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 - Sep 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 27.64%
SLY SPDR S&P 600 Small Cap ETF 5.81%
EFA iShares MSCI EAFE ETF 0.03%
EEM iShares MSCI Emerging Markets ETF 0.25%
VNQ Vanguard Real Estate ETF 1.86%
TLT iShares 20+ Year Treasury Bond ETF 33.74%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 17.88%
GLD SPDR Gold Shares 12.79%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio8.37%11.84%0.61
Tangency Portfolio8.86%7.78%0.99

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)9.12%10.34%14.92%0.6160.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)8.02%10.22%19.90%0.4560.00%100.00%
3iShares MSCI EAFE ETF (EFA)3.38%4.99%17.47%0.2200.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)4.76%7.43%22.38%0.2810.00%100.00%
5Vanguard Real Estate ETF (VNQ)6.40%9.33%22.97%0.3560.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)7.37%8.31%13.46%0.5320.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.80%6.09%7.43%0.6650.00%100.00%
8SPDR Gold Shares (GLD)8.72%10.40%17.65%0.5240.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.15% annualized).

Asset Correlations

Asset Correlations
NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.920.890.790.72-0.330.330.07
SPDR S&P 600 Small Cap ETFSLY0.921.000.810.740.75-0.380.280.04
iShares MSCI EAFE ETFEFA0.890.811.000.880.69-0.280.400.16
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-0.33-0.38-0.28-0.25-0.021.000.470.22
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.330.280.400.380.470.471.000.28
SPDR Gold SharesGLD0.070.040.160.300.110.220.281.00
Based on monthly returns from Jan 2006 to Sep 2020
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
115.92%0.60%0.00%0.00%0.00%16.71%61.45%5.33%7.38%7.08%0.881
216.49%0.63%0.00%0.00%0.00%17.23%60.17%5.49%7.43%7.08%0.887
317.01%0.68%0.00%0.00%0.00%17.76%58.90%5.65%7.47%7.08%0.893
417.49%0.78%0.00%0.00%0.00%18.29%57.62%5.82%7.51%7.08%0.898
517.97%0.87%0.00%0.00%0.01%18.83%56.35%5.99%7.55%7.09%0.904
618.40%0.96%0.00%0.00%0.02%19.34%55.11%6.17%7.60%7.09%0.909
718.81%1.07%0.00%0.00%0.04%19.85%53.88%6.35%7.64%7.10%0.914
819.21%1.19%0.00%0.00%0.06%20.36%52.63%6.54%7.68%7.11%0.919
919.60%1.33%0.00%0.00%0.08%20.88%51.39%6.73%7.72%7.12%0.924
1019.97%1.47%0.00%0.00%0.10%21.39%50.16%6.92%7.76%7.13%0.928
1120.32%1.61%0.00%0.00%0.13%21.89%48.93%7.12%7.81%7.14%0.932
1220.67%1.76%0.00%0.00%0.16%22.39%47.70%7.32%7.85%7.15%0.937
1321.01%1.91%0.00%0.00%0.20%22.89%46.46%7.52%7.89%7.16%0.941
1421.36%2.06%0.00%0.00%0.23%23.40%45.22%7.72%7.93%7.18%0.945
1521.70%2.21%0.00%0.01%0.27%23.90%43.99%7.92%7.97%7.19%0.948
1622.04%2.36%0.00%0.01%0.31%24.41%42.74%8.13%8.02%7.21%0.952
1722.37%2.52%0.00%0.02%0.35%24.91%41.50%8.33%8.06%7.23%0.956
1822.68%2.69%0.00%0.02%0.39%25.40%40.28%8.54%8.10%7.25%0.959
1922.99%2.85%0.00%0.03%0.44%25.89%39.04%8.76%8.14%7.27%0.962
2023.30%3.01%0.00%0.03%0.49%26.38%37.81%8.98%8.18%7.29%0.965
2123.60%3.17%0.00%0.04%0.55%26.87%36.58%9.19%8.22%7.31%0.968
2223.90%3.34%0.00%0.05%0.61%27.35%35.34%9.41%8.27%7.33%0.971
2324.19%3.51%0.00%0.05%0.67%27.84%34.11%9.63%8.31%7.35%0.973
2424.48%3.67%0.00%0.06%0.73%28.32%32.87%9.86%8.35%7.38%0.976
2524.78%3.84%0.00%0.07%0.79%28.81%31.62%10.09%8.39%7.41%0.978
2625.08%4.01%0.00%0.08%0.85%29.29%30.38%10.31%8.43%7.43%0.980
2725.36%4.17%0.00%0.09%0.93%29.75%29.17%10.53%8.48%7.46%0.982
2825.63%4.34%0.00%0.10%1.00%30.20%27.98%10.76%8.52%7.49%0.984
2925.88%4.51%0.00%0.12%1.08%30.65%26.79%10.98%8.56%7.52%0.985
3026.13%4.68%0.01%0.13%1.16%31.08%25.61%11.20%8.60%7.55%0.987
3126.38%4.84%0.01%0.15%1.25%31.51%24.45%11.42%8.64%7.58%0.988
3226.62%5.00%0.01%0.16%1.34%31.92%23.31%11.64%8.67%7.61%0.989
3326.86%5.15%0.02%0.17%1.43%32.33%22.17%11.87%8.71%7.64%0.990
3427.09%5.31%0.02%0.19%1.54%32.72%21.04%12.09%8.75%7.68%0.991
3527.30%5.47%0.02%0.21%1.64%33.09%19.94%12.32%8.79%7.71%0.991
3627.48%5.64%0.03%0.23%1.75%33.42%18.90%12.55%8.83%7.74%0.991
3727.64%5.81%0.03%0.25%1.86%33.74%17.88%12.79%8.86%7.78%0.991
3827.79%5.98%0.03%0.27%1.98%34.04%16.88%13.02%8.90%7.81%0.991
3927.92%6.16%0.04%0.29%2.11%34.32%15.91%13.25%8.93%7.85%0.991
4028.02%6.35%0.04%0.31%2.24%34.59%14.97%13.48%8.96%7.89%0.990
4128.10%6.54%0.04%0.33%2.38%34.84%14.05%13.71%8.99%7.93%0.990
4228.16%6.74%0.05%0.35%2.53%35.05%13.18%13.95%9.02%7.96%0.989
4328.21%6.93%0.05%0.37%2.67%35.23%12.34%14.19%9.05%8.00%0.988
4428.25%7.13%0.06%0.40%2.82%35.37%11.53%14.44%9.08%8.04%0.987
4528.27%7.32%0.06%0.42%2.98%35.50%10.75%14.70%9.11%8.08%0.985
4628.26%7.52%0.06%0.45%3.14%35.59%10.02%14.97%9.14%8.12%0.984
4728.22%7.72%0.06%0.47%3.30%35.65%9.33%15.25%9.16%8.16%0.982
4828.17%7.91%0.07%0.50%3.47%35.67%8.68%15.53%9.19%8.20%0.981
4928.11%8.10%0.08%0.53%3.63%35.69%8.03%15.83%9.21%8.24%0.979
5028.05%8.28%0.09%0.56%3.79%35.66%7.44%16.12%9.24%8.28%0.977
5128.00%8.45%0.09%0.60%3.96%35.61%6.87%16.42%9.26%8.32%0.974
5227.93%8.62%0.10%0.63%4.14%35.52%6.35%16.73%9.28%8.36%0.972
5327.86%8.79%0.10%0.65%4.31%35.39%5.86%17.04%9.30%8.41%0.970
5427.77%8.96%0.11%0.68%4.48%35.23%5.41%17.36%9.32%8.45%0.967
5527.65%9.13%0.11%0.71%4.66%35.07%4.99%17.68%9.34%8.49%0.965
5627.52%9.30%0.12%0.74%4.84%34.90%4.58%18.00%9.36%8.53%0.962
5727.39%9.46%0.13%0.77%5.02%34.72%4.18%18.34%9.37%8.58%0.959
5827.23%9.62%0.14%0.81%5.21%34.49%3.83%18.67%9.39%8.62%0.956
5927.05%9.78%0.14%0.86%5.40%34.24%3.52%19.02%9.41%8.67%0.953
6026.88%9.93%0.15%0.91%5.58%33.97%3.22%19.37%9.42%8.71%0.949
6126.70%10.07%0.16%0.96%5.77%33.68%2.92%19.73%9.43%8.76%0.946
6226.56%10.20%0.16%1.00%5.97%33.37%2.64%20.10%9.45%8.81%0.942
6326.41%10.33%0.16%1.05%6.17%33.02%2.41%20.46%9.46%8.86%0.939
6426.27%10.44%0.16%1.09%6.38%32.63%2.20%20.82%9.48%8.91%0.935
6526.12%10.55%0.16%1.14%6.61%32.21%2.02%21.19%9.49%8.96%0.931
6625.97%10.64%0.16%1.18%6.85%31.79%1.86%21.55%9.50%9.01%0.927
6725.80%10.73%0.16%1.22%7.11%31.35%1.71%21.91%9.51%9.07%0.922
6825.61%10.84%0.17%1.26%7.36%30.92%1.56%22.27%9.52%9.13%0.918
6925.40%10.97%0.17%1.31%7.61%30.48%1.42%22.64%9.54%9.18%0.913
7025.20%11.08%0.17%1.35%7.87%30.02%1.29%23.02%9.55%9.24%0.909
7125.00%11.20%0.18%1.38%8.12%29.54%1.17%23.41%9.56%9.30%0.904
7224.80%11.31%0.18%1.41%8.38%29.04%1.06%23.81%9.57%9.36%0.899
7324.60%11.43%0.18%1.44%8.66%28.54%0.96%24.18%9.58%9.43%0.894
7424.36%11.55%0.19%1.47%8.94%28.06%0.86%24.56%9.59%9.49%0.889
7524.11%11.67%0.19%1.50%9.23%27.58%0.77%24.94%9.60%9.56%0.884
7623.86%11.80%0.20%1.53%9.52%27.07%0.69%25.34%9.61%9.62%0.879
7723.61%11.94%0.20%1.55%9.83%26.53%0.61%25.73%9.62%9.69%0.874
7823.39%12.07%0.20%1.57%10.14%25.98%0.55%26.10%9.63%9.76%0.869
7923.15%12.20%0.21%1.60%10.47%25.42%0.48%26.48%9.64%9.84%0.863
8022.89%12.35%0.21%1.62%10.80%24.85%0.42%26.86%9.65%9.91%0.857
8122.58%12.52%0.21%1.65%11.16%24.29%0.36%27.23%9.66%9.99%0.852
8222.24%12.70%0.22%1.68%11.51%23.74%0.31%27.60%9.67%10.07%0.846
8321.85%12.91%0.22%1.71%11.89%23.18%0.26%27.98%9.68%10.16%0.840
8421.42%13.15%0.22%1.75%12.26%22.61%0.22%28.37%9.68%10.24%0.833
8520.91%13.45%0.24%1.81%12.65%22.03%0.18%28.73%9.69%10.33%0.827
8620.33%13.78%0.29%1.87%13.04%21.43%0.15%29.10%9.70%10.43%0.820
8719.70%14.10%0.33%1.96%13.48%20.84%0.13%29.47%9.70%10.52%0.812
8818.97%14.46%0.37%2.07%13.93%20.26%0.11%29.83%9.70%10.63%0.805
8918.17%14.83%0.42%2.19%14.38%19.71%0.09%30.21%9.70%10.73%0.797
9017.28%15.21%0.44%2.36%14.85%19.18%0.07%30.61%9.70%10.83%0.789
9116.33%15.60%0.46%2.53%15.35%18.63%0.05%31.04%9.70%10.94%0.782
9215.40%15.99%0.48%2.70%15.86%18.10%0.04%31.43%9.70%11.05%0.774
9314.41%16.50%0.50%2.84%16.41%17.56%0.02%31.76%9.70%11.17%0.766
9413.46%16.88%0.51%2.98%17.02%17.07%0.01%32.08%9.70%11.28%0.758
9512.47%17.31%0.53%3.08%17.63%16.66%0.00%32.32%9.70%11.39%0.751
9611.40%17.72%0.54%3.28%18.35%16.25%0.00%32.47%9.70%11.51%0.743
9710.25%18.17%0.44%3.52%19.15%15.89%0.00%32.57%9.69%11.63%0.735
989.05%18.44%0.29%3.73%20.30%15.61%0.00%32.57%9.69%11.76%0.726
998.06%18.33%0.15%4.02%21.53%15.24%0.00%32.68%9.68%11.91%0.717
1007.50%18.12%0.00%4.00%22.88%15.00%0.00%32.50%9.68%12.03%0.710
*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 (1.15% 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 Sep 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