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 - Nov 2018)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 51.52%
Long Term Treasury 48.48%
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Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1US Stock Market11.46%12.74%15.07%0.5470.00%100.00%
2Long Term Treasury8.17%8.81%10.96%0.3930.00%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 (4.50% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.06
Long Term Treasury0.061.00
Based on monthly returns from Jan 1978 to Nov 2018
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%8.81%10.96%0.393
21.01%98.99%8.85%10.86%0.400
32.02%97.98%8.89%10.76%0.408
43.03%96.97%8.93%10.66%0.415
54.04%95.96%8.97%10.57%0.422
65.05%94.95%9.01%10.48%0.430
76.06%93.94%9.05%10.39%0.437
87.07%92.93%9.09%10.30%0.445
98.08%91.92%9.12%10.22%0.452
109.09%90.91%9.16%10.14%0.460
1110.10%89.90%9.20%10.06%0.467
1211.11%88.89%9.24%9.99%0.474
1312.12%87.88%9.28%9.91%0.482
1413.13%86.87%9.32%9.84%0.489
1514.14%85.86%9.36%9.78%0.497
1615.15%84.85%9.40%9.71%0.504
1716.16%83.84%9.44%9.65%0.511
1817.17%82.83%9.48%9.59%0.518
1918.18%81.82%9.52%9.54%0.526
2019.19%80.81%9.56%9.48%0.533
2120.20%79.80%9.60%9.44%0.540
2221.21%78.79%9.63%9.39%0.546
2322.22%77.78%9.67%9.35%0.553
2423.23%76.77%9.71%9.31%0.559
2524.24%75.76%9.75%9.28%0.566
2625.25%74.75%9.79%9.24%0.572
2726.26%73.74%9.83%9.22%0.578
2827.27%72.73%9.87%9.19%0.584
2928.28%71.72%9.91%9.17%0.590
3029.29%70.71%9.95%9.15%0.595
3130.30%69.70%9.99%9.14%0.600
3231.31%68.69%10.03%9.13%0.605
3332.32%67.68%10.07%9.12%0.610
3433.33%66.67%10.11%9.12%0.614
3534.34%65.66%10.15%9.12%0.619
3635.35%64.65%10.19%9.12%0.623
3736.36%63.64%10.23%9.13%0.627
3837.37%62.63%10.27%9.14%0.630
3938.38%61.62%10.31%9.16%0.633
4039.39%60.61%10.34%9.18%0.636
4140.40%59.60%10.38%9.20%0.639
4241.41%58.59%10.42%9.23%0.642
4342.42%57.58%10.46%9.26%0.644
4443.43%56.57%10.50%9.29%0.646
4544.44%55.56%10.54%9.33%0.647
4645.45%54.55%10.58%9.37%0.649
4746.46%53.54%10.62%9.41%0.650
4847.47%52.53%10.66%9.46%0.651
4948.48%51.52%10.70%9.51%0.652
5049.49%50.51%10.74%9.56%0.652
5150.51%49.49%10.78%9.62%0.653
5251.52%48.48%10.82%9.68%0.653
5352.53%47.47%10.86%9.74%0.653
5453.54%46.46%10.90%9.80%0.652
5554.55%45.45%10.94%9.87%0.652
5655.56%44.44%10.98%9.94%0.651
5756.57%43.43%11.02%10.02%0.650
5857.58%42.42%11.06%10.10%0.649
5958.59%41.41%11.10%10.17%0.648
6059.60%40.40%11.14%10.26%0.647
6160.61%39.39%11.18%10.34%0.645
6261.62%38.38%11.22%10.43%0.644
6362.63%37.37%11.26%10.52%0.642
6463.64%36.36%11.30%10.61%0.640
6564.65%35.35%11.34%10.71%0.638
6665.66%34.34%11.38%10.80%0.636
6766.67%33.33%11.42%10.90%0.634
6867.68%32.32%11.46%11.00%0.632
6968.69%31.31%11.50%11.11%0.630
7069.70%30.30%11.54%11.21%0.627
7170.71%29.29%11.58%11.32%0.625
7271.72%28.28%11.62%11.43%0.623
7372.73%27.27%11.66%11.54%0.620
7473.74%26.26%11.70%11.65%0.617
7574.75%25.25%11.74%11.77%0.615
7675.76%24.24%11.78%11.88%0.612
7776.77%23.23%11.82%12.00%0.610
7877.78%22.22%11.86%12.12%0.607
7978.79%21.21%11.90%12.24%0.604
8079.80%20.20%11.94%12.36%0.601
8180.81%19.19%11.98%12.49%0.599
8281.82%18.18%12.02%12.61%0.596
8382.83%17.17%12.06%12.74%0.593
8483.84%16.16%12.10%12.87%0.590
8584.85%15.15%12.14%13.00%0.587
8685.86%14.14%12.18%13.13%0.585
8786.87%13.13%12.22%13.26%0.582
8887.88%12.12%12.26%13.39%0.579
8988.89%11.11%12.30%13.53%0.576
9089.90%10.10%12.34%13.66%0.574
9190.91%9.09%12.38%13.80%0.571
9291.92%8.08%12.42%13.94%0.568
9392.93%7.07%12.46%14.07%0.565
9493.94%6.06%12.50%14.21%0.563
9594.95%5.05%12.54%14.35%0.560
9695.96%4.04%12.58%14.50%0.557
9796.97%3.03%12.62%14.64%0.555
9897.98%2.02%12.66%14.78%0.552
9998.99%1.01%12.70%14.93%0.549
100100.00%0.00%12.74%15.07%0.547
*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 (4.50% 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