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 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 24.63%
SLY SPDR S&P 600 Small Cap ETF 10.12%
EFA iShares MSCI EAFE ETF 0.01%
EEM iShares MSCI Emerging Markets ETF 0.67%
VNQ Vanguard Real Estate ETF 1.12%
TLT iShares 20+ Year Treasury Bond ETF 32.08%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 19.72%
GLD SPDR Gold Shares 11.65%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio9.00%11.93%0.66
Tangency Portfolio9.09%7.87%1.01

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)9.80%11.05%15.07%0.6580.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)9.86%12.17%20.34%0.5430.00%100.00%
3iShares MSCI EAFE ETF (EFA)4.33%6.01%17.76%0.2750.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)5.87%8.56%22.36%0.3320.00%100.00%
5Vanguard Real Estate ETF (VNQ)6.92%9.85%22.92%0.3800.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)7.02%7.96%13.40%0.5100.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.94%6.23%7.42%0.6860.00%100.00%
8SPDR Gold Shares (GLD)8.62%10.30%17.65%0.5190.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.13% annualized).

Asset Correlations

Asset Correlations
NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.910.890.790.72-0.320.340.06
SPDR S&P 600 Small Cap ETFSLY0.911.000.810.740.74-0.370.300.02
iShares MSCI EAFE ETFEFA0.890.811.000.880.70-0.270.410.14
iShares MSCI Emerging Markets ETFEEM0.790.740.881.000.62-0.250.380.29
Vanguard Real Estate ETFVNQ0.720.740.700.621.00-0.010.470.10
iShares 20+ Year Treasury Bond ETFTLT-0.32-0.37-0.27-0.25-0.011.000.470.21
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.340.300.410.380.470.471.000.27
SPDR Gold SharesGLD0.060.020.140.290.100.210.271.00
Based on monthly returns from Jan 2006 to Dec 2020
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
114.17%0.63%0.00%0.00%0.00%14.71%64.72%5.76%7.42%7.09%0.887
214.77%0.69%0.00%0.00%0.00%15.19%63.43%5.91%7.47%7.09%0.894
315.31%0.78%0.00%0.00%0.00%15.68%62.18%6.05%7.52%7.09%0.900
415.81%0.91%0.00%0.00%0.00%16.16%60.94%6.18%7.56%7.10%0.906
516.27%1.05%0.00%0.00%0.00%16.64%59.73%6.32%7.60%7.10%0.911
616.69%1.22%0.00%0.00%0.00%17.11%58.53%6.45%7.65%7.11%0.917
717.08%1.41%0.00%0.01%0.00%17.59%57.33%6.58%7.69%7.11%0.922
817.45%1.62%0.00%0.01%0.01%18.08%56.12%6.72%7.74%7.12%0.927
917.80%1.84%0.00%0.02%0.01%18.56%54.91%6.85%7.78%7.13%0.932
1018.15%2.05%0.00%0.03%0.02%19.05%53.71%7.00%7.82%7.14%0.937
1118.48%2.28%0.00%0.04%0.03%19.53%52.49%7.14%7.87%7.15%0.942
1218.77%2.55%0.00%0.04%0.05%20.03%51.27%7.29%7.91%7.16%0.947
1319.04%2.82%0.00%0.05%0.06%20.52%50.06%7.44%7.96%7.18%0.951
1419.31%3.09%0.00%0.06%0.08%21.01%48.85%7.60%8.00%7.19%0.955
1519.57%3.37%0.00%0.07%0.10%21.49%47.64%7.75%8.05%7.21%0.959
1619.83%3.65%0.00%0.08%0.13%21.98%46.43%7.91%8.09%7.22%0.963
1720.09%3.92%0.00%0.10%0.15%22.47%45.20%8.07%8.14%7.24%0.967
1820.35%4.20%0.00%0.11%0.17%22.97%43.97%8.22%8.18%7.26%0.971
1920.61%4.49%0.00%0.13%0.20%23.46%42.73%8.38%8.23%7.28%0.974
2020.86%4.78%0.00%0.14%0.22%23.96%41.49%8.55%8.27%7.30%0.978
2121.11%5.08%0.00%0.16%0.25%24.45%40.24%8.71%8.32%7.33%0.981
2221.36%5.37%0.01%0.18%0.28%24.95%38.98%8.88%8.37%7.35%0.984
2321.61%5.67%0.01%0.20%0.30%25.45%37.72%9.05%8.41%7.37%0.987
2421.85%5.97%0.01%0.22%0.33%25.95%36.45%9.22%8.46%7.40%0.990
2522.08%6.27%0.01%0.25%0.36%26.45%35.18%9.39%8.51%7.43%0.993
2622.31%6.57%0.01%0.28%0.40%26.94%33.92%9.57%8.55%7.46%0.995
2722.54%6.87%0.02%0.31%0.44%27.43%32.66%9.74%8.60%7.48%0.998
2822.77%7.16%0.02%0.33%0.48%27.93%31.39%9.92%8.65%7.52%1.000
2923.00%7.46%0.02%0.36%0.52%28.41%30.13%10.09%8.69%7.55%1.002
3023.23%7.75%0.02%0.39%0.56%28.88%28.89%10.27%8.74%7.58%1.004
3123.43%8.05%0.02%0.42%0.62%29.33%27.69%10.45%8.78%7.61%1.005
3223.62%8.35%0.01%0.46%0.67%29.77%26.49%10.63%8.83%7.65%1.006
3323.81%8.66%0.01%0.49%0.73%30.20%25.30%10.81%8.87%7.68%1.008
3423.99%8.96%0.01%0.52%0.79%30.60%24.14%10.99%8.92%7.72%1.009
3524.17%9.24%0.01%0.56%0.87%30.99%23.00%11.16%8.96%7.76%1.009
3624.33%9.53%0.01%0.59%0.95%31.37%21.88%11.33%9.00%7.79%1.010
3724.48%9.83%0.01%0.63%1.03%31.75%20.78%11.49%9.04%7.83%1.010
3824.63%10.12%0.01%0.67%1.12%32.08%19.72%11.65%9.09%7.87%1.010
3924.74%10.42%0.01%0.72%1.21%32.40%18.67%11.83%9.13%7.91%1.010
4024.83%10.72%0.01%0.77%1.31%32.70%17.64%12.01%9.17%7.96%1.010
4124.93%11.02%0.01%0.82%1.42%32.98%16.63%12.20%9.21%8.00%1.009
4224.98%11.34%0.01%0.87%1.53%33.22%15.68%12.38%9.24%8.04%1.008
4325.01%11.67%0.01%0.92%1.65%33.42%14.77%12.56%9.28%8.09%1.007
4425.03%11.99%0.00%0.97%1.79%33.59%13.90%12.74%9.32%8.14%1.006
4525.01%12.32%0.00%1.02%1.93%33.72%13.08%12.92%9.35%8.18%1.005
4624.96%12.67%0.00%1.07%2.07%33.80%12.31%13.11%9.39%8.23%1.003
4724.87%13.02%0.00%1.13%2.22%33.84%11.61%13.31%9.42%8.28%1.001
4824.76%13.37%0.00%1.19%2.37%33.82%10.97%13.51%9.45%8.33%0.998
4924.64%13.72%0.00%1.25%2.54%33.79%10.35%13.71%9.48%8.38%0.996
5024.49%14.07%0.00%1.32%2.70%33.74%9.77%13.92%9.51%8.43%0.993
5124.34%14.42%0.00%1.38%2.88%33.66%9.21%14.12%9.54%8.49%0.991
5224.17%14.77%0.00%1.44%3.06%33.54%8.69%14.32%9.56%8.54%0.988
5324.01%15.10%0.00%1.51%3.25%33.40%8.19%14.54%9.59%8.59%0.984
5423.87%15.43%0.00%1.57%3.44%33.22%7.71%14.77%9.62%8.65%0.981
5523.73%15.75%0.00%1.64%3.63%33.02%7.24%14.99%9.65%8.71%0.977
5623.59%16.08%0.00%1.70%3.82%32.80%6.78%15.22%9.67%8.77%0.974
5723.47%16.41%0.00%1.77%4.01%32.54%6.36%15.45%9.70%8.83%0.970
5823.36%16.73%0.00%1.83%4.21%32.24%5.96%15.67%9.73%8.90%0.966
5923.22%17.05%0.00%1.90%4.41%31.93%5.58%15.91%9.75%8.96%0.962
6023.07%17.39%0.00%1.96%4.63%31.58%5.23%16.15%9.78%9.03%0.957
6122.93%17.72%0.00%2.03%4.84%31.21%4.90%16.38%9.80%9.10%0.953
6222.83%18.02%0.00%2.09%5.06%30.82%4.57%16.61%9.83%9.17%0.948
6322.74%18.30%0.00%2.15%5.30%30.40%4.26%16.85%9.85%9.25%0.943
6422.67%18.56%0.00%2.22%5.54%29.95%3.97%17.09%9.88%9.32%0.938
6522.60%18.82%0.00%2.28%5.79%29.49%3.69%17.33%9.90%9.40%0.933
6622.53%19.07%0.00%2.35%6.04%29.00%3.45%17.57%9.93%9.48%0.927
6722.45%19.31%0.00%2.41%6.29%28.49%3.22%17.82%9.95%9.56%0.922
6822.38%19.55%0.00%2.47%6.55%27.97%3.00%18.08%9.97%9.65%0.916
6922.29%19.79%0.00%2.54%6.81%27.44%2.81%18.32%9.99%9.73%0.911
7022.18%20.06%0.00%2.61%7.08%26.89%2.63%18.56%10.02%9.82%0.905
7122.07%20.31%0.00%2.68%7.36%26.32%2.47%18.79%10.04%9.91%0.899
7221.94%20.58%0.00%2.74%7.64%25.75%2.32%19.02%10.06%10.00%0.893
7321.81%20.83%0.00%2.80%7.95%25.18%2.18%19.25%10.08%10.09%0.887
7421.68%21.08%0.00%2.86%8.26%24.60%2.05%19.47%10.10%10.19%0.880
7521.53%21.36%0.00%2.92%8.56%24.02%1.93%19.67%10.12%10.28%0.874
7621.34%21.68%0.00%2.98%8.87%23.44%1.82%19.86%10.14%10.38%0.868
7721.13%22.01%0.00%3.04%9.18%22.87%1.71%20.06%10.16%10.48%0.861
7820.94%22.31%0.00%3.11%9.50%22.29%1.60%20.25%10.18%10.58%0.855
7920.74%22.60%0.00%3.19%9.82%21.70%1.50%20.45%10.20%10.68%0.849
8020.56%22.87%0.00%3.27%10.17%21.11%1.41%20.62%10.22%10.79%0.842
8120.39%23.13%0.00%3.35%10.50%20.52%1.32%20.79%10.24%10.89%0.836
8220.18%23.42%0.00%3.44%10.85%19.99%1.21%20.91%10.25%11.00%0.829
8319.89%23.78%0.00%3.53%11.19%19.48%1.10%21.02%10.27%11.11%0.823
8419.49%24.21%0.00%3.65%11.56%18.98%1.01%21.11%10.29%11.22%0.816
8519.08%24.62%0.00%3.78%11.94%18.50%0.92%21.16%10.30%11.33%0.809
8618.67%25.05%0.00%3.93%12.32%18.02%0.84%21.18%10.32%11.45%0.802
8718.24%25.49%0.00%4.07%12.70%17.55%0.77%21.19%10.33%11.56%0.796
8817.73%25.96%0.00%4.25%13.10%17.09%0.69%21.18%10.35%11.69%0.789
8917.10%26.45%0.00%4.51%13.51%16.66%0.62%21.15%10.36%11.81%0.781
9016.39%26.98%0.00%4.80%13.97%16.23%0.54%21.10%10.37%11.94%0.773
9115.53%27.55%0.00%5.10%14.46%15.84%0.47%21.04%10.38%12.08%0.765
9214.50%28.23%0.00%5.42%14.99%15.47%0.41%20.98%10.39%12.22%0.757
9313.45%28.91%0.00%5.78%15.50%15.10%0.35%20.91%10.39%12.36%0.749
9412.46%29.60%0.00%6.15%16.01%14.76%0.28%20.74%10.40%12.51%0.741
9511.49%30.22%0.00%6.51%16.57%14.45%0.23%20.54%10.41%12.66%0.733
9610.53%30.73%0.00%6.85%17.20%14.17%0.18%20.32%10.41%12.80%0.725
979.60%31.09%0.00%7.25%17.85%13.93%0.14%20.14%10.41%12.93%0.718
988.66%31.32%0.00%7.62%18.80%13.62%0.09%19.89%10.40%13.09%0.708
997.75%31.42%0.00%7.99%19.89%13.53%0.05%19.37%10.39%13.24%0.699
1006.50%32.00%0.00%8.50%20.50%13.50%0.00%19.00%10.38%13.37%0.692
*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 (1.13% 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 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