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 - Sep 2021)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 23.72%
Short Term Treasury 63.79%
Intermediate Term Treasury 2.26%
Long Term Treasury 10.22%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio7.90%4.82%0.69

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market13.29%15.38%0.5340.00%100.00%
2Short Term Treasury5.82%3.08%0.4350.00%100.00%
3Intermediate Term Treasury7.15%5.88%0.4420.00%100.00%
4Long Term Treasury8.97%11.14%0.3860.00%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 TreasuryIntermediate Term TreasuryLong Term Treasury
US Stock Market1.000.040.050.02
Short Term Treasury0.041.000.920.71
Intermediate Term Treasury0.050.921.000.88
Long Term Treasury0.020.710.881.00
Based on monthly returns from Jan 1978 to Sep 2021
Efficient Frontier Points
#US Stock MarketShort Term TreasuryIntermediate Term TreasuryLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
13.07%96.93%0.00%0.00%6.04%3.05%0.510
24.05%95.95%0.00%0.00%6.11%3.05%0.532
35.03%94.97%0.00%0.00%6.18%3.06%0.552
46.01%93.99%0.00%0.00%6.25%3.08%0.570
56.99%93.01%0.00%0.00%6.33%3.11%0.587
67.97%92.03%0.00%0.00%6.40%3.14%0.602
78.95%91.05%0.00%0.00%6.47%3.18%0.616
89.93%90.07%0.00%0.00%6.54%3.23%0.627
910.90%89.10%0.00%0.00%6.61%3.28%0.638
1011.88%88.12%0.00%0.00%6.68%3.34%0.647
1112.86%87.14%0.00%0.00%6.75%3.41%0.654
1213.84%86.16%0.00%0.00%6.83%3.48%0.660
1314.82%85.18%0.00%0.00%6.90%3.55%0.665
1415.61%83.95%0.00%0.44%6.97%3.63%0.669
1516.24%82.51%0.00%1.25%7.04%3.72%0.672
1616.87%81.06%0.00%2.07%7.11%3.80%0.675
1717.50%79.62%0.00%2.88%7.18%3.89%0.677
1818.13%78.18%0.00%3.69%7.26%3.97%0.679
1918.76%76.73%0.00%4.51%7.33%4.06%0.681
2019.39%75.29%0.00%5.32%7.40%4.15%0.682
2120.02%73.85%0.00%6.13%7.47%4.25%0.683
2220.65%72.40%0.00%6.95%7.54%4.34%0.684
2321.28%70.96%0.00%7.76%7.62%4.43%0.685
2421.91%69.52%0.00%8.58%7.69%4.53%0.685
2522.54%68.08%0.00%9.39%7.76%4.63%0.685
2623.16%66.63%0.00%10.20%7.83%4.72%0.685
2723.72%63.79%2.26%10.22%7.90%4.82%0.685
2824.28%60.89%4.63%10.20%7.98%4.92%0.685
2924.83%57.99%6.99%10.18%8.05%5.02%0.685
3025.39%55.09%9.36%10.16%8.12%5.12%0.685
3125.94%52.19%11.73%10.14%8.19%5.22%0.685
3226.50%49.29%14.09%10.12%8.27%5.32%0.684
3327.05%46.39%16.46%10.10%8.34%5.42%0.684
3427.61%43.49%18.83%10.08%8.41%5.52%0.684
3528.16%40.58%21.19%10.06%8.48%5.62%0.683
3628.72%37.68%23.56%10.04%8.55%5.72%0.683
3729.27%34.78%25.92%10.02%8.63%5.83%0.683
3829.83%31.88%28.29%10.00%8.70%5.93%0.682
3930.38%28.98%30.66%9.98%8.77%6.03%0.682
4030.94%26.08%33.02%9.96%8.85%6.13%0.681
4131.49%23.18%35.39%9.94%8.92%6.24%0.681
4232.05%20.27%37.76%9.92%8.99%6.34%0.680
4332.61%17.37%40.12%9.90%9.06%6.44%0.680
4433.16%14.47%42.49%9.88%9.14%6.55%0.679
4533.72%11.57%44.85%9.86%9.21%6.65%0.679
4634.27%8.67%47.22%9.84%9.28%6.76%0.678
4734.83%5.77%49.59%9.82%9.36%6.86%0.678
4835.38%2.87%51.95%9.80%9.43%6.96%0.677
4935.94%0.00%54.26%9.80%9.50%7.07%0.677
5036.68%0.00%52.01%11.31%9.58%7.17%0.676
5137.42%0.00%49.76%12.82%9.65%7.28%0.676
5238.16%0.00%47.51%14.33%9.72%7.39%0.675
5338.91%0.00%45.25%15.84%9.80%7.50%0.674
5439.65%0.00%43.00%17.35%9.87%7.61%0.673
5540.39%0.00%40.75%18.86%9.94%7.72%0.673
5641.13%0.00%38.50%20.37%10.02%7.83%0.672
5741.87%0.00%36.25%21.88%10.09%7.94%0.671
5842.61%0.00%33.99%23.39%10.16%8.05%0.670
5943.36%0.00%31.74%24.90%10.24%8.16%0.669
6044.10%0.00%29.49%26.41%10.31%8.28%0.667
6144.84%0.00%27.24%27.92%10.38%8.39%0.666
6245.58%0.00%24.99%29.43%10.46%8.51%0.665
6346.32%0.00%22.74%30.94%10.53%8.63%0.664
6447.06%0.00%20.48%32.45%10.60%8.74%0.663
6547.81%0.00%18.23%33.96%10.68%8.86%0.662
6648.55%0.00%15.98%35.47%10.75%8.98%0.660
6749.29%0.00%13.73%36.98%10.83%9.10%0.659
6850.03%0.00%11.48%38.49%10.90%9.22%0.658
6950.77%0.00%9.22%40.00%10.97%9.34%0.657
7051.52%0.00%6.97%41.51%11.05%9.46%0.656
7152.26%0.00%4.72%43.02%11.12%9.58%0.654
7253.00%0.00%2.47%44.53%11.20%9.70%0.653
7353.74%0.00%0.22%46.04%11.27%9.82%0.652
7455.36%0.00%0.00%44.64%11.35%9.95%0.650
7557.08%0.00%0.00%42.92%11.42%10.08%0.648
7658.80%0.00%0.00%41.20%11.49%10.22%0.646
7760.51%0.00%0.00%39.49%11.57%10.37%0.643
7862.23%0.00%0.00%37.77%11.64%10.53%0.640
7963.95%0.00%0.00%36.05%11.72%10.70%0.636
8065.66%0.00%0.00%34.34%11.79%10.87%0.632
8167.38%0.00%0.00%32.62%11.87%11.05%0.628
8269.10%0.00%0.00%30.90%11.94%11.24%0.624
8370.81%0.00%0.00%29.19%12.02%11.43%0.619
8472.53%0.00%0.00%27.47%12.09%11.63%0.614
8574.25%0.00%0.00%25.75%12.17%11.83%0.609
8675.96%0.00%0.00%24.04%12.24%12.04%0.604
8777.68%0.00%0.00%22.32%12.32%12.25%0.599
8879.40%0.00%0.00%20.60%12.39%12.47%0.594
8981.12%0.00%0.00%18.88%12.47%12.69%0.589
9082.83%0.00%0.00%17.17%12.54%12.92%0.584
9184.55%0.00%0.00%15.45%12.62%13.15%0.579
9286.27%0.00%0.00%13.73%12.69%13.39%0.574
9387.98%0.00%0.00%12.02%12.77%13.63%0.569
9489.70%0.00%0.00%10.30%12.84%13.87%0.563
9591.42%0.00%0.00%8.58%12.92%14.11%0.558
9693.13%0.00%0.00%6.87%12.99%14.36%0.553
9794.85%0.00%0.00%5.15%13.07%14.61%0.549
9896.57%0.00%0.00%3.43%13.14%14.87%0.544
9998.28%0.00%0.00%1.72%13.22%15.12%0.539
100100.00%0.00%0.00%0.00%13.29%15.38%0.534
*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 1978 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