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%0.4680.00%100.00%
2iShares Core US Aggregate Bond ETF (AGG)4.10%4.18%4.06%0.9710.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (0.24% 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%1.020
24.89%95.11%4.36%4.01%1.028
35.86%94.14%4.40%4.02%1.034
46.83%93.17%4.43%4.04%1.039
57.80%92.20%4.47%4.06%1.042
68.77%91.23%4.50%4.09%1.043
79.74%90.26%4.54%4.12%1.043
810.71%89.29%4.57%4.16%1.042
911.68%88.32%4.61%4.21%1.039
1012.65%87.35%4.65%4.26%1.035
1113.62%86.38%4.68%4.32%1.029
1214.59%85.41%4.72%4.38%1.023
1315.56%84.44%4.75%4.45%1.015
1416.53%83.47%4.79%4.52%1.007
1517.50%82.50%4.82%4.60%0.998
1618.47%81.53%4.86%4.68%0.989
1719.44%80.56%4.90%4.76%0.979
1820.41%79.59%4.93%4.85%0.968
1921.39%78.61%4.97%4.94%0.957
2022.36%77.64%5.00%5.04%0.946
2123.33%76.67%5.04%5.14%0.935
2224.30%75.70%5.07%5.24%0.924
2325.27%74.73%5.11%5.34%0.912
2426.24%73.76%5.15%5.45%0.901
2527.21%72.79%5.18%5.56%0.890
2628.18%71.82%5.22%5.67%0.878
2729.15%70.85%5.25%5.79%0.867
2830.12%69.88%5.29%5.90%0.856
2931.09%68.91%5.33%6.02%0.845
3032.06%67.94%5.36%6.14%0.834
3133.03%66.97%5.40%6.27%0.824
3234.00%66.00%5.43%6.39%0.813
3334.97%65.03%5.47%6.52%0.803
3435.94%64.06%5.51%6.64%0.793
3536.91%63.09%5.54%6.77%0.783
3637.88%62.12%5.58%6.90%0.774
3738.86%61.14%5.61%7.03%0.765
3839.83%60.17%5.65%7.17%0.756
3940.80%59.20%5.69%7.30%0.747
4041.77%58.23%5.72%7.43%0.738
4142.74%57.26%5.76%7.57%0.730
4243.71%56.29%5.79%7.71%0.721
4344.68%55.32%5.83%7.84%0.713
4445.65%54.35%5.87%7.98%0.705
4546.62%53.38%5.90%8.12%0.698
4647.59%52.41%5.94%8.26%0.690
4748.56%51.44%5.97%8.40%0.683
4849.53%50.47%6.01%8.54%0.676
4950.50%49.50%6.05%8.69%0.669
5051.47%48.53%6.08%8.83%0.662
5152.44%47.56%6.12%8.97%0.656
5253.41%46.59%6.16%9.12%0.649
5354.38%45.62%6.19%9.26%0.643
5455.35%44.65%6.23%9.41%0.637
5556.33%43.67%6.26%9.55%0.631
5657.30%42.70%6.30%9.70%0.625
5758.27%41.73%6.34%9.84%0.620
5859.24%40.76%6.37%9.99%0.614
5960.21%39.79%6.41%10.14%0.609
6061.18%38.82%6.45%10.29%0.604
6162.15%37.85%6.48%10.43%0.599
6263.12%36.88%6.52%10.58%0.594
6364.09%35.91%6.55%10.73%0.589
6465.06%34.94%6.59%10.88%0.584
6566.03%33.97%6.63%11.03%0.580
6667.00%33.00%6.66%11.18%0.575
6767.97%32.03%6.70%11.33%0.571
6868.94%31.06%6.74%11.48%0.566
6969.91%30.09%6.77%11.63%0.562
7070.88%29.12%6.81%11.78%0.558
7171.85%28.15%6.85%11.93%0.554
7272.82%27.18%6.88%12.08%0.550
7373.79%26.21%6.92%12.23%0.546
7474.77%25.23%6.95%12.39%0.543
7575.74%24.26%6.99%12.54%0.539
7676.71%23.29%7.03%12.69%0.535
7777.68%22.32%7.06%12.84%0.532
7878.65%21.35%7.10%13.00%0.528
7979.62%20.38%7.14%13.15%0.525
8080.59%19.41%7.17%13.30%0.522
8181.56%18.44%7.21%13.45%0.518
8282.53%17.47%7.25%13.61%0.515
8383.50%16.50%7.28%13.76%0.512
8484.47%15.53%7.32%13.91%0.509
8585.44%14.56%7.36%14.07%0.506
8686.41%13.59%7.39%14.22%0.503
8787.38%12.62%7.43%14.38%0.500
8888.35%11.65%7.47%14.53%0.498
8989.32%10.68%7.50%14.68%0.495
9090.29%9.71%7.54%14.84%0.492
9191.26%8.74%7.58%14.99%0.490
9292.24%7.76%7.61%15.15%0.487
9393.21%6.79%7.65%15.30%0.484
9494.18%5.82%7.69%15.46%0.482
9595.15%4.85%7.72%15.61%0.480
9696.12%3.88%7.76%15.77%0.477
9797.09%2.91%7.80%15.92%0.475
9898.06%1.94%7.83%16.08%0.472
9999.03%0.97%7.87%16.24%0.470
100100.00%0.00%7.91%16.39%0.468
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (0.24% 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 1-month treasury bill returns as the risk free rate