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 - Jan 2020)

Portfolio Allocations

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

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio11.02%9.50%0.68

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1US Stock Market11.58%12.86%15.09%0.5480.00%100.00%
2Long Term Treasury8.60%9.25%11.09%0.4210.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (4.58% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.04
Long Term Treasury0.041.00
Based on monthly returns from Jan 1978 to Jan 2020
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.25%11.09%0.421
21.01%98.99%9.29%10.99%0.428
32.02%97.98%9.32%10.88%0.436
43.03%96.97%9.36%10.78%0.443
54.04%95.96%9.40%10.68%0.450
65.05%94.95%9.43%10.59%0.458
76.06%93.94%9.47%10.49%0.465
87.07%92.93%9.50%10.40%0.473
98.08%91.92%9.54%10.31%0.481
109.09%90.91%9.58%10.23%0.488
1110.10%89.90%9.61%10.14%0.496
1211.11%88.89%9.65%10.06%0.503
1312.12%87.88%9.68%9.99%0.511
1413.13%86.87%9.72%9.91%0.518
1514.14%85.86%9.76%9.84%0.526
1615.15%84.85%9.79%9.77%0.533
1716.16%83.84%9.83%9.70%0.541
1817.17%82.83%9.86%9.64%0.548
1918.18%81.82%9.90%9.58%0.555
2019.19%80.81%9.94%9.52%0.562
2120.20%79.80%9.97%9.47%0.569
2221.21%78.79%10.01%9.42%0.576
2322.22%77.78%10.04%9.37%0.583
2423.23%76.77%10.08%9.33%0.589
2524.24%75.76%10.12%9.29%0.596
2625.25%74.75%10.15%9.25%0.602
2726.26%73.74%10.19%9.22%0.608
2827.27%72.73%10.23%9.19%0.614
2928.28%71.72%10.26%9.17%0.619
3029.29%70.71%10.30%9.15%0.625
3130.30%69.70%10.33%9.13%0.630
3231.31%68.69%10.37%9.11%0.635
3332.32%67.68%10.41%9.10%0.640
3433.33%66.67%10.44%9.10%0.644
3534.34%65.66%10.48%9.10%0.648
3635.35%64.65%10.52%9.10%0.652
3736.36%63.64%10.55%9.10%0.656
3837.37%62.63%10.59%9.11%0.659
3938.38%61.62%10.62%9.12%0.662
4039.39%60.61%10.66%9.14%0.665
4140.40%59.60%10.70%9.16%0.667
4241.41%58.59%10.73%9.18%0.670
4342.42%57.58%10.77%9.21%0.672
4443.43%56.57%10.81%9.24%0.673
4544.44%55.56%10.84%9.28%0.675
4645.45%54.55%10.88%9.32%0.676
4746.46%53.54%10.92%9.36%0.677
4847.47%52.53%10.95%9.40%0.677
4948.48%51.52%10.99%9.45%0.678
5049.49%50.51%11.02%9.50%0.678
5150.51%49.49%11.06%9.56%0.678
5251.52%48.48%11.10%9.62%0.677
5352.53%47.47%11.13%9.68%0.677
5453.54%46.46%11.17%9.74%0.676
5554.55%45.45%11.21%9.81%0.675
5655.56%44.44%11.24%9.88%0.674
5756.57%43.43%11.28%9.96%0.672
5857.58%42.42%11.32%10.04%0.671
5958.59%41.41%11.35%10.12%0.669
6059.60%40.40%11.39%10.20%0.667
6160.61%39.39%11.43%10.28%0.665
6261.62%38.38%11.46%10.37%0.663
6362.63%37.37%11.50%10.46%0.661
6463.64%36.36%11.54%10.56%0.659
6564.65%35.35%11.57%10.65%0.656
6665.66%34.34%11.61%10.75%0.654
6766.67%33.33%11.65%10.85%0.651
6867.68%32.32%11.68%10.95%0.648
6968.69%31.31%11.72%11.06%0.645
7069.70%30.30%11.76%11.16%0.643
7170.71%29.29%11.79%11.27%0.640
7271.72%28.28%11.83%11.38%0.637
7372.73%27.27%11.87%11.49%0.634
7473.74%26.26%11.90%11.61%0.630
7574.75%25.25%11.94%11.72%0.627
7675.76%24.24%11.98%11.84%0.624
7776.77%23.23%12.01%11.96%0.621
7877.78%22.22%12.05%12.08%0.618
7978.79%21.21%12.09%12.21%0.615
8079.80%20.20%12.12%12.33%0.611
8180.81%19.19%12.16%12.46%0.608
8281.82%18.18%12.20%12.59%0.605
8382.83%17.17%12.23%12.72%0.602
8483.84%16.16%12.27%12.85%0.598
8584.85%15.15%12.31%12.98%0.595
8685.86%14.14%12.34%13.11%0.592
8786.87%13.13%12.38%13.25%0.589
8887.88%12.12%12.42%13.38%0.585
8988.89%11.11%12.45%13.52%0.582
9089.90%10.10%12.49%13.66%0.579
9190.91%9.09%12.53%13.79%0.576
9291.92%8.08%12.56%13.94%0.573
9392.93%7.07%12.60%14.08%0.570
9493.94%6.06%12.64%14.22%0.567
9594.95%5.05%12.68%14.36%0.563
9695.96%4.04%12.71%14.51%0.560
9796.97%3.03%12.75%14.65%0.557
9897.98%2.02%12.79%14.80%0.554
9998.99%1.01%12.82%14.94%0.551
100100.00%0.00%12.86%15.09%0.548
*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 (4.58% 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 Jan 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