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 - Jun 2021)

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 26.06%
SLY SPDR S&P 600 Small Cap ETF 9.85%
EFA iShares MSCI EAFE ETF 0.04%
EEM iShares MSCI Emerging Markets ETF 0.65%
VNQ Vanguard Real Estate ETF 1.47%
TLT iShares 20+ Year Treasury Bond ETF 30.99%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 19.84%
GLD SPDR Gold Shares 11.10%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio9.19%11.76%0.66
Tangency Portfolio9.00%7.88%0.96

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)11.71%14.91%0.6730.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)13.32%20.14%0.5700.00%100.00%
3iShares MSCI EAFE ETF (EFA)6.44%17.52%0.2950.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)8.76%22.01%0.3330.00%100.00%
5Vanguard Real Estate ETF (VNQ)10.93%22.66%0.4110.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)7.16%13.45%0.4350.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)5.91%7.39%0.6310.00%100.00%
8SPDR Gold Shares (GLD)9.49%17.71%0.4520.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

Asset Correlations
NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.910.890.780.72-0.320.340.05
SPDR S&P 600 Small Cap ETFSLY0.911.000.810.740.74-0.380.270.01
iShares MSCI EAFE ETFEFA0.890.811.000.880.69-0.270.400.14
iShares MSCI Emerging Markets ETFEEM0.780.740.881.000.61-0.250.380.29
Vanguard Real Estate ETFVNQ0.720.740.690.611.00-0.020.460.10
iShares 20+ Year Treasury Bond ETFTLT-0.32-0.38-0.27-0.25-0.021.000.490.21
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.340.270.400.380.460.491.000.27
SPDR Gold SharesGLD0.050.010.140.290.100.210.271.00
Based on monthly returns from Jan 2006 to Jun 2021
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
113.61%1.17%0.01%0.00%0.00%13.81%65.68%5.72%7.14%7.08%0.823
214.26%1.26%0.00%0.00%0.00%14.31%64.30%5.86%7.20%7.08%0.830
314.86%1.38%0.00%0.00%0.00%14.82%62.93%6.01%7.25%7.08%0.837
415.42%1.52%0.00%0.00%0.00%15.32%61.57%6.16%7.31%7.08%0.844
515.94%1.69%0.00%0.00%0.00%15.82%60.23%6.32%7.36%7.09%0.851
616.42%1.88%0.00%0.00%0.00%16.33%58.90%6.47%7.41%7.10%0.857
716.88%2.08%0.00%0.01%0.01%16.84%57.57%6.62%7.47%7.10%0.863
817.33%2.29%0.00%0.02%0.01%17.34%56.25%6.77%7.52%7.11%0.869
917.77%2.50%0.00%0.02%0.02%17.84%54.93%6.92%7.57%7.12%0.875
1018.19%2.72%0.00%0.03%0.03%18.34%53.62%7.07%7.63%7.13%0.880
1118.59%2.96%0.00%0.03%0.05%18.85%52.32%7.22%7.68%7.15%0.886
1218.98%3.20%0.00%0.04%0.06%19.35%51.00%7.37%7.73%7.16%0.891
1319.37%3.44%0.00%0.04%0.08%19.86%49.70%7.52%7.78%7.17%0.896
1419.74%3.68%0.00%0.05%0.10%20.37%48.39%7.67%7.84%7.19%0.901
1520.09%3.93%0.00%0.07%0.13%20.87%47.09%7.82%7.89%7.21%0.905
1620.44%4.18%0.00%0.08%0.16%21.38%45.80%7.96%7.94%7.23%0.910
1720.78%4.44%0.00%0.10%0.19%21.88%44.51%8.11%7.99%7.25%0.914
1821.12%4.69%0.00%0.11%0.22%22.39%43.22%8.25%8.04%7.27%0.918
1921.46%4.94%0.00%0.13%0.25%22.90%41.92%8.40%8.10%7.29%0.922
2021.80%5.20%0.00%0.15%0.28%23.41%40.61%8.54%8.15%7.31%0.925
2122.13%5.46%0.00%0.17%0.31%23.93%39.31%8.69%8.20%7.34%0.929
2222.45%5.72%0.00%0.20%0.35%24.44%38.00%8.84%8.25%7.36%0.932
2322.78%5.97%0.01%0.22%0.39%24.96%36.69%8.98%8.30%7.39%0.935
2423.08%6.24%0.01%0.25%0.43%25.47%35.39%9.13%8.36%7.42%0.938
2523.39%6.50%0.01%0.27%0.47%25.98%34.09%9.28%8.41%7.45%0.941
2623.70%6.76%0.01%0.30%0.52%26.48%32.80%9.43%8.46%7.48%0.944
2723.99%7.03%0.02%0.33%0.57%26.95%31.53%9.59%8.51%7.51%0.946
2824.27%7.30%0.02%0.36%0.63%27.42%30.27%9.75%8.56%7.54%0.949
2924.54%7.57%0.02%0.39%0.69%27.89%29.02%9.90%8.61%7.57%0.951
3024.80%7.84%0.02%0.41%0.76%28.34%27.79%10.05%8.66%7.61%0.952
3125.04%8.10%0.03%0.44%0.84%28.79%26.56%10.19%8.71%7.64%0.954
3225.27%8.38%0.03%0.48%0.93%29.22%25.35%10.34%8.76%7.68%0.955
3325.47%8.66%0.03%0.51%1.02%29.63%24.17%10.50%8.81%7.72%0.957
3425.66%8.95%0.03%0.54%1.13%30.04%23.00%10.65%8.86%7.76%0.957
3525.82%9.24%0.03%0.58%1.24%30.41%21.88%10.80%8.91%7.80%0.958
3625.95%9.55%0.04%0.61%1.35%30.72%20.83%10.95%8.96%7.84%0.959
3726.06%9.85%0.04%0.65%1.47%30.99%19.84%11.10%9.00%7.88%0.959
3826.16%10.15%0.04%0.68%1.60%31.24%18.87%11.26%9.04%7.93%0.959
3926.23%10.46%0.04%0.72%1.72%31.46%17.94%11.42%9.09%7.97%0.959
4026.29%10.78%0.05%0.76%1.85%31.66%17.03%11.58%9.13%8.01%0.958
4126.33%11.10%0.05%0.80%1.98%31.85%16.13%11.75%9.17%8.06%0.958
4226.35%11.44%0.05%0.84%2.12%32.03%15.26%11.92%9.22%8.10%0.957
4326.39%11.76%0.05%0.88%2.25%32.15%14.44%12.08%9.26%8.15%0.956
4426.40%12.08%0.06%0.93%2.40%32.24%13.66%12.25%9.30%8.20%0.955
4526.40%12.39%0.06%0.97%2.55%32.30%12.92%12.42%9.34%8.25%0.954
4626.40%12.69%0.07%1.01%2.72%32.34%12.19%12.59%9.37%8.30%0.953
4726.41%12.99%0.07%1.05%2.89%32.31%11.51%12.77%9.41%8.35%0.951
4826.43%13.28%0.08%1.10%3.07%32.23%10.86%12.95%9.45%8.40%0.949
4926.42%13.57%0.08%1.14%3.26%32.16%10.23%13.13%9.49%8.46%0.947
5026.39%13.85%0.08%1.19%3.47%32.06%9.63%13.32%9.53%8.52%0.945
5126.35%14.13%0.09%1.24%3.68%31.91%9.08%13.51%9.56%8.57%0.942
5226.30%14.41%0.09%1.28%3.90%31.73%8.56%13.72%9.60%8.63%0.939
5326.25%14.69%0.10%1.33%4.11%31.53%8.06%13.94%9.63%8.69%0.937
5426.19%14.98%0.10%1.37%4.33%31.29%7.59%14.15%9.67%8.75%0.934
5526.13%15.26%0.09%1.41%4.56%31.03%7.14%14.37%9.70%8.82%0.931
5626.09%15.53%0.09%1.46%4.79%30.74%6.70%14.60%9.74%8.88%0.927
5726.03%15.81%0.09%1.50%5.02%30.45%6.29%14.81%9.77%8.95%0.924
5825.98%16.08%0.09%1.54%5.25%30.14%5.89%15.03%9.81%9.02%0.920
5925.92%16.34%0.09%1.58%5.51%29.80%5.51%15.23%9.84%9.09%0.917
6025.88%16.58%0.09%1.63%5.79%29.44%5.15%15.44%9.87%9.16%0.913
6125.84%16.82%0.10%1.66%6.07%29.07%4.79%15.65%9.91%9.24%0.909
6225.78%17.06%0.10%1.70%6.36%28.68%4.46%15.87%9.94%9.31%0.904
6325.74%17.29%0.10%1.73%6.65%28.23%4.16%16.10%9.97%9.39%0.900
6425.72%17.50%0.10%1.76%6.94%27.78%3.86%16.33%10.01%9.47%0.895
6525.70%17.71%0.11%1.80%7.24%27.31%3.59%16.55%10.04%9.56%0.891
6625.65%17.94%0.11%1.83%7.55%26.82%3.32%16.77%10.07%9.64%0.886
6725.60%18.18%0.11%1.86%7.86%26.28%3.09%17.02%10.11%9.73%0.881
6825.51%18.41%0.11%1.90%8.19%25.74%2.87%17.26%10.14%9.82%0.876
6925.41%18.64%0.11%1.94%8.53%25.19%2.67%17.50%10.17%9.92%0.871
7025.31%18.87%0.12%1.98%8.88%24.63%2.49%17.73%10.20%10.01%0.865
7125.16%19.13%0.12%2.02%9.23%24.07%2.33%17.95%10.23%10.11%0.860
7224.96%19.43%0.12%2.07%9.58%23.50%2.17%18.16%10.26%10.20%0.854
7324.76%19.75%0.13%2.11%9.93%22.93%2.04%18.37%10.29%10.30%0.849
7424.54%20.09%0.13%2.15%10.28%22.34%1.91%18.57%10.32%10.41%0.843
7524.32%20.42%0.13%2.19%10.64%21.76%1.80%18.74%10.35%10.51%0.837
7624.09%20.77%0.14%2.24%10.99%21.18%1.68%18.91%10.38%10.62%0.832
7723.82%21.12%0.14%2.29%11.36%20.62%1.57%19.07%10.41%10.72%0.826
7823.55%21.47%0.15%2.35%11.73%20.07%1.46%19.21%10.44%10.83%0.820
7923.25%21.82%0.15%2.43%12.13%19.52%1.36%19.34%10.47%10.94%0.814
8022.92%22.15%0.16%2.53%12.55%18.98%1.26%19.45%10.50%11.06%0.808
8122.58%22.50%0.16%2.65%12.99%18.44%1.17%19.52%10.52%11.17%0.802
8222.23%22.84%0.17%2.76%13.44%17.92%1.08%19.56%10.55%11.29%0.795
8321.91%23.16%0.17%2.87%13.91%17.39%0.99%19.59%10.58%11.41%0.789
8421.57%23.50%0.18%2.97%14.38%16.85%0.91%19.63%10.60%11.54%0.783
8521.16%23.92%0.18%3.08%14.85%16.30%0.83%19.68%10.63%11.67%0.776
8620.71%24.38%0.16%3.21%15.32%15.76%0.76%19.71%10.66%11.80%0.770
8720.21%24.87%0.14%3.34%15.78%15.23%0.69%19.73%10.69%11.93%0.764
8819.61%25.45%0.12%3.49%16.25%14.70%0.62%19.76%10.72%12.07%0.757
8918.90%26.12%0.10%3.70%16.70%14.19%0.56%19.74%10.75%12.21%0.750
9018.20%26.78%0.08%3.89%17.15%13.67%0.50%19.73%10.78%12.36%0.744
9117.43%27.47%0.06%4.07%17.65%13.17%0.44%19.71%10.81%12.51%0.737
9216.65%28.25%0.04%4.25%18.17%12.67%0.38%19.60%10.84%12.67%0.730
9315.82%29.06%0.02%4.49%18.70%12.17%0.32%19.43%10.88%12.84%0.723
9414.81%29.84%0.00%4.76%19.35%11.68%0.26%19.30%10.91%13.01%0.715
9513.84%30.54%0.00%5.01%20.00%11.23%0.21%19.16%10.93%13.18%0.708
9612.89%31.11%0.00%5.30%20.70%10.85%0.17%18.99%10.95%13.34%0.701
9711.94%31.61%0.00%5.62%21.50%10.47%0.12%18.74%10.97%13.51%0.693
9811.02%31.93%0.00%6.01%22.35%10.12%0.08%18.49%10.98%13.68%0.685
999.94%32.48%0.00%6.39%23.15%9.78%0.04%18.21%11.00%13.85%0.678
1008.00%34.00%0.00%7.50%23.00%9.50%0.00%18.00%11.01%14.03%0.670
*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.
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 Jun 2021
  • 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