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 1978 - Aug 2020)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 47.47%
Long Term Treasury 52.53%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio11.10%9.44%0.70

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market11.64%12.98%15.40%0.5490.00%100.00%
2Long Term Treasury8.77%9.43%11.13%0.4410.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (4.53% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.02
Long Term Treasury0.021.00
Based on provided custom correlation matrix
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.43%11.13%0.441
21.01%98.99%9.47%11.02%0.448
32.02%97.98%9.50%10.91%0.456
43.03%96.97%9.54%10.81%0.464
54.04%95.96%9.57%10.71%0.471
65.05%94.95%9.61%10.61%0.479
76.06%93.94%9.64%10.51%0.487
87.07%92.93%9.68%10.42%0.495
98.08%91.92%9.72%10.33%0.503
109.09%90.91%9.75%10.24%0.510
1110.10%89.90%9.79%10.15%0.518
1211.11%88.89%9.82%10.07%0.526
1312.12%87.88%9.86%9.99%0.534
1413.13%86.87%9.89%9.91%0.541
1514.14%85.86%9.93%9.84%0.549
1615.15%84.85%9.96%9.76%0.557
1716.16%83.84%10.00%9.70%0.564
1817.17%82.83%10.03%9.63%0.572
1918.18%81.82%10.07%9.57%0.579
2019.19%80.81%10.11%9.51%0.586
2120.20%79.80%10.14%9.46%0.594
2221.21%78.79%10.18%9.41%0.601
2322.22%77.78%10.21%9.36%0.607
2423.23%76.77%10.25%9.32%0.614
2524.24%75.76%10.28%9.28%0.621
2625.25%74.75%10.32%9.24%0.627
2726.26%73.74%10.35%9.21%0.633
2827.27%72.73%10.39%9.18%0.639
2928.28%71.72%10.43%9.16%0.644
3029.29%70.71%10.46%9.14%0.650
3130.30%69.70%10.50%9.12%0.655
3231.31%68.69%10.53%9.11%0.660
3332.32%67.68%10.57%9.10%0.664
3433.33%66.67%10.60%9.09%0.668
3534.34%65.66%10.64%9.09%0.672
3635.35%64.65%10.68%9.09%0.676
3736.36%63.64%10.71%9.10%0.680
3837.37%62.63%10.75%9.11%0.683
3938.38%61.62%10.78%9.13%0.685
4039.39%60.61%10.82%9.15%0.688
4140.40%59.60%10.85%9.17%0.690
4241.41%58.59%10.89%9.20%0.692
4342.42%57.58%10.93%9.23%0.694
4443.43%56.57%10.96%9.26%0.695
4544.44%55.56%11.00%9.30%0.696
4645.45%54.55%11.03%9.34%0.697
4746.46%53.54%11.07%9.39%0.697
4847.47%52.53%11.10%9.44%0.697
4948.48%51.52%11.14%9.49%0.697
5049.49%50.51%11.18%9.55%0.697
5150.51%49.49%11.21%9.61%0.696
5251.52%48.48%11.25%9.67%0.695
5352.53%47.47%11.28%9.73%0.694
5453.54%46.46%11.32%9.80%0.693
5554.55%45.45%11.36%9.88%0.691
5655.56%44.44%11.39%9.95%0.690
5756.57%43.43%11.43%10.03%0.688
5857.58%42.42%11.46%10.11%0.686
5958.59%41.41%11.50%10.20%0.684
6059.60%40.40%11.54%10.29%0.681
6160.61%39.39%11.57%10.38%0.679
6261.62%38.38%11.61%10.47%0.676
6362.63%37.37%11.64%10.57%0.674
6463.64%36.36%11.68%10.66%0.671
6564.65%35.35%11.72%10.77%0.668
6665.66%34.34%11.75%10.87%0.665
6766.67%33.33%11.79%10.97%0.662
6867.68%32.32%11.82%11.08%0.658
6968.69%31.31%11.86%11.19%0.655
7069.70%30.30%11.90%11.30%0.652
7170.71%29.29%11.93%11.42%0.649
7271.72%28.28%11.97%11.53%0.645
7372.73%27.27%12.00%11.65%0.642
7473.74%26.26%12.04%11.77%0.638
7574.75%25.25%12.08%11.89%0.635
7675.76%24.24%12.11%12.02%0.631
7776.77%23.23%12.15%12.14%0.628
7877.78%22.22%12.18%12.27%0.624
7978.79%21.21%12.22%12.40%0.621
8079.80%20.20%12.26%12.53%0.617
8180.81%19.19%12.29%12.66%0.613
8281.82%18.18%12.33%12.79%0.610
8382.83%17.17%12.37%12.93%0.606
8483.84%16.16%12.40%13.07%0.603
8584.85%15.15%12.44%13.20%0.599
8685.86%14.14%12.47%13.34%0.596
8786.87%13.13%12.51%13.48%0.592
8887.88%12.12%12.55%13.62%0.589
8988.89%11.11%12.58%13.77%0.585
9089.90%10.10%12.62%13.91%0.582
9190.91%9.09%12.66%14.05%0.578
9291.92%8.08%12.69%14.20%0.575
9392.93%7.07%12.73%14.35%0.572
9493.94%6.06%12.76%14.49%0.568
9594.95%5.05%12.80%14.64%0.565
9695.96%4.04%12.84%14.79%0.562
9796.97%3.03%12.87%14.94%0.559
9897.98%2.02%12.91%15.09%0.555
9998.99%1.01%12.95%15.25%0.552
100100.00%0.00%12.98%15.40%0.549
*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 (4.53% annualized).
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 Aug 2020
  • 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