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 - Dec 2018)

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 Market11.17%12.46%15.14%0.5260.00%100.00%
2Long Term Treasury8.30%8.94%10.97%0.4040.00%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 Market1.000.05
Long Term Treasury0.051.00
Based on monthly returns from Jan 1978 to Dec 2018
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%8.94%10.97%0.404
21.01%98.99%8.97%10.87%0.411
32.02%97.98%9.01%10.77%0.419
43.03%96.97%9.04%10.68%0.426
54.04%95.96%9.08%10.58%0.433
65.05%94.95%9.11%10.49%0.440
76.06%93.94%9.15%10.40%0.447
87.07%92.93%9.18%10.31%0.454
98.08%91.92%9.22%10.23%0.462
109.09%90.91%9.25%10.14%0.469
1110.10%89.90%9.29%10.06%0.476
1211.11%88.89%9.32%9.99%0.483
1312.12%87.88%9.36%9.91%0.490
1413.13%86.87%9.40%9.84%0.497
1514.14%85.86%9.43%9.77%0.504
1615.15%84.85%9.47%9.71%0.511
1716.16%83.84%9.50%9.65%0.518
1817.17%82.83%9.54%9.59%0.525
1918.18%81.82%9.57%9.53%0.532
2019.19%80.81%9.61%9.48%0.539
2120.20%79.80%9.64%9.43%0.545
2221.21%78.79%9.68%9.39%0.552
2322.22%77.78%9.71%9.34%0.558
2423.23%76.77%9.75%9.30%0.564
2524.24%75.76%9.78%9.27%0.570
2625.25%74.75%9.82%9.24%0.576
2726.26%73.74%9.85%9.21%0.582
2827.27%72.73%9.89%9.18%0.587
2928.28%71.72%9.92%9.16%0.592
3029.29%70.71%9.96%9.14%0.597
3130.30%69.70%10.00%9.13%0.602
3231.31%68.69%10.03%9.12%0.607
3332.32%67.68%10.07%9.11%0.611
3433.33%66.67%10.10%9.11%0.615
3534.34%65.66%10.14%9.11%0.619
3635.35%64.65%10.17%9.12%0.622
3736.36%63.64%10.21%9.12%0.626
3837.37%62.63%10.24%9.14%0.629
3938.38%61.62%10.28%9.15%0.631
4039.39%60.61%10.31%9.17%0.634
4140.40%59.60%10.35%9.19%0.636
4241.41%58.59%10.39%9.22%0.638
4342.42%57.58%10.42%9.25%0.640
4443.43%56.57%10.46%9.29%0.642
4544.44%55.56%10.49%9.32%0.643
4645.45%54.55%10.53%9.36%0.644
4746.46%53.54%10.56%9.41%0.645
4847.47%52.53%10.60%9.45%0.645
4948.48%51.52%10.63%9.51%0.645
5049.49%50.51%10.67%9.56%0.645
5150.51%49.49%10.71%9.62%0.645
5251.52%48.48%10.74%9.68%0.645
5352.53%47.47%10.78%9.74%0.644
5453.54%46.46%10.81%9.81%0.644
5554.55%45.45%10.85%9.88%0.643
5655.56%44.44%10.88%9.95%0.642
5756.57%43.43%10.92%10.03%0.640
5857.58%42.42%10.96%10.10%0.639
5958.59%41.41%10.99%10.18%0.637
6059.60%40.40%11.03%10.27%0.636
6160.61%39.39%11.06%10.35%0.634
6261.62%38.38%11.10%10.44%0.632
6362.63%37.37%11.13%10.53%0.630
6463.64%36.36%11.17%10.63%0.628
6564.65%35.35%11.21%10.72%0.625
6665.66%34.34%11.24%10.82%0.623
6766.67%33.33%11.28%10.92%0.621
6867.68%32.32%11.31%11.02%0.618
6968.69%31.31%11.35%11.13%0.615
7069.70%30.30%11.38%11.24%0.613
7170.71%29.29%11.42%11.34%0.610
7271.72%28.28%11.46%11.45%0.607
7372.73%27.27%11.49%11.57%0.604
7473.74%26.26%11.53%11.68%0.602
7574.75%25.25%11.56%11.80%0.599
7675.76%24.24%11.60%11.91%0.596
7776.77%23.23%11.63%12.03%0.593
7877.78%22.22%11.67%12.15%0.590
7978.79%21.21%11.71%12.28%0.587
8079.80%20.20%11.74%12.40%0.584
8180.81%19.19%11.78%12.53%0.581
8281.82%18.18%11.81%12.65%0.578
8382.83%17.17%11.85%12.78%0.575
8483.84%16.16%11.89%12.91%0.572
8584.85%15.15%11.92%13.04%0.569
8685.86%14.14%11.96%13.18%0.566
8786.87%13.13%11.99%13.31%0.563
8887.88%12.12%12.03%13.44%0.560
8988.89%11.11%12.07%13.58%0.557
9089.90%10.10%12.10%13.72%0.554
9190.91%9.09%12.14%13.85%0.551
9291.92%8.08%12.17%13.99%0.548
9392.93%7.07%12.21%14.13%0.546
9493.94%6.06%12.25%14.27%0.543
9594.95%5.05%12.28%14.42%0.540
9695.96%4.04%12.32%14.56%0.537
9796.97%3.03%12.35%14.70%0.534
9897.98%2.02%12.39%14.85%0.531
9998.99%1.01%12.43%14.99%0.529
100100.00%0.00%12.46%15.14%0.526
*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