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 2008 - Dec 2015)

Portfolio Allocations

Tangency Portfolio
Ticker Name Allocation
SPY SPDR S&P 500 ETF Trust 8.77%
AGG iShares Core US Aggregate Bond ETF 91.23%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio4.50%4.09%1.01

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)7.91%16.39%0.4500.00%100.00%
2iShares Core US Aggregate Bond ETF (AGG)4.18%4.06%0.9450.00%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
NameTickerSPYAGG
SPDR S&P 500 ETF TrustSPY1.000.09
iShares Core US Aggregate Bond ETFAGG0.091.00
Based on monthly returns from Jan 2008 to Dec 2015
Efficient Frontier Points
#SPYAGGExpected Return*Standard Deviation*Sharpe Ratio*
13.92%96.08%4.32%4.01%0.992
24.89%95.11%4.36%4.01%1.000
35.86%94.14%4.40%4.02%1.006
46.83%93.17%4.43%4.04%1.010
57.80%92.20%4.47%4.06%1.013
68.77%91.23%4.50%4.09%1.015
79.74%90.26%4.54%4.12%1.014
810.71%89.29%4.57%4.16%1.013
911.68%88.32%4.61%4.21%1.010
1012.65%87.35%4.65%4.26%1.006
1113.62%86.38%4.68%4.32%1.000
1214.59%85.41%4.72%4.38%0.994
1315.56%84.44%4.75%4.45%0.987
1416.53%83.47%4.79%4.52%0.978
1517.50%82.50%4.82%4.60%0.970
1618.47%81.53%4.86%4.68%0.960
1719.44%80.56%4.90%4.76%0.950
1820.41%79.59%4.93%4.85%0.940
1921.39%78.61%4.97%4.94%0.930
2022.36%77.64%5.00%5.04%0.919
2123.33%76.67%5.04%5.14%0.908
2224.30%75.70%5.07%5.24%0.897
2325.27%74.73%5.11%5.34%0.886
2426.24%73.76%5.15%5.45%0.874
2527.21%72.79%5.18%5.56%0.863
2628.18%71.82%5.22%5.67%0.852
2729.15%70.85%5.25%5.79%0.841
2830.12%69.88%5.29%5.90%0.830
2931.09%68.91%5.33%6.02%0.820
3032.06%67.94%5.36%6.14%0.809
3133.03%66.97%5.40%6.27%0.799
3234.00%66.00%5.43%6.39%0.789
3334.97%65.03%5.47%6.52%0.779
3435.94%64.06%5.51%6.64%0.769
3536.91%63.09%5.54%6.77%0.759
3637.88%62.12%5.58%6.90%0.750
3738.86%61.14%5.61%7.03%0.741
3839.83%60.17%5.65%7.17%0.732
3940.80%59.20%5.69%7.30%0.723
4041.77%58.23%5.72%7.43%0.715
4142.74%57.26%5.76%7.57%0.707
4243.71%56.29%5.79%7.71%0.698
4344.68%55.32%5.83%7.84%0.691
4445.65%54.35%5.87%7.98%0.683
4546.62%53.38%5.90%8.12%0.675
4647.59%52.41%5.94%8.26%0.668
4748.56%51.44%5.97%8.40%0.661
4849.53%50.47%6.01%8.54%0.654
4950.50%49.50%6.05%8.69%0.647
5051.47%48.53%6.08%8.83%0.641
5152.44%47.56%6.12%8.97%0.634
5253.41%46.59%6.16%9.12%0.628
5354.38%45.62%6.19%9.26%0.622
5455.35%44.65%6.23%9.41%0.616
5556.33%43.67%6.26%9.55%0.610
5657.30%42.70%6.30%9.70%0.605
5758.27%41.73%6.34%9.84%0.599
5859.24%40.76%6.37%9.99%0.594
5960.21%39.79%6.41%10.14%0.588
6061.18%38.82%6.45%10.29%0.583
6162.15%37.85%6.48%10.43%0.578
6263.12%36.88%6.52%10.58%0.573
6364.09%35.91%6.55%10.73%0.569
6465.06%34.94%6.59%10.88%0.564
6566.03%33.97%6.63%11.03%0.560
6667.00%33.00%6.66%11.18%0.555
6767.97%32.03%6.70%11.33%0.551
6868.94%31.06%6.74%11.48%0.547
6969.91%30.09%6.77%11.63%0.542
7070.88%29.12%6.81%11.78%0.538
7171.85%28.15%6.85%11.93%0.534
7272.82%27.18%6.88%12.08%0.531
7373.79%26.21%6.92%12.23%0.527
7474.77%25.23%6.95%12.39%0.523
7575.74%24.26%6.99%12.54%0.520
7676.71%23.29%7.03%12.69%0.516
7777.68%22.32%7.06%12.84%0.513
7878.65%21.35%7.10%13.00%0.509
7979.62%20.38%7.14%13.15%0.506
8080.59%19.41%7.17%13.30%0.503
8181.56%18.44%7.21%13.45%0.499
8282.53%17.47%7.25%13.61%0.496
8383.50%16.50%7.28%13.76%0.493
8484.47%15.53%7.32%13.91%0.490
8585.44%14.56%7.36%14.07%0.487
8686.41%13.59%7.39%14.22%0.485
8787.38%12.62%7.43%14.38%0.482
8888.35%11.65%7.47%14.53%0.479
8989.32%10.68%7.50%14.68%0.476
9090.29%9.71%7.54%14.84%0.474
9191.26%8.74%7.58%14.99%0.471
9292.24%7.76%7.61%15.15%0.468
9393.21%6.79%7.65%15.30%0.466
9494.18%5.82%7.69%15.46%0.464
9595.15%4.85%7.72%15.61%0.461
9696.12%3.88%7.76%15.77%0.459
9797.09%2.91%7.80%15.92%0.456
9898.06%1.94%7.83%16.08%0.454
9999.03%0.97%7.87%16.24%0.452
100100.00%0.00%7.91%16.39%0.450
*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 2008 to Dec 2015
  • 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