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.

1
%
%
%
2
%
%
%
3
%
%
%
4
%
%
%
5
%
%
%
6
%
%
%
7
%
%
%
8
%
%
%
9
%
%
%
10
%
%
%
Total
%

Asset Groups
Min. Weight
Max. Weight
A
%
%
B
%
%
C
%
%
D
%
%
E
%
%
F
%
%

Efficient Frontier Results (Jan 1977 - Sep 2021)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 24.87%
Short Term Treasury 44.48%
Intermediate Term Treasury 30.65%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio7.88%5.02%0.65

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%
3Intermediate Term Treasury7.01%5.84%0.4190.00%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 TreasuryIntermediate Term Treasury
US Stock Market1.000.050.05
Short Term Treasury0.051.000.92
Intermediate Term Treasury0.050.921.00
Based on monthly returns from Jan 1977 to Sep 2021
Efficient Frontier Points
#US Stock MarketShort Term TreasuryIntermediate Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
12.95%97.05%0.00%5.96%3.03%0.480
23.93%96.07%0.00%6.03%3.03%0.501
34.91%95.09%0.00%6.09%3.04%0.520
45.89%94.11%0.00%6.16%3.06%0.538
56.87%93.13%0.00%6.23%3.09%0.555
67.85%92.15%0.00%6.30%3.12%0.569
78.83%91.17%0.00%6.37%3.16%0.583
89.81%90.19%0.00%6.44%3.21%0.594
910.79%89.21%0.00%6.50%3.26%0.604
1011.77%88.23%0.00%6.57%3.32%0.613
1112.75%87.25%0.00%6.64%3.39%0.620
1213.73%86.27%0.00%6.71%3.46%0.627
1314.71%85.29%0.00%6.78%3.53%0.631
1415.69%84.31%0.00%6.85%3.61%0.635
1516.67%83.33%0.00%6.92%3.70%0.638
1617.55%81.89%0.55%6.98%3.79%0.640
1718.12%79.01%2.87%7.05%3.88%0.642
1818.68%76.14%5.18%7.12%3.97%0.644
1919.24%73.26%7.50%7.19%4.06%0.645
2019.81%70.38%9.81%7.26%4.15%0.646
2120.37%67.50%12.13%7.33%4.25%0.647
2220.93%64.62%14.44%7.40%4.34%0.647
2321.49%61.75%16.76%7.47%4.44%0.648
2422.06%58.87%19.07%7.54%4.53%0.649
2522.62%55.99%21.39%7.61%4.63%0.649
2623.18%53.11%23.70%7.67%4.73%0.649
2723.74%50.24%26.02%7.74%4.83%0.649
2824.31%47.36%28.33%7.81%4.93%0.650
2924.87%44.48%30.65%7.88%5.02%0.650
3025.43%41.60%32.96%7.95%5.12%0.650
3126.00%38.73%35.28%8.02%5.22%0.650
3226.56%35.85%37.59%8.09%5.32%0.649
3327.12%32.97%39.91%8.16%5.42%0.649
3427.68%30.09%42.22%8.23%5.53%0.649
3528.25%27.21%44.54%8.30%5.63%0.649
3628.81%24.34%46.85%8.37%5.73%0.649
3729.37%21.46%49.17%8.44%5.83%0.648
3829.94%18.58%51.48%8.51%5.93%0.648
3930.50%15.70%53.80%8.58%6.04%0.648
4031.06%12.83%56.11%8.65%6.14%0.647
4131.62%9.95%58.43%8.72%6.24%0.647
4232.19%7.07%60.74%8.79%6.35%0.647
4332.75%4.19%63.06%8.86%6.45%0.646
4433.31%1.31%65.37%8.93%6.55%0.646
4534.22%0.00%65.78%9.00%6.66%0.646
4635.42%0.00%64.58%9.07%6.76%0.645
4736.61%0.00%63.39%9.14%6.88%0.644
4837.81%0.00%62.19%9.21%6.99%0.642
4939.00%0.00%61.00%9.28%7.11%0.641
5040.20%0.00%59.80%9.35%7.23%0.639
5141.40%0.00%58.60%9.42%7.36%0.637
5242.59%0.00%57.41%9.49%7.48%0.635
5343.79%0.00%56.21%9.56%7.61%0.632
5444.98%0.00%55.02%9.63%7.75%0.630
5546.18%0.00%53.82%9.70%7.88%0.627
5647.38%0.00%52.62%9.77%8.02%0.625
5748.57%0.00%51.43%9.84%8.16%0.622
5849.77%0.00%50.23%9.91%8.30%0.619
5950.96%0.00%49.04%9.98%8.45%0.616
6052.16%0.00%47.84%10.05%8.59%0.613
6153.36%0.00%46.64%10.12%8.74%0.610
6254.55%0.00%45.45%10.19%8.89%0.607
6355.75%0.00%44.25%10.26%9.04%0.604
6456.94%0.00%43.06%10.33%9.19%0.601
6558.14%0.00%41.86%10.40%9.35%0.598
6659.34%0.00%40.66%10.47%9.50%0.595
6760.53%0.00%39.47%10.54%9.66%0.592
6861.73%0.00%38.27%10.61%9.81%0.589
6962.92%0.00%37.08%10.69%9.97%0.586
7064.12%0.00%35.88%10.76%10.13%0.583
7165.32%0.00%34.68%10.83%10.30%0.581
7266.51%0.00%33.49%10.90%10.46%0.578
7367.71%0.00%32.29%10.97%10.62%0.575
7468.90%0.00%31.10%11.04%10.79%0.572
7570.10%0.00%29.90%11.11%10.95%0.569
7671.30%0.00%28.70%11.18%11.12%0.567
7772.49%0.00%27.51%11.25%11.28%0.564
7873.69%0.00%26.31%11.33%11.45%0.562
7974.88%0.00%25.12%11.40%11.62%0.559
8076.08%0.00%23.92%11.47%11.79%0.556
8177.28%0.00%22.72%11.54%11.96%0.554
8278.47%0.00%21.53%11.61%12.13%0.551
8379.67%0.00%20.33%11.68%12.30%0.549
8480.86%0.00%19.14%11.75%12.47%0.547
8582.06%0.00%17.94%11.83%12.64%0.544
8683.26%0.00%16.74%11.90%12.82%0.542
8784.45%0.00%15.55%11.97%12.99%0.540
8885.65%0.00%14.35%12.04%13.17%0.537
8986.84%0.00%13.16%12.11%13.34%0.535
9088.04%0.00%11.96%12.18%13.51%0.533
9189.24%0.00%10.76%12.26%13.69%0.531
9290.43%0.00%9.57%12.33%13.87%0.529
9391.63%0.00%8.37%12.40%14.04%0.527
9492.82%0.00%7.18%12.47%14.22%0.525
9594.02%0.00%5.98%12.54%14.40%0.523
9695.22%0.00%4.78%12.62%14.57%0.521
9796.41%0.00%3.59%12.69%14.75%0.519
9897.61%0.00%2.39%12.76%14.93%0.517
9998.80%0.00%1.20%12.83%15.11%0.515
100100.00%0.00%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