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%1.04

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)6.46%7.91%16.39%0.4660.00%100.00%
2iShares Core US Aggregate Bond ETF (AGG)4.10%4.18%4.06%0.9640.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (0.26% annualized).

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%1.013
24.89%95.11%4.36%4.01%1.021
35.86%94.14%4.40%4.02%1.027
46.83%93.17%4.43%4.04%1.032
57.80%92.20%4.47%4.06%1.035
68.77%91.23%4.50%4.09%1.037
79.74%90.26%4.54%4.12%1.037
810.71%89.29%4.57%4.16%1.035
911.68%88.32%4.61%4.21%1.032
1012.65%87.35%4.65%4.26%1.028
1113.62%86.38%4.68%4.32%1.023
1214.59%85.41%4.72%4.38%1.016
1315.56%84.44%4.75%4.45%1.009
1416.53%83.47%4.79%4.52%1.001
1517.50%82.50%4.82%4.60%0.992
1618.47%81.53%4.86%4.68%0.983
1719.44%80.56%4.90%4.76%0.973
1820.41%79.59%4.93%4.85%0.962
1921.39%78.61%4.97%4.94%0.952
2022.36%77.64%5.00%5.04%0.941
2123.33%76.67%5.04%5.14%0.930
2224.30%75.70%5.07%5.24%0.918
2325.27%74.73%5.11%5.34%0.907
2426.24%73.76%5.15%5.45%0.896
2527.21%72.79%5.18%5.56%0.885
2628.18%71.82%5.22%5.67%0.873
2729.15%70.85%5.25%5.79%0.862
2830.12%69.88%5.29%5.90%0.851
2931.09%68.91%5.33%6.02%0.840
3032.06%67.94%5.36%6.14%0.830
3133.03%66.97%5.40%6.27%0.819
3234.00%66.00%5.43%6.39%0.809
3334.97%65.03%5.47%6.52%0.799
3435.94%64.06%5.51%6.64%0.789
3536.91%63.09%5.54%6.77%0.779
3637.88%62.12%5.58%6.90%0.770
3738.86%61.14%5.61%7.03%0.761
3839.83%60.17%5.65%7.17%0.752
3940.80%59.20%5.69%7.30%0.743
4041.77%58.23%5.72%7.43%0.734
4142.74%57.26%5.76%7.57%0.726
4243.71%56.29%5.79%7.71%0.718
4344.68%55.32%5.83%7.84%0.710
4445.65%54.35%5.87%7.98%0.702
4546.62%53.38%5.90%8.12%0.694
4647.59%52.41%5.94%8.26%0.687
4748.56%51.44%5.97%8.40%0.680
4849.53%50.47%6.01%8.54%0.673
4950.50%49.50%6.05%8.69%0.666
5051.47%48.53%6.08%8.83%0.659
5152.44%47.56%6.12%8.97%0.653
5253.41%46.59%6.16%9.12%0.646
5354.38%45.62%6.19%9.26%0.640
5455.35%44.65%6.23%9.41%0.634
5556.33%43.67%6.26%9.55%0.628
5657.30%42.70%6.30%9.70%0.623
5758.27%41.73%6.34%9.84%0.617
5859.24%40.76%6.37%9.99%0.612
5960.21%39.79%6.41%10.14%0.606
6061.18%38.82%6.45%10.29%0.601
6162.15%37.85%6.48%10.43%0.596
6263.12%36.88%6.52%10.58%0.591
6364.09%35.91%6.55%10.73%0.586
6465.06%34.94%6.59%10.88%0.582
6566.03%33.97%6.63%11.03%0.577
6667.00%33.00%6.66%11.18%0.573
6767.97%32.03%6.70%11.33%0.568
6868.94%31.06%6.74%11.48%0.564
6969.91%30.09%6.77%11.63%0.560
7070.88%29.12%6.81%11.78%0.556
7171.85%28.15%6.85%11.93%0.552
7272.82%27.18%6.88%12.08%0.548
7373.79%26.21%6.92%12.23%0.544
7474.77%25.23%6.95%12.39%0.540
7575.74%24.26%6.99%12.54%0.537
7676.71%23.29%7.03%12.69%0.533
7777.68%22.32%7.06%12.84%0.530
7878.65%21.35%7.10%13.00%0.526
7979.62%20.38%7.14%13.15%0.523
8080.59%19.41%7.17%13.30%0.520
8181.56%18.44%7.21%13.45%0.516
8282.53%17.47%7.25%13.61%0.513
8383.50%16.50%7.28%13.76%0.510
8484.47%15.53%7.32%13.91%0.507
8585.44%14.56%7.36%14.07%0.504
8686.41%13.59%7.39%14.22%0.501
8787.38%12.62%7.43%14.38%0.498
8888.35%11.65%7.47%14.53%0.496
8989.32%10.68%7.50%14.68%0.493
9090.29%9.71%7.54%14.84%0.490
9191.26%8.74%7.58%14.99%0.488
9292.24%7.76%7.61%15.15%0.485
9393.21%6.79%7.65%15.30%0.483
9494.18%5.82%7.69%15.46%0.480
9595.15%4.85%7.72%15.61%0.478
9696.12%3.88%7.76%15.77%0.475
9797.09%2.91%7.80%15.92%0.473
9898.06%1.94%7.83%16.08%0.471
9999.03%0.97%7.87%16.24%0.469
100100.00%0.00%7.91%16.39%0.466
*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 (0.26% annualized).
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