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 - Apr 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 27.54%
SLY SPDR S&P 600 Small Cap ETF 11.80%
EFA iShares MSCI EAFE ETF 0.09%
EEM iShares MSCI Emerging Markets ETF 0.19%
VNQ Vanguard Real Estate ETF 2.90%
TLT iShares 20+ Year Treasury Bond ETF 29.21%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 9.32%
GLD SPDR Gold Shares 18.95%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio8.15%11.76%0.58
Max Sharpe Ratio Portfolio8.61%8.71%0.83

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)10.97%15.04%0.6260.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)11.87%19.93%0.5130.00%100.00%
3iShares MSCI EAFE ETF (EFA)5.38%17.33%0.2430.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)6.72%21.69%0.2530.00%100.00%
5Vanguard Real Estate ETF (VNQ)10.74%22.54%0.4080.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)5.71%13.55%0.3330.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)4.61%7.58%0.4590.00%100.00%
8SPDR Gold Shares (GLD)9.45%17.37%0.4620.00%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 TrustSPY1.000.900.890.760.73-0.250.370.07
SPDR S&P 600 Small Cap ETFSLY0.901.000.810.740.74-0.340.300.03
iShares MSCI EAFE ETFEFA0.890.811.000.870.70-0.230.420.15
iShares MSCI Emerging Markets ETFEEM0.760.740.871.000.60-0.220.390.28
Vanguard Real Estate ETFVNQ0.730.740.700.601.00-0.000.460.11
iShares 20+ Year Treasury Bond ETFTLT-0.25-0.34-0.23-0.22-0.001.000.520.21
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.370.300.420.390.460.521.000.27
SPDR Gold SharesGLD0.070.030.150.280.110.210.271.00
Based on monthly returns from Jan 2006 to Apr 2022
Efficient Frontier Points
#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return*Standard Deviation*Sharpe Ratio*
110.24%1.56%0.04%0.00%0.00%10.10%71.07%6.99%5.80%7.32%0.630
210.82%1.66%0.03%0.00%0.00%10.51%69.73%7.24%5.86%7.32%0.638
311.39%1.76%0.02%0.00%0.00%10.95%68.40%7.49%5.92%7.32%0.645
411.92%1.88%0.02%0.00%0.00%11.38%67.08%7.72%5.98%7.32%0.653
512.44%2.02%0.01%0.00%0.00%11.83%65.76%7.95%6.04%7.33%0.660
612.96%2.16%0.01%0.00%0.00%12.28%64.42%8.17%6.10%7.33%0.667
713.46%2.31%0.00%0.00%0.00%12.74%63.09%8.40%6.15%7.34%0.674
813.94%2.46%0.00%0.00%0.01%13.19%61.77%8.63%6.21%7.34%0.681
914.41%2.63%0.00%0.00%0.02%13.64%60.45%8.86%6.27%7.35%0.687
1014.85%2.80%0.00%0.00%0.03%14.09%59.14%9.09%6.33%7.36%0.694
1115.28%2.98%0.00%0.00%0.05%14.54%57.83%9.31%6.38%7.38%0.700
1215.71%3.16%0.00%0.00%0.07%14.99%56.52%9.54%6.44%7.39%0.706
1316.14%3.35%0.00%0.00%0.09%15.46%55.20%9.77%6.50%7.40%0.712
1416.55%3.54%0.00%0.00%0.12%15.92%53.87%10.00%6.56%7.42%0.718
1516.96%3.74%0.00%0.00%0.14%16.39%52.53%10.23%6.61%7.43%0.724
1617.36%3.95%0.00%0.00%0.16%16.87%51.19%10.47%6.67%7.45%0.729
1717.76%4.16%0.00%0.00%0.18%17.34%49.85%10.70%6.73%7.47%0.735
1818.17%4.37%0.00%0.01%0.21%17.81%48.51%10.93%6.79%7.49%0.740
1918.56%4.58%0.00%0.01%0.24%18.28%47.16%11.17%6.85%7.51%0.746
2018.96%4.79%0.00%0.01%0.27%18.76%45.81%11.40%6.91%7.53%0.751
2119.36%5.00%0.00%0.01%0.30%19.24%44.45%11.64%6.96%7.55%0.756
2219.75%5.22%0.00%0.01%0.33%19.72%43.09%11.87%7.02%7.58%0.761
2320.13%5.44%0.00%0.01%0.37%20.21%41.73%12.11%7.08%7.60%0.766
2420.51%5.67%0.00%0.01%0.40%20.69%40.36%12.35%7.14%7.63%0.770
2520.89%5.89%0.00%0.01%0.44%21.18%38.99%12.60%7.20%7.66%0.775
2621.26%6.12%0.01%0.01%0.48%21.67%37.61%12.84%7.26%7.69%0.779
2721.63%6.34%0.01%0.02%0.52%22.15%36.25%13.09%7.32%7.72%0.783
2821.99%6.57%0.01%0.02%0.56%22.63%34.89%13.33%7.38%7.75%0.787
2922.35%6.80%0.02%0.02%0.61%23.10%33.53%13.57%7.44%7.78%0.791
3022.70%7.03%0.02%0.02%0.66%23.57%32.19%13.81%7.50%7.81%0.795
3123.05%7.26%0.02%0.03%0.71%24.04%30.84%14.06%7.56%7.85%0.798
3223.38%7.49%0.03%0.03%0.76%24.51%29.50%14.30%7.62%7.88%0.802
3323.72%7.72%0.03%0.04%0.82%24.96%28.18%14.54%7.67%7.92%0.805
3424.05%7.95%0.03%0.04%0.89%25.41%26.86%14.77%7.73%7.95%0.808
3524.38%8.17%0.04%0.05%0.95%25.85%25.55%15.01%7.79%7.99%0.811
3624.68%8.40%0.04%0.06%1.03%26.27%24.27%15.25%7.85%8.03%0.814
3724.97%8.63%0.04%0.06%1.11%26.67%23.03%15.48%7.90%8.07%0.816
3825.24%8.86%0.05%0.07%1.20%27.04%21.83%15.71%7.96%8.11%0.818
3925.50%9.09%0.05%0.08%1.30%27.40%20.64%15.94%8.01%8.15%0.820
4025.75%9.32%0.05%0.09%1.40%27.71%19.51%16.17%8.07%8.20%0.822
4125.96%9.55%0.06%0.10%1.52%28.01%18.40%16.40%8.12%8.24%0.824
4226.14%9.80%0.06%0.11%1.64%28.28%17.34%16.62%8.17%8.28%0.825
4326.33%10.04%0.06%0.12%1.77%28.53%16.30%16.85%8.22%8.33%0.827
4426.52%10.27%0.07%0.13%1.90%28.76%15.27%17.08%8.27%8.37%0.828
4526.71%10.51%0.07%0.14%2.03%28.94%14.29%17.32%8.32%8.42%0.829
4626.89%10.73%0.07%0.15%2.16%29.09%13.35%17.57%8.37%8.47%0.830
4727.05%10.95%0.08%0.15%2.30%29.20%12.44%17.83%8.42%8.51%0.831
4827.19%11.17%0.08%0.16%2.44%29.28%11.58%18.09%8.47%8.56%0.831
4927.32%11.38%0.08%0.17%2.59%29.31%10.77%18.37%8.52%8.61%0.831
5027.43%11.60%0.09%0.18%2.74%29.29%10.02%18.65%8.56%8.66%0.832
5127.54%11.80%0.09%0.19%2.90%29.21%9.32%18.95%8.61%8.71%0.832
5227.65%11.97%0.09%0.20%3.06%29.06%8.70%19.28%8.65%8.76%0.832
5327.74%12.15%0.09%0.21%3.22%28.86%8.12%19.61%8.69%8.81%0.831
5427.83%12.30%0.10%0.22%3.39%28.63%7.58%19.95%8.74%8.86%0.831
5527.90%12.46%0.10%0.22%3.57%28.34%7.09%20.31%8.78%8.92%0.830
5627.94%12.61%0.11%0.23%3.76%28.02%6.65%20.68%8.82%8.97%0.829
5727.98%12.76%0.12%0.24%3.95%27.68%6.22%21.05%8.86%9.03%0.828
5828.00%12.92%0.12%0.25%4.15%27.34%5.80%21.42%8.90%9.09%0.827
5928.02%13.08%0.13%0.26%4.35%26.99%5.40%21.79%8.94%9.14%0.825
6028.04%13.23%0.13%0.27%4.55%26.62%5.00%22.16%8.98%9.20%0.824
6128.05%13.37%0.14%0.27%4.76%26.23%4.63%22.54%9.02%9.26%0.822
6228.08%13.51%0.14%0.28%4.96%25.82%4.28%22.92%9.05%9.33%0.821
6328.12%13.64%0.15%0.29%5.17%25.39%3.94%23.30%9.09%9.39%0.819
6428.16%13.76%0.15%0.31%5.39%24.95%3.61%23.67%9.13%9.46%0.817
6528.19%13.88%0.16%0.33%5.61%24.48%3.31%24.03%9.17%9.52%0.815
6628.20%14.02%0.16%0.35%5.84%24.00%3.03%24.40%9.21%9.59%0.813
6728.20%14.15%0.17%0.37%6.07%23.49%2.76%24.78%9.25%9.66%0.810
6828.18%14.30%0.18%0.40%6.30%22.97%2.51%25.17%9.28%9.74%0.808
6928.15%14.44%0.18%0.42%6.54%22.45%2.26%25.56%9.32%9.81%0.805
7028.11%14.59%0.19%0.44%6.78%21.92%2.02%25.95%9.36%9.89%0.803
7128.05%14.75%0.19%0.46%7.02%21.40%1.81%26.32%9.39%9.96%0.800
7227.97%14.92%0.20%0.48%7.25%20.87%1.63%26.68%9.43%10.03%0.797
7327.87%15.08%0.20%0.51%7.51%20.34%1.46%27.02%9.46%10.11%0.794
7427.76%15.25%0.21%0.55%7.77%19.83%1.31%27.33%9.49%10.18%0.791
7527.66%15.41%0.21%0.59%8.03%19.31%1.18%27.60%9.52%10.26%0.788
7627.54%15.57%0.22%0.65%8.30%18.80%1.06%27.87%9.55%10.33%0.785
7727.39%15.74%0.22%0.70%8.58%18.30%0.93%28.14%9.58%10.41%0.782
7827.22%15.94%0.23%0.75%8.86%17.81%0.82%28.37%9.61%10.49%0.779
7926.99%16.14%0.23%0.80%9.15%17.34%0.72%28.62%9.63%10.56%0.776
8026.70%16.34%0.24%0.86%9.46%16.88%0.65%28.88%9.66%10.63%0.772
8126.42%16.55%0.24%0.91%9.77%16.41%0.57%29.13%9.68%10.71%0.769
8226.09%16.80%0.24%0.97%10.09%15.94%0.50%29.37%9.71%10.79%0.766
8325.70%17.10%0.25%1.03%10.40%15.48%0.44%29.60%9.73%10.86%0.762
8425.24%17.42%0.25%1.09%10.76%15.04%0.38%29.81%9.76%10.95%0.758
8524.77%17.76%0.25%1.15%11.14%14.57%0.33%30.03%9.78%11.03%0.755
8624.19%18.13%0.26%1.22%11.57%14.12%0.27%30.23%9.80%11.12%0.751
8723.50%18.58%0.27%1.29%12.04%13.67%0.23%30.43%9.83%11.21%0.746
8822.71%19.06%0.27%1.36%12.56%13.24%0.18%30.60%9.85%11.31%0.742
8921.87%19.53%0.28%1.44%13.10%12.84%0.15%30.79%9.87%11.40%0.737
9020.95%20.08%0.29%1.51%13.65%12.44%0.12%30.97%9.89%11.50%0.733
9120.02%20.64%0.29%1.59%14.18%12.03%0.10%31.15%9.91%11.60%0.728
9218.96%21.31%0.30%1.66%14.73%11.65%0.08%31.30%9.93%11.70%0.723
9317.83%22.00%0.31%1.74%15.27%11.31%0.06%31.49%9.95%11.80%0.719
9416.59%22.68%0.31%1.81%15.88%10.96%0.04%31.73%9.97%11.90%0.714
9515.28%23.34%0.32%1.87%16.55%10.64%0.03%31.97%9.98%12.00%0.709
9614.02%23.87%0.33%1.89%17.28%10.35%0.02%32.25%10.00%12.09%0.705
9712.81%24.15%0.33%1.85%18.10%10.08%0.01%32.67%10.01%12.18%0.701
9811.58%24.41%0.22%1.78%19.01%9.90%0.01%33.10%10.02%12.25%0.697
999.93%25.05%0.11%1.66%19.90%9.87%0.00%33.49%10.03%12.33%0.694
1007.00%25.50%0.00%1.50%22.00%10.00%0.00%34.00%10.03%12.45%0.687
*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 Apr 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