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 1972 - Sep 2021)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 29.60%
Intermediate Term Treasury 70.40%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio8.50%6.28%0.58

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market12.14%15.58%0.4500.00%100.00%
2Intermediate Term Treasury7.00%5.74%0.3960.00%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 MarketIntermediate Term Treasury
US Stock Market1.000.05
Intermediate Term Treasury0.051.00
Based on monthly returns from Jan 1972 to Sep 2021
Efficient Frontier Points
#US Stock MarketIntermediate Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
110.65%89.35%7.53%5.47%0.507
211.55%88.45%7.58%5.47%0.515
312.46%87.54%7.62%5.48%0.522
413.36%86.64%7.67%5.49%0.529
514.26%85.74%7.72%5.50%0.536
615.16%84.84%7.76%5.52%0.542
716.07%83.93%7.81%5.54%0.547
816.97%83.03%7.85%5.57%0.552
917.87%82.13%7.90%5.60%0.557
1018.77%81.23%7.94%5.63%0.561
1119.68%80.32%7.99%5.66%0.565
1220.58%79.42%8.04%5.70%0.569
1321.48%78.52%8.08%5.75%0.572
1422.38%77.62%8.13%5.80%0.575
1523.29%76.71%8.17%5.85%0.577
1624.19%75.81%8.22%5.90%0.579
1725.09%74.91%8.27%5.96%0.581
1825.99%74.01%8.31%6.02%0.582
1926.90%73.10%8.36%6.08%0.583
2027.80%72.20%8.40%6.14%0.584
2128.70%71.30%8.45%6.21%0.584
2229.60%70.40%8.50%6.28%0.584
2330.51%69.49%8.54%6.36%0.584
2431.41%68.59%8.59%6.43%0.584
2532.31%67.69%8.63%6.51%0.584
2633.21%66.79%8.68%6.59%0.583
2734.12%65.88%8.73%6.68%0.582
2835.02%64.98%8.77%6.76%0.581
2935.92%64.08%8.82%6.85%0.580
3036.82%63.18%8.87%6.94%0.578
3137.73%62.27%8.91%7.03%0.577
3238.63%61.37%8.96%7.13%0.575
3339.53%60.47%9.00%7.22%0.574
3440.43%59.57%9.05%7.32%0.572
3541.34%58.66%9.10%7.42%0.570
3642.24%57.76%9.14%7.52%0.568
3743.14%56.86%9.19%7.62%0.566
3844.04%55.96%9.24%7.72%0.564
3944.95%55.05%9.28%7.83%0.562
4045.85%54.15%9.33%7.93%0.560
4146.75%53.25%9.37%8.04%0.558
4247.65%52.35%9.42%8.15%0.556
4348.56%51.44%9.47%8.26%0.553
4449.46%50.54%9.51%8.37%0.551
4550.36%49.64%9.56%8.48%0.549
4651.26%48.74%9.61%8.59%0.547
4752.17%47.83%9.65%8.71%0.544
4853.07%46.93%9.70%8.82%0.542
4953.97%46.03%9.75%8.94%0.540
5054.87%45.13%9.79%9.06%0.538
5155.78%44.22%9.84%9.18%0.535
5256.68%43.32%9.89%9.29%0.533
5357.58%42.42%9.93%9.41%0.531
5458.48%41.52%9.98%9.53%0.529
5559.39%40.61%10.03%9.65%0.526
5660.29%39.71%10.07%9.78%0.524
5761.19%38.81%10.12%9.90%0.522
5862.09%37.91%10.17%10.02%0.520
5963.00%37.00%10.21%10.15%0.518
6063.90%36.10%10.26%10.27%0.516
6164.80%35.20%10.31%10.40%0.514
6265.70%34.30%10.35%10.52%0.512
6366.61%33.39%10.40%10.65%0.509
6467.51%32.49%10.45%10.77%0.507
6568.41%31.59%10.49%10.90%0.505
6669.31%30.69%10.54%11.03%0.503
6770.22%29.78%10.59%11.16%0.502
6871.12%28.88%10.63%11.29%0.500
6972.02%27.98%10.68%11.41%0.498
7072.92%27.08%10.73%11.54%0.496
7173.83%26.17%10.77%11.67%0.494
7274.73%25.27%10.82%11.80%0.492
7375.63%24.37%10.87%11.94%0.490
7476.53%23.47%10.92%12.07%0.489
7577.44%22.56%10.96%12.20%0.487
7678.34%21.66%11.01%12.33%0.485
7779.24%20.76%11.06%12.46%0.483
7880.14%19.86%11.10%12.59%0.482
7981.05%18.95%11.15%12.73%0.480
8081.95%18.05%11.20%12.86%0.478
8182.85%17.15%11.24%12.99%0.477
8283.75%16.25%11.29%13.13%0.475
8384.66%15.34%11.34%13.26%0.473
8485.56%14.44%11.39%13.40%0.472
8586.46%13.54%11.43%13.53%0.470
8687.36%12.64%11.48%13.67%0.469
8788.27%11.73%11.53%13.80%0.467
8889.17%10.83%11.57%13.94%0.466
8990.07%9.93%11.62%14.07%0.464
9090.97%9.03%11.67%14.21%0.463
9191.88%8.12%11.72%14.34%0.462
9292.78%7.22%11.76%14.48%0.460
9393.68%6.32%11.81%14.62%0.459
9494.58%5.42%11.86%14.75%0.457
9595.49%4.51%11.91%14.89%0.456
9696.39%3.61%11.95%15.03%0.455
9797.29%2.71%12.00%15.16%0.453
9898.19%1.81%12.05%15.30%0.452
9999.10%0.90%12.10%15.44%0.451
100100.00%0.00%12.14%15.58%0.450
*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 1972 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