Efficient Frontier

This online tool calculates and plots 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 provide the best possible expected return for the level of risk in the portfolio. 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 - Mar 2019)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 49.49%
Long Term Treasury 50.51%
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Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1US Stock Market11.46%12.75%15.15%0.5460.00%100.00%
2Long Term Treasury8.36%9.00%10.97%0.4120.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (4.49% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.05
Long Term Treasury0.051.00
Based on monthly returns from Jan 1978 to Mar 2019
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.00%10.97%0.412
21.01%98.99%9.04%10.87%0.419
32.02%97.98%9.08%10.77%0.426
43.03%96.97%9.12%10.67%0.434
54.04%95.96%9.15%10.58%0.441
65.05%94.95%9.19%10.48%0.449
76.06%93.94%9.23%10.39%0.456
87.07%92.93%9.27%10.31%0.464
98.08%91.92%9.30%10.22%0.471
109.09%90.91%9.34%10.14%0.479
1110.10%89.90%9.38%10.06%0.486
1211.11%88.89%9.41%9.98%0.494
1312.12%87.88%9.45%9.91%0.501
1413.13%86.87%9.49%9.84%0.509
1514.14%85.86%9.53%9.77%0.516
1615.15%84.85%9.56%9.70%0.523
1716.16%83.84%9.60%9.64%0.531
1817.17%82.83%9.64%9.58%0.538
1918.18%81.82%9.68%9.53%0.545
2019.19%80.81%9.71%9.48%0.552
2120.20%79.80%9.75%9.43%0.559
2221.21%78.79%9.79%9.38%0.565
2322.22%77.78%9.83%9.34%0.572
2423.23%76.77%9.86%9.30%0.578
2524.24%75.76%9.90%9.26%0.585
2625.25%74.75%9.94%9.23%0.591
2726.26%73.74%9.98%9.20%0.597
2827.27%72.73%10.01%9.18%0.602
2928.28%71.72%10.05%9.16%0.608
3029.29%70.71%10.09%9.14%0.613
3130.30%69.70%10.13%9.13%0.618
3231.31%68.69%10.16%9.11%0.623
3332.32%67.68%10.20%9.11%0.628
3433.33%66.67%10.24%9.11%0.632
3534.34%65.66%10.28%9.11%0.636
3635.35%64.65%10.31%9.11%0.640
3736.36%63.64%10.35%9.12%0.643
3837.37%62.63%10.39%9.13%0.647
3938.38%61.62%10.43%9.15%0.650
4039.39%60.61%10.47%9.17%0.652
4140.40%59.60%10.50%9.19%0.655
4241.41%58.59%10.54%9.22%0.657
4342.42%57.58%10.58%9.25%0.659
4443.43%56.57%10.62%9.28%0.661
4544.44%55.56%10.65%9.32%0.662
4645.45%54.55%10.69%9.36%0.663
4746.46%53.54%10.73%9.40%0.664
4847.47%52.53%10.77%9.45%0.665
4948.48%51.52%10.81%9.50%0.665
5049.49%50.51%10.84%9.56%0.665
5150.51%49.49%10.88%9.61%0.665
5251.52%48.48%10.92%9.67%0.665
5352.53%47.47%10.96%9.74%0.664
5453.54%46.46%10.99%9.81%0.664
5554.55%45.45%11.03%9.87%0.663
5655.56%44.44%11.07%9.95%0.662
5756.57%43.43%11.11%10.02%0.661
5857.58%42.42%11.15%10.10%0.659
5958.59%41.41%11.18%10.18%0.658
6059.60%40.40%11.22%10.27%0.656
6160.61%39.39%11.26%10.35%0.654
6261.62%38.38%11.30%10.44%0.652
6362.63%37.37%11.34%10.53%0.650
6463.64%36.36%11.37%10.63%0.648
6564.65%35.35%11.41%10.72%0.646
6665.66%34.34%11.45%10.82%0.644
6766.67%33.33%11.49%10.92%0.641
6867.68%32.32%11.53%11.02%0.639
6968.69%31.31%11.56%11.13%0.636
7069.70%30.30%11.60%11.24%0.633
7170.71%29.29%11.64%11.34%0.631
7271.72%28.28%11.68%11.45%0.628
7372.73%27.27%11.72%11.57%0.625
7473.74%26.26%11.75%11.68%0.622
7574.75%25.25%11.79%11.80%0.619
7675.76%24.24%11.83%11.92%0.616
7776.77%23.23%11.87%12.04%0.613
7877.78%22.22%11.91%12.16%0.610
7978.79%21.21%11.94%12.28%0.607
8079.80%20.20%11.98%12.40%0.604
8180.81%19.19%12.02%12.53%0.601
8281.82%18.18%12.06%12.66%0.598
8382.83%17.17%12.10%12.78%0.595
8483.84%16.16%12.14%12.91%0.592
8584.85%15.15%12.17%13.05%0.589
8685.86%14.14%12.21%13.18%0.586
8786.87%13.13%12.25%13.31%0.583
8887.88%12.12%12.29%13.45%0.580
8988.89%11.11%12.33%13.58%0.577
9089.90%10.10%12.37%13.72%0.574
9190.91%9.09%12.40%13.86%0.571
9291.92%8.08%12.44%14.00%0.568
9392.93%7.07%12.48%14.14%0.565
9493.94%6.06%12.52%14.28%0.563
9594.95%5.05%12.56%14.42%0.560
9695.96%4.04%12.60%14.56%0.557
9796.97%3.03%12.63%14.71%0.554
9897.98%2.02%12.67%14.85%0.551
9998.99%1.01%12.71%15.00%0.548
100100.00%0.00%12.75%15.15%0.546
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (4.49% annualized).
Notes on results:
  • Past performance is not a guarantee of future returns.
  • The efficient frontier is based on the monthly returns, volatilities and correlations of the specified assets and the related portfolio allocations assume monthly rebalancing.
  • 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 1-month treasury bill returns as the risk free rate