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 2019)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 50.23%
Long Term Treasury 49.77%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio10.98%9.54%0.67

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market11.60%12.89%15.11%0.5490.00%100.00%
2Long Term Treasury8.43%9.08%11.06%0.4060.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (4.59% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.04
Long Term Treasury0.041.00
Based on provided custom correlation matrix
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
134.31%65.69%10.38%9.08%0.637
234.97%65.03%10.40%9.09%0.640
335.64%64.36%10.43%9.09%0.642
436.30%63.70%10.45%9.09%0.645
536.96%63.04%10.48%9.10%0.647
637.63%62.37%10.50%9.10%0.649
738.29%61.71%10.53%9.11%0.651
838.95%61.05%10.55%9.12%0.653
939.62%60.38%10.58%9.14%0.655
1040.28%59.72%10.60%9.15%0.657
1140.94%59.06%10.63%9.17%0.659
1241.61%58.39%10.65%9.18%0.660
1342.27%57.73%10.68%9.20%0.662
1442.93%57.07%10.70%9.22%0.663
1543.60%56.40%10.73%9.24%0.664
1644.26%55.74%10.75%9.27%0.665
1744.93%55.07%10.78%9.29%0.666
1845.59%54.41%10.80%9.32%0.667
1946.25%53.75%10.83%9.35%0.668
2046.92%53.08%10.85%9.38%0.668
2147.58%52.42%10.88%9.41%0.669
2248.24%51.76%10.90%9.44%0.669
2348.91%51.09%10.93%9.47%0.669
2449.57%50.43%10.96%9.51%0.670
2550.23%49.77%10.98%9.54%0.670
2650.90%49.10%11.01%9.58%0.670
2751.56%48.44%11.03%9.62%0.669
2852.22%47.78%11.06%9.66%0.669
2952.89%47.11%11.08%9.70%0.669
3053.55%46.45%11.11%9.75%0.669
3154.21%45.79%11.13%9.79%0.668
3254.88%45.12%11.16%9.84%0.667
3355.54%44.46%11.18%9.89%0.667
3456.21%43.79%11.21%9.94%0.666
3556.87%43.13%11.23%9.99%0.665
3657.53%42.47%11.26%10.04%0.664
3758.20%41.80%11.28%10.09%0.664
3858.86%41.14%11.31%10.14%0.662
3959.52%40.48%11.33%10.20%0.661
4060.19%39.81%11.36%10.25%0.660
4160.85%39.15%11.39%10.31%0.659
4261.51%38.49%11.41%10.37%0.658
4362.18%37.82%11.44%10.43%0.657
4462.84%37.16%11.46%10.49%0.655
4563.50%36.50%11.49%10.55%0.654
4664.17%35.83%11.51%10.61%0.652
4764.83%35.17%11.54%10.68%0.651
4865.50%34.50%11.56%10.74%0.649
4966.16%33.84%11.59%10.81%0.648
5066.82%33.18%11.61%10.87%0.646
5167.49%32.51%11.64%10.94%0.644
5268.15%31.85%11.66%11.01%0.643
5368.81%31.19%11.69%11.08%0.641
5469.48%30.52%11.72%11.15%0.639
5570.14%29.86%11.74%11.22%0.637
5670.80%29.20%11.77%11.29%0.636
5771.47%28.53%11.79%11.36%0.634
5872.13%27.87%11.82%11.44%0.632
5972.79%27.21%11.84%11.51%0.630
6073.46%26.54%11.87%11.59%0.628
6174.12%25.88%11.89%11.66%0.626
6274.78%25.22%11.92%11.74%0.624
6375.45%24.55%11.94%11.82%0.622
6476.11%23.89%11.97%11.90%0.620
6576.78%23.22%11.99%11.98%0.618
6677.44%22.56%12.02%12.06%0.616
6778.10%21.90%12.05%12.14%0.614
6878.77%21.23%12.07%12.22%0.612
6979.43%20.57%12.10%12.30%0.610
7080.09%19.91%12.12%12.38%0.608
7180.76%19.24%12.15%12.46%0.606
7281.42%18.58%12.17%12.55%0.604
7382.08%17.92%12.20%12.63%0.602
7482.75%17.25%12.22%12.72%0.600
7583.41%16.59%12.25%12.80%0.598
7684.07%15.93%12.28%12.89%0.596
7784.74%15.26%12.30%12.98%0.594
7885.40%14.60%12.33%13.06%0.592
7986.07%13.93%12.35%13.15%0.590
8086.73%13.27%12.38%13.24%0.588
8187.39%12.61%12.40%13.33%0.586
8288.06%11.94%12.43%13.42%0.584
8388.72%11.28%12.45%13.51%0.582
8489.38%10.62%12.48%13.60%0.580
8590.05%9.95%12.51%13.69%0.578
8690.71%9.29%12.53%13.78%0.576
8791.37%8.63%12.56%13.87%0.574
8892.04%7.96%12.58%13.97%0.572
8992.70%7.30%12.61%14.06%0.570
9093.36%6.64%12.63%14.15%0.568
9194.03%5.97%12.66%14.25%0.566
9294.69%5.31%12.68%14.34%0.565
9395.35%4.65%12.71%14.43%0.563
9496.02%3.98%12.74%14.53%0.561
9596.68%3.32%12.76%14.62%0.559
9697.35%2.65%12.79%14.72%0.557
9798.01%1.99%12.81%14.82%0.555
9898.67%1.33%12.84%14.91%0.553
9999.34%0.66%12.86%15.01%0.551
100100.00%0.00%12.89%15.11%0.549
*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 (4.59% 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 2019
  • 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