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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9
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10
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Total
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Asset Groups
Min. Weight
Max. Weight
A
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B
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C
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D
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E
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F
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Efficient Frontier Results (Jan 2006 - Dec 2022)

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 26.63%
SLY SPDR S&P 600 Small Cap ETF 13.30%
EFA iShares MSCI EAFE ETF 0.23%
EEM iShares MSCI Emerging Markets ETF 0.79%
VNQ Vanguard Real Estate ETF 4.30%
TLT iShares 20+ Year Treasury Bond ETF 26.09%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 9.82%
GLD SPDR Gold Shares 18.85%
Save portfolio »

Performance Summary

PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio7.17%12.13%0.50
Max Sharpe Ratio Portfolio7.64%9.45%0.69

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 Dec 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

Efficient Frontier Assets

#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)9.80%15.51%0.5600.00%100.00%
2SPDR S&P 600 Small Cap ETF (SLY)10.77%20.31%0.4760.00%100.00%
3iShares MSCI EAFE ETF (EFA)5.07%17.73%0.2230.00%100.00%
4iShares MSCI Emerging Markets ETF (EEM)5.87%21.84%0.2180.00%100.00%
5Vanguard Real Estate ETF (VNQ)8.80%22.70%0.3390.00%100.00%
6iShares 20+ Year Treasury Bond ETF (TLT)4.44%13.74%0.2430.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)4.14%7.97%0.3810.00%100.00%
8SPDR Gold Shares (GLD)8.50%17.25%0.4290.00%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 TrustSPY1.000.900.880.750.74-0.190.410.08
SPDR S&P 600 Small Cap ETFSLY0.901.000.810.720.74-0.290.340.03
iShares MSCI EAFE ETFEFA0.880.811.000.870.71-0.160.470.17
iShares MSCI Emerging Markets ETFEEM0.750.720.871.000.61-0.160.420.30
Vanguard Real Estate ETFVNQ0.740.740.710.611.000.040.490.12
iShares 20+ Year Treasury Bond ETFTLT-0.19-0.29-0.16-0.160.041.000.550.23
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.410.340.470.420.490.551.000.28
SPDR Gold SharesGLD0.080.030.170.300.120.230.281.00
Based on monthly returns from Jan 2006 to Dec 2022

Efficient Frontier Portfolios

#SPYSLYEFAEEMVNQTLTLQDGLDExpected Return *Standard Deviation *Sharpe Ratio *
18.91%1.52%0.02%0.00%0.00%8.63%72.33%8.59%5.15%7.75%0.522
29.47%1.61%0.01%0.00%0.00%8.95%71.21%8.74%5.19%7.75%0.528
39.99%1.74%0.01%0.00%0.00%9.29%70.07%8.90%5.24%7.75%0.533
410.48%1.87%0.01%0.00%0.01%9.66%68.91%9.06%5.28%7.76%0.539
510.96%2.03%0.00%0.01%0.01%10.04%67.74%9.22%5.33%7.76%0.544
611.43%2.19%0.00%0.01%0.02%10.43%66.55%9.37%5.37%7.77%0.550
711.91%2.36%0.00%0.01%0.03%10.81%65.33%9.54%5.42%7.78%0.555
812.36%2.55%0.00%0.02%0.04%11.21%64.11%9.71%5.47%7.78%0.561
912.80%2.75%0.00%0.02%0.06%11.63%62.86%9.88%5.52%7.79%0.566
1013.24%2.94%0.00%0.03%0.08%12.06%61.61%10.04%5.56%7.81%0.571
1113.67%3.15%0.00%0.04%0.10%12.49%60.35%10.20%5.61%7.82%0.577
1214.10%3.35%0.00%0.04%0.12%12.92%59.09%10.37%5.66%7.83%0.582
1314.50%3.58%0.00%0.05%0.15%13.36%57.83%10.53%5.70%7.85%0.587
1414.90%3.81%0.00%0.06%0.17%13.80%56.57%10.68%5.75%7.86%0.591
1515.28%4.06%0.00%0.07%0.20%14.26%55.28%10.85%5.80%7.88%0.596
1615.65%4.32%0.00%0.08%0.24%14.72%53.97%11.03%5.85%7.90%0.601
1716.01%4.56%0.01%0.09%0.28%15.18%52.66%11.20%5.90%7.92%0.605
1816.37%4.81%0.02%0.10%0.33%15.64%51.34%11.39%5.95%7.94%0.610
1916.74%5.05%0.03%0.12%0.38%16.12%50.00%11.57%5.99%7.96%0.614
2017.09%5.30%0.04%0.13%0.43%16.59%48.66%11.75%6.04%7.99%0.619
2117.45%5.55%0.04%0.15%0.49%17.06%47.33%11.94%6.09%8.01%0.623
2217.81%5.79%0.05%0.17%0.55%17.53%45.99%12.12%6.14%8.04%0.627
2318.16%6.03%0.06%0.19%0.61%17.99%44.66%12.31%6.19%8.07%0.631
2418.51%6.27%0.06%0.21%0.68%18.46%43.32%12.50%6.24%8.10%0.634
2518.86%6.51%0.07%0.23%0.75%18.92%41.98%12.68%6.29%8.13%0.638
2619.22%6.74%0.08%0.24%0.82%19.39%40.64%12.87%6.34%8.16%0.642
2719.59%6.97%0.09%0.26%0.89%19.85%39.30%13.06%6.39%8.19%0.645
2819.95%7.21%0.09%0.28%0.96%20.31%37.95%13.25%6.44%8.22%0.648
2920.30%7.45%0.10%0.30%1.04%20.77%36.62%13.44%6.48%8.26%0.652
3020.64%7.70%0.11%0.31%1.11%21.22%35.28%13.63%6.53%8.29%0.655
3120.97%7.94%0.11%0.33%1.19%21.67%33.96%13.82%6.58%8.33%0.658
3221.29%8.20%0.12%0.35%1.28%22.10%32.65%14.01%6.63%8.37%0.661
3321.62%8.44%0.12%0.38%1.36%22.53%31.35%14.20%6.68%8.41%0.663
3421.94%8.69%0.13%0.39%1.45%22.95%30.05%14.40%6.73%8.45%0.666
3522.25%8.94%0.14%0.41%1.55%23.35%28.77%14.60%6.78%8.49%0.669
3622.55%9.19%0.14%0.43%1.64%23.74%27.51%14.80%6.83%8.53%0.671
3722.85%9.45%0.15%0.45%1.74%24.12%26.24%15.00%6.88%8.57%0.673
3823.13%9.71%0.15%0.47%1.84%24.49%25.01%15.21%6.92%8.62%0.676
3923.41%9.96%0.16%0.49%1.95%24.83%23.79%15.41%6.97%8.66%0.678
4023.70%10.22%0.16%0.50%2.06%25.15%22.59%15.62%7.02%8.71%0.680
4123.97%10.47%0.17%0.52%2.17%25.45%21.42%15.83%7.07%8.75%0.681
4224.20%10.73%0.17%0.54%2.30%25.71%20.29%16.05%7.12%8.80%0.683
4324.43%10.99%0.18%0.56%2.44%25.93%19.21%16.27%7.16%8.85%0.685
4424.63%11.24%0.18%0.58%2.58%26.12%18.17%16.50%7.21%8.90%0.686
4524.84%11.48%0.19%0.60%2.74%26.30%17.15%16.71%7.25%8.95%0.687
4625.05%11.72%0.19%0.62%2.89%26.43%16.16%16.94%7.30%9.00%0.688
4725.26%11.96%0.20%0.64%3.04%26.56%15.19%17.16%7.34%9.06%0.689
4825.46%12.18%0.20%0.66%3.21%26.61%14.28%17.39%7.39%9.11%0.690
4925.66%12.39%0.21%0.68%3.39%26.62%13.43%17.62%7.43%9.17%0.690
5025.85%12.58%0.21%0.70%3.57%26.59%12.63%17.86%7.47%9.22%0.691
5126.05%12.77%0.22%0.72%3.75%26.51%11.88%18.10%7.52%9.28%0.691
5226.24%12.96%0.22%0.74%3.93%26.41%11.15%18.34%7.56%9.34%0.692
5326.44%13.13%0.23%0.77%4.11%26.26%10.47%18.59%7.60%9.39%0.692
5426.63%13.30%0.23%0.79%4.30%26.09%9.82%18.85%7.64%9.45%0.692
5526.81%13.47%0.24%0.81%4.48%25.89%9.19%19.11%7.68%9.51%0.692
5626.99%13.64%0.24%0.84%4.67%25.65%8.61%19.37%7.73%9.57%0.692
5727.13%13.82%0.25%0.86%4.87%25.37%8.07%19.63%7.77%9.64%0.691
5827.26%14.01%0.25%0.88%5.07%25.07%7.57%19.89%7.81%9.70%0.691
5927.38%14.20%0.25%0.90%5.27%24.75%7.09%20.16%7.85%9.77%0.690
6027.49%14.41%0.25%0.92%5.48%24.42%6.61%20.42%7.89%9.83%0.690
6127.61%14.59%0.25%0.94%5.69%24.06%6.17%20.69%7.93%9.90%0.689
6227.72%14.78%0.24%0.96%5.91%23.69%5.75%20.95%7.97%9.97%0.688
6327.74%15.02%0.24%0.99%6.13%23.31%5.35%21.21%8.00%10.04%0.687
6427.77%15.25%0.24%1.01%6.36%22.92%4.98%21.47%8.04%10.11%0.686
6527.81%15.47%0.24%1.04%6.60%22.48%4.63%21.72%8.08%10.19%0.685
6627.86%15.67%0.24%1.07%6.86%22.05%4.30%21.95%8.12%10.26%0.683
6727.89%15.88%0.24%1.10%7.12%21.61%3.98%22.17%8.15%10.34%0.682
6827.90%16.09%0.24%1.16%7.38%21.13%3.68%22.42%8.19%10.42%0.680
6927.91%16.28%0.24%1.21%7.65%20.65%3.40%22.66%8.23%10.50%0.678
7027.90%16.47%0.24%1.26%7.93%20.14%3.15%22.90%8.26%10.59%0.676
7127.88%16.68%0.24%1.32%8.21%19.62%2.91%23.14%8.30%10.67%0.674
7227.83%16.91%0.24%1.37%8.50%19.09%2.68%23.36%8.33%10.76%0.672
7327.79%17.15%0.25%1.45%8.80%18.55%2.45%23.57%8.37%10.85%0.670
7427.73%17.40%0.25%1.51%9.10%18.02%2.23%23.76%8.40%10.94%0.667
7527.66%17.65%0.25%1.58%9.42%17.49%2.02%23.94%8.44%11.04%0.665
7627.55%17.94%0.23%1.67%9.73%16.97%1.83%24.09%8.47%11.13%0.662
7727.41%18.24%0.21%1.76%10.05%16.46%1.66%24.22%8.50%11.23%0.659
7827.22%18.57%0.18%1.85%10.38%15.93%1.50%24.36%8.54%11.33%0.656
7927.04%18.93%0.16%1.95%10.72%15.39%1.36%24.45%8.57%11.43%0.653
8026.86%19.29%0.14%2.05%11.07%14.83%1.23%24.52%8.60%11.54%0.650
8126.66%19.66%0.12%2.15%11.44%14.28%1.12%24.56%8.64%11.65%0.647
8226.41%20.05%0.12%2.26%11.81%13.74%1.03%24.59%8.67%11.76%0.643
8326.13%20.44%0.12%2.36%12.19%13.21%0.94%24.61%8.69%11.86%0.640
8425.83%20.86%0.12%2.47%12.56%12.70%0.85%24.61%8.72%11.97%0.636
8525.51%21.28%0.12%2.57%12.96%12.20%0.77%24.58%8.75%12.09%0.633
8625.17%21.72%0.12%2.67%13.38%11.71%0.69%24.54%8.78%12.20%0.629
8724.79%22.17%0.12%2.77%13.82%11.22%0.61%24.50%8.81%12.32%0.625
8824.32%22.69%0.11%2.87%14.30%10.77%0.53%24.40%8.83%12.44%0.621
8923.70%23.30%0.11%2.97%14.82%10.35%0.46%24.29%8.86%12.56%0.617
9022.92%24.01%0.10%3.08%15.36%9.94%0.40%24.19%8.88%12.69%0.613
9122.01%24.83%0.09%3.19%15.92%9.55%0.34%24.08%8.91%12.82%0.609
9220.93%25.77%0.09%3.29%16.48%9.17%0.28%23.98%8.93%12.95%0.604
9319.68%26.87%0.09%3.38%17.06%8.82%0.22%23.88%8.95%13.09%0.600
9418.34%27.97%0.09%3.47%17.70%8.50%0.18%23.76%8.98%13.24%0.595
9516.95%29.13%0.07%3.55%18.36%8.20%0.14%23.59%9.00%13.38%0.590
9615.55%30.19%0.06%3.61%19.11%7.95%0.10%23.42%9.02%13.52%0.585
9714.19%31.12%0.04%3.66%19.96%7.74%0.07%23.22%9.03%13.66%0.581
9812.87%31.49%0.03%3.82%21.11%7.60%0.04%23.04%9.03%13.79%0.575
9911.37%31.90%0.01%3.97%22.31%7.54%0.02%22.88%9.02%13.91%0.570
1009.50%33.49%0.00%3.50%23.00%7.50%0.00%23.00%9.05%14.01%0.568
*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.