Efficient Frontier

This tool uses mean-variance optimization to calculate and plot 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 that provide the best possible expected return for the level of risk in the portfolio. Monte Carlo method can be used for more robust optimization that resamples the optimization inputs in order to mitigate the impact of input estimation errors and improve diversification. 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 Groups
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Efficient Frontier Results (Jan 1978 - Jul 2019)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 49.07%
Long Term Treasury 50.93%
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Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1US Stock Market11.50%12.80%15.16%0.5490.00%100.00%
2Long Term Treasury8.45%9.09%10.97%0.4210.00%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 (4.47% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.05
Long Term Treasury0.051.00
Based on monthly returns from Jan 1978 to Jul 2019
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
133.65%66.35%10.32%9.08%0.645
234.32%65.68%10.35%9.08%0.647
334.99%65.01%10.37%9.08%0.650
435.66%64.34%10.40%9.09%0.652
536.33%63.67%10.42%9.09%0.655
637.01%62.99%10.45%9.10%0.657
737.68%62.32%10.47%9.11%0.659
838.35%61.65%10.50%9.12%0.661
939.02%60.98%10.52%9.13%0.663
1039.69%60.31%10.55%9.15%0.664
1140.36%59.64%10.57%9.16%0.666
1241.03%58.97%10.60%9.18%0.667
1341.70%58.30%10.62%9.20%0.669
1442.37%57.63%10.65%9.22%0.670
1543.04%56.96%10.67%9.24%0.671
1643.71%56.29%10.69%9.26%0.672
1744.38%55.62%10.72%9.29%0.673
1845.05%54.95%10.74%9.32%0.674
1945.72%54.28%10.77%9.34%0.674
2046.39%53.61%10.79%9.37%0.675
2147.06%52.94%10.82%9.40%0.675
2247.73%52.27%10.84%9.44%0.676
2348.40%51.60%10.87%9.47%0.676
2449.07%50.93%10.89%9.51%0.676
2549.74%50.26%10.92%9.54%0.676
2650.41%49.59%10.94%9.58%0.676
2751.08%48.92%10.97%9.62%0.675
2851.75%48.25%10.99%9.66%0.675
2952.42%47.58%11.02%9.71%0.675
3053.09%46.91%11.04%9.75%0.674
3153.76%46.24%11.07%9.80%0.674
3254.43%45.57%11.09%9.84%0.673
3355.10%44.90%11.12%9.89%0.672
3455.77%44.23%11.14%9.94%0.671
3556.44%43.56%11.17%9.99%0.670
3657.11%42.89%11.19%10.04%0.669
3757.78%42.22%11.22%10.10%0.668
3858.45%41.55%11.24%10.15%0.667
3959.12%40.88%11.27%10.21%0.666
4059.79%40.21%11.29%10.26%0.665
4160.46%39.54%11.32%10.32%0.664
4261.13%38.87%11.34%10.38%0.662
4361.80%38.20%11.37%10.44%0.661
4462.47%37.53%11.39%10.50%0.659
4563.14%36.86%11.42%10.56%0.658
4663.81%36.19%11.44%10.63%0.656
4764.48%35.52%11.47%10.69%0.655
4865.15%34.85%11.49%10.76%0.653
4965.82%34.18%11.52%10.82%0.651
5066.49%33.51%11.54%10.89%0.650
5167.16%32.84%11.57%10.96%0.648
5267.83%32.17%11.59%11.03%0.646
5368.50%31.50%11.62%11.10%0.644
5469.17%30.83%11.64%11.17%0.642
5569.84%30.16%11.67%11.24%0.640
5670.51%29.49%11.69%11.31%0.639
5771.18%28.82%11.72%11.39%0.637
5871.85%28.15%11.74%11.46%0.635
5972.52%27.48%11.77%11.54%0.633
6073.19%26.81%11.79%11.61%0.631
6173.86%26.14%11.82%11.69%0.629
6274.53%25.47%11.84%11.77%0.627
6375.20%24.80%11.87%11.84%0.625
6475.87%24.13%11.89%11.92%0.623
6576.54%23.46%11.92%12.00%0.621
6677.21%22.79%11.94%12.08%0.619
6777.88%22.12%11.97%12.17%0.616
6878.55%21.45%11.99%12.25%0.614
6979.22%20.78%12.02%12.33%0.612
7079.89%20.11%12.04%12.41%0.610
7180.57%19.43%12.07%12.50%0.608
7281.24%18.76%12.09%12.58%0.606
7381.91%18.09%12.12%12.67%0.604
7482.58%17.42%12.14%12.75%0.602
7583.25%16.75%12.17%12.84%0.600
7683.92%16.08%12.20%12.93%0.598
7784.59%15.41%12.22%13.01%0.596
7885.26%14.74%12.25%13.10%0.593
7985.93%14.07%12.27%13.19%0.591
8086.60%13.40%12.30%13.28%0.589
8187.27%12.73%12.32%13.37%0.587
8287.94%12.06%12.35%13.46%0.585
8388.61%11.39%12.37%13.55%0.583
8489.28%10.72%12.40%13.64%0.581
8589.95%10.05%12.42%13.73%0.579
8690.62%9.38%12.45%13.83%0.577
8791.29%8.71%12.47%13.92%0.575
8891.96%8.04%12.50%14.01%0.573
8992.63%7.37%12.52%14.11%0.571
9093.30%6.70%12.55%14.20%0.569
9193.97%6.03%12.57%14.30%0.567
9294.64%5.36%12.60%14.39%0.565
9395.31%4.69%12.62%14.49%0.563
9495.98%4.02%12.65%14.58%0.561
9596.65%3.35%12.67%14.68%0.559
9697.32%2.68%12.70%14.77%0.557
9797.99%2.01%12.72%14.87%0.555
9898.66%1.34%12.75%14.97%0.553
9999.33%0.67%12.78%15.07%0.551
100100.00%0.00%12.80%15.16%0.549
*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 (4.47% annualized).
Notes on results:
  • Past performance is not a guarantee of future returns.
  • The efficient frontier is based on the monthly returns, volatilities, and correlations of the specified assets.
  • The displayed standard deviation and expected return in the efficient frontier are annualized from the monthly returns
  • Ex-ante Sharpe Ratio for the efficient frontier data points is calculated using historical 1-month treasury bill returns as the risk free rate