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 1986 - Sep 2021)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 9.96%
Short Term Treasury 90.04%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio5.31%2.28%0.93

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market12.27%15.34%0.5590.00%100.00%
2Short Term Treasury4.57%2.07%0.6820.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

Asset Correlations
AssetUS Stock MarketShort Term Treasury
US Stock Market1.00-0.11
Short Term Treasury-0.111.00
Based on monthly returns from Jan 1986 to Sep 2021
Efficient Frontier Points
#US Stock MarketShort Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
13.10%96.90%4.80%2.02%0.812
24.08%95.92%4.87%2.02%0.844
35.06%94.94%4.94%2.04%0.871
46.04%93.96%5.02%2.07%0.893
57.02%92.98%5.09%2.11%0.910
68.00%92.00%5.16%2.16%0.921
78.98%91.02%5.24%2.22%0.928
89.96%90.04%5.31%2.28%0.931
910.93%89.07%5.38%2.36%0.931
1011.91%88.09%5.46%2.44%0.928
1112.89%87.11%5.53%2.53%0.922
1213.87%86.13%5.60%2.63%0.915
1314.85%85.15%5.68%2.73%0.907
1415.83%84.17%5.75%2.84%0.898
1516.81%83.19%5.83%2.95%0.888
1617.79%82.21%5.90%3.06%0.878
1718.76%81.24%5.97%3.18%0.868
1819.74%80.26%6.05%3.30%0.857
1920.72%79.28%6.12%3.42%0.847
2021.70%78.30%6.20%3.55%0.837
2122.68%77.32%6.27%3.67%0.827
2223.66%76.34%6.34%3.80%0.817
2324.64%75.36%6.42%3.93%0.808
2425.62%74.38%6.49%4.07%0.799
2526.59%73.41%6.57%4.20%0.790
2627.57%72.43%6.64%4.34%0.781
2728.55%71.45%6.71%4.47%0.773
2829.53%70.47%6.79%4.61%0.765
2930.51%69.49%6.86%4.75%0.758
3031.49%68.51%6.94%4.89%0.750
3132.47%67.53%7.01%5.03%0.743
3233.45%66.55%7.09%5.17%0.737
3334.42%65.58%7.16%5.31%0.730
3435.40%64.60%7.24%5.45%0.724
3536.38%63.62%7.31%5.60%0.718
3637.36%62.64%7.39%5.74%0.712
3738.34%61.66%7.46%5.89%0.707
3839.32%60.68%7.54%6.03%0.701
3940.30%59.70%7.61%6.17%0.696
4041.28%58.72%7.69%6.32%0.691
4142.25%57.75%7.76%6.47%0.687
4243.23%56.77%7.84%6.61%0.682
4344.21%55.79%7.91%6.76%0.678
4445.19%54.81%7.99%6.91%0.673
4546.17%53.83%8.06%7.05%0.669
4647.15%52.85%8.14%7.20%0.665
4748.13%51.87%8.21%7.35%0.661
4849.11%50.89%8.29%7.50%0.658
4950.08%49.92%8.36%7.64%0.654
5051.06%48.94%8.44%7.79%0.651
5152.04%47.96%8.51%7.94%0.647
5253.02%46.98%8.59%8.09%0.644
5354.00%46.00%8.66%8.24%0.641
5454.98%45.02%8.74%8.39%0.638
5555.96%44.04%8.82%8.54%0.635
5656.94%43.06%8.89%8.68%0.632
5757.91%42.09%8.97%8.83%0.629
5858.89%41.11%9.04%8.98%0.627
5959.87%40.13%9.12%9.13%0.624
6060.85%39.15%9.20%9.28%0.622
6161.83%38.17%9.27%9.43%0.619
6262.81%37.19%9.35%9.58%0.617
6363.79%36.21%9.42%9.73%0.614
6464.77%35.23%9.50%9.88%0.612
6565.74%34.26%9.58%10.03%0.610
6666.72%33.28%9.65%10.19%0.608
6767.70%32.30%9.73%10.34%0.606
6868.68%31.32%9.80%10.49%0.604
6969.66%30.34%9.88%10.64%0.602
7070.64%29.36%9.96%10.79%0.600
7171.62%28.38%10.03%10.94%0.598
7272.60%27.40%10.11%11.09%0.596
7373.57%26.43%10.19%11.24%0.594
7474.55%25.45%10.26%11.39%0.593
7575.53%24.47%10.34%11.54%0.591
7676.51%23.49%10.42%11.69%0.589
7777.49%22.51%10.49%11.85%0.588
7878.47%21.53%10.57%12.00%0.586
7979.45%20.55%10.65%12.15%0.585
8080.42%19.58%10.72%12.30%0.583
8181.40%18.60%10.80%12.45%0.582
8282.38%17.62%10.88%12.60%0.580
8383.36%16.64%10.95%12.76%0.579
8484.34%15.66%11.03%12.91%0.577
8585.32%14.68%11.11%13.06%0.576
8686.30%13.70%11.19%13.21%0.575
8787.28%12.72%11.26%13.36%0.573
8888.25%11.75%11.34%13.51%0.572
8989.23%10.77%11.42%13.67%0.571
9090.21%9.79%11.50%13.82%0.570
9191.19%8.81%11.57%13.97%0.569
9292.17%7.83%11.65%14.12%0.567
9393.15%6.85%11.73%14.27%0.566
9494.13%5.87%11.81%14.43%0.565
9595.11%4.89%11.88%14.58%0.564
9696.08%3.92%11.96%14.73%0.563
9797.06%2.94%12.04%14.88%0.562
9898.04%1.96%12.12%15.03%0.561
9999.02%0.98%12.19%15.19%0.560
100100.00%0.00%12.27%15.34%0.559
*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.
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.
  • Historical asset statistics are based on monthly returns from Jan 1986 to Sep 2021
  • 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 3-month treasury bill returns as the risk free rate