Efficient Frontier

This online tool calculates and plots the efficient frontier for the specified asset classes, mutual funds, ETFs or stocks for the specified time period. The efficient frontier shows the set of optimal portfolios provide the best possible expected return for the level of risk in the portfolio. You can also use the efficient frontier forecast tool to specify expected future returns for the assets. The required inputs for the efficient frontier include the portfolio assets. You can optionally specify the asset allocation and allocation constraints for the portfolio assets. If an asset allocation is specified, the provided portfolio will be rendered on the efficient frontier chart.

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Asset 4
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Asset 5
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Asset 6
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Asset 7
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Asset 8
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Asset 9
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Asset 10
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Efficient Frontier Results (Jan 1978 - Dec 2016)

Portfolio Allocations

Tangency Portfolio
Asset Allocation
Save portfolio »
US Stock Market 42.42%
Long Term Treasury 57.58%

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe Ratio
1US Stock Market12.71%15.31%0.830
2Long Term Treasury9.22%11.11%0.830

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
Based on monthly returns from Jan 1978 to Dec 2016
US Stock Market1.000.06
Long Term Treasury0.061.00
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected ReturnStandard DeviationSharpe Ratio*
*Ex ante Sharpe Ratio calculated directly from the expected return and standard deviation
10.00%100.00%9.22%11.11%0.830
21.01%98.99%9.26%11.01%0.841
32.02%97.98%9.29%10.91%0.852
43.03%96.97%9.33%10.82%0.862
54.04%95.96%9.36%10.72%0.873
65.05%94.95%9.40%10.63%0.884
76.06%93.94%9.43%10.54%0.895
87.07%92.93%9.47%10.45%0.906
98.08%91.92%9.50%10.36%0.917
109.09%90.91%9.54%10.28%0.927
1110.10%89.90%9.57%10.20%0.938
1211.11%88.89%9.61%10.12%0.949
1312.12%87.88%9.64%10.05%0.959
1413.13%86.87%9.67%9.98%0.970
1514.14%85.86%9.71%9.91%0.980
1615.15%84.85%9.74%9.85%0.990
1716.16%83.84%9.78%9.78%1.000
1817.17%82.83%9.81%9.72%1.009
1918.18%81.82%9.85%9.67%1.019
2019.19%80.81%9.88%9.62%1.028
2120.20%79.80%9.92%9.57%1.037
2221.21%78.79%9.95%9.52%1.046
2322.22%77.78%9.99%9.48%1.054
2423.23%76.77%10.02%9.44%1.062
2524.24%75.76%10.06%9.40%1.070
2625.25%74.75%10.09%9.37%1.077
2726.26%73.74%10.13%9.34%1.084
2827.27%72.73%10.16%9.32%1.091
2928.28%71.72%10.20%9.30%1.097
3029.29%70.71%10.23%9.28%1.103
3130.30%69.70%10.27%9.26%1.108
3231.31%68.69%10.30%9.25%1.113
3332.32%67.68%10.34%9.25%1.118
3433.33%66.67%10.37%9.25%1.122
3534.34%65.66%10.41%9.25%1.126
3635.35%64.65%10.44%9.25%1.129
3736.36%63.64%10.48%9.26%1.132
3837.37%62.63%10.51%9.27%1.134
3938.38%61.62%10.55%9.29%1.136
4039.39%60.61%10.58%9.31%1.137
4140.40%59.60%10.62%9.33%1.138
4241.41%58.59%10.65%9.36%1.139
4342.42%57.58%10.69%9.39%1.139
4443.43%56.57%10.72%9.42%1.138
4544.44%55.56%10.76%9.46%1.138
4645.45%54.55%10.79%9.50%1.136
4746.46%53.54%10.83%9.54%1.135
4847.47%52.53%10.86%9.59%1.133
4948.48%51.52%10.90%9.64%1.130
5049.49%50.51%10.93%9.70%1.128
5150.51%49.49%10.97%9.75%1.125
5251.52%48.48%11.01%9.81%1.121
5352.53%47.47%11.04%9.88%1.118
5453.54%46.46%11.08%9.94%1.114
5554.55%45.45%11.11%10.01%1.109
5655.56%44.44%11.15%10.09%1.105
5756.57%43.43%11.18%10.16%1.100
5857.58%42.42%11.22%10.24%1.095
5958.59%41.41%11.25%10.32%1.090
6059.60%40.40%11.29%10.41%1.085
6160.61%39.39%11.32%10.49%1.079
6261.62%38.38%11.36%10.58%1.073
6362.63%37.37%11.39%10.67%1.067
6463.64%36.36%11.43%10.77%1.061
6564.65%35.35%11.46%10.86%1.055
6665.66%34.34%11.50%10.96%1.049
6766.67%33.33%11.53%11.06%1.043
6867.68%32.32%11.57%11.17%1.036
6968.69%31.31%11.61%11.27%1.030
7069.70%30.30%11.64%11.38%1.023
7170.71%29.29%11.68%11.49%1.016
7271.72%28.28%11.71%11.60%1.010
7372.73%27.27%11.75%11.71%1.003
7473.74%26.26%11.78%11.83%0.996
7574.75%25.25%11.82%11.94%0.990
7675.76%24.24%11.85%12.06%0.983
7776.77%23.23%11.89%12.18%0.976
7877.78%22.22%11.92%12.30%0.969
7978.79%21.21%11.96%12.43%0.962
8079.80%20.20%12.00%12.55%0.956
8180.81%19.19%12.03%12.68%0.949
8281.82%18.18%12.07%12.80%0.942
8382.83%17.17%12.10%12.93%0.936
8483.84%16.16%12.14%13.06%0.929
8584.85%15.15%12.17%13.20%0.922
8685.86%14.14%12.21%13.33%0.916
8786.87%13.13%12.24%13.46%0.909
8887.88%12.12%12.28%13.60%0.903
8988.89%11.11%12.31%13.74%0.897
9089.90%10.10%12.35%13.87%0.890
9190.91%9.09%12.39%14.01%0.884
9291.92%8.08%12.42%14.15%0.878
9392.93%7.07%12.46%14.29%0.872
9493.94%6.06%12.49%14.44%0.865
9594.95%5.05%12.53%14.58%0.859
9695.96%4.04%12.56%14.72%0.853
9796.97%3.03%12.60%14.87%0.848
9897.98%2.02%12.64%15.01%0.842
9998.99%1.01%12.67%15.16%0.836
100100.00%0.00%12.71%15.31%0.830
Notes on results:
  • Standard deviation and expected return in the efficient frontier are annualized from the monthly returns