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 - Jun 2021)

Portfolio Allocations

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

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio11.20%9.61%0.66

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market13.37%15.40%0.5370.00%100.00%
2Long Term Treasury9.01%11.15%0.3870.00%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 Jun 2021
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%9.01%11.15%0.387
21.01%98.99%9.06%11.04%0.394
32.02%97.98%9.10%10.93%0.402
43.03%96.97%9.14%10.83%0.409
54.04%95.96%9.19%10.73%0.417
65.05%94.95%9.23%10.63%0.424
76.06%93.94%9.27%10.53%0.432
87.07%92.93%9.32%10.43%0.440
98.08%91.92%9.36%10.34%0.448
109.09%90.91%9.40%10.25%0.455
1110.10%89.90%9.45%10.17%0.463
1211.11%88.89%9.49%10.08%0.471
1312.12%87.88%9.53%10.00%0.479
1413.13%86.87%9.58%9.93%0.487
1514.14%85.86%9.62%9.85%0.494
1615.15%84.85%9.66%9.78%0.502
1716.16%83.84%9.71%9.71%0.510
1817.17%82.83%9.75%9.65%0.517
1918.18%81.82%9.80%9.59%0.525
2019.19%80.81%9.84%9.53%0.532
2120.20%79.80%9.88%9.47%0.539
2221.21%78.79%9.93%9.42%0.547
2322.22%77.78%9.97%9.38%0.554
2423.23%76.77%10.01%9.33%0.560
2524.24%75.76%10.06%9.29%0.567
2625.25%74.75%10.10%9.25%0.574
2726.26%73.74%10.14%9.22%0.580
2827.27%72.73%10.19%9.19%0.586
2928.28%71.72%10.23%9.17%0.592
3029.29%70.71%10.27%9.15%0.598
3130.30%69.70%10.32%9.13%0.603
3231.31%68.69%10.36%9.12%0.609
3332.32%67.68%10.41%9.11%0.614
3433.33%66.67%10.45%9.10%0.618
3534.34%65.66%10.49%9.10%0.623
3635.35%64.65%10.54%9.11%0.627
3736.36%63.64%10.58%9.11%0.631
3837.37%62.63%10.62%9.12%0.634
3938.38%61.62%10.67%9.14%0.638
4039.39%60.61%10.71%9.16%0.641
4140.40%59.60%10.76%9.18%0.644
4241.41%58.59%10.80%9.21%0.646
4342.42%57.58%10.84%9.24%0.648
4443.43%56.57%10.89%9.27%0.650
4544.44%55.56%10.93%9.31%0.652
4645.45%54.55%10.98%9.35%0.653
4746.46%53.54%11.02%9.40%0.654
4847.47%52.53%11.06%9.44%0.655
4948.48%51.52%11.11%9.50%0.656
5049.49%50.51%11.15%9.55%0.656
5150.51%49.49%11.20%9.61%0.656
5251.52%48.48%11.24%9.68%0.656
5352.53%47.47%11.28%9.74%0.656
5453.54%46.46%11.33%9.81%0.655
5554.55%45.45%11.37%9.88%0.654
5655.56%44.44%11.42%9.96%0.653
5756.57%43.43%11.46%10.04%0.652
5857.58%42.42%11.50%10.12%0.651
5958.59%41.41%11.55%10.21%0.649
6059.60%40.40%11.59%10.29%0.648
6160.61%39.39%11.64%10.38%0.646
6261.62%38.38%11.68%10.48%0.644
6362.63%37.37%11.72%10.57%0.642
6463.64%36.36%11.77%10.67%0.640
6564.65%35.35%11.81%10.77%0.638
6665.66%34.34%11.86%10.87%0.635
6766.67%33.33%11.90%10.98%0.633
6867.68%32.32%11.95%11.09%0.630
6968.69%31.31%11.99%11.20%0.628
7069.70%30.30%12.03%11.31%0.625
7170.71%29.29%12.08%11.42%0.622
7271.72%28.28%12.12%11.54%0.619
7372.73%27.27%12.17%11.66%0.617
7473.74%26.26%12.21%11.78%0.614
7574.75%25.25%12.26%11.90%0.611
7675.76%24.24%12.30%12.02%0.608
7776.77%23.23%12.35%12.15%0.605
7877.78%22.22%12.39%12.27%0.602
7978.79%21.21%12.43%12.40%0.599
8079.80%20.20%12.48%12.53%0.596
8180.81%19.19%12.52%12.66%0.593
8281.82%18.18%12.57%12.80%0.590
8382.83%17.17%12.61%12.93%0.587
8483.84%16.16%12.66%13.07%0.584
8584.85%15.15%12.70%13.21%0.580
8685.86%14.14%12.75%13.34%0.577
8786.87%13.13%12.79%13.48%0.574
8887.88%12.12%12.84%13.62%0.571
8988.89%11.11%12.88%13.77%0.568
9089.90%10.10%12.92%13.91%0.565
9190.91%9.09%12.97%14.06%0.562
9291.92%8.08%13.01%14.20%0.559
9392.93%7.07%13.06%14.35%0.557
9493.94%6.06%13.10%14.50%0.554
9594.95%5.05%13.15%14.64%0.551
9695.96%4.04%13.19%14.79%0.548
9796.97%3.03%13.24%14.94%0.545
9897.98%2.02%13.28%15.10%0.542
9998.99%1.01%13.33%15.25%0.539
100100.00%0.00%13.37%15.40%0.537
*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:
  • Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
  • All portfolio returns presented are hypothetical and backtested. Hypothetical returns do not reflect trading costs, transaction fees, or taxes.
  • 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 information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
  • 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.
  • 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 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