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 1986 - Sep 2021)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 22.49%
Intermediate Term Treasury 77.51%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio7.52%4.84%0.87

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market12.27%15.34%0.5590.00%100.00%
2Intermediate Term Treasury6.18%4.78%0.6180.00%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 Market1.00-0.09
Intermediate Term Treasury-0.091.00
Based on monthly returns from Jan 1986 to Sep 2021
Efficient Frontier Points
#US Stock MarketIntermediate Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
110.78%89.22%6.82%4.44%0.802
211.68%88.32%6.87%4.44%0.813
312.58%87.42%6.93%4.45%0.823
413.48%86.52%6.98%4.46%0.832
514.38%85.62%7.03%4.48%0.840
615.28%84.72%7.09%4.50%0.847
716.18%83.82%7.14%4.53%0.853
817.08%82.92%7.20%4.56%0.858
917.99%82.01%7.25%4.59%0.863
1018.89%81.11%7.30%4.63%0.866
1119.79%80.21%7.36%4.68%0.869
1220.69%79.31%7.41%4.73%0.870
1321.59%78.41%7.47%4.78%0.871
1422.49%77.51%7.52%4.84%0.871
1523.39%76.61%7.58%4.90%0.871
1624.29%75.71%7.63%4.96%0.870
1725.20%74.80%7.68%5.03%0.868
1826.10%73.90%7.74%5.10%0.866
1927.00%73.00%7.79%5.18%0.863
2027.90%72.10%7.85%5.26%0.860
2128.80%71.20%7.90%5.34%0.856
2229.70%70.30%7.96%5.42%0.852
2330.60%69.40%8.01%5.51%0.848
2431.50%68.50%8.06%5.60%0.844
2532.41%67.59%8.12%5.69%0.839
2633.31%66.69%8.17%5.78%0.834
2734.21%65.79%8.23%5.88%0.829
2835.11%64.89%8.28%5.98%0.824
2936.01%63.99%8.34%6.08%0.819
3036.91%63.09%8.39%6.18%0.813
3137.81%62.19%8.45%6.28%0.808
3238.71%61.29%8.50%6.39%0.802
3339.62%60.38%8.55%6.50%0.797
3440.52%59.48%8.61%6.61%0.792
3541.42%58.58%8.66%6.72%0.786
3642.32%57.68%8.72%6.83%0.781
3743.22%56.78%8.77%6.94%0.775
3844.12%55.88%8.83%7.06%0.770
3945.02%54.98%8.88%7.17%0.764
4045.92%54.08%8.94%7.29%0.759
4146.83%53.17%8.99%7.41%0.754
4247.73%52.27%9.05%7.53%0.748
4348.63%51.37%9.10%7.65%0.743
4449.53%50.47%9.16%7.77%0.738
4550.43%49.57%9.21%7.89%0.733
4651.33%48.67%9.27%8.01%0.728
4752.23%47.77%9.32%8.14%0.723
4853.13%46.87%9.38%8.26%0.719
4954.04%45.96%9.43%8.39%0.714
5054.94%45.06%9.49%8.52%0.709
5155.84%44.16%9.54%8.64%0.705
5256.74%43.26%9.60%8.77%0.700
5357.64%42.36%9.65%8.90%0.696
5458.54%41.46%9.71%9.03%0.692
5559.44%40.56%9.76%9.16%0.687
5660.34%39.66%9.82%9.29%0.683
5761.25%38.75%9.87%9.42%0.679
5862.15%37.85%9.93%9.55%0.675
5963.05%36.95%9.98%9.68%0.671
6063.95%36.05%10.04%9.81%0.667
6164.85%35.15%10.09%9.94%0.663
6265.75%34.25%10.15%10.08%0.660
6366.65%33.35%10.21%10.21%0.656
6467.55%32.45%10.26%10.34%0.652
6568.46%31.54%10.32%10.48%0.649
6669.36%30.64%10.37%10.61%0.646
6770.26%29.74%10.43%10.75%0.642
6871.16%28.84%10.48%10.88%0.639
6972.06%27.94%10.54%11.02%0.636
7072.96%27.04%10.59%11.15%0.632
7173.86%26.14%10.65%11.29%0.629
7274.76%25.24%10.70%11.43%0.626
7375.67%24.33%10.76%11.56%0.623
7476.57%23.43%10.82%11.70%0.620
7577.47%22.53%10.87%11.84%0.617
7678.37%21.63%10.93%11.98%0.614
7779.27%20.73%10.98%12.11%0.612
7880.17%19.83%11.04%12.25%0.609
7981.07%18.93%11.09%12.39%0.606
8081.97%18.03%11.15%12.53%0.603
8182.88%17.12%11.21%12.67%0.601
8283.78%16.22%11.26%12.81%0.598
8384.68%15.32%11.32%12.95%0.596
8485.58%14.42%11.37%13.09%0.593
8586.48%13.52%11.43%13.23%0.591
8687.38%12.62%11.49%13.36%0.588
8788.28%11.72%11.54%13.50%0.586
8889.18%10.82%11.60%13.65%0.584
8990.09%9.91%11.65%13.79%0.581
9090.99%9.01%11.71%13.93%0.579
9191.89%8.11%11.77%14.07%0.577
9292.79%7.21%11.82%14.21%0.575
9393.69%6.31%11.88%14.35%0.573
9494.59%5.41%11.93%14.49%0.571
9595.49%4.51%11.99%14.63%0.569
9696.39%3.61%12.05%14.77%0.567
9797.30%2.70%12.10%14.91%0.565
9898.20%1.80%12.16%15.06%0.563
9999.10%0.90%12.22%15.20%0.561
100100.00%0.00%12.27%15.34%0.559
*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 1986 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