Efficient Frontier

Efficient Frontier Overview

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.

Efficient Frontier Configuration

Efficient Frontier Assets
Allocation
Min. Weight
Max. Weight
Group
EF #1
EF #2
1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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%
Total
%
Asset Groups
Min. Weight
Max. Weight
A
%
%
B
%
%
C
%
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D
%
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E
%
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F
%
%

Efficient Frontier Results (Jan 2006 - May 2023)

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 »

Max Sharpe Ratio Portfolio

Ticker Name Allocation
SPY SPDR S&P 500 ETF Trust 32.54%
SLY SPDR S&P 600 Small Cap ETF 11.64%
EFA iShares MSCI EAFE ETF 0.25%
EEM iShares MSCI Emerging Markets ETF 0.23%
VNQ Vanguard Real Estate ETF 1.88%
TLT iShares 20+ Year Treasury Bond ETF 25.03%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 6.76%
GLD SPDR Gold Shares 21.66%
Save portfolio »

Performance Summary

PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio7.23%12.20%0.50
Max Sharpe Ratio Portfolio8.03%9.59%0.71

Efficient Frontier

Notes and Disclosures
  • IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
  • 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. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
  • Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
  • Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
  • 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.
  • Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
  • Portfolio optimization is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. 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 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 May 2023
  • 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

Efficient Frontier Assets

#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)10.11%15.42%0.5790.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)10.43%20.25%0.4560.00%100.00%
3iShares MSCI EAFE ETF (EFA)5.40%17.71%0.2380.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)5.82%21.79%0.2120.00%100.00%
5Vanguard Real Estate ETF (VNQ)8.51%22.64%0.3230.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)4.61%13.82%0.2470.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)4.25%8.09%0.3790.00%100.00%
8SPDR Gold Shares (GLD)8.74%17.24%0.4380.00%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

NameTickerSPYSLYEFAEEMVNQTLTLQDGLD
SPDR S&P 500 ETF TrustSPY1.000.900.880.750.74-0.170.430.09
SPDR S&P 600 Small Cap ETFSLY0.901.000.810.720.75-0.270.340.03
iShares MSCI EAFE ETFEFA0.880.811.000.870.71-0.130.480.18
iShares MSCI Emerging Markets ETFEEM0.750.720.871.000.61-0.130.440.31
Vanguard Real Estate ETFVNQ0.740.750.710.611.000.060.490.13
iShares 20+ Year Treasury Bond ETFTLT-0.17-0.27-0.13-0.130.061.000.570.25
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.430.340.480.440.490.571.000.30
SPDR Gold SharesGLD0.090.030.180.310.130.250.301.00
Based on monthly returns from Jan 2006 to May 2023

Efficient Frontier Portfolios

#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return *Standard Deviation *Sharpe Ratio *
19.04%1.50%0.00%0.00%0.00%7.78%73.61%8.08%5.27%7.90%0.516
29.62%1.55%0.01%0.00%0.00%8.11%72.40%8.31%5.31%7.90%0.522
310.18%1.63%0.02%0.00%0.00%8.47%71.17%8.53%5.36%7.90%0.528
410.75%1.71%0.02%0.00%0.00%8.85%69.92%8.75%5.41%7.91%0.534
511.31%1.80%0.03%0.00%0.00%9.23%68.66%8.96%5.46%7.91%0.540
611.85%1.91%0.04%0.00%0.00%9.63%67.40%9.17%5.51%7.92%0.546
712.37%2.03%0.04%0.00%0.00%10.04%66.14%9.38%5.56%7.92%0.552
812.90%2.15%0.05%0.00%0.00%10.45%64.87%9.59%5.61%7.93%0.557
913.41%2.28%0.06%0.00%0.00%10.87%63.59%9.79%5.66%7.94%0.563
1013.92%2.42%0.06%0.00%0.00%11.28%62.32%10.00%5.71%7.95%0.568
1114.42%2.56%0.07%0.00%0.00%11.70%61.04%10.21%5.76%7.96%0.574
1214.92%2.71%0.07%0.00%0.00%12.12%59.76%10.42%5.81%7.97%0.579
1315.42%2.86%0.08%0.00%0.00%12.55%58.46%10.63%5.86%7.99%0.584
1415.92%3.01%0.09%0.00%0.01%12.98%57.15%10.84%5.91%8.00%0.590
1516.41%3.17%0.09%0.00%0.01%13.42%55.84%11.06%5.96%8.02%0.595
1616.89%3.34%0.10%0.00%0.02%13.85%54.52%11.27%6.01%8.03%0.600
1717.35%3.52%0.10%0.01%0.04%14.29%53.22%11.49%6.06%8.05%0.604
1817.80%3.69%0.10%0.01%0.06%14.72%51.92%11.71%6.10%8.07%0.609
1918.25%3.87%0.10%0.01%0.08%15.16%50.61%11.93%6.15%8.09%0.614
2018.70%4.05%0.10%0.02%0.10%15.60%49.29%12.15%6.20%8.11%0.618
2119.15%4.23%0.10%0.02%0.12%16.04%47.96%12.37%6.25%8.13%0.623
2219.60%4.41%0.10%0.02%0.15%16.48%46.64%12.60%6.30%8.16%0.627
2320.05%4.59%0.10%0.03%0.17%16.92%45.33%12.82%6.35%8.18%0.631
2420.50%4.77%0.10%0.03%0.20%17.35%44.01%13.05%6.41%8.21%0.636
2520.95%4.94%0.10%0.03%0.23%17.79%42.68%13.27%6.46%8.23%0.640
2621.41%5.12%0.10%0.04%0.26%18.22%41.34%13.50%6.51%8.26%0.644
2721.87%5.31%0.10%0.04%0.29%18.67%40.00%13.73%6.56%8.29%0.648
2822.34%5.49%0.10%0.04%0.31%19.11%38.64%13.97%6.61%8.32%0.652
2922.80%5.67%0.11%0.05%0.34%19.55%37.29%14.20%6.66%8.35%0.655
3023.26%5.85%0.11%0.05%0.37%20.00%35.93%14.44%6.71%8.38%0.659
3123.72%6.03%0.12%0.05%0.40%20.45%34.56%14.67%6.77%8.41%0.663
3224.19%6.22%0.12%0.06%0.43%20.89%33.19%14.91%6.82%8.45%0.666
3324.65%6.41%0.12%0.06%0.45%21.34%31.82%15.15%6.87%8.48%0.670
3425.11%6.60%0.13%0.06%0.48%21.78%30.46%15.39%6.92%8.52%0.673
3525.54%6.79%0.13%0.07%0.52%22.21%29.12%15.63%6.97%8.56%0.676
3625.97%6.99%0.13%0.07%0.56%22.62%27.79%15.87%7.02%8.59%0.679
3726.40%7.18%0.14%0.07%0.60%23.02%26.49%16.11%7.08%8.63%0.682
3826.81%7.38%0.14%0.08%0.64%23.38%25.22%16.34%7.13%8.67%0.685
3927.20%7.58%0.15%0.08%0.69%23.73%24.00%16.58%7.17%8.71%0.687
4027.59%7.77%0.15%0.08%0.74%24.05%22.80%16.82%7.22%8.75%0.690
4127.97%7.97%0.15%0.09%0.78%24.37%21.61%17.06%7.27%8.79%0.692
4228.33%8.18%0.16%0.10%0.83%24.67%20.43%17.30%7.32%8.83%0.694
4328.69%8.38%0.16%0.10%0.88%24.97%19.27%17.54%7.37%8.87%0.696
4429.04%8.59%0.17%0.11%0.93%25.24%18.14%17.79%7.42%8.92%0.698
4529.36%8.81%0.17%0.12%0.98%25.47%17.05%18.04%7.46%8.96%0.700
4629.67%9.04%0.17%0.12%1.03%25.67%16.00%18.29%7.51%9.00%0.702
4729.97%9.27%0.18%0.13%1.08%25.84%14.99%18.54%7.55%9.05%0.704
4830.26%9.51%0.18%0.13%1.13%25.97%14.01%18.80%7.60%9.09%0.705
4930.54%9.74%0.19%0.14%1.18%26.07%13.08%19.06%7.65%9.14%0.707
5030.81%9.97%0.20%0.15%1.23%26.12%12.20%19.33%7.69%9.18%0.708
5131.05%10.20%0.20%0.16%1.29%26.10%11.38%19.61%7.73%9.23%0.709
5231.30%10.42%0.21%0.16%1.36%26.06%10.58%19.90%7.78%9.28%0.710
5331.53%10.63%0.22%0.17%1.44%25.97%9.85%20.19%7.82%9.33%0.711
5431.74%10.84%0.22%0.18%1.52%25.84%9.17%20.49%7.86%9.38%0.712
5531.96%11.04%0.23%0.19%1.60%25.68%8.52%20.78%7.90%9.43%0.712
5632.17%11.24%0.24%0.20%1.69%25.49%7.90%21.07%7.95%9.48%0.713
5732.36%11.44%0.24%0.21%1.78%25.28%7.31%21.37%7.99%9.54%0.713
5832.54%11.64%0.25%0.23%1.88%25.03%6.76%21.66%8.03%9.59%0.713
5932.72%11.83%0.24%0.26%1.98%24.75%6.26%21.96%8.06%9.64%0.713
6032.89%12.01%0.24%0.30%2.08%24.43%5.79%22.27%8.10%9.70%0.713
6133.04%12.19%0.24%0.33%2.18%24.09%5.33%22.58%8.14%9.76%0.713
6233.20%12.38%0.23%0.37%2.29%23.73%4.91%22.90%8.18%9.82%0.712
6333.34%12.57%0.23%0.40%2.39%23.35%4.50%23.22%8.22%9.88%0.712
6433.45%12.79%0.23%0.44%2.49%22.93%4.13%23.54%8.26%9.94%0.711
6533.54%13.03%0.22%0.47%2.60%22.50%3.79%23.85%8.29%10.00%0.710
6633.63%13.25%0.22%0.51%2.71%22.05%3.47%24.17%8.33%10.06%0.710
6733.68%13.49%0.22%0.55%2.83%21.58%3.19%24.47%8.36%10.13%0.708
6833.71%13.74%0.22%0.59%2.95%21.11%2.91%24.77%8.40%10.20%0.707
6933.73%14.01%0.22%0.62%3.07%20.62%2.67%25.06%8.43%10.26%0.706
7033.72%14.29%0.23%0.66%3.19%20.11%2.44%25.36%8.47%10.33%0.705
7133.69%14.59%0.24%0.69%3.32%19.60%2.23%25.64%8.50%10.40%0.703
7233.63%14.92%0.25%0.73%3.45%19.08%2.04%25.91%8.54%10.47%0.701
7333.55%15.25%0.26%0.76%3.59%18.55%1.86%26.18%8.57%10.55%0.700
7433.45%15.62%0.26%0.80%3.72%18.02%1.70%26.43%8.60%10.62%0.698
7533.29%16.03%0.27%0.84%3.86%17.49%1.54%26.68%8.63%10.70%0.696
7633.10%16.46%0.28%0.89%4.01%16.96%1.40%26.91%8.66%10.78%0.694
7732.87%16.91%0.29%0.93%4.16%16.44%1.26%27.15%8.69%10.86%0.691
7832.65%17.36%0.29%0.97%4.33%15.92%1.11%27.36%8.73%10.94%0.689
7932.41%17.83%0.30%1.01%4.52%15.42%0.98%27.53%8.75%11.02%0.687
8032.12%18.34%0.31%1.06%4.70%14.91%0.87%27.70%8.78%11.10%0.684
8131.82%18.87%0.32%1.11%4.86%14.40%0.76%27.86%8.81%11.19%0.681
8231.54%19.39%0.32%1.16%5.03%13.87%0.67%28.02%8.84%11.28%0.679
8331.21%19.93%0.33%1.21%5.20%13.33%0.58%28.22%8.87%11.36%0.676
8430.84%20.50%0.33%1.26%5.36%12.81%0.50%28.40%8.90%11.45%0.673
8530.43%21.10%0.33%1.32%5.53%12.31%0.42%28.57%8.92%11.54%0.670
8630.02%21.69%0.33%1.37%5.70%11.83%0.34%28.72%8.95%11.63%0.668
8729.51%22.30%0.33%1.43%5.93%11.36%0.27%28.87%8.97%11.72%0.664
8828.97%22.94%0.33%1.50%6.15%10.89%0.22%28.99%9.00%11.81%0.661
8928.46%23.58%0.33%1.58%6.36%10.44%0.18%29.07%9.02%11.90%0.658
9027.93%24.26%0.33%1.65%6.58%9.99%0.15%29.11%9.04%11.99%0.655
9127.38%24.96%0.34%1.73%6.79%9.55%0.12%29.12%9.06%12.08%0.651
9226.73%25.73%0.34%1.82%6.99%9.12%0.10%29.18%9.08%12.18%0.648
9326.02%26.49%0.34%1.91%7.21%8.70%0.08%29.27%9.10%12.27%0.645
9425.31%27.18%0.35%2.01%7.42%8.30%0.06%29.37%9.11%12.36%0.641
9524.59%27.81%0.38%2.11%7.64%7.93%0.04%29.50%9.13%12.44%0.638
9623.84%28.38%0.40%2.22%7.86%7.59%0.02%29.69%9.14%12.52%0.635
9722.75%29.00%0.42%2.29%8.32%7.24%0.02%29.97%9.14%12.60%0.631
9821.50%29.69%0.44%2.37%9.05%6.84%0.01%30.10%9.15%12.71%0.626
9920.04%30.21%0.47%2.42%10.06%6.41%0.00%30.41%9.15%12.82%0.621
10018.00%31.50%1.00%2.50%11.00%6.00%0.00%30.00%9.14%13.00%0.611
*Annualized 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.