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 - Feb 2021)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 50.51%
Long Term Treasury 49.49%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio11.12%9.63%0.69

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market11.83%13.18%15.44%0.5640.00%100.00%
2Long Term Treasury8.38%9.04%11.15%0.4100.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (4.47% 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 Feb 2021
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.04%11.15%0.410
21.01%98.99%9.08%11.04%0.418
32.02%97.98%9.13%10.93%0.426
43.03%96.97%9.17%10.83%0.434
54.04%95.96%9.21%10.72%0.441
65.05%94.95%9.25%10.62%0.449
76.06%93.94%9.29%10.53%0.458
87.07%92.93%9.33%10.43%0.466
98.08%91.92%9.37%10.34%0.474
109.09%90.91%9.41%10.25%0.482
1110.10%89.90%9.46%10.17%0.490
1211.11%88.89%9.50%10.08%0.498
1312.12%87.88%9.54%10.00%0.506
1413.13%86.87%9.58%9.93%0.514
1514.14%85.86%9.62%9.85%0.522
1615.15%84.85%9.66%9.78%0.530
1716.16%83.84%9.70%9.71%0.538
1817.17%82.83%9.74%9.65%0.546
1918.18%81.82%9.79%9.59%0.554
2019.19%80.81%9.83%9.53%0.562
2120.20%79.80%9.87%9.48%0.569
2221.21%78.79%9.91%9.43%0.577
2322.22%77.78%9.95%9.38%0.584
2423.23%76.77%9.99%9.33%0.591
2524.24%75.76%10.03%9.30%0.598
2625.25%74.75%10.08%9.26%0.605
2726.26%73.74%10.12%9.23%0.612
2827.27%72.73%10.16%9.20%0.618
2928.28%71.72%10.20%9.17%0.624
3029.29%70.71%10.24%9.15%0.630
3130.30%69.70%10.28%9.14%0.636
3231.31%68.69%10.32%9.13%0.641
3332.32%67.68%10.37%9.12%0.646
3433.33%66.67%10.41%9.11%0.651
3534.34%65.66%10.45%9.11%0.656
3635.35%64.65%10.49%9.11%0.660
3736.36%63.64%10.53%9.12%0.664
3837.37%62.63%10.57%9.13%0.668
3938.38%61.62%10.62%9.15%0.671
4039.39%60.61%10.66%9.17%0.674
4140.40%59.60%10.70%9.19%0.677
4241.41%58.59%10.74%9.22%0.680
4342.42%57.58%10.78%9.25%0.682
4443.43%56.57%10.82%9.28%0.684
4544.44%55.56%10.87%9.32%0.686
4645.45%54.55%10.91%9.37%0.687
4746.46%53.54%10.95%9.41%0.688
4847.47%52.53%10.99%9.46%0.689
4948.48%51.52%11.03%9.51%0.689
5049.49%50.51%11.07%9.57%0.690
5150.51%49.49%11.12%9.63%0.690
5251.52%48.48%11.16%9.69%0.689
5352.53%47.47%11.20%9.76%0.689
5453.54%46.46%11.24%9.83%0.688
5554.55%45.45%11.28%9.90%0.687
5655.56%44.44%11.32%9.98%0.686
5756.57%43.43%11.37%10.06%0.685
5857.58%42.42%11.41%10.14%0.684
5958.59%41.41%11.45%10.23%0.682
6059.60%40.40%11.49%10.32%0.680
6160.61%39.39%11.53%10.41%0.678
6261.62%38.38%11.58%10.50%0.676
6362.63%37.37%11.62%10.60%0.674
6463.64%36.36%11.66%10.69%0.672
6564.65%35.35%11.70%10.80%0.670
6665.66%34.34%11.74%10.90%0.667
6766.67%33.33%11.79%11.01%0.664
6867.68%32.32%11.83%11.11%0.662
6968.69%31.31%11.87%11.22%0.659
7069.70%30.30%11.91%11.34%0.656
7170.71%29.29%11.95%11.45%0.653
7271.72%28.28%12.00%11.57%0.650
7372.73%27.27%12.04%11.69%0.647
7473.74%26.26%12.08%11.81%0.644
7574.75%25.25%12.12%11.93%0.641
7675.76%24.24%12.16%12.05%0.638
7776.77%23.23%12.21%12.18%0.635
7877.78%22.22%12.25%12.31%0.632
7978.79%21.21%12.29%12.43%0.629
8079.80%20.20%12.33%12.56%0.626
8180.81%19.19%12.38%12.70%0.622
8281.82%18.18%12.42%12.83%0.619
8382.83%17.17%12.46%12.97%0.616
8483.84%16.16%12.50%13.10%0.613
8584.85%15.15%12.54%13.24%0.610
8685.86%14.14%12.59%13.38%0.606
8786.87%13.13%12.63%13.52%0.603
8887.88%12.12%12.67%13.66%0.600
8988.89%11.11%12.71%13.80%0.597
9089.90%10.10%12.76%13.95%0.594
9190.91%9.09%12.80%14.09%0.591
9291.92%8.08%12.84%14.24%0.588
9392.93%7.07%12.88%14.39%0.585
9493.94%6.06%12.93%14.53%0.582
9594.95%5.05%12.97%14.68%0.579
9695.96%4.04%13.01%14.83%0.576
9796.97%3.03%13.05%14.98%0.573
9897.98%2.02%13.10%15.14%0.570
9998.99%1.01%13.14%15.29%0.567
100100.00%0.00%13.18%15.44%0.564
*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 (4.47% 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 Feb 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