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 - Jan 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 Market11.37%12.67%15.17%0.5390.00%100.00%
2Long Term Treasury8.29%8.93%10.96%0.4050.00%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 Jan 2019
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%8.93%10.96%0.405
21.01%98.99%8.97%10.86%0.412
32.02%97.98%9.01%10.76%0.419
43.03%96.97%9.04%10.66%0.427
54.04%95.96%9.08%10.57%0.434
65.05%94.95%9.12%10.48%0.441
76.06%93.94%9.16%10.39%0.449
87.07%92.93%9.19%10.30%0.456
98.08%91.92%9.23%10.22%0.463
109.09%90.91%9.27%10.13%0.471
1110.10%89.90%9.30%10.05%0.478
1211.11%88.89%9.34%9.98%0.486
1312.12%87.88%9.38%9.90%0.493
1413.13%86.87%9.42%9.83%0.500
1514.14%85.86%9.45%9.77%0.508
1615.15%84.85%9.49%9.70%0.515
1716.16%83.84%9.53%9.64%0.522
1817.17%82.83%9.57%9.58%0.529
1918.18%81.82%9.60%9.53%0.536
2019.19%80.81%9.64%9.47%0.543
2120.20%79.80%9.68%9.42%0.550
2221.21%78.79%9.72%9.38%0.557
2322.22%77.78%9.75%9.34%0.563
2423.23%76.77%9.79%9.30%0.570
2524.24%75.76%9.83%9.26%0.576
2625.25%74.75%9.87%9.23%0.582
2726.26%73.74%9.90%9.20%0.588
2827.27%72.73%9.94%9.18%0.593
2928.28%71.72%9.98%9.16%0.599
3029.29%70.71%10.02%9.14%0.604
3130.30%69.70%10.05%9.13%0.609
3231.31%68.69%10.09%9.12%0.614
3332.32%67.68%10.13%9.11%0.618
3433.33%66.67%10.17%9.11%0.622
3534.34%65.66%10.20%9.11%0.627
3635.35%64.65%10.24%9.12%0.630
3736.36%63.64%10.28%9.12%0.634
3837.37%62.63%10.32%9.14%0.637
3938.38%61.62%10.35%9.15%0.640
4039.39%60.61%10.39%9.17%0.643
4140.40%59.60%10.43%9.20%0.645
4241.41%58.59%10.47%9.22%0.647
4342.42%57.58%10.50%9.25%0.649
4443.43%56.57%10.54%9.29%0.651
4544.44%55.56%10.58%9.33%0.652
4645.45%54.55%10.62%9.37%0.653
4746.46%53.54%10.65%9.41%0.654
4847.47%52.53%10.69%9.46%0.655
4948.48%51.52%10.73%9.51%0.655
5049.49%50.51%10.77%9.57%0.656
5150.51%49.49%10.81%9.63%0.656
5251.52%48.48%10.84%9.69%0.655
5352.53%47.47%10.88%9.75%0.655
5453.54%46.46%10.92%9.82%0.654
5554.55%45.45%10.96%9.89%0.653
5655.56%44.44%10.99%9.96%0.652
5756.57%43.43%11.03%10.04%0.651
5857.58%42.42%11.07%10.12%0.650
5958.59%41.41%11.11%10.20%0.649
6059.60%40.40%11.15%10.28%0.647
6160.61%39.39%11.18%10.37%0.645
6261.62%38.38%11.22%10.46%0.643
6362.63%37.37%11.26%10.55%0.641
6463.64%36.36%11.30%10.64%0.639
6564.65%35.35%11.33%10.74%0.637
6665.66%34.34%11.37%10.84%0.635
6766.67%33.33%11.41%10.94%0.632
6867.68%32.32%11.45%11.04%0.630
6968.69%31.31%11.49%11.15%0.627
7069.70%30.30%11.52%11.25%0.625
7170.71%29.29%11.56%11.36%0.622
7271.72%28.28%11.60%11.47%0.619
7372.73%27.27%11.64%11.59%0.617
7473.74%26.26%11.68%11.70%0.614
7574.75%25.25%11.71%11.82%0.611
7675.76%24.24%11.75%11.94%0.608
7776.77%23.23%11.79%12.06%0.605
7877.78%22.22%11.83%12.18%0.602
7978.79%21.21%11.87%12.30%0.599
8079.80%20.20%11.91%12.42%0.596
8180.81%19.19%11.94%12.55%0.593
8281.82%18.18%11.98%12.68%0.591
8382.83%17.17%12.02%12.81%0.588
8483.84%16.16%12.06%12.94%0.585
8584.85%15.15%12.10%13.07%0.582
8685.86%14.14%12.13%13.20%0.579
8786.87%13.13%12.17%13.33%0.576
8887.88%12.12%12.21%13.47%0.573
8988.89%11.11%12.25%13.61%0.570
9089.90%10.10%12.29%13.74%0.567
9190.91%9.09%12.32%13.88%0.564
9291.92%8.08%12.36%14.02%0.561
9392.93%7.07%12.40%14.16%0.558
9493.94%6.06%12.44%14.30%0.555
9594.95%5.05%12.48%14.45%0.553
9695.96%4.04%12.52%14.59%0.550
9796.97%3.03%12.55%14.73%0.547
9897.98%2.02%12.59%14.88%0.544
9998.99%1.01%12.63%15.02%0.542
100100.00%0.00%12.67%15.17%0.539
*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