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 - Jul 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 27.28%
SLY SPDR S&P 600 Small Cap ETF 5.23%
EEM iShares MSCI Emerging Markets ETF 0.77%
VNQ Vanguard Real Estate ETF 1.22%
TLT iShares 20+ Year Treasury Bond ETF 33.25%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 18.95%
GLD SPDR Gold Shares 13.31%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio8.53%11.89%0.62
Tangency Portfolio9.04%7.75%1.02

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)9.01%10.22%14.87%0.6090.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)8.19%10.39%19.95%0.4630.00%100.00%
3iShares MSCI EAFE ETF (EFA)3.23%4.86%17.52%0.2110.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)4.69%7.38%22.49%0.2760.00%100.00%
5Vanguard Real Estate ETF (VNQ)6.64%9.61%23.09%0.3660.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)7.78%8.73%13.45%0.5630.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)6.04%6.32%7.45%0.6930.00%100.00%
8SPDR Gold Shares (GLD)9.17%10.86%17.70%0.5480.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.16% annualized).

Asset Correlations

Asset Correlations
NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.920.890.790.72-0.330.340.07
SPDR S&P 600 Small Cap ETFSLY0.921.000.810.740.75-0.380.290.03
iShares MSCI EAFE ETFEFA0.890.811.000.880.69-0.270.410.16
iShares MSCI Emerging Markets ETFEEM0.790.740.881.000.62-0.250.380.30
Vanguard Real Estate ETFVNQ0.720.750.690.621.00-0.020.470.11
iShares 20+ Year Treasury Bond ETFTLT-0.33-0.38-0.27-0.25-0.021.000.470.22
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.340.290.410.380.470.471.000.28
SPDR Gold SharesGLD0.070.030.160.300.110.220.281.00
Based on provided custom correlation matrix
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
115.48%0.69%0.05%0.00%0.00%16.68%61.74%5.35%7.59%7.10%0.906
216.01%0.73%0.04%0.00%0.00%17.17%60.50%5.56%7.63%7.10%0.912
316.53%0.76%0.03%0.00%0.00%17.66%59.26%5.77%7.67%7.10%0.917
417.02%0.81%0.02%0.00%0.00%18.15%58.03%5.98%7.72%7.10%0.923
517.47%0.87%0.02%0.00%0.01%18.63%56.82%6.19%7.76%7.11%0.928
617.90%0.96%0.01%0.00%0.01%19.11%55.60%6.41%7.80%7.11%0.934
718.31%1.04%0.01%0.00%0.02%19.60%54.40%6.62%7.84%7.12%0.939
818.70%1.14%0.01%0.01%0.03%20.08%53.21%6.83%7.88%7.12%0.943
919.07%1.25%0.00%0.03%0.04%20.56%52.03%7.03%7.92%7.13%0.948
1019.43%1.36%0.00%0.04%0.05%21.03%50.85%7.23%7.96%7.14%0.952
1119.79%1.47%0.00%0.06%0.06%21.50%49.67%7.44%8.00%7.15%0.956
1220.14%1.60%0.00%0.07%0.07%21.98%48.49%7.65%8.04%7.16%0.961
1320.47%1.73%0.00%0.09%0.08%22.46%47.30%7.86%8.08%7.17%0.965
1420.81%1.87%0.00%0.10%0.10%22.94%46.11%8.07%8.12%7.19%0.969
1521.13%2.00%0.00%0.12%0.12%23.42%44.93%8.28%8.16%7.20%0.972
1621.44%2.14%0.00%0.14%0.14%23.89%43.76%8.48%8.20%7.21%0.976
1721.74%2.29%0.00%0.16%0.16%24.36%42.60%8.69%8.24%7.23%0.979
1822.03%2.44%0.00%0.18%0.18%24.83%41.43%8.90%8.28%7.25%0.982
1922.32%2.59%0.00%0.20%0.20%25.31%40.26%9.12%8.32%7.26%0.985
2022.62%2.74%0.00%0.22%0.22%25.78%39.09%9.33%8.36%7.28%0.989
2122.91%2.90%0.00%0.24%0.24%26.26%37.90%9.54%8.40%7.30%0.991
2223.21%3.05%0.00%0.27%0.27%26.74%36.72%9.76%8.44%7.32%0.994
2323.50%3.19%0.00%0.29%0.30%27.21%35.53%9.98%8.48%7.34%0.997
2423.78%3.35%0.00%0.32%0.33%27.68%34.35%10.20%8.52%7.36%0.999
2524.06%3.49%0.00%0.34%0.38%28.14%33.18%10.42%8.56%7.38%1.002
2624.33%3.62%0.00%0.37%0.42%28.59%32.03%10.64%8.60%7.41%1.004
2724.60%3.76%0.00%0.40%0.47%29.04%30.87%10.86%8.64%7.43%1.006
2824.86%3.91%0.00%0.43%0.51%29.49%29.72%11.08%8.67%7.46%1.008
2925.12%4.04%0.00%0.46%0.57%29.92%28.58%11.31%8.71%7.48%1.009
3025.38%4.18%0.00%0.49%0.63%30.34%27.46%11.53%8.75%7.51%1.011
3125.65%4.31%0.00%0.52%0.69%30.75%26.34%11.75%8.79%7.54%1.012
3225.93%4.43%0.00%0.55%0.75%31.15%25.22%11.96%8.83%7.57%1.013
3326.20%4.56%0.00%0.58%0.82%31.56%24.10%12.19%8.87%7.59%1.014
3426.45%4.69%0.00%0.61%0.89%31.95%23.00%12.41%8.90%7.63%1.015
3526.66%4.84%0.00%0.65%0.96%32.31%21.95%12.64%8.94%7.66%1.016
3626.88%4.96%0.00%0.69%1.04%32.63%20.93%12.86%8.97%7.69%1.016
3727.08%5.10%0.00%0.73%1.13%32.95%19.93%13.08%9.01%7.72%1.017
3827.28%5.23%0.00%0.77%1.22%33.25%18.95%13.31%9.04%7.75%1.017
3927.44%5.37%0.00%0.81%1.31%33.54%17.99%13.53%9.08%7.78%1.017
4027.60%5.52%0.00%0.86%1.40%33.81%17.05%13.76%9.11%7.82%1.017
4127.74%5.67%0.00%0.90%1.50%34.08%16.11%13.99%9.14%7.85%1.016
4227.87%5.83%0.00%0.95%1.60%34.33%15.19%14.23%9.17%7.89%1.016
4327.96%6.00%0.00%1.00%1.70%34.55%14.31%14.48%9.20%7.92%1.015
4428.03%6.17%0.00%1.05%1.81%34.74%13.47%14.73%9.23%7.96%1.014
4528.08%6.34%0.00%1.10%1.93%34.88%12.69%14.98%9.26%7.99%1.013
4628.11%6.51%0.00%1.15%2.05%34.96%11.96%15.25%9.29%8.03%1.012
4728.10%6.68%0.00%1.21%2.19%35.00%11.28%15.53%9.32%8.07%1.011
4828.08%6.84%0.00%1.26%2.34%35.00%10.65%15.83%9.34%8.11%1.009
4928.03%7.00%0.00%1.32%2.50%34.98%10.06%16.12%9.36%8.15%1.007
5027.99%7.15%0.00%1.37%2.65%34.94%9.48%16.42%9.39%8.19%1.005
5127.95%7.30%0.00%1.42%2.81%34.85%8.94%16.73%9.41%8.23%1.003
5227.89%7.46%0.00%1.48%2.97%34.74%8.42%17.05%9.43%8.27%1.000
5327.80%7.63%0.00%1.53%3.13%34.60%7.94%17.38%9.45%8.31%0.998
5427.68%7.79%0.00%1.58%3.30%34.45%7.48%17.72%9.47%8.35%0.995
5527.56%7.95%0.00%1.64%3.47%34.30%7.05%18.04%9.49%8.39%0.992
5627.42%8.11%0.00%1.70%3.64%34.13%6.64%18.36%9.51%8.44%0.989
5727.27%8.26%0.00%1.77%3.83%33.96%6.24%18.68%9.53%8.48%0.986
5827.11%8.41%0.00%1.85%4.01%33.78%5.87%18.99%9.54%8.52%0.983
5926.95%8.56%0.00%1.92%4.20%33.57%5.50%19.30%9.56%8.57%0.980
6026.78%8.70%0.00%2.00%4.39%33.34%5.16%19.64%9.58%8.62%0.976
6126.61%8.84%0.00%2.08%4.59%33.09%4.83%19.97%9.59%8.67%0.973
6226.42%8.99%0.00%2.15%4.79%32.83%4.52%20.31%9.61%8.71%0.969
6326.23%9.14%0.00%2.23%4.99%32.55%4.21%20.64%9.62%8.76%0.965
6426.04%9.29%0.00%2.30%5.21%32.27%3.92%20.98%9.64%8.82%0.961
6525.84%9.43%0.00%2.38%5.43%31.97%3.65%21.31%9.65%8.87%0.957
6625.63%9.57%0.00%2.47%5.65%31.67%3.38%21.64%9.66%8.92%0.953
6725.42%9.71%0.00%2.56%5.87%31.35%3.13%21.97%9.68%8.97%0.949
6825.23%9.82%0.00%2.65%6.11%31.00%2.90%22.29%9.69%9.03%0.944
6925.05%9.92%0.00%2.74%6.36%30.64%2.67%22.62%9.70%9.09%0.940
7024.84%10.04%0.00%2.84%6.62%30.26%2.45%22.96%9.71%9.15%0.935
7124.61%10.17%0.00%2.94%6.89%29.88%2.24%23.28%9.73%9.21%0.930
7224.36%10.30%0.00%3.04%7.17%29.51%2.04%23.59%9.74%9.27%0.925
7324.06%10.47%0.00%3.15%7.44%29.13%1.86%23.89%9.75%9.34%0.919
7423.74%10.66%0.00%3.25%7.72%28.75%1.70%24.18%9.76%9.40%0.914
7523.41%10.84%0.00%3.35%8.03%28.35%1.56%24.47%9.77%9.47%0.909
7623.09%11.00%0.00%3.44%8.35%27.94%1.42%24.77%9.77%9.53%0.903
7722.77%11.16%0.00%3.54%8.67%27.50%1.28%25.09%9.78%9.60%0.898
7822.42%11.34%0.00%3.63%8.99%27.08%1.15%25.38%9.79%9.67%0.892
7922.03%11.54%0.00%3.73%9.32%26.65%1.04%25.68%9.80%9.75%0.886
8021.65%11.73%0.00%3.84%9.66%26.21%0.92%26.00%9.81%9.82%0.881
8121.22%11.95%0.00%3.94%10.01%25.75%0.81%26.32%9.82%9.90%0.875
8220.75%12.16%0.00%4.05%10.39%25.30%0.71%26.63%9.83%9.98%0.868
8320.29%12.39%0.00%4.16%10.79%24.82%0.62%26.92%9.83%10.06%0.862
8419.80%12.63%0.00%4.28%11.20%24.32%0.55%27.22%9.84%10.15%0.855
8519.31%12.88%0.00%4.40%11.61%23.82%0.48%27.50%9.85%10.23%0.848
8618.80%13.13%0.00%4.56%12.01%23.32%0.42%27.76%9.85%10.32%0.842
8718.26%13.37%0.00%4.73%12.44%22.82%0.36%28.02%9.86%10.42%0.835
8817.72%13.59%0.00%4.90%12.91%22.30%0.31%28.27%9.86%10.51%0.827
8917.14%13.79%0.00%5.10%13.41%21.76%0.27%28.53%9.86%10.62%0.820
9016.53%13.95%0.00%5.34%13.92%21.21%0.24%28.81%9.86%10.72%0.812
9115.83%14.17%0.00%5.60%14.45%20.70%0.20%29.05%9.86%10.83%0.804
9214.94%14.44%0.00%5.90%15.08%20.19%0.18%29.27%9.86%10.95%0.795
9314.10%14.67%0.00%6.20%15.79%19.65%0.15%29.44%9.86%11.08%0.785
9413.22%15.00%0.00%6.48%16.54%19.06%0.13%29.58%9.86%11.22%0.775
9512.31%15.43%0.00%6.75%17.32%18.42%0.10%29.67%9.86%11.37%0.765
9611.30%15.95%0.00%6.98%18.15%17.77%0.08%29.78%9.86%11.52%0.755
9710.18%16.46%0.00%7.16%19.04%17.10%0.06%30.01%9.86%11.69%0.744
988.96%16.87%0.00%7.45%20.03%16.45%0.04%30.20%9.86%11.86%0.733
997.72%16.82%0.00%8.04%21.24%15.81%0.02%30.36%9.85%12.05%0.721
1006.50%16.99%0.00%8.50%23.50%14.50%0.00%30.01%9.84%12.41%0.699
*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 (1.16% 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 Jul 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