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 2022)

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 »
Max Sharpe Ratio Portfolio
Ticker Name Allocation
SPY SPDR S&P 500 ETF Trust 24.37%
SLY SPDR S&P 600 Small Cap ETF 12.93%
EFA iShares MSCI EAFE ETF 0.04%
EEM iShares MSCI Emerging Markets ETF 0.35%
VNQ Vanguard Real Estate ETF 4.45%
TLT iShares 20+ Year Treasury Bond ETF 30.31%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 10.15%
GLD SPDR Gold Shares 17.39%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio6.81%12.03%0.48
Max Sharpe Ratio Portfolio7.24%9.10%0.68

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)9.47%15.40%0.5460.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)10.35%20.16%0.4610.00%100.00%
3iShares MSCI EAFE ETF (EFA)4.11%17.53%0.1740.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)5.30%21.67%0.1960.00%100.00%
5Vanguard Real Estate ETF (VNQ)8.65%22.78%0.3330.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)4.59%13.64%0.2590.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)3.94%7.86%0.3670.00%100.00%
8SPDR Gold Shares (GLD)8.05%17.26%0.4050.00%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 TrustSPY1.000.900.890.760.74-0.200.410.08
SPDR S&P 600 Small Cap ETFSLY0.901.000.820.740.74-0.290.340.03
iShares MSCI EAFE ETFEFA0.890.821.000.870.71-0.180.450.16
iShares MSCI Emerging Markets ETFEEM0.760.740.871.000.61-0.190.400.29
Vanguard Real Estate ETFVNQ0.740.740.710.611.000.040.480.12
iShares 20+ Year Treasury Bond ETFTLT-0.20-0.29-0.18-0.190.041.000.540.22
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.410.340.450.400.480.541.000.26
SPDR Gold SharesGLD0.080.030.160.290.120.220.261.00
Based on monthly returns from Jan 2006 to Sep 2022
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
18.79%1.49%0.03%0.00%0.00%9.77%71.32%8.60%4.94%7.63%0.508
29.44%1.55%0.03%0.00%0.00%10.21%70.02%8.76%4.99%7.63%0.515
310.06%1.62%0.02%0.00%0.00%10.67%68.73%8.90%5.04%7.64%0.521
410.65%1.71%0.02%0.00%0.00%11.13%67.44%9.05%5.09%7.64%0.527
511.20%1.82%0.01%0.00%0.01%11.59%66.18%9.19%5.13%7.64%0.533
611.74%1.93%0.01%0.00%0.02%12.06%64.90%9.34%5.18%7.65%0.538
712.25%2.07%0.01%0.00%0.02%12.53%63.62%9.49%5.23%7.66%0.544
812.73%2.24%0.00%0.00%0.03%13.01%62.34%9.64%5.27%7.67%0.549
913.20%2.43%0.00%0.00%0.04%13.49%61.05%9.79%5.32%7.68%0.555
1013.65%2.62%0.00%0.00%0.06%13.98%59.75%9.94%5.37%7.69%0.560
1114.05%2.82%0.00%0.01%0.08%14.48%58.47%10.09%5.41%7.70%0.565
1214.43%3.04%0.00%0.01%0.11%14.97%57.19%10.24%5.46%7.71%0.570
1314.80%3.27%0.00%0.01%0.14%15.47%55.92%10.39%5.50%7.73%0.575
1415.15%3.51%0.00%0.01%0.17%15.96%54.65%10.54%5.55%7.74%0.580
1515.51%3.74%0.00%0.02%0.20%16.46%53.37%10.70%5.60%7.76%0.585
1615.87%3.98%0.00%0.03%0.23%16.97%52.08%10.85%5.64%7.78%0.589
1716.22%4.22%0.00%0.03%0.26%17.47%50.79%11.00%5.69%7.79%0.594
1816.58%4.45%0.00%0.04%0.29%17.98%49.49%11.16%5.73%7.81%0.598
1916.95%4.69%0.01%0.05%0.32%18.49%48.18%11.31%5.78%7.83%0.602
2017.31%4.93%0.01%0.06%0.36%19.00%46.87%11.47%5.83%7.86%0.607
2117.66%5.17%0.01%0.07%0.40%19.51%45.55%11.64%5.87%7.88%0.611
2218.02%5.40%0.01%0.08%0.44%20.01%44.24%11.80%5.92%7.90%0.615
2318.36%5.63%0.01%0.09%0.49%20.51%42.94%11.97%5.97%7.93%0.619
2418.70%5.87%0.01%0.10%0.54%21.02%41.63%12.13%6.01%7.95%0.623
2519.03%6.11%0.01%0.11%0.60%21.52%40.33%12.30%6.06%7.98%0.627
2619.36%6.35%0.01%0.12%0.65%22.02%39.02%12.46%6.11%8.01%0.630
2719.69%6.59%0.01%0.12%0.71%22.53%37.71%12.63%6.15%8.04%0.634
2820.01%6.83%0.02%0.13%0.77%23.03%36.41%12.81%6.20%8.07%0.637
2920.34%7.07%0.02%0.14%0.83%23.53%35.10%12.98%6.25%8.10%0.641
3020.66%7.31%0.02%0.15%0.89%24.02%33.79%13.15%6.29%8.13%0.644
3120.97%7.55%0.02%0.16%0.96%24.53%32.49%13.31%6.34%8.16%0.647
3221.29%7.78%0.02%0.17%1.04%25.01%31.20%13.49%6.39%8.19%0.650
3321.60%8.02%0.02%0.18%1.11%25.50%29.90%13.66%6.43%8.23%0.653
3421.90%8.25%0.02%0.19%1.19%25.96%28.64%13.84%6.48%8.26%0.655
3522.19%8.48%0.02%0.20%1.28%26.41%27.38%14.02%6.52%8.30%0.658
3622.47%8.72%0.02%0.21%1.38%26.83%26.16%14.20%6.57%8.34%0.661
3722.74%8.95%0.03%0.22%1.48%27.23%24.97%14.38%6.61%8.38%0.663
3822.99%9.20%0.03%0.23%1.59%27.62%23.79%14.56%6.66%8.41%0.665
3923.21%9.43%0.03%0.24%1.71%27.98%22.66%14.74%6.70%8.45%0.667
4023.40%9.68%0.03%0.25%1.84%28.29%21.60%14.92%6.74%8.49%0.669
4123.56%9.93%0.03%0.26%1.99%28.58%20.55%15.10%6.78%8.53%0.671
4223.70%10.18%0.03%0.26%2.16%28.86%19.52%15.29%6.83%8.58%0.672
4323.84%10.42%0.03%0.27%2.33%29.13%18.50%15.48%6.87%8.62%0.673
4423.96%10.66%0.03%0.28%2.50%29.38%17.51%15.67%6.91%8.66%0.675
4524.07%10.91%0.03%0.29%2.68%29.62%16.53%15.86%6.95%8.71%0.676
4624.13%11.19%0.04%0.30%2.87%29.85%15.58%16.04%6.99%8.75%0.677
4724.18%11.47%0.04%0.31%3.06%30.03%14.69%16.23%7.02%8.80%0.678
4824.21%11.74%0.04%0.31%3.27%30.16%13.85%16.42%7.06%8.85%0.678
4924.24%12.00%0.04%0.32%3.48%30.24%13.06%16.61%7.10%8.89%0.679
5024.27%12.26%0.04%0.33%3.71%30.29%12.30%16.80%7.13%8.94%0.679
5124.29%12.50%0.04%0.34%3.95%30.33%11.56%16.99%7.17%8.99%0.679
5224.32%12.72%0.04%0.35%4.20%30.33%10.85%17.19%7.21%9.04%0.680
5324.37%12.93%0.04%0.35%4.45%30.31%10.15%17.39%7.24%9.10%0.680
5424.39%13.14%0.04%0.36%4.71%30.26%9.50%17.60%7.28%9.15%0.680
5524.41%13.35%0.05%0.37%4.98%30.19%8.85%17.81%7.31%9.20%0.679
5624.42%13.56%0.05%0.38%5.24%30.09%8.24%18.02%7.35%9.26%0.679
5724.45%13.76%0.05%0.39%5.50%29.95%7.67%18.24%7.38%9.31%0.679
5824.49%13.95%0.05%0.40%5.77%29.77%7.12%18.46%7.42%9.37%0.679
5924.52%14.14%0.05%0.40%6.04%29.57%6.59%18.69%7.45%9.43%0.678
6024.56%14.34%0.05%0.41%6.30%29.32%6.09%18.93%7.49%9.48%0.678
6124.58%14.55%0.05%0.41%6.57%29.05%5.63%19.17%7.52%9.54%0.677
6224.60%14.74%0.05%0.41%6.85%28.72%5.20%19.42%7.56%9.61%0.676
6324.62%14.93%0.05%0.42%7.13%28.35%4.81%19.69%7.59%9.67%0.675
6424.64%15.12%0.06%0.42%7.41%27.97%4.42%19.96%7.63%9.74%0.675
6524.67%15.31%0.06%0.43%7.69%27.57%4.06%20.22%7.66%9.80%0.673
6624.68%15.49%0.06%0.43%7.97%27.15%3.73%20.48%7.70%9.87%0.672
6724.70%15.67%0.06%0.44%8.26%26.71%3.42%20.74%7.73%9.94%0.671
6824.72%15.87%0.06%0.44%8.56%26.23%3.14%20.99%7.77%10.01%0.670
6924.70%16.08%0.06%0.45%8.87%25.74%2.88%21.22%7.80%10.09%0.668
7024.67%16.31%0.06%0.47%9.17%25.23%2.64%21.46%7.83%10.16%0.666
7124.63%16.56%0.06%0.48%9.48%24.70%2.40%21.69%7.87%10.24%0.665
7224.59%16.81%0.07%0.49%9.78%24.16%2.18%21.91%7.90%10.32%0.663
7324.55%17.08%0.07%0.51%10.09%23.59%1.98%22.14%7.94%10.41%0.661
7424.50%17.36%0.07%0.53%10.40%22.98%1.79%22.37%7.97%10.50%0.658
7524.46%17.61%0.08%0.56%10.72%22.36%1.62%22.59%8.01%10.59%0.656
7624.41%17.88%0.08%0.58%11.05%21.74%1.46%22.80%8.04%10.68%0.654
7724.35%18.16%0.08%0.61%11.38%21.09%1.32%23.01%8.08%10.78%0.651
7824.26%18.47%0.08%0.64%11.71%20.44%1.18%23.20%8.11%10.88%0.648
7924.16%18.80%0.08%0.67%12.06%19.80%1.06%23.36%8.15%10.98%0.645
8024.04%19.13%0.09%0.70%12.42%19.16%0.94%23.51%8.18%11.08%0.642
8123.95%19.44%0.10%0.75%12.78%18.50%0.83%23.65%8.21%11.19%0.639
8223.83%19.75%0.12%0.80%13.16%17.88%0.72%23.74%8.25%11.30%0.636
8323.65%20.10%0.13%0.85%13.55%17.27%0.63%23.83%8.28%11.40%0.633
8423.46%20.48%0.13%0.89%13.95%16.66%0.54%23.89%8.31%11.52%0.629
8523.23%20.88%0.14%0.93%14.35%16.06%0.47%23.93%8.34%11.63%0.626
8623.01%21.31%0.13%0.98%14.76%15.46%0.41%23.94%8.37%11.75%0.622
8722.80%21.72%0.12%1.03%15.22%14.82%0.35%23.94%8.40%11.87%0.619
8822.50%22.23%0.12%1.09%15.67%14.19%0.30%23.90%8.44%12.00%0.615
8922.16%22.76%0.11%1.16%16.15%13.57%0.24%23.84%8.47%12.14%0.610
9021.77%23.34%0.10%1.22%16.65%12.96%0.20%23.76%8.50%12.27%0.606
9121.25%24.03%0.09%1.27%17.15%12.37%0.15%23.68%8.53%12.42%0.602
9220.74%24.70%0.08%1.33%17.65%11.83%0.12%23.56%8.56%12.55%0.598
9320.19%25.37%0.07%1.38%18.18%11.33%0.09%23.38%8.59%12.69%0.593
9419.41%26.15%0.06%1.45%18.80%10.87%0.06%23.20%8.62%12.84%0.589
9518.57%26.94%0.05%1.52%19.47%10.48%0.05%22.93%8.64%12.99%0.584
9617.62%27.71%0.04%1.59%20.19%10.12%0.04%22.71%8.66%13.13%0.579
9716.78%28.51%0.03%1.65%20.87%9.78%0.02%22.35%8.68%13.28%0.574
9815.79%29.41%0.02%1.76%21.67%9.49%0.02%21.84%8.70%13.45%0.568
9914.64%30.14%0.01%1.90%22.63%9.32%0.01%21.36%8.71%13.61%0.562
10013.50%30.50%0.00%2.00%23.50%9.50%0.00%21.00%8.70%13.69%0.558
*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.
Notes on results:
  • 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 Sep 2022
  • 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