Efficient Frontier

Efficient Frontier Overview

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.

Efficient Frontier Configuration

Efficient Frontier Assets
Allocation
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Asset Groups
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D
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E
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Efficient Frontier Results (Jan 1978 - Dec 2021)

Max Sharpe Ratio Portfolio

Asset Class Allocation
US Stock Market 24.49%
Short Term Treasury 63.68%
Long Term Treasury 11.83%
Save portfolio »

Performance Summary

PortfolioExpected ReturnStandard DeviationSharpe Ratio
Max Sharpe Ratio Portfolio7.71%4.92%0.69

Efficient Frontier

Notes and Disclosures
  • IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
  • 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. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
  • Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
  • Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
  • 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.
  • Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
  • Portfolio optimization is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. 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 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 Dec 2021
  • 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

Efficient Frontier Assets

#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market12.68%15.37%0.5450.00%100.00%
2Short Term Treasury5.62%3.08%0.4290.00%100.00%
3Intermediate Term Treasury6.87%5.87%0.4380.00%100.00%
4Long Term Treasury8.64%11.12%0.3900.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

AssetUS Stock MarketShort Term TreasuryIntermediate Term TreasuryLong Term Treasury
US Stock Market1.000.040.040.02
Short Term Treasury0.041.000.920.70
Intermediate Term Treasury0.040.921.000.88
Long Term Treasury0.020.700.881.00
Based on monthly returns from Jan 1978 to Dec 2021

Efficient Frontier Portfolios

#US Stock MarketShort Term TreasuryIntermediate Term TreasuryLong Term TreasuryExpected Return *Standard Deviation *Sharpe Ratio *
13.12%96.88%0.00%0.00%5.84%3.04%0.507
24.10%95.90%0.00%0.00%5.91%3.04%0.529
35.08%94.92%0.00%0.00%5.98%3.06%0.550
46.06%93.94%0.00%0.00%6.05%3.08%0.569
57.03%92.97%0.00%0.00%6.12%3.10%0.586
68.01%91.99%0.00%0.00%6.19%3.13%0.602
78.99%91.01%0.00%0.00%6.26%3.18%0.616
89.97%90.03%0.00%0.00%6.33%3.22%0.628
910.95%89.05%0.00%0.00%6.40%3.28%0.639
1011.93%88.07%0.00%0.00%6.47%3.34%0.648
1112.91%87.09%0.00%0.00%6.53%3.40%0.656
1213.88%86.12%0.00%0.00%6.60%3.47%0.663
1314.86%85.14%0.00%0.00%6.67%3.55%0.668
1415.65%83.90%0.00%0.45%6.74%3.63%0.672
1516.28%82.46%0.00%1.26%6.81%3.71%0.676
1616.91%81.01%0.00%2.07%6.88%3.79%0.679
1717.54%79.57%0.00%2.89%6.95%3.88%0.682
1818.18%78.12%0.00%3.70%7.02%3.97%0.684
1918.81%76.68%0.00%4.51%7.09%4.06%0.686
2019.44%75.23%0.00%5.33%7.16%4.15%0.688
2120.07%73.79%0.00%6.14%7.22%4.24%0.689
2220.70%72.35%0.00%6.95%7.29%4.33%0.690
2321.33%70.90%0.00%7.76%7.36%4.43%0.691
2421.97%69.46%0.00%8.58%7.43%4.52%0.692
2522.60%68.01%0.00%9.39%7.50%4.62%0.692
2623.23%66.57%0.00%10.20%7.57%4.72%0.692
2723.86%65.12%0.00%11.02%7.64%4.82%0.693
2824.49%63.68%0.00%11.83%7.71%4.92%0.693
2925.10%61.82%0.66%12.41%7.78%5.02%0.693
3025.67%58.99%2.90%12.45%7.85%5.12%0.692
3126.24%56.15%5.13%12.48%7.92%5.22%0.692
3226.81%53.31%7.37%12.52%7.98%5.32%0.692
3327.37%50.47%9.61%12.55%8.05%5.42%0.692
3427.94%47.63%11.84%12.59%8.12%5.52%0.691
3528.51%44.79%14.08%12.62%8.19%5.63%0.691
3629.08%41.95%16.32%12.65%8.26%5.73%0.691
3729.64%39.11%18.55%12.69%8.33%5.83%0.690
3830.21%36.27%20.79%12.72%8.40%5.94%0.690
3930.78%33.43%23.03%12.76%8.47%6.04%0.690
4031.35%30.60%25.26%12.79%8.54%6.14%0.689
4131.91%27.76%27.50%12.83%8.61%6.25%0.689
4232.48%24.92%29.74%12.86%8.67%6.35%0.688
4333.05%22.08%31.98%12.90%8.74%6.46%0.688
4433.62%19.24%34.21%12.93%8.81%6.56%0.687
4534.18%16.40%36.45%12.97%8.88%6.67%0.687
4634.75%13.56%38.69%13.00%8.95%6.77%0.686
4735.32%10.72%40.92%13.04%9.02%6.88%0.686
4835.89%7.88%43.16%13.07%9.09%6.98%0.685
4936.45%5.05%45.40%13.11%9.16%7.09%0.685
5037.02%2.21%47.63%13.14%9.23%7.19%0.684
5137.62%0.00%48.88%13.50%9.30%7.30%0.684
5238.36%0.00%46.64%15.00%9.37%7.41%0.683
5339.10%0.00%44.41%16.49%9.43%7.52%0.683
5439.83%0.00%42.18%17.99%9.50%7.62%0.682
5540.57%0.00%39.95%19.49%9.57%7.73%0.681
5641.30%0.00%37.72%20.98%9.64%7.84%0.681
5742.04%0.00%35.49%22.48%9.71%7.96%0.680
5842.77%0.00%33.25%23.98%9.78%8.07%0.679
5943.51%0.00%31.02%25.47%9.85%8.18%0.678
6044.24%0.00%28.79%26.97%9.92%8.29%0.677
6144.98%0.00%26.56%28.46%9.99%8.41%0.676
6245.71%0.00%24.33%29.96%10.06%8.52%0.675
6346.45%0.00%22.10%31.46%10.12%8.64%0.674
6447.18%0.00%19.86%32.95%10.19%8.76%0.673
6547.92%0.00%17.63%34.45%10.26%8.87%0.672
6648.65%0.00%15.40%35.95%10.33%8.99%0.671
6749.39%0.00%13.17%37.44%10.40%9.11%0.670
6850.12%0.00%10.94%38.94%10.47%9.23%0.668
6950.86%0.00%8.71%40.44%10.54%9.34%0.667
7051.59%0.00%6.47%41.93%10.61%9.46%0.666
7152.33%0.00%4.24%43.43%10.68%9.58%0.665
7253.06%0.00%2.01%44.93%10.75%9.70%0.664
7353.90%0.00%0.00%46.10%10.82%9.83%0.663
7455.60%0.00%0.00%44.40%10.88%9.95%0.661
7557.31%0.00%0.00%42.69%10.95%10.09%0.659
7659.02%0.00%0.00%40.98%11.02%10.23%0.657
7760.73%0.00%0.00%39.27%11.09%10.38%0.654
7862.43%0.00%0.00%37.57%11.16%10.54%0.651
7964.14%0.00%0.00%35.86%11.23%10.71%0.647
8065.85%0.00%0.00%34.15%11.30%10.88%0.643
8167.56%0.00%0.00%32.44%11.37%11.06%0.639
8269.26%0.00%0.00%30.74%11.44%11.24%0.634
8370.97%0.00%0.00%29.03%11.51%11.44%0.630
8472.68%0.00%0.00%27.32%11.57%11.63%0.625
8574.39%0.00%0.00%25.61%11.64%11.84%0.620
8676.09%0.00%0.00%23.91%11.71%12.05%0.615
8777.80%0.00%0.00%22.20%11.78%12.26%0.610
8879.51%0.00%0.00%20.49%11.85%12.48%0.605
8981.22%0.00%0.00%18.78%11.92%12.70%0.600
9082.92%0.00%0.00%17.08%11.99%12.92%0.595
9184.63%0.00%0.00%15.37%12.06%13.15%0.590
9286.34%0.00%0.00%13.66%12.13%13.39%0.584
9388.05%0.00%0.00%11.95%12.20%13.63%0.579
9489.75%0.00%0.00%10.25%12.27%13.87%0.574
9591.46%0.00%0.00%8.54%12.33%14.11%0.569
9693.17%0.00%0.00%6.83%12.40%14.36%0.564
9794.88%0.00%0.00%5.12%12.47%14.61%0.559
9896.58%0.00%0.00%3.42%12.54%14.86%0.554
9998.29%0.00%0.00%1.71%12.61%15.12%0.550
100100.00%0.00%0.00%0.00%12.68%15.37%0.545
*Annualized 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.