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. 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 - May 2019)

Portfolio Allocations

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

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1US Stock Market11.33%12.63%15.17%0.5370.00%100.00%
2Long Term Treasury8.45%9.09%10.99%0.4200.00%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 (4.48% 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 May 2019
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.09%10.99%0.420
21.01%98.99%9.13%10.89%0.427
32.02%97.98%9.16%10.79%0.434
43.03%96.97%9.20%10.69%0.441
54.04%95.96%9.23%10.60%0.449
65.05%94.95%9.27%10.50%0.456
76.06%93.94%9.30%10.41%0.463
87.07%92.93%9.34%10.32%0.471
98.08%91.92%9.37%10.23%0.478
109.09%90.91%9.41%10.15%0.486
1110.10%89.90%9.44%10.07%0.493
1211.11%88.89%9.48%9.99%0.500
1312.12%87.88%9.51%9.92%0.508
1413.13%86.87%9.55%9.84%0.515
1514.14%85.86%9.59%9.77%0.522
1615.15%84.85%9.62%9.71%0.530
1716.16%83.84%9.66%9.64%0.537
1817.17%82.83%9.69%9.58%0.544
1918.18%81.82%9.73%9.53%0.551
2019.19%80.81%9.76%9.47%0.558
2120.20%79.80%9.80%9.42%0.564
2221.21%78.79%9.83%9.38%0.571
2322.22%77.78%9.87%9.33%0.578
2423.23%76.77%9.90%9.29%0.584
2524.24%75.76%9.94%9.26%0.590
2625.25%74.75%9.97%9.22%0.596
2726.26%73.74%10.01%9.19%0.602
2827.27%72.73%10.05%9.17%0.607
2928.28%71.72%10.08%9.15%0.613
3029.29%70.71%10.12%9.13%0.618
3130.30%69.70%10.15%9.11%0.623
3231.31%68.69%10.19%9.10%0.627
3332.32%67.68%10.22%9.09%0.632
3433.33%66.67%10.26%9.09%0.636
3534.34%65.66%10.29%9.09%0.640
3635.35%64.65%10.33%9.10%0.643
3736.36%63.64%10.37%9.10%0.647
3837.37%62.63%10.40%9.11%0.650
3938.38%61.62%10.44%9.13%0.653
4039.39%60.61%10.47%9.15%0.655
4140.40%59.60%10.51%9.17%0.657
4241.41%58.59%10.54%9.20%0.659
4342.42%57.58%10.58%9.23%0.661
4443.43%56.57%10.61%9.26%0.662
4544.44%55.56%10.65%9.30%0.664
4645.45%54.55%10.69%9.34%0.665
4746.46%53.54%10.72%9.38%0.665
4847.47%52.53%10.76%9.43%0.666
4948.48%51.52%10.79%9.48%0.666
5049.49%50.51%10.83%9.54%0.666
5150.51%49.49%10.86%9.60%0.666
5251.52%48.48%10.90%9.66%0.665
5352.53%47.47%10.94%9.72%0.664
5453.54%46.46%10.97%9.79%0.663
5554.55%45.45%11.01%9.86%0.662
5655.56%44.44%11.04%9.93%0.661
5756.57%43.43%11.08%10.01%0.660
5857.58%42.42%11.11%10.09%0.658
5958.59%41.41%11.15%10.17%0.656
6059.60%40.40%11.19%10.25%0.654
6160.61%39.39%11.22%10.34%0.652
6261.62%38.38%11.26%10.43%0.650
6362.63%37.37%11.29%10.52%0.648
6463.64%36.36%11.33%10.61%0.646
6564.65%35.35%11.37%10.71%0.643
6665.66%34.34%11.40%10.81%0.641
6766.67%33.33%11.44%10.91%0.638
6867.68%32.32%11.47%11.01%0.635
6968.69%31.31%11.51%11.12%0.632
7069.70%30.30%11.55%11.23%0.629
7170.71%29.29%11.58%11.34%0.627
7271.72%28.28%11.62%11.45%0.624
7372.73%27.27%11.65%11.56%0.621
7473.74%26.26%11.69%11.68%0.618
7574.75%25.25%11.73%11.79%0.614
7675.76%24.24%11.76%11.91%0.611
7776.77%23.23%11.80%12.03%0.608
7877.78%22.22%11.83%12.15%0.605
7978.79%21.21%11.87%12.28%0.602
8079.80%20.20%11.91%12.40%0.599
8180.81%19.19%11.94%12.53%0.596
8281.82%18.18%11.98%12.66%0.592
8382.83%17.17%12.01%12.79%0.589
8483.84%16.16%12.05%12.92%0.586
8584.85%15.15%12.09%13.05%0.583
8685.86%14.14%12.12%13.18%0.580
8786.87%13.13%12.16%13.32%0.577
8887.88%12.12%12.19%13.45%0.573
8988.89%11.11%12.23%13.59%0.570
9089.90%10.10%12.27%13.73%0.567
9190.91%9.09%12.30%13.87%0.564
9291.92%8.08%12.34%14.01%0.561
9392.93%7.07%12.37%14.15%0.558
9493.94%6.06%12.41%14.29%0.555
9594.95%5.05%12.45%14.44%0.552
9695.96%4.04%12.48%14.58%0.549
9796.97%3.03%12.52%14.73%0.546
9897.98%2.02%12.56%14.87%0.543
9998.99%1.01%12.59%15.02%0.540
100100.00%0.00%12.63%15.17%0.537
*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 (4.48% 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