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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 based on historical returns or forward-looking capital market assumptions 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. 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
Expected Return
Volatility
Min. Weight
Max. Weight
Group
1
%
%
%
%
%
2
%
%
%
%
%
3
%
%
%
%
%
4
%
%
%
%
%
5
%
%
%
%
%
6
%
%
%
%
%
7
%
%
%
%
%
8
%
%
%
%
%
9
%
%
%
%
%
10
%
%
%
%
%
Total
%
Asset Groups
Min. Weight
Max. Weight
A
%
%
B
%
%
C
%
%
D
%
%
E
%
%
F
%
%

Efficient Frontier Results (Jan 1978 - Aug 2026)

Note: The time period was constrained by the available data for Long Term Treasury [Jan 1978 - Aug 2026].

Max Sharpe Ratio Portfolio

Asset Class Allocation
US Stock Market 65.48%
Long Term Treasury 34.52%

Performance Summary

PortfolioExpected ReturnStandard DeviationSharpe Ratio
Max Sharpe Ratio Portfolio10.75%11.17%0.58

Efficient Frontier

Efficient Frontier Assets

#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market12.63%15.44%0.5410.00%100.00%
2Long Term Treasury7.17%11.48%0.2520.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using U.S. 3-Month Treasury Bill Rate returns as the risk-free rate.

Asset Correlations

AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.09
Long Term Treasury0.091.00
Based on monthly returns from Jan 1978 to Aug 2026

Efficient Frontier Portfolios

#US Stock MarketLong Term TreasuryExpected Return *Standard Deviation *Sharpe Ratio *
134.28%65.72%9.04%9.58%0.497
234.94%65.06%9.08%9.58%0.501
335.60%64.40%9.11%9.59%0.504
436.27%63.73%9.15%9.59%0.508
536.93%63.07%9.19%9.60%0.511
637.60%62.40%9.22%9.60%0.515
738.26%61.74%9.26%9.61%0.518
838.92%61.08%9.30%9.62%0.521
939.59%60.41%9.33%9.63%0.525
1040.25%59.75%9.37%9.65%0.528
1140.91%59.09%9.40%9.66%0.531
1241.58%58.42%9.44%9.68%0.533
1342.24%57.76%9.48%9.70%0.536
1442.91%57.09%9.51%9.71%0.539
1543.57%56.43%9.55%9.74%0.541
1644.23%55.77%9.59%9.76%0.544
1744.90%55.10%9.62%9.78%0.546
1845.56%54.44%9.66%9.81%0.549
1946.23%53.77%9.69%9.83%0.551
2046.89%53.11%9.73%9.86%0.553
2147.55%52.45%9.77%9.89%0.555
2248.22%51.78%9.80%9.92%0.557
2348.88%51.12%9.84%9.95%0.559
2449.55%50.45%9.88%9.99%0.560
2550.21%49.79%9.91%10.02%0.562
2650.87%49.13%9.95%10.06%0.564
2751.54%48.46%9.98%10.10%0.565
2852.20%47.80%10.02%10.14%0.567
2952.86%47.14%10.06%10.18%0.568
3053.53%46.47%10.09%10.22%0.569
3154.19%45.81%10.13%10.26%0.570
3254.86%45.14%10.17%10.31%0.571
3355.52%44.48%10.20%10.35%0.572
3456.18%43.82%10.24%10.40%0.573
3556.85%43.15%10.28%10.45%0.574
3657.51%42.49%10.31%10.50%0.575
3758.18%41.82%10.35%10.55%0.575
3858.84%41.16%10.38%10.60%0.576
3959.50%40.50%10.42%10.65%0.577
4060.17%39.83%10.46%10.70%0.577
4160.83%39.17%10.49%10.76%0.578
4261.49%38.51%10.53%10.82%0.578
4362.16%37.84%10.57%10.87%0.578
4462.82%37.18%10.60%10.93%0.578
4563.49%36.51%10.64%10.99%0.579
4664.15%35.85%10.67%11.05%0.579
4764.81%35.19%10.71%11.11%0.579
4865.48%34.52%10.75%11.17%0.579
4966.14%33.86%10.78%11.24%0.579
5066.81%33.19%10.82%11.30%0.579
5167.47%32.53%10.86%11.37%0.579
5268.13%31.87%10.89%11.43%0.578
5368.80%31.20%10.93%11.50%0.578
5469.46%30.54%10.96%11.57%0.578
5570.13%29.87%11.00%11.64%0.578
5670.79%29.21%11.04%11.71%0.577
5771.45%28.55%11.07%11.78%0.577
5872.12%27.88%11.11%11.85%0.576
5972.78%27.22%11.15%11.92%0.576
6073.44%26.56%11.18%12.00%0.575
6174.11%25.89%11.22%12.07%0.575
6274.77%25.23%11.25%12.14%0.574
6375.44%24.56%11.29%12.22%0.574
6476.10%23.90%11.33%12.30%0.573
6576.76%23.24%11.36%12.37%0.573
6677.43%22.57%11.40%12.45%0.572
6778.09%21.91%11.44%12.53%0.571
6878.76%21.24%11.47%12.61%0.571
6979.42%20.58%11.51%12.69%0.570
7080.08%19.92%11.54%12.77%0.569
7180.75%19.25%11.58%12.85%0.568
7281.41%18.59%11.62%12.93%0.568
7382.08%17.92%11.65%13.01%0.567
7482.74%17.26%11.69%13.10%0.566
7583.40%16.60%11.73%13.18%0.565
7684.07%15.93%11.76%13.26%0.564
7784.73%15.27%11.80%13.35%0.563
7885.39%14.61%11.84%13.43%0.562
7986.06%13.94%11.87%13.52%0.562
8086.72%13.28%11.91%13.61%0.561
8187.39%12.61%11.94%13.69%0.560
8288.05%11.95%11.98%13.78%0.559
8388.71%11.29%12.02%13.87%0.558
8489.38%10.62%12.05%13.96%0.557
8590.04%9.96%12.09%14.05%0.556
8690.71%9.29%12.13%14.14%0.555
8791.37%8.63%12.16%14.23%0.554
8892.03%7.97%12.20%14.32%0.553
8992.70%7.30%12.23%14.41%0.552
9093.36%6.64%12.27%14.50%0.551
9194.02%5.98%12.31%14.59%0.550
9294.69%5.31%12.34%14.69%0.549
9395.35%4.65%12.38%14.78%0.548
9496.02%3.98%12.42%14.87%0.547
9596.68%3.32%12.45%14.97%0.546
9697.34%2.66%12.49%15.06%0.545
9798.01%1.99%12.52%15.15%0.544
9898.67%1.33%12.56%15.25%0.543
9999.34%0.66%12.60%15.34%0.542
100100.00%0.00%12.63%15.44%0.541
*Annualized ex-ante values shown for portfolio return and volatility. Ex-ante Sharpe Ratio calculated using historical U.S. 3-Month Treasury Bill Rate returns as the risk-free rate.

  • 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. Other investments not considered may have characteristics similar or superior to those being analyzed.
  • 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 Aug 2026
  • 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 U.S. 3-Month Treasury Bill Rate returns as the risk free rate