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 1977 - Sep 2021)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 20.59%
Short Term Treasury 79.41%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio7.19%4.07%0.64

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market12.90%15.29%0.5140.00%100.00%
2Short Term Treasury5.75%3.06%0.4120.00%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 Treasury
US Stock Market1.000.05
Short Term Treasury0.051.00
Based on monthly returns from Jan 1977 to Sep 2021
Efficient Frontier Points
#US Stock MarketShort Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
12.95%97.05%5.96%3.03%0.480
23.93%96.07%6.03%3.03%0.501
34.91%95.09%6.09%3.04%0.520
45.89%94.11%6.16%3.06%0.538
56.87%93.13%6.23%3.09%0.555
67.85%92.15%6.30%3.12%0.569
78.83%91.17%6.37%3.16%0.583
89.81%90.19%6.44%3.21%0.594
910.79%89.21%6.50%3.26%0.604
1011.77%88.23%6.57%3.32%0.613
1112.75%87.25%6.64%3.39%0.620
1213.73%86.27%6.71%3.46%0.627
1314.71%85.29%6.78%3.53%0.631
1415.69%84.31%6.85%3.61%0.635
1516.67%83.33%6.92%3.70%0.638
1617.65%82.35%6.98%3.79%0.640
1718.63%81.37%7.05%3.88%0.642
1819.61%80.39%7.12%3.97%0.642
1920.59%79.41%7.19%4.07%0.643
2021.58%78.42%7.26%4.18%0.642
2122.56%77.44%7.33%4.28%0.642
2223.54%76.46%7.40%4.39%0.640
2324.52%75.48%7.47%4.50%0.639
2425.50%74.50%7.54%4.61%0.637
2526.48%73.52%7.61%4.73%0.635
2627.46%72.54%7.67%4.85%0.633
2728.44%71.56%7.74%4.97%0.631
2829.42%70.58%7.81%5.09%0.629
2930.40%69.60%7.88%5.21%0.627
3031.38%68.62%7.95%5.33%0.624
3132.36%67.64%8.02%5.46%0.622
3233.34%66.66%8.09%5.58%0.619
3334.32%65.68%8.16%5.71%0.617
3435.30%64.70%8.23%5.84%0.614
3536.28%63.72%8.30%5.97%0.612
3637.26%62.74%8.37%6.10%0.609
3738.24%61.76%8.44%6.23%0.606
3839.22%60.78%8.51%6.37%0.604
3940.20%59.80%8.58%6.50%0.602
4041.18%58.82%8.65%6.63%0.599
4142.16%57.84%8.72%6.77%0.597
4243.14%56.86%8.79%6.91%0.594
4344.12%55.88%8.86%7.04%0.592
4445.10%54.90%8.93%7.18%0.590
4546.08%53.92%9.00%7.32%0.587
4647.06%52.94%9.07%7.45%0.585
4748.04%51.96%9.14%7.59%0.583
4849.02%50.98%9.21%7.73%0.581
4950.00%50.00%9.28%7.87%0.579
5050.98%49.02%9.35%8.01%0.577
5151.96%48.04%9.42%8.15%0.575
5252.94%47.06%9.49%8.29%0.573
5353.93%46.07%9.56%8.43%0.571
5454.91%45.09%9.63%8.57%0.569
5555.89%44.11%9.70%8.72%0.567
5656.87%43.13%9.77%8.86%0.565
5757.85%42.15%9.84%9.00%0.564
5858.83%41.17%9.91%9.14%0.562
5959.81%40.19%9.98%9.29%0.560
6060.79%39.21%10.05%9.43%0.559
6161.77%38.23%10.12%9.57%0.557
6262.75%37.25%10.19%9.72%0.555
6363.73%36.27%10.26%9.86%0.554
6464.71%35.29%10.33%10.00%0.552
6565.69%34.31%10.40%10.15%0.551
6666.67%33.33%10.47%10.29%0.549
6767.65%32.35%10.54%10.44%0.548
6868.63%31.37%10.61%10.58%0.547
6969.61%30.39%10.69%10.73%0.545
7070.59%29.41%10.76%10.87%0.544
7171.57%28.43%10.83%11.02%0.542
7272.55%27.45%10.90%11.16%0.541
7373.53%26.47%10.97%11.31%0.540
7474.51%25.49%11.04%11.46%0.539
7575.49%24.51%11.11%11.60%0.537
7676.47%23.53%11.18%11.75%0.536
7777.45%22.55%11.25%11.89%0.535
7878.43%21.57%11.33%12.04%0.534
7979.41%20.59%11.40%12.19%0.533
8080.39%19.61%11.47%12.33%0.532
8181.37%18.63%11.54%12.48%0.531
8282.35%17.65%11.61%12.63%0.530
8383.33%16.67%11.68%12.78%0.529
8484.31%15.69%11.75%12.92%0.528
8585.30%14.70%11.83%13.07%0.527
8686.28%13.72%11.90%13.22%0.526
8787.26%12.74%11.97%13.36%0.525
8888.24%11.76%12.04%13.51%0.524
8989.22%10.78%12.11%13.66%0.523
9090.20%9.80%12.18%13.81%0.522
9191.18%8.82%12.26%13.95%0.521
9292.16%7.84%12.33%14.10%0.520
9393.14%6.86%12.40%14.25%0.519
9494.12%5.88%12.47%14.40%0.518
9595.10%4.90%12.54%14.55%0.518
9696.08%3.92%12.62%14.69%0.517
9797.06%2.94%12.69%14.84%0.516
9898.04%1.96%12.76%14.99%0.515
9999.02%0.98%12.83%15.14%0.514
100100.00%0.00%12.90%15.29%0.514
*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 1977 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