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 - Apr 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 Portfolio11.15%9.62%0.65

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market13.35%15.43%0.5330.00%100.00%
2Long Term Treasury8.95%11.16%0.3790.00%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 Apr 2021
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
10.00%100.00%8.95%11.16%0.379
21.01%98.99%8.99%11.05%0.387
32.02%97.98%9.04%10.94%0.394
43.03%96.97%9.08%10.84%0.402
54.04%95.96%9.12%10.74%0.409
65.05%94.95%9.17%10.64%0.417
76.06%93.94%9.21%10.54%0.425
87.07%92.93%9.25%10.44%0.432
98.08%91.92%9.30%10.35%0.440
109.09%90.91%9.34%10.26%0.448
1110.10%89.90%9.39%10.18%0.456
1211.11%88.89%9.43%10.09%0.463
1312.12%87.88%9.47%10.01%0.471
1413.13%86.87%9.52%9.93%0.479
1514.14%85.86%9.56%9.86%0.487
1615.15%84.85%9.61%9.79%0.494
1716.16%83.84%9.65%9.72%0.502
1817.17%82.83%9.69%9.66%0.510
1918.18%81.82%9.74%9.59%0.517
2019.19%80.81%9.78%9.54%0.524
2120.20%79.80%9.83%9.48%0.532
2221.21%78.79%9.87%9.43%0.539
2322.22%77.78%9.91%9.38%0.546
2423.23%76.77%9.96%9.34%0.553
2524.24%75.76%10.00%9.30%0.559
2625.25%74.75%10.05%9.26%0.566
2726.26%73.74%10.09%9.23%0.572
2827.27%72.73%10.13%9.20%0.578
2928.28%71.72%10.18%9.18%0.584
3029.29%70.71%10.22%9.16%0.590
3130.30%69.70%10.27%9.14%0.596
3231.31%68.69%10.31%9.13%0.601
3332.32%67.68%10.35%9.12%0.606
3433.33%66.67%10.40%9.11%0.611
3534.34%65.66%10.44%9.11%0.615
3635.35%64.65%10.49%9.11%0.619
3736.36%63.64%10.53%9.12%0.623
3837.37%62.63%10.57%9.13%0.627
3938.38%61.62%10.62%9.15%0.630
4039.39%60.61%10.66%9.17%0.634
4140.40%59.60%10.71%9.19%0.636
4241.41%58.59%10.75%9.22%0.639
4342.42%57.58%10.80%9.25%0.641
4443.43%56.57%10.84%9.28%0.643
4544.44%55.56%10.89%9.32%0.645
4645.45%54.55%10.93%9.36%0.646
4746.46%53.54%10.97%9.41%0.647
4847.47%52.53%11.02%9.46%0.648
4948.48%51.52%11.06%9.51%0.649
5049.49%50.51%11.11%9.56%0.649
5150.51%49.49%11.15%9.62%0.649
5251.52%48.48%11.20%9.69%0.649
5352.53%47.47%11.24%9.75%0.649
5453.54%46.46%11.28%9.82%0.649
5554.55%45.45%11.33%9.90%0.648
5655.56%44.44%11.37%9.97%0.647
5756.57%43.43%11.42%10.05%0.646
5857.58%42.42%11.46%10.13%0.645
5958.59%41.41%11.51%10.22%0.643
6059.60%40.40%11.55%10.31%0.642
6160.61%39.39%11.60%10.40%0.640
6261.62%38.38%11.64%10.49%0.638
6362.63%37.37%11.69%10.59%0.636
6463.64%36.36%11.73%10.69%0.634
6564.65%35.35%11.78%10.79%0.632
6665.66%34.34%11.82%10.89%0.630
6766.67%33.33%11.86%11.00%0.627
6867.68%32.32%11.91%11.10%0.625
6968.69%31.31%11.95%11.21%0.622
7069.70%30.30%12.00%11.33%0.620
7170.71%29.29%12.04%11.44%0.617
7271.72%28.28%12.09%11.56%0.614
7372.73%27.27%12.13%11.67%0.611
7473.74%26.26%12.18%11.79%0.609
7574.75%25.25%12.22%11.92%0.606
7675.76%24.24%12.27%12.04%0.603
7776.77%23.23%12.31%12.17%0.600
7877.78%22.22%12.36%12.29%0.597
7978.79%21.21%12.40%12.42%0.594
8079.80%20.20%12.45%12.55%0.591
8180.81%19.19%12.49%12.69%0.588
8281.82%18.18%12.54%12.82%0.585
8382.83%17.17%12.58%12.95%0.582
8483.84%16.16%12.63%13.09%0.579
8584.85%15.15%12.67%13.23%0.576
8685.86%14.14%12.72%13.37%0.573
8786.87%13.13%12.76%13.51%0.570
8887.88%12.12%12.81%13.65%0.567
8988.89%11.11%12.85%13.79%0.564
9089.90%10.10%12.90%13.93%0.562
9190.91%9.09%12.94%14.08%0.559
9291.92%8.08%12.99%14.23%0.556
9392.93%7.07%13.03%14.37%0.553
9493.94%6.06%13.08%14.52%0.550
9594.95%5.05%13.12%14.67%0.547
9695.96%4.04%13.17%14.82%0.544
9796.97%3.03%13.21%14.97%0.542
9897.98%2.02%13.26%15.12%0.539
9998.99%1.01%13.30%15.28%0.536
100100.00%0.00%13.35%15.43%0.533
*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 Apr 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