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 2006 - Mar 2021)

Portfolio Allocations

Provided Portfolio
Ticker Name Allocation
SPY SPDR S&P 500 ETF Trust 12.50%
SLY SPDR S&P 600 Small Cap ETF 12.50%
EFA iShares MSCI EAFE ETF 12.50%
EEM iShares MSCI Emerging Markets ETF 12.50%
VNQ Vanguard Real Estate ETF 12.50%
TLT iShares 20+ Year Treasury Bond ETF 12.50%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 12.50%
GLD SPDR Gold Shares 12.50%
Save portfolio »
Tangency Portfolio
Ticker Name Allocation
SPY SPDR S&P 500 ETF Trust 26.02%
SLY SPDR S&P 600 Small Cap ETF 11.30%
EEM iShares MSCI Emerging Markets ETF 0.36%
VNQ Vanguard Real Estate ETF 1.69%
TLT iShares 20+ Year Treasury Bond ETF 30.79%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 15.85%
GLD SPDR Gold Shares 13.99%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio8.92%11.83%0.66
Tangency Portfolio8.93%8.09%0.97

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)10.07%11.31%14.99%0.6810.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)10.91%13.24%20.30%0.5970.00%100.00%
3iShares MSCI EAFE ETF (EFA)4.53%6.18%17.63%0.2870.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)5.99%8.64%22.19%0.3390.00%100.00%
5Vanguard Real Estate ETF (VNQ)7.39%10.30%22.77%0.4030.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)5.86%6.80%13.51%0.4210.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.45%5.74%7.44%0.6220.00%100.00%
8SPDR Gold Shares (GLD)7.70%9.36%17.63%0.4680.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.11% annualized).

Asset Correlations

Asset Correlations
NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.910.890.780.72-0.320.340.06
SPDR S&P 600 Small Cap ETFSLY0.911.000.810.740.74-0.380.270.01
iShares MSCI EAFE ETFEFA0.890.811.000.880.70-0.270.410.14
iShares MSCI Emerging Markets ETFEEM0.780.740.881.000.62-0.250.380.29
Vanguard Real Estate ETFVNQ0.720.740.700.621.00-0.020.460.10
iShares 20+ Year Treasury Bond ETFTLT-0.32-0.38-0.27-0.25-0.021.000.490.22
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.340.270.410.380.460.491.000.28
SPDR Gold SharesGLD0.060.010.140.290.100.220.281.00
Based on monthly returns from Jan 2006 to Mar 2021
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
114.51%0.67%0.00%0.00%0.00%14.23%64.83%5.76%6.94%7.11%0.819
215.15%0.73%0.00%0.00%0.00%14.69%63.49%5.93%6.99%7.11%0.826
315.73%0.81%0.00%0.00%0.00%15.13%62.22%6.11%7.04%7.12%0.833
416.26%0.91%0.00%0.01%0.00%15.56%60.97%6.29%7.09%7.12%0.839
516.77%1.03%0.00%0.01%0.00%15.99%59.72%6.48%7.14%7.12%0.845
617.23%1.18%0.00%0.02%0.01%16.43%58.47%6.66%7.18%7.13%0.851
717.69%1.35%0.00%0.02%0.01%16.88%57.21%6.85%7.23%7.14%0.857
818.12%1.54%0.00%0.02%0.01%17.33%55.93%7.05%7.28%7.15%0.863
918.51%1.74%0.00%0.03%0.02%17.78%54.68%7.24%7.33%7.15%0.869
1018.87%1.98%0.00%0.03%0.03%18.23%53.43%7.43%7.38%7.17%0.875
1119.20%2.23%0.00%0.04%0.04%18.69%52.18%7.64%7.43%7.18%0.880
1219.51%2.48%0.00%0.04%0.06%19.14%50.94%7.84%7.48%7.19%0.885
1319.82%2.75%0.00%0.04%0.07%19.59%49.69%8.04%7.53%7.20%0.890
1420.14%3.00%0.00%0.05%0.09%20.04%48.44%8.24%7.58%7.22%0.895
1520.47%3.26%0.00%0.05%0.10%20.49%47.18%8.44%7.63%7.24%0.900
1620.79%3.52%0.00%0.06%0.12%20.95%45.92%8.65%7.68%7.25%0.905
1721.11%3.79%0.00%0.06%0.14%21.40%44.65%8.85%7.73%7.27%0.910
1821.42%4.07%0.00%0.06%0.16%21.86%43.38%9.05%7.78%7.29%0.914
1921.72%4.35%0.00%0.07%0.19%22.31%42.10%9.26%7.83%7.31%0.919
2022.03%4.63%0.00%0.07%0.22%22.76%40.83%9.47%7.88%7.34%0.923
2122.31%4.92%0.00%0.08%0.25%23.21%39.55%9.68%7.94%7.36%0.927
2222.59%5.21%0.00%0.08%0.28%23.66%38.28%9.89%7.99%7.39%0.931
2322.85%5.52%0.00%0.09%0.31%24.11%37.01%10.11%8.04%7.41%0.934
2423.10%5.83%0.00%0.10%0.35%24.56%35.74%10.32%8.09%7.44%0.938
2523.35%6.13%0.00%0.11%0.40%25.01%34.47%10.54%8.14%7.47%0.941
2623.59%6.43%0.00%0.12%0.45%25.46%33.20%10.75%8.19%7.50%0.944
2723.83%6.72%0.00%0.13%0.51%25.91%31.93%10.97%8.24%7.53%0.947
2824.08%7.01%0.00%0.14%0.56%26.36%30.65%11.18%8.30%7.56%0.949
2924.33%7.31%0.00%0.16%0.62%26.80%29.38%11.40%8.35%7.60%0.952
3024.58%7.60%0.00%0.17%0.69%27.23%28.13%11.61%8.40%7.63%0.954
3124.81%7.90%0.00%0.18%0.75%27.65%26.88%11.83%8.45%7.67%0.956
3225.03%8.19%0.00%0.20%0.83%28.07%25.64%12.05%8.50%7.71%0.958
3325.25%8.49%0.00%0.21%0.90%28.48%24.41%12.26%8.55%7.74%0.960
3425.45%8.79%0.00%0.23%0.98%28.86%23.21%12.48%8.60%7.78%0.962
3525.61%9.12%0.00%0.24%1.06%29.21%22.07%12.69%8.65%7.82%0.963
3625.74%9.46%0.00%0.26%1.15%29.53%20.96%12.90%8.70%7.87%0.964
3725.85%9.81%0.00%0.28%1.25%29.84%19.87%13.11%8.75%7.91%0.965
3825.92%10.18%0.00%0.30%1.35%30.11%18.81%13.33%8.79%7.95%0.965
3925.96%10.55%0.00%0.32%1.46%30.36%17.80%13.54%8.84%8.00%0.966
4025.99%10.92%0.00%0.34%1.57%30.58%16.82%13.77%8.89%8.04%0.966
4126.02%11.30%0.00%0.36%1.69%30.79%15.85%13.99%8.93%8.09%0.966
4226.02%11.68%0.00%0.39%1.81%30.95%14.93%14.22%8.98%8.14%0.966
4326.02%12.04%0.00%0.41%1.95%31.08%14.06%14.45%9.02%8.19%0.966
4425.98%12.42%0.00%0.44%2.09%31.17%13.22%14.68%9.06%8.24%0.965
4525.93%12.81%0.00%0.46%2.22%31.22%12.43%14.92%9.11%8.29%0.964
4625.87%13.18%0.00%0.49%2.36%31.23%11.70%15.17%9.15%8.34%0.963
4725.78%13.56%0.00%0.51%2.50%31.19%11.02%15.42%9.19%8.39%0.962
4825.67%13.94%0.00%0.54%2.65%31.13%10.38%15.69%9.22%8.44%0.960
4925.54%14.32%0.00%0.56%2.80%31.01%9.81%15.96%9.26%8.50%0.959
5025.40%14.70%0.00%0.59%2.96%30.85%9.27%16.22%9.30%8.55%0.957
5125.27%15.08%0.00%0.61%3.12%30.67%8.76%16.49%9.34%8.61%0.955
5225.11%15.47%0.00%0.64%3.28%30.46%8.29%16.76%9.37%8.67%0.953
5324.93%15.86%0.00%0.66%3.45%30.22%7.84%17.04%9.41%8.73%0.950
5424.77%16.25%0.00%0.68%3.62%29.96%7.41%17.31%9.44%8.79%0.948
5524.61%16.62%0.00%0.71%3.80%29.68%6.98%17.59%9.48%8.85%0.945
5624.45%17.00%0.00%0.73%3.99%29.38%6.57%17.88%9.51%8.91%0.942
5724.31%17.35%0.00%0.75%4.18%29.06%6.17%18.17%9.55%8.98%0.939
5824.20%17.69%0.00%0.78%4.38%28.70%5.79%18.47%9.59%9.05%0.936
5924.10%18.01%0.00%0.80%4.58%28.32%5.42%18.78%9.62%9.12%0.933
6024.00%18.32%0.00%0.83%4.78%27.91%5.07%19.09%9.66%9.19%0.929
6123.91%18.61%0.00%0.87%4.99%27.50%4.73%19.40%9.69%9.27%0.926
6223.81%18.89%0.00%0.91%5.20%27.08%4.40%19.70%9.72%9.34%0.922
6323.71%19.16%0.00%0.95%5.42%26.66%4.09%20.00%9.76%9.41%0.918
6423.62%19.42%0.00%1.00%5.64%26.22%3.79%20.31%9.79%9.49%0.914
6523.56%19.65%0.00%1.05%5.87%25.75%3.51%20.61%9.82%9.57%0.910
6623.50%19.87%0.00%1.10%6.10%25.27%3.24%20.91%9.85%9.65%0.905
6723.42%20.09%0.00%1.15%6.35%24.80%2.97%21.21%9.88%9.73%0.901
6823.35%20.31%0.00%1.21%6.60%24.34%2.71%21.49%9.91%9.81%0.897
6923.27%20.53%0.00%1.26%6.85%23.85%2.46%21.77%9.94%9.90%0.892
7023.17%20.78%0.00%1.31%7.11%23.36%2.23%22.05%9.98%9.98%0.888
7123.06%21.04%0.00%1.37%7.36%22.86%2.01%22.31%10.01%10.07%0.883
7222.88%21.34%0.00%1.42%7.62%22.37%1.81%22.56%10.04%10.16%0.878
7322.68%21.65%0.00%1.49%7.88%21.89%1.61%22.81%10.07%10.25%0.874
7422.46%21.96%0.00%1.55%8.14%21.40%1.43%23.06%10.10%10.34%0.869
7522.25%22.27%0.00%1.62%8.41%20.91%1.26%23.28%10.12%10.43%0.864
7622.06%22.58%0.00%1.70%8.69%20.40%1.10%23.48%10.15%10.52%0.859
7721.85%22.90%0.00%1.78%8.97%19.90%0.96%23.65%10.18%10.62%0.854
7821.62%23.23%0.00%1.87%9.26%19.39%0.84%23.78%10.21%10.72%0.849
7921.35%23.59%0.00%1.96%9.56%18.89%0.73%23.93%10.24%10.82%0.844
8021.04%23.97%0.00%2.06%9.85%18.38%0.64%24.06%10.27%10.92%0.838
8120.67%24.39%0.00%2.16%10.15%17.90%0.56%24.17%10.29%11.02%0.833
8220.26%24.85%0.00%2.26%10.48%17.42%0.49%24.25%10.32%11.12%0.828
8319.78%25.35%0.00%2.36%10.85%16.94%0.42%24.30%10.35%11.23%0.822
8419.29%25.85%0.00%2.47%11.25%16.44%0.37%24.32%10.37%11.35%0.816
8518.73%26.42%0.00%2.59%11.67%15.95%0.32%24.31%10.40%11.47%0.810
8618.14%27.02%0.00%2.72%12.08%15.46%0.28%24.30%10.43%11.59%0.804
8717.49%27.65%0.00%2.85%12.50%14.97%0.25%24.29%10.46%11.72%0.798
8816.82%28.31%0.00%2.97%12.91%14.47%0.22%24.30%10.49%11.85%0.791
8916.10%29.01%0.00%3.10%13.34%13.98%0.19%24.29%10.52%11.98%0.785
9015.40%29.73%0.00%3.23%13.79%13.50%0.17%24.18%10.55%12.12%0.779
9114.77%30.41%0.00%3.37%14.29%13.03%0.15%24.00%10.58%12.26%0.772
9214.12%31.09%0.00%3.50%14.78%12.56%0.13%23.82%10.61%12.40%0.766
9313.49%31.75%0.00%3.64%15.31%12.09%0.11%23.61%10.64%12.55%0.759
9412.82%32.26%0.00%3.74%15.96%11.64%0.10%23.49%10.67%12.70%0.752
9512.16%32.80%0.00%3.83%16.62%11.17%0.08%23.34%10.69%12.84%0.746
9611.53%33.28%0.00%3.80%17.50%10.66%0.06%23.17%10.72%13.00%0.739
9710.82%33.63%0.00%3.70%18.52%10.18%0.05%23.11%10.74%13.16%0.732
9810.00%33.85%0.00%3.68%19.63%9.66%0.03%23.15%10.76%13.31%0.725
998.72%34.30%0.00%3.83%21.00%9.07%0.01%23.07%10.78%13.53%0.715
1007.00%35.50%0.00%4.00%22.00%8.50%0.00%23.00%10.82%13.75%0.706
*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 (1.11% 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 2006 to Mar 2021
  • The efficient frontier is based on the monthly returns, volatilities, and correlations of the specified assets
  • Monte Carlo method was used to resample the efficient frontier inputs to mitigate the impact of input estimation errors
  • 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