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.

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 - Jun 2022)

Portfolio Allocations

Max Sharpe Ratio Portfolio
Asset Class Allocation
US Stock Market 52.53%
Long Term Treasury 47.47%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Max Sharpe Ratio Portfolio10.61%9.88%0.59

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market12.70%15.48%0.5010.00%100.00%
2Long Term Treasury8.33%11.22%0.3350.00%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 Market1.000.04
Long Term Treasury0.041.00
Based on monthly returns from Jan 1978 to Jun 2022
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%8.33%11.22%0.335
21.01%98.99%8.37%11.12%0.342
32.02%97.98%8.41%11.01%0.349
43.03%96.97%8.46%10.91%0.356
54.04%95.96%8.50%10.81%0.363
65.05%94.95%8.54%10.71%0.370
76.06%93.94%8.59%10.62%0.377
87.07%92.93%8.63%10.53%0.384
98.08%91.92%8.67%10.44%0.391
109.09%90.91%8.72%10.35%0.399
1110.10%89.90%8.76%10.27%0.406
1211.11%88.89%8.80%10.19%0.413
1312.12%87.88%8.85%10.11%0.420
1413.13%86.87%8.89%10.03%0.427
1514.14%85.86%8.93%9.96%0.435
1615.15%84.85%8.98%9.89%0.442
1716.16%83.84%9.02%9.83%0.449
1817.17%82.83%9.07%9.76%0.456
1918.18%81.82%9.11%9.70%0.463
2019.19%80.81%9.15%9.65%0.470
2120.20%79.80%9.20%9.60%0.476
2221.21%78.79%9.24%9.55%0.483
2322.22%77.78%9.28%9.50%0.490
2423.23%76.77%9.33%9.46%0.496
2524.24%75.76%9.37%9.42%0.502
2625.25%74.75%9.42%9.39%0.508
2726.26%73.74%9.46%9.36%0.514
2827.27%72.73%9.50%9.33%0.520
2928.28%71.72%9.55%9.30%0.526
3029.29%70.71%9.59%9.29%0.531
3130.30%69.70%9.64%9.27%0.537
3231.31%68.69%9.68%9.26%0.542
3332.32%67.68%9.72%9.25%0.547
3433.33%66.67%9.77%9.25%0.551
3534.34%65.66%9.81%9.25%0.556
3635.35%64.65%9.86%9.25%0.560
3736.36%63.64%9.90%9.26%0.564
3837.37%62.63%9.94%9.27%0.567
3938.38%61.62%9.99%9.28%0.571
4039.39%60.61%10.03%9.30%0.574
4140.40%59.60%10.08%9.33%0.577
4241.41%58.59%10.12%9.35%0.579
4342.42%57.58%10.16%9.38%0.582
4443.43%56.57%10.21%9.42%0.584
4544.44%55.56%10.25%9.45%0.586
4645.45%54.55%10.30%9.50%0.588
4746.46%53.54%10.34%9.54%0.589
4847.47%52.53%10.38%9.59%0.590
4948.48%51.52%10.43%9.64%0.591
5049.49%50.51%10.47%9.70%0.592
5150.51%49.49%10.52%9.76%0.593
5251.52%48.48%10.56%9.82%0.593
5352.53%47.47%10.61%9.88%0.593
5453.54%46.46%10.65%9.95%0.593
5554.55%45.45%10.69%10.03%0.593
5655.56%44.44%10.74%10.10%0.592
5756.57%43.43%10.78%10.18%0.592
5857.58%42.42%10.83%10.26%0.591
5958.59%41.41%10.87%10.34%0.590
6059.60%40.40%10.92%10.43%0.589
6160.61%39.39%10.96%10.52%0.588
6261.62%38.38%11.00%10.61%0.587
6362.63%37.37%11.05%10.70%0.585
6463.64%36.36%11.09%10.80%0.584
6564.65%35.35%11.14%10.90%0.582
6665.66%34.34%11.18%11.00%0.581
6766.67%33.33%11.23%11.11%0.579
6867.68%32.32%11.27%11.21%0.577
6968.69%31.31%11.32%11.32%0.575
7069.70%30.30%11.36%11.43%0.573
7170.71%29.29%11.40%11.54%0.571
7271.72%28.28%11.45%11.66%0.569
7372.73%27.27%11.49%11.77%0.566
7473.74%26.26%11.54%11.89%0.564
7574.75%25.25%11.58%12.01%0.562
7675.76%24.24%11.63%12.13%0.560
7776.77%23.23%11.67%12.26%0.557
7877.78%22.22%11.72%12.38%0.555
7978.79%21.21%11.76%12.51%0.552
8079.80%20.20%11.81%12.64%0.550
8180.81%19.19%11.85%12.77%0.548
8281.82%18.18%11.90%12.90%0.545
8382.83%17.17%11.94%13.03%0.543
8483.84%16.16%11.99%13.17%0.540
8584.85%15.15%12.03%13.30%0.538
8685.86%14.14%12.08%13.44%0.535
8786.87%13.13%12.12%13.58%0.533
8887.88%12.12%12.16%13.72%0.530
8988.89%11.11%12.21%13.86%0.528
9089.90%10.10%12.25%14.00%0.525
9190.91%9.09%12.30%14.14%0.523
9291.92%8.08%12.34%14.29%0.520
9392.93%7.07%12.39%14.43%0.518
9493.94%6.06%12.43%14.58%0.516
9594.95%5.05%12.48%14.73%0.513
9695.96%4.04%12.52%14.87%0.511
9796.97%3.03%12.57%15.02%0.508
9897.98%2.02%12.61%15.17%0.506
9998.99%1.01%12.66%15.32%0.504
100100.00%0.00%12.70%15.48%0.501
*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 Jun 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