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 - Oct 2022)

Portfolio Allocations

Max Sharpe Ratio Portfolio
Asset Class Allocation
US Stock Market 56.57%
Long Term Treasury 43.43%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Max Sharpe Ratio Portfolio10.12%10.30%0.57

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market12.03%15.60%0.4990.00%100.00%
2Long Term Treasury7.62%11.32%0.2980.00%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 Market1.000.05
Long Term Treasury0.051.00
Based on monthly returns from Jan 1978 to Oct 2022
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return *Standard Deviation *Sharpe Ratio *
10.00%100.00%7.62%11.32%0.298
21.01%98.99%7.67%11.22%0.305
32.02%97.98%7.71%11.11%0.312
43.03%96.97%7.76%11.01%0.319
54.04%95.96%7.80%10.91%0.326
65.05%94.95%7.85%10.82%0.333
76.06%93.94%7.89%10.72%0.340
87.07%92.93%7.93%10.63%0.347
98.08%91.92%7.98%10.54%0.354
109.09%90.91%8.02%10.46%0.361
1110.10%89.90%8.07%10.37%0.368
1211.11%88.89%8.11%10.29%0.376
1312.12%87.88%8.16%10.22%0.383
1413.13%86.87%8.20%10.14%0.390
1514.14%85.86%8.25%10.07%0.397
1615.15%84.85%8.29%10.00%0.404
1716.16%83.84%8.34%9.94%0.411
1817.17%82.83%8.38%9.87%0.419
1918.18%81.82%8.42%9.82%0.426
2019.19%80.81%8.47%9.76%0.433
2120.20%79.80%8.51%9.71%0.439
2221.21%78.79%8.56%9.66%0.446
2322.22%77.78%8.60%9.62%0.453
2423.23%76.77%8.65%9.57%0.460
2524.24%75.76%8.69%9.54%0.466
2625.25%74.75%8.74%9.50%0.472
2726.26%73.74%8.78%9.47%0.479
2827.27%72.73%8.82%9.45%0.485
2928.28%71.72%8.87%9.42%0.491
3029.29%70.71%8.91%9.40%0.496
3130.30%69.70%8.96%9.39%0.502
3231.31%68.69%9.00%9.38%0.507
3332.32%67.68%9.05%9.37%0.512
3433.33%66.67%9.09%9.37%0.517
3534.34%65.66%9.14%9.37%0.522
3635.35%64.65%9.18%9.37%0.527
3736.36%63.64%9.23%9.38%0.531
3837.37%62.63%9.27%9.39%0.535
3938.38%61.62%9.31%9.41%0.539
4039.39%60.61%9.36%9.43%0.542
4140.40%59.60%9.40%9.45%0.546
4241.41%58.59%9.45%9.48%0.549
4342.42%57.58%9.49%9.51%0.552
4443.43%56.57%9.54%9.54%0.554
4544.44%55.56%9.58%9.58%0.557
4645.45%54.55%9.63%9.62%0.559
4746.46%53.54%9.67%9.67%0.561
4847.47%52.53%9.72%9.71%0.563
4948.48%51.52%9.76%9.77%0.564
5049.49%50.51%9.80%9.82%0.566
5150.51%49.49%9.85%9.88%0.567
5251.52%48.48%9.89%9.94%0.568
5352.53%47.47%9.94%10.01%0.569
5453.54%46.46%9.98%10.08%0.569
5554.55%45.45%10.03%10.15%0.569
5655.56%44.44%10.07%10.22%0.570
5756.57%43.43%10.12%10.30%0.570
5857.58%42.42%10.16%10.38%0.570
5958.59%41.41%10.21%10.47%0.569
6059.60%40.40%10.25%10.55%0.569
6160.61%39.39%10.29%10.64%0.568
6261.62%38.38%10.34%10.73%0.568
6362.63%37.37%10.38%10.83%0.567
6463.64%36.36%10.43%10.92%0.566
6564.65%35.35%10.47%11.02%0.565
6665.66%34.34%10.52%11.13%0.564
6766.67%33.33%10.56%11.23%0.562
6867.68%32.32%10.61%11.34%0.561
6968.69%31.31%10.65%11.44%0.560
7069.70%30.30%10.70%11.55%0.558
7170.71%29.29%10.74%11.67%0.557
7271.72%28.28%10.78%11.78%0.555
7372.73%27.27%10.83%11.90%0.553
7473.74%26.26%10.87%12.02%0.551
7574.75%25.25%10.92%12.14%0.550
7675.76%24.24%10.96%12.26%0.548
7776.77%23.23%11.01%12.38%0.546
7877.78%22.22%11.05%12.51%0.544
7978.79%21.21%11.10%12.63%0.542
8079.80%20.20%11.14%12.76%0.540
8180.81%19.19%11.18%12.89%0.538
8281.82%18.18%11.23%13.02%0.536
8382.83%17.17%11.27%13.16%0.534
8483.84%16.16%11.32%13.29%0.532
8584.85%15.15%11.36%13.43%0.530
8685.86%14.14%11.41%13.56%0.528
8786.87%13.13%11.45%13.70%0.526
8887.88%12.12%11.50%13.84%0.524
8988.89%11.11%11.54%13.98%0.522
9089.90%10.10%11.59%14.12%0.520
9190.91%9.09%11.63%14.27%0.518
9291.92%8.08%11.67%14.41%0.515
9392.93%7.07%11.72%14.56%0.513
9493.94%6.06%11.76%14.70%0.511
9594.95%5.05%11.81%14.85%0.509
9695.96%4.04%11.85%15.00%0.507
9796.97%3.03%11.90%15.15%0.505
9897.98%2.02%11.94%15.30%0.503
9998.99%1.01%11.99%15.45%0.501
100100.00%0.00%12.03%15.60%0.499
*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, 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 Oct 2022
  • 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