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 - Jun 2020)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 46.46%
Long Term Treasury 53.54%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio10.97%9.39%0.68

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market11.37%12.70%15.39%0.5300.00%100.00%
2Long Term Treasury8.83%9.48%11.11%0.4450.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (4.54% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.02
Long Term Treasury0.021.00
Based on provided custom correlation matrix
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.48%11.11%0.445
21.01%98.99%9.52%11.00%0.452
32.02%97.98%9.55%10.89%0.459
43.03%96.97%9.58%10.79%0.467
54.04%95.96%9.61%10.69%0.474
65.05%94.95%9.64%10.59%0.482
76.06%93.94%9.68%10.49%0.489
87.07%92.93%9.71%10.40%0.497
98.08%91.92%9.74%10.31%0.504
109.09%90.91%9.77%10.22%0.512
1110.10%89.90%9.81%10.13%0.519
1211.11%88.89%9.84%10.05%0.527
1312.12%87.88%9.87%9.97%0.534
1413.13%86.87%9.90%9.90%0.541
1514.14%85.86%9.93%9.82%0.549
1615.15%84.85%9.97%9.75%0.556
1716.16%83.84%10.00%9.68%0.563
1817.17%82.83%10.03%9.62%0.570
1918.18%81.82%10.06%9.56%0.577
2019.19%80.81%10.10%9.50%0.584
2120.20%79.80%10.13%9.45%0.591
2221.21%78.79%10.16%9.40%0.597
2322.22%77.78%10.19%9.35%0.604
2423.23%76.77%10.22%9.31%0.610
2524.24%75.76%10.26%9.27%0.616
2625.25%74.75%10.29%9.23%0.622
2726.26%73.74%10.32%9.20%0.628
2827.27%72.73%10.35%9.17%0.633
2928.28%71.72%10.39%9.15%0.638
3029.29%70.71%10.42%9.13%0.643
3130.30%69.70%10.45%9.11%0.648
3231.31%68.69%10.48%9.10%0.652
3332.32%67.68%10.51%9.09%0.657
3433.33%66.67%10.55%9.09%0.661
3534.34%65.66%10.58%9.09%0.664
3635.35%64.65%10.61%9.09%0.667
3736.36%63.64%10.64%9.10%0.670
3837.37%62.63%10.68%9.11%0.673
3938.38%61.62%10.71%9.12%0.676
4039.39%60.61%10.74%9.14%0.678
4140.40%59.60%10.77%9.17%0.680
4241.41%58.59%10.81%9.19%0.681
4342.42%57.58%10.84%9.22%0.682
4443.43%56.57%10.87%9.26%0.683
4544.44%55.56%10.90%9.30%0.684
4645.45%54.55%10.94%9.34%0.684
4746.46%53.54%10.97%9.39%0.684
4847.47%52.53%11.00%9.44%0.684
4948.48%51.52%11.03%9.49%0.684
5049.49%50.51%11.07%9.54%0.683
5150.51%49.49%11.10%9.60%0.682
5251.52%48.48%11.13%9.67%0.681
5352.53%47.47%11.16%9.73%0.680
5453.54%46.46%11.20%9.80%0.678
5554.55%45.45%11.23%9.88%0.677
5655.56%44.44%11.26%9.95%0.675
5756.57%43.43%11.29%10.03%0.673
5857.58%42.42%11.33%10.11%0.671
5958.59%41.41%11.36%10.20%0.668
6059.60%40.40%11.39%10.29%0.666
6160.61%39.39%11.42%10.38%0.663
6261.62%38.38%11.46%10.47%0.660
6362.63%37.37%11.49%10.56%0.657
6463.64%36.36%11.52%10.66%0.654
6564.65%35.35%11.55%10.76%0.651
6665.66%34.34%11.59%10.87%0.648
6766.67%33.33%11.62%10.97%0.645
6867.68%32.32%11.65%11.08%0.642
6968.69%31.31%11.68%11.19%0.638
7069.70%30.30%11.72%11.30%0.635
7170.71%29.29%11.75%11.41%0.631
7271.72%28.28%11.78%11.53%0.628
7372.73%27.27%11.81%11.65%0.624
7473.74%26.26%11.85%11.77%0.621
7574.75%25.25%11.88%11.89%0.617
7675.76%24.24%11.91%12.01%0.613
7776.77%23.23%11.95%12.14%0.610
7877.78%22.22%11.98%12.26%0.606
7978.79%21.21%12.01%12.39%0.603
8079.80%20.20%12.04%12.52%0.599
8180.81%19.19%12.08%12.65%0.595
8281.82%18.18%12.11%12.79%0.592
8382.83%17.17%12.14%12.92%0.588
8483.84%16.16%12.17%13.06%0.584
8584.85%15.15%12.21%13.19%0.581
8685.86%14.14%12.24%13.33%0.577
8786.87%13.13%12.27%13.47%0.574
8887.88%12.12%12.31%13.61%0.570
8988.89%11.11%12.34%13.75%0.567
9089.90%10.10%12.37%13.90%0.563
9190.91%9.09%12.40%14.04%0.560
9291.92%8.08%12.44%14.19%0.556
9392.93%7.07%12.47%14.33%0.553
9493.94%6.06%12.50%14.48%0.550
9594.95%5.05%12.54%14.63%0.546
9695.96%4.04%12.57%14.78%0.543
9796.97%3.03%12.60%14.93%0.540
9897.98%2.02%12.63%15.08%0.536
9998.99%1.01%12.67%15.23%0.533
100100.00%0.00%12.70%15.39%0.530
*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 (4.54% 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 Jun 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