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 - Dec 2020)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 48.48%
Long Term Treasury 51.52%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio11.16%9.52%0.70

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market11.81%13.16%15.47%0.5600.00%100.00%
2Long Term Treasury8.65%9.31%11.11%0.4340.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (4.49% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.02
Long Term Treasury0.021.00
Based on monthly returns from Jan 1978 to Dec 2020
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.31%11.11%0.434
21.01%98.99%9.35%11.00%0.441
32.02%97.98%9.38%10.89%0.449
43.03%96.97%9.42%10.79%0.457
54.04%95.96%9.46%10.69%0.465
65.05%94.95%9.50%10.59%0.473
76.06%93.94%9.54%10.49%0.481
87.07%92.93%9.58%10.40%0.489
98.08%91.92%9.61%10.31%0.497
109.09%90.91%9.65%10.22%0.505
1110.10%89.90%9.69%10.13%0.513
1211.11%88.89%9.73%10.05%0.521
1312.12%87.88%9.77%9.97%0.529
1413.13%86.87%9.81%9.90%0.537
1514.14%85.86%9.85%9.82%0.545
1615.15%84.85%9.88%9.75%0.553
1716.16%83.84%9.92%9.69%0.561
1817.17%82.83%9.96%9.62%0.568
1918.18%81.82%10.00%9.56%0.576
2019.19%80.81%10.04%9.50%0.584
2120.20%79.80%10.08%9.45%0.591
2221.21%78.79%10.12%9.40%0.598
2322.22%77.78%10.15%9.36%0.605
2423.23%76.77%10.19%9.31%0.612
2524.24%75.76%10.23%9.27%0.619
2625.25%74.75%10.27%9.24%0.625
2726.26%73.74%10.31%9.21%0.632
2827.27%72.73%10.35%9.18%0.638
2928.28%71.72%10.39%9.16%0.644
3029.29%70.71%10.42%9.14%0.649
3130.30%69.70%10.46%9.12%0.655
3231.31%68.69%10.50%9.11%0.660
3332.32%67.68%10.54%9.10%0.664
3433.33%66.67%10.58%9.10%0.669
3534.34%65.66%10.62%9.10%0.673
3635.35%64.65%10.66%9.11%0.677
3736.36%63.64%10.69%9.11%0.681
3837.37%62.63%10.73%9.13%0.684
3938.38%61.62%10.77%9.14%0.687
4039.39%60.61%10.81%9.16%0.690
4140.40%59.60%10.85%9.19%0.692
4241.41%58.59%10.89%9.21%0.694
4342.42%57.58%10.93%9.25%0.696
4443.43%56.57%10.97%9.28%0.698
4544.44%55.56%11.01%9.32%0.699
4645.45%54.55%11.04%9.36%0.700
4746.46%53.54%11.08%9.41%0.700
4847.47%52.53%11.12%9.46%0.701
4948.48%51.52%11.16%9.52%0.701
5049.49%50.51%11.20%9.57%0.701
5150.51%49.49%11.24%9.63%0.700
5251.52%48.48%11.28%9.70%0.700
5352.53%47.47%11.32%9.77%0.699
5453.54%46.46%11.36%9.84%0.698
5554.55%45.45%11.39%9.91%0.696
5655.56%44.44%11.43%9.99%0.695
5756.57%43.43%11.47%10.07%0.693
5857.58%42.42%11.51%10.15%0.691
5958.59%41.41%11.55%10.24%0.690
6059.60%40.40%11.59%10.33%0.687
6160.61%39.39%11.63%10.42%0.685
6261.62%38.38%11.67%10.51%0.683
6362.63%37.37%11.71%10.61%0.680
6463.64%36.36%11.75%10.71%0.677
6564.65%35.35%11.78%10.81%0.675
6665.66%34.34%11.82%10.91%0.672
6766.67%33.33%11.86%11.02%0.669
6867.68%32.32%11.90%11.13%0.666
6968.69%31.31%11.94%11.24%0.663
7069.70%30.30%11.98%11.35%0.660
7170.71%29.29%12.02%11.47%0.656
7271.72%28.28%12.06%11.58%0.653
7372.73%27.27%12.10%11.70%0.650
7473.74%26.26%12.14%11.82%0.647
7574.75%25.25%12.18%11.95%0.643
7675.76%24.24%12.22%12.07%0.640
7776.77%23.23%12.25%12.20%0.636
7877.78%22.22%12.29%12.33%0.633
7978.79%21.21%12.33%12.45%0.630
8079.80%20.20%12.37%12.59%0.626
8180.81%19.19%12.41%12.72%0.623
8281.82%18.18%12.45%12.85%0.619
8382.83%17.17%12.49%12.99%0.616
8483.84%16.16%12.53%13.12%0.612
8584.85%15.15%12.57%13.26%0.609
8685.86%14.14%12.61%13.40%0.606
8786.87%13.13%12.65%13.54%0.602
8887.88%12.12%12.69%13.68%0.599
8988.89%11.11%12.73%13.83%0.596
9089.90%10.10%12.77%13.97%0.592
9190.91%9.09%12.81%14.12%0.589
9291.92%8.08%12.84%14.26%0.586
9392.93%7.07%12.88%14.41%0.582
9493.94%6.06%12.92%14.56%0.579
9594.95%5.05%12.96%14.71%0.576
9695.96%4.04%13.00%14.86%0.573
9796.97%3.03%13.04%15.01%0.570
9897.98%2.02%13.08%15.16%0.567
9998.99%1.01%13.12%15.31%0.564
100100.00%0.00%13.16%15.47%0.560
*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 (4.49% annualized).
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 Dec 2020
  • 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