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 - Nov 2019)

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 24.02%
SLY SPDR S&P 600 Small Cap ETF 9.15%
EFA iShares MSCI EAFE ETF 0.19%
EEM iShares MSCI Emerging Markets ETF 0.54%
VNQ Vanguard Real Estate ETF 1.91%
TLT iShares 20+ Year Treasury Bond ETF 28.57%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 23.72%
GLD SPDR Gold Shares 11.90%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio8.40%11.47%0.63
Tangency Portfolio8.33%7.54%0.95

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)9.04%10.14%14.14%0.6350.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)9.57%11.53%18.82%0.5510.00%100.00%
3iShares MSCI EAFE ETF (EFA)3.91%5.47%17.20%0.2510.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)4.58%7.19%22.18%0.2720.00%100.00%
5Vanguard Real Estate ETF (VNQ)7.79%10.70%22.78%0.4190.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)6.56%7.48%13.36%0.4730.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.58%5.86%7.22%0.6510.00%100.00%
8SPDR Gold Shares (GLD)7.32%9.00%17.77%0.4410.00%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 (1.16% annualized).

Asset Correlations

Asset Correlations
NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.910.890.790.71-0.310.280.03
SPDR S&P 600 Small Cap ETFSLY0.911.000.790.730.73-0.360.210.00
iShares MSCI EAFE ETFEFA0.890.791.000.880.67-0.240.370.15
iShares MSCI Emerging Markets ETFEEM0.790.730.881.000.60-0.230.350.29
Vanguard Real Estate ETFVNQ0.710.730.670.601.000.010.430.09
iShares 20+ Year Treasury Bond ETFTLT-0.31-0.36-0.24-0.230.011.000.520.22
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.280.210.370.350.430.521.000.26
SPDR Gold SharesGLD0.030.000.150.290.090.220.261.00
Based on monthly returns from Jan 2006 to Nov 2019
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
116.82%0.90%0.00%0.00%0.00%12.88%64.23%5.18%6.99%6.84%0.853
217.28%1.02%0.00%0.00%0.00%13.38%62.95%5.38%7.03%6.84%0.859
317.66%1.19%0.00%0.00%0.00%13.86%61.72%5.57%7.07%6.84%0.864
418.03%1.37%0.00%0.00%0.00%14.35%60.48%5.77%7.11%6.84%0.870
518.38%1.55%0.00%0.01%0.01%14.84%59.25%5.96%7.15%6.85%0.875
618.69%1.76%0.00%0.01%0.03%15.33%58.02%6.16%7.19%6.85%0.880
718.97%1.97%0.01%0.01%0.04%15.81%56.82%6.35%7.23%6.86%0.885
819.23%2.21%0.01%0.02%0.06%16.30%55.63%6.54%7.26%6.87%0.889
919.46%2.46%0.02%0.02%0.08%16.78%54.44%6.73%7.30%6.88%0.893
1019.69%2.70%0.02%0.03%0.11%17.24%53.28%6.92%7.34%6.89%0.898
1119.91%2.95%0.03%0.03%0.15%17.70%52.12%7.11%7.38%6.90%0.902
1220.11%3.21%0.03%0.04%0.18%18.15%50.97%7.30%7.42%6.92%0.905
1320.29%3.47%0.04%0.05%0.23%18.61%49.82%7.49%7.46%6.93%0.909
1420.46%3.73%0.05%0.06%0.27%19.07%48.67%7.69%7.49%6.95%0.912
1520.65%3.99%0.05%0.08%0.32%19.53%47.50%7.88%7.53%6.96%0.916
1620.84%4.25%0.06%0.09%0.36%19.99%46.33%8.08%7.57%6.98%0.919
1721.03%4.51%0.06%0.10%0.42%20.45%45.15%8.28%7.61%7.00%0.922
1821.22%4.77%0.07%0.11%0.48%20.91%43.96%8.48%7.65%7.02%0.925
1921.41%5.02%0.07%0.13%0.54%21.38%42.77%8.68%7.69%7.04%0.928
2021.60%5.27%0.08%0.15%0.61%21.85%41.56%8.88%7.73%7.07%0.930
2121.79%5.52%0.08%0.17%0.67%22.32%40.36%9.08%7.77%7.09%0.933
2221.97%5.77%0.09%0.20%0.75%22.78%39.16%9.29%7.81%7.12%0.935
2322.16%6.02%0.09%0.22%0.82%23.25%37.95%9.49%7.85%7.14%0.937
2422.35%6.27%0.10%0.25%0.89%23.72%36.73%9.69%7.89%7.17%0.939
2522.53%6.53%0.11%0.27%0.97%24.19%35.52%9.89%7.93%7.20%0.941
2622.70%6.78%0.11%0.30%1.05%24.66%34.31%10.09%7.97%7.23%0.943
2722.88%7.03%0.12%0.32%1.13%25.13%33.10%10.28%8.01%7.26%0.944
2823.05%7.29%0.13%0.35%1.21%25.61%31.88%10.48%8.05%7.29%0.945
2923.21%7.55%0.14%0.38%1.29%26.07%30.68%10.68%8.09%7.32%0.947
3023.38%7.81%0.14%0.41%1.38%26.52%29.48%10.88%8.13%7.36%0.948
3123.54%8.08%0.15%0.43%1.47%26.96%28.30%11.08%8.17%7.39%0.949
3223.69%8.34%0.16%0.46%1.57%27.38%27.13%11.28%8.21%7.43%0.950
3323.83%8.61%0.17%0.49%1.67%27.80%25.96%11.48%8.25%7.46%0.950
3423.93%8.89%0.18%0.51%1.78%28.19%24.83%11.69%8.29%7.50%0.951
3524.02%9.15%0.19%0.54%1.91%28.57%23.72%11.90%8.33%7.54%0.951
3624.09%9.42%0.20%0.57%2.05%28.92%22.65%12.11%8.36%7.58%0.950
3724.13%9.70%0.21%0.60%2.19%29.25%21.59%12.33%8.40%7.63%0.950
3824.18%9.98%0.22%0.63%2.33%29.56%20.56%12.54%8.44%7.67%0.950
3924.21%10.27%0.23%0.66%2.48%29.86%19.54%12.76%8.48%7.71%0.949
4024.23%10.56%0.24%0.69%2.63%30.12%18.56%12.98%8.51%7.76%0.948
4124.21%10.84%0.25%0.72%2.80%30.34%17.64%13.20%8.55%7.80%0.947
4224.18%11.12%0.26%0.75%2.98%30.53%16.75%13.42%8.58%7.85%0.946
4324.15%11.39%0.27%0.79%3.15%30.71%15.89%13.65%8.61%7.89%0.945
4424.11%11.66%0.28%0.83%3.33%30.86%15.07%13.87%8.65%7.94%0.943
4524.06%11.93%0.29%0.87%3.52%30.97%14.27%14.10%8.68%7.99%0.942
4624.00%12.19%0.30%0.91%3.71%31.07%13.50%14.33%8.71%8.04%0.940
4723.92%12.45%0.30%0.95%3.90%31.12%12.76%14.58%8.74%8.08%0.938
4823.83%12.72%0.31%0.99%4.10%31.16%12.05%14.83%8.77%8.13%0.936
4923.76%12.98%0.32%1.03%4.30%31.17%11.37%15.08%8.80%8.19%0.934
5023.67%13.23%0.33%1.07%4.51%31.16%10.70%15.33%8.83%8.24%0.931
5123.57%13.48%0.34%1.11%4.72%31.12%10.06%15.60%8.86%8.29%0.929
5223.47%13.73%0.36%1.16%4.93%31.05%9.44%15.87%8.89%8.34%0.926
5323.35%13.97%0.38%1.20%5.16%30.95%8.86%16.13%8.91%8.40%0.923
5423.22%14.21%0.41%1.25%5.38%30.83%8.31%16.40%8.94%8.45%0.920
5523.10%14.42%0.43%1.30%5.62%30.69%7.78%16.66%8.96%8.51%0.917
5622.98%14.62%0.46%1.36%5.85%30.51%7.29%16.95%8.99%8.57%0.914
5722.85%14.81%0.48%1.41%6.09%30.29%6.84%17.24%9.01%8.63%0.910
5822.73%15.00%0.50%1.46%6.33%30.04%6.40%17.53%9.03%8.69%0.907
5922.61%15.18%0.52%1.52%6.59%29.78%5.99%17.81%9.06%8.75%0.903
6022.50%15.35%0.54%1.58%6.84%29.51%5.58%18.09%9.08%8.81%0.899
6122.37%15.53%0.55%1.64%7.10%29.24%5.20%18.37%9.10%8.87%0.895
6222.22%15.70%0.57%1.70%7.37%28.96%4.83%18.65%9.12%8.93%0.892
6322.00%15.90%0.58%1.76%7.66%28.66%4.51%18.92%9.14%9.00%0.887
6421.78%16.10%0.60%1.83%7.95%28.33%4.21%19.21%9.16%9.06%0.883
6521.55%16.29%0.62%1.90%8.23%27.98%3.94%19.50%9.18%9.13%0.879
6621.33%16.46%0.63%1.97%8.52%27.62%3.69%19.77%9.20%9.20%0.875
6721.13%16.62%0.65%2.05%8.81%27.26%3.45%20.04%9.22%9.26%0.870
6820.90%16.79%0.67%2.13%9.11%26.87%3.21%20.33%9.24%9.34%0.865
6920.65%16.96%0.68%2.21%9.41%26.47%3.00%20.61%9.25%9.41%0.861
7020.42%17.13%0.69%2.29%9.73%26.06%2.81%20.87%9.27%9.48%0.856
7120.17%17.28%0.70%2.38%10.06%25.64%2.63%21.13%9.29%9.55%0.851
7219.94%17.43%0.71%2.47%10.40%25.21%2.46%21.38%9.31%9.63%0.846
7319.72%17.57%0.72%2.56%10.74%24.76%2.29%21.63%9.32%9.71%0.841
7419.47%17.69%0.74%2.67%11.12%24.31%2.14%21.87%9.34%9.79%0.836
7519.20%17.82%0.75%2.79%11.50%23.86%1.99%22.09%9.35%9.87%0.830
7618.94%17.95%0.76%2.91%11.88%23.41%1.84%22.30%9.37%9.95%0.825
7718.68%18.07%0.77%3.03%12.28%22.96%1.70%22.51%9.38%10.04%0.820
7818.32%18.26%0.79%3.16%12.67%22.50%1.57%22.74%9.40%10.13%0.814
7917.88%18.50%0.80%3.28%13.10%22.04%1.44%22.97%9.42%10.22%0.808
8017.36%18.76%0.81%3.42%13.54%21.59%1.32%23.20%9.43%10.32%0.802
8116.78%19.05%0.82%3.57%14.01%21.14%1.20%23.43%9.45%10.41%0.796
8216.22%19.33%0.83%3.72%14.47%20.70%1.07%23.65%9.47%10.51%0.790
8315.57%19.62%0.84%3.89%14.94%20.30%0.96%23.88%9.48%10.61%0.784
8414.91%19.91%0.85%4.06%15.42%19.90%0.85%24.11%9.49%10.71%0.778
8514.25%20.20%0.86%4.23%15.90%19.48%0.77%24.31%9.51%10.81%0.772
8613.55%20.50%0.87%4.39%16.41%19.07%0.70%24.51%9.52%10.91%0.767
8712.86%20.75%0.87%4.54%16.94%18.70%0.63%24.69%9.53%11.01%0.761
8812.14%21.00%0.89%4.70%17.50%18.34%0.57%24.86%9.54%11.11%0.755
8911.39%21.27%0.90%4.87%18.05%17.98%0.50%25.04%9.56%11.21%0.749
9010.58%21.54%0.91%5.04%18.65%17.61%0.43%25.23%9.57%11.32%0.743
919.74%21.80%0.93%5.21%19.28%17.23%0.38%25.43%9.58%11.43%0.737
928.91%22.04%0.92%5.40%19.94%16.86%0.33%25.58%9.59%11.54%0.731
938.07%22.27%0.87%5.62%20.62%16.54%0.28%25.73%9.60%11.65%0.725
947.24%22.39%0.82%5.82%21.34%16.28%0.23%25.87%9.61%11.75%0.720
956.43%22.50%0.75%6.00%22.05%16.05%0.19%26.02%9.62%11.85%0.714
965.56%22.48%0.65%6.21%22.90%15.82%0.15%26.24%9.63%11.96%0.709
974.74%22.04%0.61%6.52%23.81%15.54%0.11%26.64%9.63%12.06%0.702
983.95%21.46%0.57%6.76%24.88%15.29%0.07%27.03%9.62%12.17%0.696
993.17%21.08%0.54%6.98%25.79%15.19%0.03%27.22%9.62%12.26%0.690
1002.50%20.50%0.50%7.00%27.00%15.50%0.00%27.00%9.62%12.33%0.686
*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 (1.16% 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 Nov 2019
  • 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 1-month treasury bill returns as the risk free rate