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 - Mar 2020)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 45.45%
Long Term Treasury 54.55%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio10.75%9.32%0.66

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1US Stock Market10.91%12.23%15.30%0.5010.00%100.00%
2Long Term Treasury8.87%9.53%11.13%0.4450.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (4.57% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.02
Long Term Treasury0.021.00
Based on monthly returns from Jan 1978 to Mar 2020
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.53%11.13%0.445
21.01%98.99%9.56%11.02%0.452
32.02%97.98%9.58%10.92%0.459
43.03%96.97%9.61%10.81%0.466
54.04%95.96%9.64%10.71%0.473
65.05%94.95%9.66%10.61%0.480
76.06%93.94%9.69%10.52%0.487
87.07%92.93%9.72%10.42%0.494
98.08%91.92%9.75%10.33%0.501
109.09%90.91%9.77%10.24%0.508
1110.10%89.90%9.80%10.16%0.515
1211.11%88.89%9.83%10.07%0.522
1312.12%87.88%9.85%9.99%0.529
1413.13%86.87%9.88%9.91%0.536
1514.14%85.86%9.91%9.84%0.542
1615.15%84.85%9.93%9.77%0.549
1716.16%83.84%9.96%9.70%0.556
1817.17%82.83%9.99%9.64%0.562
1918.18%81.82%10.02%9.57%0.569
2019.19%80.81%10.04%9.52%0.575
2120.20%79.80%10.07%9.46%0.581
2221.21%78.79%10.10%9.41%0.587
2322.22%77.78%10.12%9.36%0.593
2423.23%76.77%10.15%9.32%0.599
2524.24%75.76%10.18%9.28%0.604
2625.25%74.75%10.20%9.24%0.610
2726.26%73.74%10.23%9.21%0.615
2827.27%72.73%10.26%9.18%0.620
2928.28%71.72%10.29%9.15%0.624
3029.29%70.71%10.31%9.13%0.629
3130.30%69.70%10.34%9.11%0.633
3231.31%68.69%10.37%9.10%0.637
3332.32%67.68%10.39%9.09%0.641
3433.33%66.67%10.42%9.08%0.644
3534.34%65.66%10.45%9.08%0.647
3635.35%64.65%10.48%9.08%0.650
3736.36%63.64%10.50%9.09%0.653
3837.37%62.63%10.53%9.10%0.655
3938.38%61.62%10.56%9.11%0.657
4039.39%60.61%10.59%9.13%0.659
4140.40%59.60%10.61%9.15%0.660
4241.41%58.59%10.64%9.18%0.661
4342.42%57.58%10.67%9.21%0.662
4443.43%56.57%10.69%9.24%0.663
4544.44%55.56%10.72%9.28%0.663
4645.45%54.55%10.75%9.32%0.663
4746.46%53.54%10.78%9.36%0.663
4847.47%52.53%10.80%9.41%0.662
4948.48%51.52%10.83%9.46%0.662
5049.49%50.51%10.86%9.52%0.661
5150.51%49.49%10.88%9.58%0.659
5251.52%48.48%10.91%9.64%0.658
5352.53%47.47%10.94%9.70%0.656
5453.54%46.46%10.97%9.77%0.655
5554.55%45.45%10.99%9.84%0.653
5655.56%44.44%11.02%9.92%0.651
5756.57%43.43%11.05%9.99%0.648
5857.58%42.42%11.08%10.07%0.646
5958.59%41.41%11.10%10.16%0.643
6059.60%40.40%11.13%10.24%0.640
6160.61%39.39%11.16%10.33%0.638
6261.62%38.38%11.18%10.42%0.635
6362.63%37.37%11.21%10.52%0.631
6463.64%36.36%11.24%10.61%0.628
6564.65%35.35%11.27%10.71%0.625
6665.66%34.34%11.29%10.82%0.622
6766.67%33.33%11.32%10.92%0.618
6867.68%32.32%11.35%11.03%0.615
6968.69%31.31%11.38%11.13%0.611
7069.70%30.30%11.40%11.24%0.608
7170.71%29.29%11.43%11.36%0.604
7271.72%28.28%11.46%11.47%0.600
7372.73%27.27%11.49%11.59%0.597
7473.74%26.26%11.51%11.71%0.593
7574.75%25.25%11.54%11.83%0.589
7675.76%24.24%11.57%11.95%0.586
7776.77%23.23%11.60%12.07%0.582
7877.78%22.22%11.62%12.20%0.578
7978.79%21.21%11.65%12.33%0.574
8079.80%20.20%11.68%12.46%0.571
8180.81%19.19%11.71%12.59%0.567
8281.82%18.18%11.73%12.72%0.563
8382.83%17.17%11.76%12.85%0.559
8483.84%16.16%11.79%12.99%0.556
8584.85%15.15%11.82%13.12%0.552
8685.86%14.14%11.84%13.26%0.548
8786.87%13.13%11.87%13.40%0.545
8887.88%12.12%11.90%13.54%0.541
8988.89%11.11%11.93%13.68%0.538
9089.90%10.10%11.95%13.82%0.534
9190.91%9.09%11.98%13.96%0.531
9291.92%8.08%12.01%14.11%0.527
9392.93%7.07%12.04%14.25%0.524
9493.94%6.06%12.06%14.40%0.520
9594.95%5.05%12.09%14.55%0.517
9695.96%4.04%12.12%14.70%0.514
9796.97%3.03%12.15%14.85%0.510
9897.98%2.02%12.17%15.00%0.507
9998.99%1.01%12.20%15.15%0.504
100100.00%0.00%12.23%15.30%0.501
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (4.57% annualized).
Notes on results:
  • Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
  • All portfolio returns presented are hypothetical and backtested. Hypothetical returns do not reflect trading costs, transaction fees, or taxes.
  • Portfolio optimization determines target weights for portfolio assets based on mathematical models that can use either historical or forecasted data as inputs. Optimization results are not guarantees of future performance.
  • The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
  • The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities.
  • The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
  • Historical asset statistics are based on monthly returns from Jan 1978 to Mar 2020
  • 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 3-month treasury bill returns as the risk free rate