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 - Feb 2020)

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 22.43%
SLY SPDR S&P 600 Small Cap ETF 9.08%
EFA iShares MSCI EAFE ETF 0.01%
EEM iShares MSCI Emerging Markets ETF 0.83%
VNQ Vanguard Real Estate ETF 1.80%
TLT iShares 20+ Year Treasury Bond ETF 30.95%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 23.13%
GLD SPDR Gold Shares 11.77%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio8.18%11.44%0.61
Tangency Portfolio8.37%7.48%0.96

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)8.46%9.56%14.22%0.5890.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)8.55%10.51%18.91%0.4930.00%100.00%
3iShares MSCI EAFE ETF (EFA)3.25%4.81%17.22%0.2110.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)4.30%6.90%22.17%0.2580.00%100.00%
5Vanguard Real Estate ETF (VNQ)7.25%10.11%22.67%0.3940.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)7.24%8.19%13.51%0.5180.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.78%6.05%7.18%0.6780.00%100.00%
8SPDR Gold Shares (GLD)7.74%9.41%17.66%0.4660.00%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 (1.19% annualized).

Asset Correlations

Asset Correlations
NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.910.890.780.71-0.330.270.03
SPDR S&P 600 Small Cap ETFSLY0.911.000.800.730.73-0.380.200.00
iShares MSCI EAFE ETFEFA0.890.801.000.880.68-0.260.360.15
iShares MSCI Emerging Markets ETFEEM0.780.730.881.000.60-0.250.340.29
Vanguard Real Estate ETFVNQ0.710.730.680.601.000.000.430.09
iShares 20+ Year Treasury Bond ETFTLT-0.33-0.38-0.26-0.250.001.000.520.21
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.270.200.360.340.430.521.000.26
SPDR Gold SharesGLD0.030.000.150.290.090.210.261.00
Based on monthly returns from Jan 2006 to Feb 2020
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
115.81%1.44%0.00%0.00%0.00%11.72%65.10%5.93%7.11%6.80%0.871
216.18%1.53%0.00%0.00%0.00%12.22%64.00%6.07%7.14%6.80%0.876
316.49%1.67%0.00%0.00%0.00%12.74%62.89%6.21%7.18%6.81%0.880
416.78%1.83%0.00%0.00%0.00%13.27%61.78%6.35%7.21%6.81%0.885
517.04%2.00%0.00%0.00%0.00%13.80%60.68%6.48%7.24%6.81%0.889
617.27%2.20%0.00%0.00%0.01%14.31%59.61%6.60%7.27%6.82%0.893
717.49%2.40%0.00%0.00%0.02%14.83%58.53%6.73%7.31%6.82%0.897
817.72%2.59%0.00%0.00%0.04%15.34%57.45%6.87%7.34%6.83%0.901
917.93%2.79%0.00%0.01%0.05%15.85%56.36%7.00%7.37%6.84%0.905
1018.10%3.03%0.00%0.02%0.07%16.37%55.28%7.14%7.40%6.84%0.908
1118.25%3.27%0.00%0.03%0.08%16.89%54.20%7.28%7.44%6.85%0.912
1218.41%3.53%0.00%0.04%0.10%17.42%53.09%7.42%7.47%6.86%0.916
1318.57%3.77%0.00%0.05%0.12%17.94%51.98%7.56%7.50%6.87%0.919
1418.73%4.02%0.00%0.06%0.14%18.47%50.86%7.71%7.54%6.89%0.922
1518.90%4.26%0.00%0.07%0.17%18.99%49.74%7.87%7.57%6.90%0.926
1619.09%4.49%0.00%0.08%0.19%19.51%48.60%8.02%7.61%6.91%0.929
1719.28%4.72%0.00%0.10%0.23%20.02%47.45%8.18%7.64%6.93%0.932
1819.45%4.96%0.01%0.13%0.26%20.55%46.30%8.35%7.68%6.94%0.935
1919.62%5.18%0.01%0.15%0.30%21.09%45.13%8.52%7.71%6.96%0.937
2019.76%5.41%0.01%0.18%0.36%21.62%43.98%8.68%7.75%6.98%0.940
2119.91%5.62%0.01%0.21%0.41%22.15%42.83%8.85%7.78%7.00%0.942
2220.05%5.84%0.01%0.25%0.47%22.68%41.68%9.01%7.81%7.02%0.944
2320.21%6.05%0.01%0.28%0.54%23.22%40.51%9.18%7.85%7.04%0.946
2420.37%6.26%0.01%0.31%0.60%23.76%39.34%9.34%7.88%7.07%0.948
2520.53%6.46%0.01%0.35%0.67%24.29%38.17%9.51%7.92%7.09%0.949
2620.70%6.66%0.01%0.38%0.74%24.82%37.00%9.68%7.95%7.12%0.951
2720.87%6.85%0.02%0.42%0.82%25.35%35.83%9.85%7.99%7.14%0.952
2821.03%7.05%0.02%0.45%0.89%25.88%34.65%10.02%8.02%7.17%0.954
2921.19%7.25%0.02%0.48%0.97%26.40%33.49%10.20%8.06%7.20%0.955
3021.34%7.45%0.02%0.52%1.06%26.92%32.33%10.37%8.09%7.22%0.956
3121.48%7.66%0.02%0.55%1.14%27.43%31.17%10.55%8.13%7.25%0.957
3221.61%7.87%0.02%0.59%1.23%27.95%30.01%10.72%8.16%7.28%0.958
3321.75%8.08%0.02%0.63%1.31%28.46%28.85%10.89%8.20%7.31%0.959
3421.89%8.29%0.02%0.67%1.40%28.97%27.69%11.07%8.23%7.35%0.959
3522.03%8.50%0.02%0.71%1.49%29.48%26.54%11.24%8.27%7.38%0.960
3622.17%8.70%0.01%0.75%1.58%29.98%25.39%11.42%8.30%7.41%0.960
3722.30%8.89%0.01%0.79%1.69%30.48%24.25%11.60%8.34%7.44%0.961
3822.43%9.08%0.01%0.83%1.80%30.95%23.13%11.77%8.37%7.48%0.961
3922.54%9.28%0.00%0.87%1.91%31.41%22.04%11.95%8.41%7.51%0.961
4022.62%9.48%0.00%0.91%2.03%31.84%20.99%12.12%8.44%7.55%0.960
4122.69%9.68%0.00%0.96%2.16%32.24%19.96%12.30%8.47%7.59%0.960
4222.75%9.88%0.00%1.00%2.29%32.63%18.95%12.49%8.50%7.62%0.960
4322.81%10.08%0.00%1.05%2.42%33.00%17.97%12.67%8.53%7.66%0.959
4422.86%10.29%0.00%1.09%2.56%33.34%17.01%12.85%8.56%7.70%0.958
4522.88%10.51%0.00%1.14%2.70%33.64%16.10%13.03%8.59%7.74%0.957
4622.86%10.74%0.00%1.20%2.85%33.89%15.25%13.22%8.62%7.78%0.956
4722.83%10.97%0.00%1.25%3.02%34.11%14.41%13.41%8.65%7.82%0.955
4822.79%11.19%0.00%1.30%3.19%34.33%13.59%13.61%8.67%7.86%0.953
4922.73%11.43%0.00%1.36%3.36%34.54%12.78%13.81%8.70%7.90%0.951
5022.64%11.67%0.00%1.42%3.54%34.72%12.00%14.01%8.73%7.94%0.950
5122.55%11.90%0.00%1.48%3.72%34.87%11.26%14.22%8.75%7.98%0.948
5222.43%12.12%0.00%1.54%3.91%34.96%10.59%14.44%8.78%8.03%0.946
5322.32%12.34%0.00%1.61%4.10%35.03%9.93%14.67%8.80%8.07%0.943
5422.20%12.55%0.00%1.67%4.31%35.07%9.30%14.90%8.82%8.11%0.941
5522.06%12.75%0.00%1.73%4.53%35.09%8.72%15.12%8.84%8.16%0.939
5621.90%12.96%0.00%1.79%4.75%35.08%8.17%15.35%8.87%8.20%0.936
5721.73%13.16%0.00%1.85%4.99%35.05%7.66%15.57%8.89%8.25%0.933
5821.56%13.33%0.00%1.91%5.24%34.99%7.18%15.79%8.90%8.30%0.930
5921.40%13.49%0.00%1.97%5.50%34.90%6.74%16.00%8.92%8.34%0.927
6021.21%13.66%0.00%2.03%5.77%34.77%6.34%16.23%8.94%8.39%0.924
6121.02%13.81%0.00%2.08%6.05%34.64%5.94%16.46%8.96%8.44%0.921
6220.82%13.96%0.00%2.14%6.34%34.49%5.56%16.68%8.97%8.49%0.917
6320.62%14.10%0.00%2.21%6.63%34.32%5.21%16.92%8.99%8.54%0.914
6420.40%14.24%0.00%2.27%6.92%34.12%4.88%17.16%9.00%8.59%0.910
6520.21%14.39%0.00%2.33%7.22%33.88%4.56%17.42%9.02%8.64%0.907
6620.01%14.52%0.00%2.40%7.52%33.63%4.25%17.67%9.03%8.69%0.903
6719.80%14.67%0.00%2.46%7.83%33.37%3.95%17.92%9.05%8.75%0.899
6819.55%14.84%0.00%2.52%8.16%33.08%3.68%18.17%9.06%8.81%0.895
6919.30%15.01%0.00%2.59%8.48%32.78%3.41%18.43%9.08%8.87%0.890
7019.08%15.16%0.00%2.66%8.79%32.47%3.15%18.69%9.09%8.92%0.886
7118.88%15.27%0.00%2.74%9.11%32.13%2.93%18.94%9.11%8.98%0.882
7218.69%15.37%0.00%2.81%9.44%31.78%2.71%19.19%9.12%9.04%0.877
7318.50%15.47%0.00%2.89%9.77%31.42%2.51%19.45%9.13%9.10%0.873
7418.30%15.57%0.00%2.97%10.12%31.05%2.30%19.69%9.14%9.17%0.868
7518.09%15.69%0.00%3.04%10.48%30.69%2.11%19.90%9.16%9.23%0.863
7617.86%15.79%0.00%3.13%10.85%30.33%1.93%20.11%9.17%9.30%0.859
7717.62%15.88%0.00%3.24%11.23%29.92%1.76%20.34%9.18%9.37%0.853
7817.38%16.00%0.00%3.36%11.63%29.48%1.61%20.56%9.19%9.44%0.848
7917.13%16.12%0.00%3.47%12.03%29.03%1.46%20.76%9.20%9.52%0.842
8016.89%16.23%0.00%3.60%12.42%28.58%1.33%20.95%9.21%9.60%0.836
8116.61%16.38%0.00%3.75%12.82%28.11%1.20%21.11%9.22%9.68%0.830
8216.34%16.55%0.00%3.91%13.21%27.63%1.09%21.27%9.23%9.76%0.824
8316.04%16.75%0.00%4.07%13.61%27.16%0.97%21.40%9.24%9.85%0.818
8415.72%16.99%0.00%4.23%14.02%26.69%0.86%21.50%9.25%9.94%0.812
8515.35%17.26%0.01%4.38%14.44%26.23%0.75%21.58%9.26%10.03%0.806
8614.97%17.51%0.04%4.53%14.87%25.79%0.66%21.63%9.27%10.12%0.799
8714.58%17.77%0.06%4.69%15.32%25.32%0.57%21.70%9.28%10.21%0.793
8814.03%18.18%0.08%4.85%15.76%24.84%0.49%21.76%9.29%10.31%0.786
8913.39%18.71%0.10%5.02%16.21%24.35%0.43%21.79%9.30%10.42%0.779
9012.65%19.28%0.13%5.18%16.70%23.87%0.37%21.82%9.31%10.53%0.772
9111.94%19.76%0.11%5.38%17.20%23.41%0.32%21.88%9.32%10.64%0.765
9211.23%20.24%0.09%5.59%17.68%22.98%0.27%21.92%9.34%10.75%0.758
9310.53%20.73%0.06%5.82%18.20%22.51%0.23%21.91%9.35%10.87%0.751
949.86%21.10%0.03%6.10%18.82%21.99%0.19%21.91%9.36%11.00%0.743
959.14%21.40%0.01%6.46%19.47%21.47%0.14%21.92%9.36%11.13%0.734
968.15%21.74%0.00%6.98%20.09%20.94%0.11%21.99%9.36%11.28%0.725
977.13%22.13%0.00%7.57%20.68%20.45%0.08%21.95%9.36%11.43%0.715
986.15%22.42%0.00%8.20%21.32%20.05%0.05%21.82%9.36%11.58%0.706
995.29%22.01%0.00%8.99%22.43%19.81%0.02%21.45%9.34%11.74%0.695
1004.50%21.00%0.00%10.00%23.50%20.00%0.00%21.00%9.31%11.86%0.685
*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 (1.19% 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 Feb 2020
  • 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