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 - Dec 2021)

Portfolio Allocations

Max Sharpe Ratio Portfolio
Asset Class Allocation
US Stock Market 50.51%
Long Term Treasury 49.49%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Max Sharpe Ratio Portfolio11.22%9.60%0.66

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market13.44%15.37%0.5450.00%100.00%
2Long Term Treasury8.99%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

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 Dec 2021
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%8.99%11.12%0.390
21.01%98.99%9.03%11.01%0.397
32.02%97.98%9.07%10.91%0.405
43.03%96.97%9.12%10.80%0.413
54.04%95.96%9.16%10.70%0.420
65.05%94.95%9.21%10.60%0.428
76.06%93.94%9.25%10.50%0.436
87.07%92.93%9.30%10.41%0.444
98.08%91.92%9.34%10.32%0.452
109.09%90.91%9.38%10.23%0.459
1110.10%89.90%9.43%10.15%0.467
1211.11%88.89%9.47%10.06%0.475
1312.12%87.88%9.52%9.98%0.483
1413.13%86.87%9.56%9.91%0.491
1514.14%85.86%9.61%9.83%0.499
1615.15%84.85%9.65%9.76%0.507
1716.16%83.84%9.70%9.69%0.514
1817.17%82.83%9.74%9.63%0.522
1918.18%81.82%9.78%9.57%0.530
2019.19%80.81%9.83%9.51%0.537
2120.20%79.80%9.87%9.46%0.545
2221.21%78.79%9.92%9.41%0.552
2322.22%77.78%9.96%9.36%0.559
2423.23%76.77%10.01%9.32%0.566
2524.24%75.76%10.05%9.28%0.573
2625.25%74.75%10.10%9.24%0.580
2726.26%73.74%10.14%9.21%0.586
2827.27%72.73%10.19%9.18%0.592
2928.28%71.72%10.23%9.15%0.598
3029.29%70.71%10.27%9.13%0.604
3130.30%69.70%10.32%9.12%0.610
3231.31%68.69%10.36%9.10%0.615
3332.32%67.68%10.41%9.10%0.620
3433.33%66.67%10.45%9.09%0.625
3534.34%65.66%10.50%9.09%0.629
3635.35%64.65%10.54%9.09%0.634
3736.36%63.64%10.59%9.10%0.638
3837.37%62.63%10.63%9.11%0.641
3938.38%61.62%10.68%9.13%0.645
4039.39%60.61%10.72%9.15%0.648
4140.40%59.60%10.77%9.17%0.651
4241.41%58.59%10.81%9.19%0.653
4342.42%57.58%10.86%9.23%0.656
4443.43%56.57%10.90%9.26%0.658
4544.44%55.56%10.95%9.30%0.659
4645.45%54.55%10.99%9.34%0.661
4746.46%53.54%11.04%9.38%0.662
4847.47%52.53%11.08%9.43%0.663
4948.48%51.52%11.13%9.49%0.663
5049.49%50.51%11.17%9.54%0.664
5150.51%49.49%11.22%9.60%0.664
5251.52%48.48%11.26%9.66%0.664
5352.53%47.47%11.31%9.73%0.664
5453.54%46.46%11.35%9.80%0.663
5554.55%45.45%11.40%9.87%0.662
5655.56%44.44%11.44%9.95%0.661
5756.57%43.43%11.49%10.03%0.660
5857.58%42.42%11.53%10.11%0.659
5958.59%41.41%11.58%10.19%0.658
6059.60%40.40%11.62%10.28%0.656
6160.61%39.39%11.67%10.37%0.654
6261.62%38.38%11.71%10.46%0.652
6362.63%37.37%11.76%10.56%0.650
6463.64%36.36%11.80%10.66%0.648
6564.65%35.35%11.85%10.76%0.646
6665.66%34.34%11.89%10.86%0.644
6766.67%33.33%11.94%10.96%0.641
6867.68%32.32%11.98%11.07%0.639
6968.69%31.31%12.03%11.18%0.636
7069.70%30.30%12.07%11.29%0.633
7170.71%29.29%12.12%11.41%0.631
7271.72%28.28%12.17%11.52%0.628
7372.73%27.27%12.21%11.64%0.625
7473.74%26.26%12.26%11.76%0.622
7574.75%25.25%12.30%11.88%0.619
7675.76%24.24%12.35%12.00%0.616
7776.77%23.23%12.39%12.13%0.613
7877.78%22.22%12.44%12.26%0.610
7978.79%21.21%12.48%12.38%0.607
8079.80%20.20%12.53%12.51%0.604
8180.81%19.19%12.57%12.64%0.601
8281.82%18.18%12.62%12.78%0.598
8382.83%17.17%12.67%12.91%0.595
8483.84%16.16%12.71%13.05%0.592
8584.85%15.15%12.76%13.18%0.589
8685.86%14.14%12.80%13.32%0.586
8786.87%13.13%12.85%13.46%0.583
8887.88%12.12%12.89%13.60%0.580
8988.89%11.11%12.94%13.74%0.577
9089.90%10.10%12.99%13.89%0.574
9190.91%9.09%13.03%14.03%0.571
9291.92%8.08%13.08%14.18%0.568
9392.93%7.07%13.12%14.32%0.565
9493.94%6.06%13.17%14.47%0.562
9594.95%5.05%13.21%14.62%0.559
9695.96%4.04%13.26%14.77%0.556
9796.97%3.03%13.31%14.92%0.553
9897.98%2.02%13.35%15.07%0.550
9998.99%1.01%13.40%15.22%0.548
100100.00%0.00%13.44%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.
Notes on results:
  • 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, 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 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