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 - Oct 2019)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 48.48%
Long Term Treasury 51.52%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio10.92%9.47%0.68

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1US Stock Market11.48%12.77%15.13%0.5490.00%100.00%
2Long Term Treasury8.56%9.21%11.06%0.4300.00%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 (4.46% 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 Oct 2019
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.21%11.06%0.430
21.01%98.99%9.24%10.96%0.437
32.02%97.98%9.28%10.86%0.444
43.03%96.97%9.32%10.76%0.452
54.04%95.96%9.35%10.66%0.459
65.05%94.95%9.39%10.56%0.467
76.06%93.94%9.42%10.47%0.474
87.07%92.93%9.46%10.38%0.482
98.08%91.92%9.49%10.29%0.490
109.09%90.91%9.53%10.21%0.497
1110.10%89.90%9.56%10.12%0.505
1211.11%88.89%9.60%10.04%0.512
1312.12%87.88%9.63%9.97%0.520
1413.13%86.87%9.67%9.89%0.527
1514.14%85.86%9.71%9.82%0.535
1615.15%84.85%9.74%9.75%0.542
1716.16%83.84%9.78%9.69%0.549
1817.17%82.83%9.81%9.62%0.557
1918.18%81.82%9.85%9.57%0.564
2019.19%80.81%9.88%9.51%0.571
2120.20%79.80%9.92%9.46%0.578
2221.21%78.79%9.95%9.41%0.585
2322.22%77.78%9.99%9.36%0.591
2423.23%76.77%10.03%9.32%0.598
2524.24%75.76%10.06%9.28%0.604
2625.25%74.75%10.10%9.25%0.610
2726.26%73.74%10.13%9.22%0.616
2827.27%72.73%10.17%9.19%0.622
2928.28%71.72%10.20%9.16%0.627
3029.29%70.71%10.24%9.14%0.633
3130.30%69.70%10.28%9.13%0.638
3231.31%68.69%10.31%9.11%0.643
3332.32%67.68%10.35%9.11%0.647
3433.33%66.67%10.38%9.10%0.651
3534.34%65.66%10.42%9.10%0.656
3635.35%64.65%10.45%9.10%0.659
3736.36%63.64%10.49%9.11%0.663
3837.37%62.63%10.53%9.12%0.666
3938.38%61.62%10.56%9.13%0.669
4039.39%60.61%10.60%9.15%0.672
4140.40%59.60%10.63%9.17%0.674
4241.41%58.59%10.67%9.19%0.676
4342.42%57.58%10.71%9.22%0.678
4443.43%56.57%10.74%9.25%0.679
4544.44%55.56%10.78%9.29%0.681
4645.45%54.55%10.81%9.33%0.682
4746.46%53.54%10.85%9.37%0.682
4847.47%52.53%10.88%9.42%0.683
4948.48%51.52%10.92%9.47%0.683
5049.49%50.51%10.96%9.52%0.683
5150.51%49.49%10.99%9.58%0.683
5251.52%48.48%11.03%9.64%0.682
5352.53%47.47%11.06%9.70%0.681
5453.54%46.46%11.10%9.76%0.681
5554.55%45.45%11.14%9.83%0.679
5655.56%44.44%11.17%9.91%0.678
5756.57%43.43%11.21%9.98%0.677
5857.58%42.42%11.24%10.06%0.675
5958.59%41.41%11.28%10.14%0.673
6059.60%40.40%11.32%10.22%0.671
6160.61%39.39%11.35%10.31%0.669
6261.62%38.38%11.39%10.40%0.667
6362.63%37.37%11.42%10.49%0.665
6463.64%36.36%11.46%10.58%0.662
6564.65%35.35%11.50%10.68%0.660
6665.66%34.34%11.53%10.78%0.657
6766.67%33.33%11.57%10.88%0.654
6867.68%32.32%11.61%10.98%0.651
6968.69%31.31%11.64%11.08%0.648
7069.70%30.30%11.68%11.19%0.645
7170.71%29.29%11.71%11.30%0.642
7271.72%28.28%11.75%11.41%0.639
7372.73%27.27%11.79%11.52%0.636
7473.74%26.26%11.82%11.64%0.633
7574.75%25.25%11.86%11.76%0.630
7675.76%24.24%11.89%11.87%0.627
7776.77%23.23%11.93%11.99%0.623
7877.78%22.22%11.97%12.12%0.620
7978.79%21.21%12.00%12.24%0.617
8079.80%20.20%12.04%12.36%0.613
8180.81%19.19%12.08%12.49%0.610
8281.82%18.18%12.11%12.62%0.607
8382.83%17.17%12.15%12.75%0.603
8483.84%16.16%12.18%12.88%0.600
8584.85%15.15%12.22%13.01%0.597
8685.86%14.14%12.26%13.14%0.594
8786.87%13.13%12.29%13.28%0.590
8887.88%12.12%12.33%13.41%0.587
8988.89%11.11%12.37%13.55%0.584
9089.90%10.10%12.40%13.69%0.581
9190.91%9.09%12.44%13.83%0.577
9291.92%8.08%12.48%13.97%0.574
9392.93%7.07%12.51%14.11%0.571
9493.94%6.06%12.55%14.25%0.568
9594.95%5.05%12.58%14.40%0.565
9695.96%4.04%12.62%14.54%0.562
9796.97%3.03%12.66%14.69%0.558
9897.98%2.02%12.69%14.83%0.555
9998.99%1.01%12.73%14.98%0.552
100100.00%0.00%12.77%15.13%0.549
*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 (4.46% annualized).
Notes on results:
  • Past performance is not a guarantee of future returns
  • Historical asset statistics are based on monthly returns from Jan 1978 to Oct 2019
  • 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