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 1978 - Sep 2021)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 50.51%
Long Term Treasury 49.49%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio11.14%9.61%0.65

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market13.29%15.38%0.5340.00%100.00%
2Long Term Treasury8.97%11.14%0.3860.00%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 MarketLong Term Treasury
US Stock Market1.000.02
Long Term Treasury0.021.00
Based on monthly returns from Jan 1978 to Sep 2021
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%8.97%11.14%0.386
21.01%98.99%9.02%11.03%0.393
32.02%97.98%9.06%10.92%0.401
43.03%96.97%9.10%10.82%0.408
54.04%95.96%9.14%10.72%0.416
65.05%94.95%9.19%10.62%0.423
76.06%93.94%9.23%10.52%0.431
87.07%92.93%9.27%10.43%0.439
98.08%91.92%9.32%10.34%0.446
109.09%90.91%9.36%10.25%0.454
1110.10%89.90%9.40%10.16%0.462
1211.11%88.89%9.45%10.08%0.470
1312.12%87.88%9.49%10.00%0.477
1413.13%86.87%9.53%9.92%0.485
1514.14%85.86%9.57%9.85%0.493
1615.15%84.85%9.62%9.78%0.500
1716.16%83.84%9.66%9.71%0.508
1817.17%82.83%9.70%9.65%0.515
1918.18%81.82%9.75%9.58%0.523
2019.19%80.81%9.79%9.53%0.530
2120.20%79.80%9.83%9.47%0.537
2221.21%78.79%9.88%9.42%0.544
2322.22%77.78%9.92%9.38%0.551
2423.23%76.77%9.96%9.33%0.558
2524.24%75.76%10.01%9.29%0.565
2625.25%74.75%10.05%9.26%0.571
2726.26%73.74%10.09%9.22%0.578
2827.27%72.73%10.14%9.20%0.584
2928.28%71.72%10.18%9.17%0.590
3029.29%70.71%10.22%9.15%0.595
3130.30%69.70%10.27%9.13%0.601
3231.31%68.69%10.31%9.12%0.606
3332.32%67.68%10.35%9.11%0.611
3433.33%66.67%10.40%9.11%0.615
3534.34%65.66%10.44%9.11%0.620
3635.35%64.65%10.48%9.11%0.624
3736.36%63.64%10.53%9.12%0.628
3837.37%62.63%10.57%9.13%0.631
3938.38%61.62%10.61%9.14%0.635
4039.39%60.61%10.66%9.16%0.638
4140.40%59.60%10.70%9.18%0.641
4241.41%58.59%10.74%9.21%0.643
4342.42%57.58%10.79%9.24%0.645
4443.43%56.57%10.83%9.27%0.647
4544.44%55.56%10.87%9.31%0.649
4645.45%54.55%10.92%9.35%0.650
4746.46%53.54%10.96%9.40%0.651
4847.47%52.53%11.00%9.45%0.652
4948.48%51.52%11.05%9.50%0.653
5049.49%50.51%11.09%9.55%0.653
5150.51%49.49%11.14%9.61%0.653
5251.52%48.48%11.18%9.68%0.653
5352.53%47.47%11.22%9.74%0.652
5453.54%46.46%11.27%9.81%0.652
5554.55%45.45%11.31%9.88%0.651
5655.56%44.44%11.35%9.96%0.650
5756.57%43.43%11.40%10.04%0.649
5857.58%42.42%11.44%10.12%0.648
5958.59%41.41%11.49%10.20%0.646
6059.60%40.40%11.53%10.29%0.645
6160.61%39.39%11.57%10.38%0.643
6261.62%38.38%11.62%10.47%0.641
6362.63%37.37%11.66%10.57%0.639
6463.64%36.36%11.70%10.67%0.637
6564.65%35.35%11.75%10.77%0.635
6665.66%34.34%11.79%10.87%0.632
6766.67%33.33%11.84%10.98%0.630
6867.68%32.32%11.88%11.08%0.627
6968.69%31.31%11.92%11.19%0.625
7069.70%30.30%11.97%11.30%0.622
7170.71%29.29%12.01%11.42%0.619
7271.72%28.28%12.06%11.53%0.616
7372.73%27.27%12.10%11.65%0.614
7473.74%26.26%12.14%11.77%0.611
7574.75%25.25%12.19%11.89%0.608
7675.76%24.24%12.23%12.01%0.605
7776.77%23.23%12.28%12.14%0.602
7877.78%22.22%12.32%12.27%0.599
7978.79%21.21%12.36%12.39%0.596
8079.80%20.20%12.41%12.52%0.593
8180.81%19.19%12.45%12.65%0.590
8281.82%18.18%12.50%12.79%0.587
8382.83%17.17%12.54%12.92%0.584
8483.84%16.16%12.58%13.06%0.581
8584.85%15.15%12.63%13.19%0.578
8685.86%14.14%12.67%13.33%0.575
8786.87%13.13%12.72%13.47%0.572
8887.88%12.12%12.76%13.61%0.569
8988.89%11.11%12.81%13.75%0.566
9089.90%10.10%12.85%13.90%0.563
9190.91%9.09%12.89%14.04%0.560
9291.92%8.08%12.94%14.19%0.557
9392.93%7.07%12.98%14.33%0.554
9493.94%6.06%13.03%14.48%0.551
9594.95%5.05%13.07%14.63%0.548
9695.96%4.04%13.12%14.78%0.545
9796.97%3.03%13.16%14.93%0.543
9897.98%2.02%13.20%15.08%0.540
9998.99%1.01%13.25%15.23%0.537
100100.00%0.00%13.29%15.38%0.534
*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 1978 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