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 - Dec 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 24.71%
SLY SPDR S&P 600 Small Cap ETF 10.43%
EFA iShares MSCI EAFE ETF 0.03%
EEM iShares MSCI Emerging Markets ETF 0.28%
VNQ Vanguard Real Estate ETF 1.40%
TLT iShares 20+ Year Treasury Bond ETF 28.99%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 21.46%
GLD SPDR Gold Shares 12.70%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio8.53%11.45%0.64
Tangency Portfolio8.44%7.55%0.96

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)9.21%10.30%14.11%0.6460.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)9.75%11.70%18.77%0.5600.00%100.00%
3iShares MSCI EAFE ETF (EFA)4.10%5.66%17.16%0.2610.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)5.11%7.74%22.20%0.2950.00%100.00%
5Vanguard Real Estate ETF (VNQ)7.80%10.69%22.71%0.4190.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)6.27%7.20%13.36%0.4500.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.59%5.86%7.20%0.6500.00%100.00%
8SPDR Gold Shares (GLD)7.55%9.23%17.73%0.4540.00%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 (1.18% annualized).

Asset Correlations

Asset Correlations
NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.910.890.790.70-0.320.280.03
SPDR S&P 600 Small Cap ETFSLY0.911.000.790.730.73-0.360.210.01
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 ETFVNQ0.700.730.670.601.000.010.430.09
iShares 20+ Year Treasury Bond ETFTLT-0.32-0.36-0.24-0.230.011.000.520.21
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.280.210.370.350.430.521.000.26
SPDR Gold SharesGLD0.030.010.150.290.090.210.261.00
Based on monthly returns from Jan 2006 to Dec 2019
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
116.73%1.13%0.00%0.00%0.00%12.58%64.01%5.55%7.01%6.82%0.855
217.26%1.24%0.00%0.00%0.00%13.11%62.63%5.75%7.05%6.82%0.861
317.71%1.39%0.00%0.00%0.00%13.62%61.33%5.95%7.10%6.82%0.867
418.08%1.58%0.00%0.00%0.00%14.12%60.06%6.16%7.14%6.82%0.873
518.41%1.80%0.00%0.00%0.00%14.62%58.81%6.36%7.18%6.83%0.878
618.72%2.04%0.00%0.00%0.00%15.12%57.56%6.56%7.22%6.84%0.883
719.01%2.29%0.00%0.00%0.01%15.61%56.32%6.75%7.26%6.84%0.888
819.27%2.56%0.00%0.00%0.02%16.11%55.08%6.96%7.30%6.85%0.893
919.53%2.84%0.00%0.00%0.02%16.61%53.83%7.16%7.34%6.86%0.898
1019.78%3.12%0.00%0.00%0.04%17.11%52.58%7.37%7.38%6.87%0.902
1120.03%3.41%0.00%0.00%0.05%17.62%51.32%7.57%7.42%6.89%0.907
1220.26%3.70%0.00%0.00%0.06%18.12%50.07%7.78%7.47%6.90%0.911
1320.49%4.00%0.00%0.00%0.08%18.63%48.81%7.99%7.51%6.91%0.915
1420.72%4.30%0.00%0.00%0.10%19.13%47.54%8.20%7.55%6.93%0.919
1520.95%4.60%0.00%0.00%0.13%19.63%46.28%8.42%7.59%6.95%0.923
1621.16%4.90%0.00%0.00%0.16%20.13%45.01%8.63%7.64%6.97%0.927
1721.39%5.20%0.00%0.00%0.19%20.63%43.74%8.84%7.68%6.99%0.930
1821.62%5.50%0.00%0.00%0.23%21.12%42.47%9.06%7.72%7.01%0.933
1921.85%5.80%0.00%0.00%0.27%21.63%41.18%9.27%7.77%7.03%0.936
2022.09%6.10%0.00%0.00%0.31%22.12%39.89%9.49%7.81%7.05%0.940
2122.32%6.38%0.00%0.01%0.36%22.61%38.61%9.71%7.85%7.08%0.942
2222.52%6.68%0.00%0.02%0.41%23.10%37.34%9.93%7.90%7.11%0.945
2322.71%6.97%0.00%0.04%0.47%23.59%36.07%10.14%7.94%7.13%0.947
2422.90%7.26%0.01%0.05%0.54%24.07%34.81%10.36%7.98%7.16%0.949
2523.10%7.55%0.01%0.07%0.60%24.56%33.54%10.57%8.02%7.20%0.951
2623.28%7.84%0.01%0.09%0.67%25.04%32.28%10.79%8.07%7.23%0.952
2723.47%8.12%0.02%0.11%0.73%25.52%31.02%11.00%8.11%7.26%0.954
2823.64%8.41%0.02%0.13%0.81%25.98%29.79%11.22%8.15%7.29%0.955
2923.81%8.71%0.02%0.16%0.88%26.45%28.55%11.43%8.19%7.33%0.957
3023.99%9.00%0.03%0.18%0.95%26.92%27.31%11.65%8.23%7.36%0.958
3124.16%9.28%0.03%0.20%1.02%27.38%26.08%11.85%8.28%7.40%0.959
3224.32%9.56%0.03%0.22%1.11%27.81%24.89%12.07%8.32%7.44%0.959
3324.46%9.85%0.03%0.24%1.20%28.22%23.72%12.28%8.36%7.48%0.960
3424.59%10.14%0.03%0.26%1.30%28.61%22.58%12.49%8.40%7.51%0.960
3524.71%10.43%0.03%0.28%1.40%28.99%21.46%12.70%8.44%7.55%0.960
3624.78%10.74%0.03%0.30%1.52%29.35%20.38%12.91%8.48%7.60%0.960
3724.83%11.05%0.02%0.33%1.64%29.68%19.33%13.12%8.51%7.64%0.960
3824.86%11.36%0.03%0.35%1.77%29.98%18.31%13.33%8.55%7.68%0.960
3924.88%11.68%0.03%0.37%1.91%30.24%17.33%13.56%8.59%7.73%0.959
4024.86%12.01%0.04%0.39%2.05%30.45%16.41%13.79%8.63%7.77%0.958
4124.82%12.32%0.05%0.41%2.20%30.63%15.54%14.03%8.66%7.82%0.957
4224.78%12.62%0.05%0.44%2.37%30.77%14.71%14.26%8.69%7.86%0.956
4324.73%12.93%0.06%0.46%2.53%30.88%13.93%14.49%8.73%7.91%0.954
4424.65%13.22%0.06%0.48%2.71%30.94%13.20%14.73%8.76%7.95%0.953
4524.57%13.52%0.07%0.50%2.88%30.99%12.49%14.97%8.79%8.00%0.951
4624.48%13.82%0.08%0.52%3.06%31.04%11.78%15.22%8.82%8.05%0.949
4724.39%14.12%0.08%0.55%3.25%31.05%11.11%15.47%8.85%8.10%0.947
4824.29%14.41%0.09%0.57%3.43%31.02%10.48%15.70%8.88%8.15%0.945
4924.19%14.70%0.09%0.60%3.63%30.95%9.89%15.95%8.91%8.20%0.943
5024.09%14.95%0.10%0.62%3.83%30.84%9.34%16.22%8.94%8.25%0.941
5123.98%15.20%0.11%0.65%4.05%30.69%8.82%16.50%8.97%8.30%0.938
5223.86%15.44%0.13%0.67%4.28%30.51%8.33%16.78%9.00%8.36%0.935
5323.74%15.69%0.14%0.69%4.50%30.30%7.87%17.07%9.03%8.41%0.932
5423.63%15.93%0.15%0.72%4.73%30.04%7.42%17.38%9.05%8.47%0.929
5523.49%16.18%0.16%0.74%4.97%29.76%7.00%17.70%9.08%8.53%0.926
5623.37%16.41%0.17%0.77%5.22%29.46%6.58%18.01%9.11%8.59%0.922
5723.24%16.65%0.18%0.79%5.47%29.13%6.20%18.33%9.14%8.66%0.919
5823.06%16.92%0.20%0.82%5.73%28.79%5.85%18.65%9.16%8.72%0.915
5922.87%17.18%0.21%0.85%5.99%28.42%5.51%18.98%9.19%8.79%0.911
6022.67%17.44%0.22%0.88%6.26%28.03%5.20%19.30%9.21%8.86%0.907
6122.46%17.71%0.23%0.91%6.53%27.63%4.91%19.62%9.24%8.92%0.903
6222.26%17.97%0.24%0.94%6.80%27.21%4.63%19.94%9.27%8.99%0.899
6322.04%18.25%0.25%0.98%7.07%26.78%4.36%20.27%9.29%9.07%0.894
6421.81%18.52%0.26%1.02%7.35%26.35%4.10%20.59%9.32%9.14%0.890
6521.58%18.78%0.26%1.07%7.64%25.93%3.85%20.89%9.34%9.21%0.885
6621.34%19.04%0.27%1.12%7.93%25.50%3.62%21.17%9.36%9.29%0.881
6721.08%19.28%0.28%1.19%8.25%25.06%3.42%21.45%9.39%9.37%0.876
6820.81%19.52%0.29%1.25%8.57%24.60%3.24%21.72%9.41%9.44%0.871
6920.52%19.75%0.30%1.32%8.89%24.15%3.06%21.99%9.43%9.52%0.866
7020.21%20.00%0.31%1.40%9.22%23.72%2.88%22.25%9.45%9.60%0.861
7119.90%20.24%0.32%1.47%9.55%23.28%2.71%22.52%9.47%9.68%0.856
7219.59%20.45%0.33%1.57%9.90%22.84%2.55%22.77%9.49%9.76%0.851
7319.28%20.66%0.33%1.66%10.25%22.38%2.39%23.03%9.51%9.85%0.846
7418.95%20.89%0.34%1.75%10.61%21.92%2.23%23.30%9.53%9.93%0.841
7518.58%21.15%0.35%1.84%10.98%21.46%2.08%23.56%9.55%10.02%0.835
7618.21%21.39%0.35%1.94%11.36%20.99%1.94%23.82%9.57%10.11%0.830
7717.82%21.65%0.34%2.04%11.77%20.50%1.81%24.07%9.59%10.20%0.824
7817.41%21.94%0.33%2.14%12.18%20.00%1.69%24.31%9.62%10.30%0.819
7916.99%22.24%0.32%2.24%12.60%19.49%1.57%24.55%9.64%10.40%0.813
8016.54%22.57%0.31%2.34%13.02%18.98%1.46%24.78%9.66%10.50%0.807
8116.08%22.89%0.30%2.44%13.46%18.50%1.35%24.97%9.68%10.60%0.802
8215.63%23.21%0.29%2.56%13.90%18.01%1.25%25.15%9.70%10.70%0.796
8315.17%23.51%0.29%2.69%14.34%17.54%1.15%25.32%9.72%10.81%0.790
8414.68%23.83%0.28%2.83%14.78%17.08%1.05%25.47%9.74%10.91%0.785
8514.17%24.14%0.28%3.01%15.23%16.59%0.97%25.62%9.76%11.02%0.779
8613.68%24.42%0.27%3.19%15.73%16.13%0.88%25.70%9.78%11.13%0.773
8713.07%24.75%0.31%3.37%16.25%15.69%0.80%25.77%9.80%11.24%0.766
8812.39%25.11%0.32%3.58%16.79%15.26%0.72%25.83%9.82%11.36%0.760
8911.69%25.47%0.32%3.80%17.34%14.86%0.65%25.86%9.83%11.48%0.754
9010.95%25.87%0.33%4.02%17.91%14.45%0.58%25.89%9.85%11.60%0.747
9110.18%26.26%0.34%4.24%18.50%14.08%0.51%25.89%9.87%11.72%0.741
929.41%26.61%0.35%4.47%19.13%13.77%0.44%25.81%9.88%11.84%0.735
938.65%26.92%0.36%4.68%19.85%13.47%0.38%25.69%9.90%11.96%0.728
947.86%27.23%0.37%4.90%20.59%13.17%0.32%25.57%9.91%12.09%0.722
957.10%27.44%0.35%5.12%21.40%12.90%0.27%25.42%9.92%12.22%0.716
966.38%27.44%0.27%5.39%22.39%12.64%0.21%25.27%9.94%12.35%0.709
975.74%27.12%0.20%5.75%23.49%12.37%0.16%25.17%9.94%12.49%0.702
985.13%26.40%0.14%6.16%24.96%12.17%0.11%24.93%9.94%12.64%0.693
994.57%25.37%0.07%6.59%26.47%12.07%0.05%24.80%9.93%12.78%0.685
1004.00%24.50%0.00%7.00%27.50%12.00%0.00%25.00%9.92%12.87%0.679
*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 (1.18% 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 Dec 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 3-month treasury bill returns as the risk free rate