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 - Dec 2019)

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 Portfolio10.99%9.56%0.67

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market11.60%12.89%15.11%0.5490.00%100.00%
2Long Term Treasury8.43%9.08%11.06%0.4060.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (4.59% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.04
Long Term Treasury0.041.00
Based on provided custom correlation matrix
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.08%11.06%0.406
21.01%98.99%9.12%10.95%0.414
32.02%97.98%9.16%10.85%0.421
43.03%96.97%9.20%10.75%0.429
54.04%95.96%9.23%10.65%0.436
65.05%94.95%9.27%10.56%0.444
76.06%93.94%9.31%10.46%0.451
87.07%92.93%9.35%10.37%0.459
98.08%91.92%9.39%10.28%0.466
109.09%90.91%9.42%10.20%0.474
1110.10%89.90%9.46%10.11%0.482
1211.11%88.89%9.50%10.03%0.489
1312.12%87.88%9.54%9.96%0.497
1413.13%86.87%9.58%9.88%0.505
1514.14%85.86%9.61%9.81%0.512
1615.15%84.85%9.65%9.74%0.520
1716.16%83.84%9.69%9.68%0.527
1817.17%82.83%9.73%9.61%0.534
1918.18%81.82%9.77%9.56%0.542
2019.19%80.81%9.80%9.50%0.549
2120.20%79.80%9.84%9.45%0.556
2221.21%78.79%9.88%9.40%0.563
2322.22%77.78%9.92%9.35%0.570
2423.23%76.77%9.96%9.31%0.577
2524.24%75.76%10.00%9.27%0.583
2625.25%74.75%10.03%9.24%0.589
2726.26%73.74%10.07%9.20%0.596
2827.27%72.73%10.11%9.18%0.602
2928.28%71.72%10.15%9.15%0.607
3029.29%70.71%10.19%9.13%0.613
3130.30%69.70%10.22%9.11%0.618
3231.31%68.69%10.26%9.10%0.623
3332.32%67.68%10.30%9.09%0.628
3433.33%66.67%10.34%9.09%0.633
3534.34%65.66%10.38%9.08%0.637
3635.35%64.65%10.42%9.09%0.641
3736.36%63.64%10.45%9.09%0.645
3837.37%62.63%10.49%9.10%0.648
3938.38%61.62%10.53%9.12%0.652
4039.39%60.61%10.57%9.13%0.655
4140.40%59.60%10.61%9.15%0.657
4241.41%58.59%10.65%9.18%0.660
4342.42%57.58%10.68%9.21%0.662
4443.43%56.57%10.72%9.24%0.664
4544.44%55.56%10.76%9.27%0.665
4645.45%54.55%10.80%9.31%0.667
4746.46%53.54%10.84%9.36%0.668
4847.47%52.53%10.88%9.40%0.669
4948.48%51.52%10.91%9.45%0.669
5049.49%50.51%10.95%9.50%0.670
5150.51%49.49%10.99%9.56%0.670
5251.52%48.48%11.03%9.62%0.669
5352.53%47.47%11.07%9.68%0.669
5453.54%46.46%11.11%9.75%0.669
5554.55%45.45%11.14%9.82%0.668
5655.56%44.44%11.18%9.89%0.667
5756.57%43.43%11.22%9.96%0.666
5857.58%42.42%11.26%10.04%0.664
5958.59%41.41%11.30%10.12%0.663
6059.60%40.40%11.34%10.20%0.661
6160.61%39.39%11.38%10.29%0.660
6261.62%38.38%11.41%10.38%0.658
6362.63%37.37%11.45%10.47%0.656
6463.64%36.36%11.49%10.56%0.653
6564.65%35.35%11.53%10.66%0.651
6665.66%34.34%11.57%10.76%0.649
6766.67%33.33%11.61%10.86%0.646
6867.68%32.32%11.65%10.96%0.644
6968.69%31.31%11.68%11.06%0.641
7069.70%30.30%11.72%11.17%0.639
7170.71%29.29%11.76%11.28%0.636
7271.72%28.28%11.80%11.39%0.633
7372.73%27.27%11.84%11.50%0.630
7473.74%26.26%11.88%11.62%0.627
7574.75%25.25%11.92%11.74%0.624
7675.76%24.24%11.96%11.85%0.621
7776.77%23.23%11.99%11.97%0.618
7877.78%22.22%12.03%12.10%0.615
7978.79%21.21%12.07%12.22%0.612
8079.80%20.20%12.11%12.34%0.609
8180.81%19.19%12.15%12.47%0.606
8281.82%18.18%12.19%12.60%0.603
8382.83%17.17%12.23%12.73%0.600
8483.84%16.16%12.27%12.86%0.597
8584.85%15.15%12.31%12.99%0.594
8685.86%14.14%12.34%13.12%0.591
8786.87%13.13%12.38%13.26%0.588
8887.88%12.12%12.42%13.39%0.585
8988.89%11.11%12.46%13.53%0.582
9089.90%10.10%12.50%13.67%0.579
9190.91%9.09%12.54%13.81%0.576
9291.92%8.08%12.58%13.95%0.573
9392.93%7.07%12.62%14.09%0.570
9493.94%6.06%12.66%14.23%0.567
9594.95%5.05%12.69%14.38%0.564
9695.96%4.04%12.73%14.52%0.561
9796.97%3.03%12.77%14.67%0.558
9897.98%2.02%12.81%14.81%0.555
9998.99%1.01%12.85%14.96%0.552
100100.00%0.00%12.89%15.11%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 (4.59% 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 Dec 2019
  • 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