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 - Aug 2019)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 47.47%
Long Term Treasury 52.53%
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Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1US Stock Market11.43%12.72%15.16%0.5450.00%100.00%
2Long Term Treasury8.69%9.34%11.07%0.4410.00%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 (4.47% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.04
Long Term Treasury0.041.00
Based on monthly returns from Jan 1978 to Aug 2019
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.34%11.07%0.441
21.01%98.99%9.38%10.96%0.448
32.02%97.98%9.41%10.86%0.455
43.03%96.97%9.44%10.76%0.463
54.04%95.96%9.48%10.66%0.470
65.05%94.95%9.51%10.57%0.478
76.06%93.94%9.55%10.48%0.485
87.07%92.93%9.58%10.39%0.492
98.08%91.92%9.61%10.30%0.500
109.09%90.91%9.65%10.21%0.507
1110.10%89.90%9.68%10.13%0.515
1211.11%88.89%9.71%10.05%0.522
1312.12%87.88%9.75%9.97%0.530
1413.13%86.87%9.78%9.90%0.537
1514.14%85.86%9.82%9.83%0.544
1615.15%84.85%9.85%9.76%0.552
1716.16%83.84%9.88%9.69%0.559
1817.17%82.83%9.92%9.63%0.566
1918.18%81.82%9.95%9.57%0.573
2019.19%80.81%9.98%9.52%0.580
2120.20%79.80%10.02%9.47%0.587
2221.21%78.79%10.05%9.42%0.593
2322.22%77.78%10.09%9.37%0.600
2423.23%76.77%10.12%9.33%0.606
2524.24%75.76%10.15%9.29%0.612
2625.25%74.75%10.19%9.26%0.618
2726.26%73.74%10.22%9.23%0.624
2827.27%72.73%10.26%9.20%0.629
2928.28%71.72%10.29%9.17%0.635
3029.29%70.71%10.32%9.15%0.640
3130.30%69.70%10.36%9.14%0.645
3231.31%68.69%10.39%9.13%0.649
3332.32%67.68%10.42%9.12%0.654
3433.33%66.67%10.46%9.11%0.658
3534.34%65.66%10.49%9.11%0.662
3635.35%64.65%10.53%9.11%0.665
3736.36%63.64%10.56%9.12%0.668
3837.37%62.63%10.59%9.13%0.671
3938.38%61.62%10.63%9.14%0.674
4039.39%60.61%10.66%9.16%0.676
4140.40%59.60%10.70%9.18%0.679
4241.41%58.59%10.73%9.21%0.680
4342.42%57.58%10.76%9.24%0.682
4443.43%56.57%10.80%9.27%0.683
4544.44%55.56%10.83%9.30%0.684
4645.45%54.55%10.87%9.34%0.685
4746.46%53.54%10.90%9.39%0.686
4847.47%52.53%10.93%9.43%0.686
4948.48%51.52%10.97%9.48%0.686
5049.49%50.51%11.00%9.54%0.686
5150.51%49.49%11.04%9.59%0.685
5251.52%48.48%11.07%9.65%0.684
5352.53%47.47%11.11%9.72%0.683
5453.54%46.46%11.14%9.78%0.682
5554.55%45.45%11.17%9.85%0.681
5655.56%44.44%11.21%9.92%0.679
5756.57%43.43%11.24%10.00%0.678
5857.58%42.42%11.28%10.08%0.676
5958.59%41.41%11.31%10.16%0.674
6059.60%40.40%11.34%10.24%0.672
6160.61%39.39%11.38%10.33%0.669
6261.62%38.38%11.41%10.42%0.667
6362.63%37.37%11.45%10.51%0.664
6463.64%36.36%11.48%10.60%0.662
6564.65%35.35%11.52%10.70%0.659
6665.66%34.34%11.55%10.80%0.656
6766.67%33.33%11.58%10.90%0.653
6867.68%32.32%11.62%11.00%0.650
6968.69%31.31%11.65%11.11%0.647
7069.70%30.30%11.69%11.21%0.644
7170.71%29.29%11.72%11.32%0.641
7271.72%28.28%11.75%11.43%0.638
7372.73%27.27%11.79%11.55%0.634
7473.74%26.26%11.82%11.66%0.631
7574.75%25.25%11.86%11.78%0.628
7675.76%24.24%11.89%11.90%0.624
7776.77%23.23%11.93%12.02%0.621
7877.78%22.22%11.96%12.14%0.617
7978.79%21.21%12.00%12.26%0.614
8079.80%20.20%12.03%12.39%0.611
8180.81%19.19%12.06%12.52%0.607
8281.82%18.18%12.10%12.64%0.604
8382.83%17.17%12.13%12.77%0.600
8483.84%16.16%12.17%12.90%0.597
8584.85%15.15%12.20%13.04%0.593
8685.86%14.14%12.24%13.17%0.590
8786.87%13.13%12.27%13.31%0.587
8887.88%12.12%12.30%13.44%0.583
8988.89%11.11%12.34%13.58%0.580
9089.90%10.10%12.37%13.72%0.577
9190.91%9.09%12.41%13.86%0.573
9291.92%8.08%12.44%14.00%0.570
9392.93%7.07%12.48%14.14%0.567
9493.94%6.06%12.51%14.28%0.563
9594.95%5.05%12.55%14.42%0.560
9695.96%4.04%12.58%14.57%0.557
9796.97%3.03%12.62%14.71%0.554
9897.98%2.02%12.65%14.86%0.551
9998.99%1.01%12.68%15.01%0.548
100100.00%0.00%12.72%15.16%0.545
*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 (4.47% 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.
  • 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