0.43%0.00%28.81%10.51%14.97%0.702
920.00%73.68%0.00%0.00%0.00%0.00%0.00%26.32%10.58%15.35%0.689
930.00%77.03%0.00%0.00%0.00%0.00%0.00%22.97%10.65%15.77%0.675
940.00%79.78%0.00%0.00%0.60%0.00%0.00%19.62%10.72%16.23%0.660
950.00%82.37%0.00%0.00%1.35%0.00%0.00%16.28%10.79%16.73%0.645
960.00%84.97%0.00%0.00%2.10%0.00%0.00%12.94%10.86%17.26%0.629
970.00%87.56%0.00%0.00%2.85%0.00%0.00%9.59%10.93%17.82%0.613
980.00%90.15%0.00%0.00%3.60%0.00%0.00%6.25%11.00%18.41%0.597
990.00%92.75%0.00%0.00%4.35%0.00%0.00%2.90%11.07%19.03%0.582
1000.00%0.14%0.00%0.00%99.86%0.00%0.00%0.00%11.13%24.85%0.448
Annual returns for the configured portfolios
YearInflationVanguard Total Stock Market ETF (VTI)iShares S&P SmallCap 600 Value ETF (IJS)iShares MSCI EAFE ETF (EFA)iShares MSCI Emerging Index Fund (EEM)Vanguard REIT ETF (VNQ)iShares 20+ Year Treasury Bond ETF (TLT)iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD)SPDR Gold Trust (GLD)Equal Weight ReturnEqual Weight Inflation Adjusted ReturnEqual Weight Year End BalanceInverse Volatility Weight ReturnInverse Volatility Weight Inflation Adjusted ReturnInverse Volatility Weight Year End BalanceOptimized Portfolio ReturnOptimized Portfolio Inflation Adjusted ReturnOptimized Portfolio Year End Balance
20062.54%15.69%19.37%25.81%31.19%35.30%0.71%4.22%22.55%19.39%16.43%$11,93915.60%12.74%$11,56017.64%14.72%$11,764
20074.08%5.37%-5.56%9.94%33.31%-16.50%10.29%3.73%30.45%8.39%4.14%$12,9417.92%3.68%$12,4755.14%1.02%$12,369
20080.09%-36.98%-29.39%-41.04%-48.88%-37.00%33.93%2.40%4.92%-21.23%-21.30%$10,194-15.60%-15.68%$10,529-12.69%-12.77%$10,799
20092.72%28.89%22.36%26.95%68.93%30.08%-21.80%8.46%24.03%23.38%20.11%$12,57718.27%15.14%$12,45317.13%14.02%$12,648
20101.50%17.42%24.69%8.15%16.51%28.37%9.05%9.33%29.27%18.79%17.04%$14,94116.84%15.12%$14,54924.75%22.91%$15,778
20112.96%0.97%-1.65%-12.25%-18.82%8.62%33.96%9.73%9.57%4.04%1.05%$15,5456.33%3.27%$15,4707.31%4.23%$16,932
20121.74%16.45%18.24%18.82%19.10%17.63%2.41%10.24%6.60%14.15%12.19%$17,74413.07%11.14%$17,49313.31%11.37%$19,186
20131.50%33.45%39.34%21.40%-3.69%2.31%-13.37%-2.00%-28.33%4.45%2.90%$18,5333.66%2.12%$18,13211.07%9.43%$21,310
20140.76%12.54%7.56%-6.20%-3.93%30.36%27.30%8.21%-2.19%8.88%8.07%$20,1809.29%8.47%$19,8178.09%7.28%$23,034
20150.73%0.36%-6.90%-1.00%-16.18%2.42%-1.79%-1.25%-10.67%-3.92%-4.62%$19,389-3.16%-3.86%$19,192-6.42%-7.10%$21,555
20162.04%12.83%31.25%1.37%10.87%8.60%1.18%6.21%8.03%10.46%8.25%$21,4179.49%7.30%$21,01421.57%19.14%$26,205
Monthly returns for the configured portfolios
YearMonthVanguard Total Stock Market ETF (VTI)iShares S&P SmallCap 600 Value ETF (IJS)iShares MSCI EAFE ETF (EFA)iShares MSCI Emerging Index Fund (EEM)Vanguard REIT ETF (VNQ)iShares 20+ Year Treasury Bond ETF (TLT)iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD)SPDR Gold Trust (GLD)Equal Weight ReturnEqual Weight Month End BalanceInverse Volatility Weight ReturnInverse Volatility Weight Month End BalanceOptimized Portfolio ReturnOptimized Portfolio Month End Balance
200613.22%8.75%5.77%14.20%7.54%-1.34%-0.44%9.93%5.95%$10,5954.42%$10,4427.53%$10,753
200620.22%0.27%-0.70%-3.85%1.86%1.11%0.68%-1.11%-0.19%$10,5750.03%$10,4450.06%$10,759
200632.05%4.86%4.01%2.17%4.73%-4.57%-1.68%3.62%1.90%$10,7761.04%$10,5533.14%$11,097
200640.96%0.18%4.79%6.52%-3.40%-2.75%-0.20%12.03%2.26%$11,0201.72%$10,7352.66%$11,392
20065-3.22%-4.55%-3.82%-11.14%-2.70%-0.19%-0.19%-1.32%-3.39%$10,646-2.64%$10,452-3.10%$11,039
200660.13%0.04%-0.06%0.21%4.95%1.18%-0.09%-4.67%0.21%$10,6690.09%$10,461-0.95%$10,934
20067-0.12%-3.10%0.81%2.34%3.89%2.16%1.46%3.15%1.33%$10,8101.26%$10,593-0.77%$10,850
200682.30%2.70%2.55%1.58%3.48%3.06%2.22%-1.38%2.07%$11,0332.11%$10,8171.75%$11,040
200692.26%1.19%0.22%-0.87%1.96%1.91%0.87%-4.53%0.38%$11,0750.55%$10,876-0.11%$11,027
2006103.53%5.52%3.75%7.06%6.03%0.85%1.00%1.29%3.63%$11,4772.99%$11,2023.78%$11,444
2006112.33%2.38%3.07%5.98%4.78%2.31%1.46%6.89%3.65%$11,8963.16%$11,5563.48%$11,842
2006121.20%0.32%3.20%5.44%-1.83%-2.69%-0.90%-1.83%0.36%$11,9390.04%$11,560-0.66%$11,764
200711.86%2.14%1.39%0.11%8.78%-1.00%0.09%2.56%1.99%$12,1771.46%$11,7291.77%$11,972
20072-1.62%-0.92%-0.12%-3.24%-2.70%3.39%2.00%2.55%-0.08%$12,1670.45%$11,7820.58%$12,041
200731.12%0.91%2.90%5.33%-2.07%-1.70%-0.68%-1.11%0.59%$12,2380.30%$11,8170.02%$12,044
200744.02%1.84%3.75%3.73%-0.13%0.90%0.89%2.05%2.13%$12,4991.98%$12,0511.75%$12,254
200753.72%4.63%2.36%5.06%-0.38%-2.31%-1.23%-2.31%1.19%$12,6490.72%$12,1381.88%$12,485
20076-1.76%-2.24%-0.32%3.68%-8.99%-1.01%-0.81%-1.94%-1.67%$12,437-1.45%$11,962-1.98%$12,238
20077-3.53%-6.26%-2.29%0.71%-8.26%3.32%-0.82%2.37%-1.85%$12,207-1.43%$11,791-2.70%$11,907
200781.47%1.33%-0.63%1.04%6.74%1.79%2.38%1.11%1.90%$12,4401.86%$12,0091.34%$12,067
200793.85%0.31%5.32%11.57%3.90%0.23%0.73%10.51%4.55%$13,0063.67%$12,4512.81%$12,407
2007101.79%1.06%4.25%11.87%2.10%1.81%0.97%6.95%3.85%$13,5073.17%$12,8452.62%$12,732
200711-4.52%-7.15%-3.62%-7.65%-9.47%5.35%1.02%-1.65%-3.46%$13,039-2.25%$12,556-3.92%$12,233
200712-0.70%-0.71%-2.99%-1.43%-5.41%-0.64%-0.81%6.65%-0.75%$12,941-0.64%$12,4751.11%$12,369
20081-6.17%-4.00%-7.85%-8.92%-0.78%2.10%2.57%10.84%-1.53%$12,743-0.79%$12,3770.57%$12,439
20082-2.50%-3.36%-1.02%1.99%-3.18%-0.46%-0.71%5.23%-0.50%$12,680-0.57%$12,307-0.81%$12,338
20083-0.90%0.83%0.42%-3.75%6.48%2.14%-0.60%-6.00%-0.17%$12,658-0.25%$12,276-0.66%$12,257
200844.89%2.64%5.44%9.14%6.38%-2.48%1.25%-4.16%2.89%$13,0232.30%$12,5570.20%$12,282
200852.02%3.92%1.19%3.16%-0.21%-2.69%-2.21%0.92%0.76%$13,1220.18%$12,5802.19%$12,550
20086-8.12%-8.41%-8.80%-9.29%-10.62%2.65%-1.29%4.52%-4.92%$12,477-3.96%$12,082-3.57%$12,102
20087-0.62%2.87%-3.32%-5.50%3.12%-0.37%0.39%-1.44%-0.61%$12,401-0.46%$12,0271.32%$12,263
200881.46%4.76%-4.25%-6.32%2.37%2.74%0.15%-9.29%-1.05%$12,271-0.65%$11,9491.00%$12,385
20089-9.24%-4.82%-11.44%-14.68%-0.11%1.47%-10.73%4.11%-5.68%$11,574-6.26%$11,201-1.68%$12,177
200810-17.48%-19.86%-20.83%-25.58%-31.73%-1.86%-1.95%-16.14%-16.93%$9,615-13.58%$9,680-16.25%$10,198
200811-8.01%-11.80%-6.37%-9.75%-22.72%14.34%3.35%12.57%-3.55%$9,273-1.37%$9,548-1.88%$10,007
2008121.78%6.57%8.88%10.35%16.67%13.64%13.80%7.73%9.93%$10,19410.27%$10,5297.92%$10,799
20091-8.05%-13.94%-13.73%-9.29%-17.53%-13.07%-1.80%5.54%-8.98%$9,278-7.83%$9,704-9.02%$9,825
20092-10.53%-13.03%-10.39%-6.27%-20.53%-1.54%-5.20%1.45%-8.25%$8,512-7.35%$8,991-7.74%$9,064
200938.26%7.58%8.39%16.86%3.61%4.04%0.47%-2.54%5.84%$9,0094.86%$9,4284.56%$9,478
2009410.99%18.89%11.52%15.56%30.68%-6.95%2.78%-3.33%10.02%$9,9117.69%$10,1549.55%$10,383
200955.46%0.67%13.19%15.94%2.62%-3.69%2.32%10.23%5.84%$10,4914.85%$10,6462.37%$10,629
200960.36%1.52%-1.43%-2.25%-3.23%0.76%2.89%-5.22%-0.82%$10,404-0.09%$10,637-0.25%$10,602
200977.74%11.00%10.04%11.01%10.77%0.58%4.63%2.38%7.27%$11,1606.48%$11,3257.32%$11,378
200983.71%3.48%4.50%-1.31%14.32%2.24%1.31%0.05%3.54%$11,5553.00%$11,6662.45%$11,657
200994.14%4.21%3.80%10.20%6.63%2.46%1.76%5.84%4.88%$12,1194.14%$12,1494.35%$12,164
200910-2.63%-6.07%-2.52%-3.44%-4.46%-2.62%-0.49%3.72%-2.32%$11,838-1.98%$11,908-3.14%$11,781
2009115.69%2.90%3.92%7.85%6.57%1.21%1.95%12.79%5.36%$12,4734.61%$12,4575.08%$12,380
2009122.86%8.10%0.70%3.27%7.37%-6.34%-2.07%-7.20%0.84%$12,577-0.04%$12,4532.17%$12,648
20101-3.57%-2.54%-5.07%-7.76%-5.52%2.69%1.25%-1.26%-2.72%$12,235-1.78%$12,231-1.44%$12,466
201023.44%4.76%0.27%1.78%5.58%-0.34%0.51%3.27%2.41%$12,5301.97%$12,4723.63%$12,919
201036.40%7.80%6.39%8.11%10.18%-2.06%0.65%-0.44%4.63%$13,1103.62%$12,9234.29%$13,474
201042.18%6.63%-2.80%-0.17%7.15%3.32%1.91%5.88%3.01%$13,5052.77%$13,2815.95%$14,276
20105-7.88%-8.54%-11.19%-9.39%-5.33%5.11%-1.31%3.05%-4.44%$12,906-3.59%$12,804-3.64%$13,756
20106-5.83%-8.27%-2.07%-1.40%-5.19%5.80%3.28%2.36%-1.42%$12,723-0.45%$12,746-3.55%$13,267
201077.02%6.71%11.61%10.93%9.59%-0.95%2.11%-5.09%5.24%$13,3904.39%$13,3062.66%$13,620
20108-4.71%-7.91%-3.80%-3.24%-1.28%8.40%2.86%5.71%-0.50%$13,3230.31%$13,347-2.12%$13,332
201099.45%10.93%9.97%11.76%4.45%-2.51%0.46%4.78%6.16%$14,1444.99%$14,0127.40%$14,319
2010104.03%4.04%3.81%3.02%4.74%-4.47%-0.26%3.68%2.32%$14,4721.65%$14,2432.68%$14,702
2010110.51%2.47%-4.82%-2.91%-1.85%-1.69%-1.62%2.11%-0.97%$14,331-1.02%$14,0981.76%$14,961
2010126.96%8.97%8.30%7.27%4.54%-3.68%-0.75%2.44%4.25%$14,9413.20%$14,5495.46%$15,778
201112.05%-0.24%2.10%-3.84%3.25%-3.08%0.04%-6.38%-0.76%$14,827-0.67%$14,451-2.18%$15,435
201123.70%4.21%3.55%-0.04%4.71%1.65%1.08%6.00%3.11%$15,2872.78%$14,8534.27%$16,094
201130.42%2.21%-2.39%6.29%-1.62%0.03%-0.54%1.60%0.75%$15,4020.45%$14,9201.73%$16,372
201142.90%1.06%5.63%2.73%5.75%2.34%2.50%8.94%3.98%$16,0153.66%$15,4653.19%$16,895
20115-1.06%-1.77%-2.21%-2.94%1.37%3.42%1.27%-1.79%-0.46%$15,941-0.07%$15,455-1.00%$16,727
20116-1.79%-1.59%-1.19%-0.93%-3.30%-2.33%-0.80%-2.43%-1.80%$15,655-1.64%$15,201-1.91%$16,408
20117-2.27%-2.77%-2.38%-1.03%1.56%4.42%2.43%8.42%1.05%$15,8191.32%$15,4011.06%$16,581
20118-6.09%-7.98%-8.75%-9.25%-5.62%9.66%0.34%12.27%-1.93%$15,514-1.04%$15,241-0.35%$16,524
20119-7.57%-10.57%-10.81%-17.89%-10.85%13.20%0.35%-11.06%-6.90%$14,443-4.75%$14,517-7.13%$15,345
20111011.37%15.34%9.63%16.27%14.29%-3.84%2.51%5.87%8.93%$15,7337.25%$15,57010.14%$16,901
201111-0.37%0.63%-2.18%-1.96%-3.80%1.98%-3.16%1.67%-0.90%$15,592-1.04%$15,4081.09%$17,085
2011120.98%2.02%-2.21%-4.30%4.85%3.44%3.49%-10.66%-0.30%$15,5450.40%$15,470-0.89%$16,932
201215.07%7.90%5.27%10.99%6.38%-0.33%2.14%11.40%6.10%$16,4935.11%$16,2627.53%$18,207
201224.22%1.71%4.83%5.27%-1.15%-2.59%1.63%-2.96%1.37%$16,7191.33%$16,478-0.08%$18,192
201233.06%2.89%0.42%-3.11%5.19%-4.23%-1.42%-1.32%0.18%$16,750-0.21%$16,4440.79%$18,335
20124-0.64%-1.91%-2.08%-1.70%2.86%4.83%1.08%-0.15%0.29%$16,7980.53%$16,532-0.47%$18,249
20125-6.23%-7.18%-11.14%-10.71%-4.51%9.03%0.76%-6.34%-4.54%$16,036-3.16%$16,009-4.54%$17,420
201264.05%4.54%7.11%5.08%5.52%-1.68%0.87%2.35%3.48%$16,5942.84%$16,4633.07%$17,955
201270.88%-0.69%0.08%-0.03%2.00%3.82%3.48%0.84%1.30%$16,8091.72%$16,7470.36%$18,020
201282.70%4.08%3.20%0.41%-0.01%-1.32%-0.05%4.94%1.74%$17,1021.45%$16,9893.48%$18,647
201292.49%3.14%2.71%5.22%-1.86%-2.53%1.10%4.67%1.87%$17,4221.62%$17,2642.67%$19,144
201210-1.81%-1.96%1.09%-0.44%-0.91%-0.48%1.35%-2.94%-0.76%$17,289-0.45%$17,186-1.98%$18,765
2012110.77%1.65%2.78%1.56%-0.26%1.16%-0.72%-0.47%0.81%$17,4290.60%$17,2901.06%$18,963
2012121.29%3.55%4.37%6.80%3.72%-2.49%-0.33%-2.43%1.81%$17,7441.17%$17,4931.17%$19,186
201315.42%5.35%3.73%-0.29%3.74%-3.19%-1.30%-0.51%1.62%$18,0311.09%$17,6832.63%$19,690
201321.28%1.63%-1.29%-2.28%1.22%1.24%1.08%-5.09%-0.28%$17,9810.03%$17,688-0.08%$19,674
201333.95%4.11%1.31%-1.02%2.87%-0.42%-0.05%0.95%1.46%$18,2441.24%$17,9072.65%$20,196
201341.61%0.12%5.02%1.22%6.73%4.68%2.17%-7.56%1.75%$18,5631.84%$18,235-1.09%$19,976
201352.44%4.29%-3.02%-4.83%-5.98%-6.76%-3.22%-6.20%-2.91%$18,023-2.86%$17,7130.05%$19,986
20136-1.43%-0.14%-2.70%-5.35%-1.98%-3.27%-3.27%-11.06%-3.65%$17,366-3.52%$17,090-3.30%$19,327
201375.75%6.56%5.32%1.32%0.90%-2.26%1.11%7.43%3.27%$17,9332.89%$17,5835.45%$20,381
20138-3.03%-3.41%-1.96%-2.54%-6.98%-1.34%-1.00%5.20%-1.88%$17,596-1.62%$17,298-0.98%$20,181
201393.90%6.59%7.82%7.21%3.49%0.66%0.74%-4.78%3.20%$18,1592.68%$17,7612.90%$20,767
2013104.27%3.48%3.26%4.17%4.52%1.43%1.81%-0.34%2.82%$18,6722.59%$18,2212.23%$21,231
2013112.70%4.25%0.55%-0.26%-5.25%-2.70%-0.14%-5.51%-0.79%$18,524-0.58%$18,1160.81%$21,403
2013122.73%1.29%2.16%-0.42%0.10%-1.87%0.22%-3.79%0.05%$18,5330.09%$18,132-0.43%$21,310
20141-3.17%-3.51%-5.20%-8.64%4.28%6.30%1.88%3.42%-0.58%$18,4260.02%$18,136-0.34%$21,238
201424.87%4.63%6.13%3.38%5.07%0.52%1.14%6.27%4.00%$19,1633.45%$18,7614.42%$22,177
201430.51%1.34%-0.46%3.88%0.49%0.73%-0.03%-3.14%0.41%$19,2420.29%$18,8150.15%$22,209
201440.06%-2.29%1.67%0.78%3.29%2.10%1.33%0.49%0.93%$19,4210.97%$18,997-0.95%$21,998
201452.10%0.62%1.60%2.95%2.40%2.95%1.51%-3.05%1.38%$19,6901.43%$19,2690.07%$22,013
201462.62%3.85%0.92%2.40%1.13%-0.25%0.01%6.32%2.13%$20,1091.73%$19,6043.84%$22,859
20147-1.99%-5.07%-2.60%1.36%0.08%0.67%-0.32%-3.63%-1.44%$19,819-1.29%$19,351-3.86%$21,977
201484.15%4.46%0.18%2.83%3.04%4.72%2.00%0.38%2.72%$20,3592.70%$19,8743.50%$22,746
20149-2.10%-5.94%-3.88%-7.77%-6.04%-2.11%-1.68%-6.18%-4.46%$19,450-3.78%$19,124-5.43%$21,511
2014102.75%7.13%-0.27%1.42%9.94%2.81%1.23%-3.05%2.74%$19,9842.36%$19,5743.98%$22,366
2014112.48%0.48%0.06%-1.54%2.00%2.97%0.91%-0.49%0.86%$20,1561.01%$19,7720.61%$22,504
201412-0.04%2.56%-4.00%-3.99%1.88%3.25%-0.02%1.31%0.12%$20,1800.23%$19,8172.36%$23,034
20151-2.74%-5.32%0.62%-0.69%6.85%9.82%3.75%8.69%2.62%$20,7092.90%$20,3910.40%$23,126
201525.74%5.86%6.34%4.41%-3.67%-6.14%-1.42%-5.91%0.65%$20,8440.26%$20,4441.16%$23,395
20153-1.16%1.03%-1.43%-1.50%1.74%1.10%0.20%-2.15%-0.27%$20,788-0.20%$20,4030.26%$23,455
201540.62%-1.82%3.65%6.85%-5.85%-3.43%-1.19%-0.17%-0.17%$20,753-0.41%$20,319-1.66%$23,066
201551.30%0.75%0.20%-4.10%-0.30%-2.37%-1.12%0.56%-0.64%$20,621-0.66%$20,1840.24%$23,121
20156-1.67%0.42%-3.12%-2.93%-4.68%-4.07%-1.88%-1.52%-2.43%$20,119-2.34%$19,713-0.73%$22,952
201571.70%-2.70%2.03%-6.31%5.77%4.55%0.83%-6.62%-0.09%$20,1010.28%$19,767-2.58%$22,360
20158-6.09%-4.62%-7.43%-8.84%-6.29%-0.69%-0.83%3.71%-3.88%$19,320-3.22%$19,131-1.98%$21,918
20159-2.92%-3.77%-4.42%-3.13%3.05%1.97%1.19%-1.80%-1.23%$19,082-0.86%$18,967-2.43%$21,385
2015107.91%6.57%6.61%6.38%5.76%-0.41%0.57%2.28%4.46%$19,9333.71%$19,6714.47%$22,340
2015110.60%2.47%-0.75%-2.52%-0.63%-0.87%-0.15%-6.75%-1.08%$19,719-0.87%$19,500-0.30%$22,273
201512-2.13%-5.08%-2.34%-3.83%1.82%-0.30%-1.08%-0.45%-1.67%$19,389-1.58%$19,192-3.23%$21,555
20161-5.72%-5.85%-5.52%-5.03%-3.44%5.57%0.12%5.41%-1.81%$19,038-1.25%$18,953-1.37%$21,260
20162-0.01%2.08%-3.33%-0.82%-0.36%3.09%1.05%10.93%1.58%$19,3391.58%$19,2534.41%$22,198
201637.11%9.41%6.58%12.96%10.48%-0.09%3.62%-0.84%6.15%$20,5295.32%$20,2765.47%$23,411
201640.66%2.13%2.22%0.41%-2.35%-0.74%1.55%5.11%1.12%$20,7591.20%$20,5202.43%$23,981
201651.73%0.44%-0.09%-3.69%2.25%0.81%-0.51%-6.14%-0.65%$20,625-0.51%$20,415-1.12%$23,711
201660.27%0.83%-2.42%4.56%6.92%6.93%3.09%8.97%3.65%$21,3773.48%$21,1253.75%$24,600
201673.98%5.06%3.98%5.38%4.26%2.10%1.29%1.98%3.50%$22,1263.07%$21,7743.86%$25,549
201680.21%1.13%0.53%0.88%-3.76%-1.01%0.18%-3.26%-0.64%$21,985-0.46%$21,674-0.27%$25,481
201690.21%0.87%1.34%2.52%-1.82%-1.51%-0.32%0.69%0.25%$22,0390.10%$21,6960.47%$25,600
201610-2.19%-3.74%-2.22%-0.83%-5.74%-4.38%-1.53%-2.94%-2.95%$21,390-2.74%$21,102-3.64%$24,668
2016114.49%13.34%-1.78%-4.42%-1.68%-8.21%-3.17%-8.36%-1.22%$21,128-1.58%$20,7684.77%$25,845
2016121.98%3.20%2.71%-0.25%4.82%-0.46%0.84%-1.91%1.37%$21,4171.19%$21,0141.39%$26,205
Portfolio return and risk metrics
MetricEqual WeightInverse Volatility WeightOptimized Portfolio
(*) Beta and market correlation are calculated against the US stock market.
Mean Return (monthly)0.64%0.61%0.80%
Mean Return (annualized)8.00%7.57%10.00%
Compound Return (monthly)0.58%0.56%0.73%
Compound Return (annualized)7.17%6.98%9.15%
Volatility (monthly)3.56%3.00%3.58%
Volatility (annualized)12.54%10.50%12.56%
Max. Drawdown-36.98%-30.00%-28.81%
Market Correlation0.870.830.84
Beta(*)0.710.570.69
Alpha (annualized)1.50%2.31%3.56%
R275.83%69.24%70.02%
Sharpe Ratio0.540.600.68
Sortino Ratio0.800.911.06
Treynor Ratio (%)9.4010.9812.43
Diversification Ratio1.441.521.50
Skewness-0.80-0.69-0.72
Excess Kurtosis4.284.073.56
Historical Value-at-Risk (95%)-4.67%-3.84%-4.14%
Delta Normal Value-at-Risk (95%)-5.86%-4.93%-5.89%
Conditional Value-at-Risk (95%)-8.61%-7.29%-8.35%
Positive Periods76 out of 132 (57.58%)81 out of 132 (61.36%)80 out of 132 (60.61%)
Gain/Loss Ratio1.221.121.19

Drawdowns for Equal Weight

Drawdowns for Equal Weight
RankDrawdown StartDrawdown EndDrawdown LengthRecovery ByRecovery TimeDrawdown
1Nov 2007Feb 20091 year 4 monthsSep 20102 years 11 months-36.98%
2May 2011Sep 20115 monthsJan 20129 months-9.81%
3Mar 2015Jan 201611 monthsJun 20161 year 4 months-8.66%
4May 2013Jun 20132 monthsOct 20136 months-6.45%
5May 2012May 20121 monthJul 20123 months-4.54%
6Aug 2016Nov 20164 months-4.51%
7Sep 2014Sep 20141 monthJan 20155 months-4.46%
8Jun 2007Jul 20072 monthsSep 20074 months-3.49%
9May 2006May 20061 monthAug 20064 months-3.39%
10Jul 2014Jul 20141 monthAug 20142 months-1.44%
11Nov 2013Jan 20143 monthsFeb 20144 months-1.32%
12Nov 2010Nov 20101 monthDec 20102 months-0.97%
13Jan 2011Jan 20111 monthFeb 20112 months-0.76%
14Oct 2012Oct 20121 monthNov 20122 months-0.76%
15Feb 2013Feb 20131 monthMar 20132 months-0.28%
16Feb 2006Feb 20061 monthMar 20062 months-0.19%
17Feb 2007Feb 20071 monthMar 20072 months-0.08%

Drawdowns for Inverse Volatility Weight

Drawdowns for Inverse Volatility Weight
RankDrawdown StartDrawdown EndDrawdown LengthRecovery ByRecovery TimeDrawdown
1Nov 2007Feb 20091 year 4 monthsMar 20102 years 5 months-30.00%
2Mar 2015Jan 201611 monthsApr 20161 year 2 months-7.29%
3May 2013Jun 20132 monthsFeb 201410 months-6.28%
4May 2011Sep 20115 monthsOct 20116 months-6.13%
5Aug 2016Nov 20164 months-4.62%
6May 2010Jun 20102 monthsJul 20103 months-4.03%
7Sep 2014Sep 20141 monthJan 20155 months-3.78%
8May 2012May 20121 monthJul 20123 months-3.16%
9Jun 2007Jul 20072 monthsSep 20074 months-2.86%
10May 2006May 20061 monthAug 20064 months-2.64%
11Jul 2014Jul 20141 monthAug 20142 months-1.29%
12Nov 2011Nov 20111 monthJan 20123 months-1.04%
13Nov 2010Nov 20101 monthDec 20102 months-1.02%
14Jan 2011Jan 20111 monthFeb 20112 months-0.67%
15May 2016May 20161 monthJun 20162 months-0.51%
16Oct 2012Oct 20121 monthNov 20122 months-0.45%
17Mar 2012Mar 20121 monthApr 20122 months-0.21%

Drawdowns for Optimized Portfolio

Drawdowns for Optimized Portfolio
RankDrawdown StartDrawdown EndDrawdown LengthRecovery ByRecovery TimeDrawdown
1Nov 2007Feb 20091 year 4 monthsFeb 20102 years 4 months-28.81%
2Apr 2015Jan 201610 monthsApr 20161 year 1 month-9.36%
3May 2011Sep 20115 monthsOct 20116 months-9.17%
4May 2010Jun 20102 monthsSep 20105 months-7.06%
5Jul 2014Sep 20143 monthsDec 20146 months-5.89%
6Apr 2012May 20122 monthsAug 20125 months-4.99%
7May 2006Jul 20063 monthsOct 20066 months-4.76%
8Jun 2007Jul 20072 monthsOct 20075 months-4.63%
9Apr 2013Jun 20133 monthsJul 20134 months-4.30%
10Oct 2016Oct 20161 monthNov 20162 months-3.64%
11Jan 2011Jan 20111 monthFeb 20112 months-2.18%
12Oct 2012Oct 20121 monthDec 20123 months-1.98%
13May 2016May 20161 monthJun 20162 months-1.12%
14Aug 2013Aug 20131 monthSep 20132 months-0.98%
15Apr 2014Apr 20141 monthJun 20143 months-0.95%
16Dec 2011Dec 20111 monthJan 20122 months-0.89%
17Dec 2013Jan 20142 monthsFeb 20143 months-0.77%
18Dec 2006Dec 20061 monthJan 20072 months-0.66%
19Aug 2016Aug 20161 monthSep 20162 months-0.27%
20Feb 2012Feb 20121 monthMar 20122 months-0.08%
21Feb 2013Feb 20131 monthMar 20132 months-0.08%

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdDevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
VTIVanguard Total Stock Market ETF7.97%15.38%33.45%-36.98%-50.84%0.510.741.00
IJSiShares S&P SmallCap 600 Value ETF9.02%19.73%39.34%-29.39%-54.13%0.490.730.92
EFAiShares MSCI EAFE ETF2.66%18.81%26.95%-41.04%-57.38%0.180.250.90
EEMiShares MSCI Emerging Index Fund3.52%24.01%68.93%-48.88%-60.44%0.220.330.81
VNQVanguard REIT ETF7.66%25.70%35.30%-37.00%-68.30%0.380.550.75
TLTiShares 20+ Year Treasury Bond ETF6.04%13.84%33.96%-21.80%-21.80%0.410.71-0.32
LQDiShares iBoxx $ Investment Grade Corporate Bond ETF5.31%7.69%10.24%-2.00%-15.11%0.570.930.28
GLDSPDR Gold Trust7.09%19.22%30.45%-28.33%-42.91%0.400.630.05

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIIJSEFAEEMVNQTLTLQDGLDEqual WeightInverse Volatility WeightOptimized Portfolio
VTIVanguard Total Stock Market ETF-0.920.900.810.75-0.330.280.050.870.830.84
IJSiShares S&P SmallCap 600 Value ETF0.92-0.780.720.77-0.340.210.010.820.770.90
EFAiShares MSCI EAFE ETF0.900.78-0.880.70-0.240.390.150.890.870.76
EEMiShares MSCI Emerging Index Fund0.810.720.88-0.63-0.240.350.290.880.840.76
VNQVanguard REIT ETF0.750.770.700.63--0.010.430.100.850.830.76
TLTiShares 20+ Year Treasury Bond ETF-0.33-0.34-0.24-0.24-0.01-0.500.19-0.000.10-0.08
LQDiShares iBoxx $ Investment Grade Corporate Bond ETF0.280.210.390.350.430.50-0.240.540.640.37
GLDSPDR Gold Trust0.050.010.150.290.100.190.24-0.370.390.42

Annual Asset Returns