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 2008 - Dec 2018)

Portfolio Allocations

Tangency Portfolio
Ticker Name Allocation
QQQ Invesco QQQ Trust 15.07%
BND Vanguard Total Bond Market ETF 84.85%
TLT iShares 20+ Year Treasury Bond ETF 0.07%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio4.93%4.04%1.10

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1iShares Gold Trust (IAU)3.70%5.42%18.27%0.2710.00%100.00%
2iShares Core S&P Small-Cap ETF (IJR)8.51%10.54%19.23%0.5240.00%100.00%
3Invesco QQQ Trust (QQQ)11.61%13.42%17.98%0.7200.00%25.00%
4Vanguard Information Technology ETF (VGT)10.84%12.77%18.60%0.6610.00%100.00%
5Vanguard High Dividend Yield ETF (VYM)7.23%8.37%14.50%0.5450.00%100.00%
6iShares Core S&P 500 ETF (IVV)7.22%8.45%15.04%0.5300.00%100.00%
7Vanguard Total Bond Market ETF (BND)3.41%3.48%3.62%0.8310.00%100.00%
8iShares 20+ Year Treasury Bond ETF (TLT)5.74%6.76%14.01%0.4490.00%40.00%
9iShares MSCI Emerging Markets ETF (EEM)-0.25%2.39%22.79%0.0840.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (0.47% annualized).

Asset Correlations

Asset Correlations
NameTickerIAUIJRQQQVGTVYMIVVBNDTLTEEM
iShares Gold TrustIAU1.00-0.04-0.03-0.04-0.020.010.450.240.25
iShares Core S&P Small-Cap ETFIJR-0.041.000.800.810.860.90-0.05-0.330.71
Invesco QQQ TrustQQQ-0.030.801.000.980.800.92-0.03-0.320.76
Vanguard Information Technology ETFVGT-0.040.810.981.000.790.91-0.05-0.340.75
Vanguard High Dividend Yield ETFVYM-0.020.860.800.791.000.950.09-0.190.75
iShares Core S&P 500 ETFIVV0.010.900.920.910.951.000.02-0.300.81
Vanguard Total Bond Market ETFBND0.45-0.05-0.03-0.050.090.021.000.820.17
iShares 20+ Year Treasury Bond ETFTLT0.24-0.33-0.32-0.34-0.19-0.300.821.00-0.21
iShares MSCI Emerging Markets ETFEEM0.250.710.760.750.750.810.17-0.211.00
Based on provided custom correlation matrix
Efficient Frontier Points
#IAUIJRQQQVGTVYMIVVBNDTLTEEMExpected Return*Standard Deviation*Sharpe Ratio*
10.00%1.97%0.00%2.80%0.00%0.00%95.23%0.00%0.00%3.87%3.51%0.967
20.00%1.76%0.00%3.94%0.00%0.00%94.29%0.00%0.00%3.95%3.52%0.990
30.00%1.55%1.73%3.24%0.00%0.00%93.48%0.00%0.00%4.04%3.53%1.011
40.00%1.33%4.13%1.84%0.00%0.00%92.70%0.00%0.00%4.13%3.55%1.030
50.00%1.11%6.52%0.43%0.00%0.00%91.93%0.00%0.00%4.22%3.58%1.047
60.00%0.81%8.06%0.00%0.00%0.00%91.12%0.00%0.00%4.31%3.62%1.061
70.00%0.48%9.23%0.00%0.00%0.00%90.30%0.00%0.00%4.40%3.66%1.074
80.00%0.14%10.39%0.00%0.00%0.00%89.47%0.00%0.00%4.48%3.70%1.083
90.00%0.00%11.41%0.00%0.00%0.00%88.59%0.00%0.00%4.57%3.76%1.091
100.00%0.00%12.33%0.00%0.00%0.00%87.67%0.00%0.00%4.66%3.82%1.097
110.00%0.00%13.26%0.00%0.00%0.00%86.74%0.00%0.00%4.75%3.89%1.100
120.00%0.00%14.18%0.00%0.00%0.00%85.82%0.00%0.00%4.84%3.96%1.102
130.00%0.00%15.07%0.00%0.00%0.00%84.85%0.07%0.00%4.93%4.04%1.102
140.00%0.00%15.70%0.00%0.00%0.00%83.36%0.94%0.00%5.02%4.13%1.102
150.00%0.00%16.33%0.00%0.00%0.00%81.87%1.80%0.00%5.11%4.21%1.101
160.00%0.00%16.96%0.00%0.00%0.00%80.38%2.66%0.00%5.20%4.30%1.100
170.00%0.00%17.59%0.00%0.00%0.00%78.88%3.52%0.00%5.28%4.38%1.098
180.00%0.00%18.22%0.00%0.00%0.00%77.39%4.39%0.00%5.37%4.47%1.097
190.00%0.00%18.85%0.00%0.00%0.00%75.90%5.25%0.00%5.46%4.56%1.096
200.00%0.00%19.48%0.00%0.00%0.00%74.41%6.11%0.00%5.55%4.65%1.094
210.00%0.00%20.11%0.00%0.00%0.00%72.92%6.98%0.00%5.64%4.73%1.092
220.00%0.00%20.74%0.00%0.00%0.00%71.42%7.84%0.00%5.73%4.82%1.091
230.00%0.00%21.37%0.00%0.00%0.00%69.93%8.70%0.00%5.82%4.91%1.089
240.00%0.00%22.00%0.00%0.00%0.00%68.44%9.56%0.00%5.91%5.01%1.087
250.00%0.00%22.63%0.00%0.00%0.00%66.95%10.43%0.00%6.00%5.10%1.085
260.00%0.00%23.25%0.00%0.00%0.00%65.46%11.29%0.00%6.09%5.19%1.083
270.10%0.00%23.87%0.00%0.00%0.00%63.90%12.13%0.00%6.18%5.28%1.081
280.23%0.00%24.48%0.00%0.00%0.00%62.33%12.96%0.00%6.27%5.37%1.079
290.43%0.00%25.00%0.00%0.00%0.00%60.53%14.04%0.00%6.36%5.47%1.077
300.61%0.20%25.00%0.41%0.00%0.00%58.68%15.10%0.00%6.45%5.56%1.075
310.76%0.27%25.00%0.98%0.00%0.00%56.98%16.01%0.00%6.54%5.66%1.072
320.90%0.33%25.00%1.55%0.00%0.00%55.28%16.93%0.00%6.63%5.76%1.070
331.05%0.40%25.00%2.12%0.00%0.00%53.59%17.85%0.00%6.72%5.86%1.067
341.19%0.47%25.00%2.69%0.00%0.00%51.89%18.76%0.00%6.81%5.95%1.065
351.34%0.53%25.00%3.26%0.00%0.00%50.19%19.68%0.00%6.90%6.05%1.063
361.48%0.60%25.00%3.82%0.00%0.00%48.49%20.60%0.00%6.99%6.15%1.060
371.63%0.67%25.00%4.39%0.00%0.00%46.79%21.52%0.00%7.08%6.25%1.058
381.77%0.74%25.00%4.96%0.00%0.00%45.10%22.43%0.00%7.17%6.35%1.055
391.92%0.80%25.00%5.53%0.00%0.00%43.40%23.35%0.00%7.26%6.45%1.053
402.06%0.87%25.00%6.10%0.00%0.00%41.70%24.27%0.00%7.36%6.55%1.051
412.21%0.94%25.00%6.67%0.00%0.00%40.00%25.18%0.00%7.45%6.65%1.049
422.35%1.00%25.00%7.24%0.00%0.00%38.30%26.10%0.00%7.54%6.75%1.047
432.50%1.07%25.00%7.81%0.00%0.00%36.61%27.02%0.00%7.63%6.85%1.044
442.64%1.14%25.00%8.38%0.00%0.00%34.91%27.94%0.00%7.72%6.95%1.042
452.79%1.20%25.00%8.95%0.00%0.00%33.21%28.85%0.00%7.81%7.06%1.040
462.93%1.27%25.00%9.52%0.00%0.00%31.51%29.77%0.00%7.90%7.16%1.038
473.08%1.34%25.00%10.09%0.00%0.00%29.81%30.69%0.00%7.99%7.26%1.036
483.22%1.41%25.00%10.65%0.00%0.00%28.11%31.60%0.00%8.08%7.36%1.034
493.37%1.47%25.00%11.22%0.00%0.00%26.42%32.52%0.00%8.18%7.46%1.032
503.51%1.54%25.00%11.79%0.00%0.00%24.72%33.44%0.00%8.27%7.56%1.031
513.66%1.61%25.00%12.36%0.00%0.00%23.02%34.35%0.00%8.36%7.67%1.029
523.80%1.67%25.00%12.93%0.00%0.00%21.32%35.27%0.00%8.45%7.77%1.027
533.95%1.74%25.00%13.50%0.00%0.00%19.62%36.19%0.00%8.54%7.87%1.025
544.09%1.81%25.00%14.07%0.00%0.00%17.93%37.11%0.00%8.63%7.98%1.023
554.24%1.87%25.00%14.64%0.00%0.00%16.23%38.02%0.00%8.73%8.08%1.022
564.38%1.94%25.00%15.21%0.00%0.00%14.53%38.94%0.00%8.82%8.18%1.020
574.52%2.01%25.00%15.78%0.00%0.00%12.83%39.86%0.00%8.91%8.29%1.019
584.82%1.87%25.00%16.75%0.00%0.00%11.56%40.00%0.00%9.00%8.39%1.017
595.15%1.70%25.00%17.80%0.00%0.00%10.36%40.00%0.00%9.09%8.50%1.015
605.47%1.52%25.00%18.84%0.00%0.00%9.16%40.00%0.00%9.19%8.61%1.013
615.80%1.35%25.00%19.89%0.00%0.00%7.96%40.00%0.00%9.28%8.72%1.010
626.12%1.17%25.00%20.94%0.00%0.00%6.76%40.00%0.00%9.37%8.83%1.008
636.45%1.00%25.00%21.99%0.00%0.00%5.57%40.00%0.00%9.46%8.95%1.005
646.77%0.82%25.00%23.03%0.00%0.00%4.37%40.00%0.00%9.56%9.06%1.002
657.10%0.65%25.00%24.08%0.00%0.00%3.17%40.00%0.00%9.65%9.18%0.999
667.43%0.48%25.00%25.13%0.00%0.00%1.97%40.00%0.00%9.74%9.30%0.996
677.75%0.30%25.00%26.17%0.00%0.00%0.77%40.00%0.00%9.83%9.43%0.993
687.57%0.00%25.00%27.43%0.00%0.00%0.00%40.00%0.00%9.93%9.55%0.990
696.32%0.00%25.00%28.68%0.00%0.00%0.00%40.00%0.00%10.02%9.69%0.986
705.06%0.00%25.00%29.94%0.00%0.00%0.00%40.00%0.00%10.11%9.83%0.981
713.81%0.00%25.00%31.19%0.00%0.00%0.00%40.00%0.00%10.20%9.98%0.975
722.56%0.00%25.00%32.44%0.00%0.00%0.00%40.00%0.00%10.30%10.14%0.969
731.30%0.00%25.00%33.70%0.00%0.00%0.00%40.00%0.00%10.39%10.31%0.962
740.05%0.00%25.00%34.95%0.00%0.00%0.00%40.00%0.00%10.48%10.49%0.955
750.00%0.00%25.00%36.48%0.00%0.00%0.00%38.52%0.00%10.58%10.70%0.945
760.00%0.00%25.00%38.02%0.00%0.00%0.00%36.98%0.00%10.67%10.92%0.934
770.00%0.00%25.00%39.56%0.00%0.00%0.00%35.44%0.00%10.76%11.15%0.923
780.00%0.00%25.00%41.10%0.00%0.00%0.00%33.90%0.00%10.86%11.40%0.911
790.00%0.00%25.00%42.64%0.00%0.00%0.00%32.36%0.00%10.95%11.65%0.899
800.00%0.00%25.00%44.18%0.00%0.00%0.00%30.82%0.00%11.04%11.92%0.887
810.00%0.00%25.00%45.72%0.00%0.00%0.00%29.28%0.00%11.14%12.19%0.875
820.00%0.00%25.00%47.27%0.00%0.00%0.00%27.73%0.00%11.23%12.47%0.863
830.00%0.00%25.00%48.81%0.00%0.00%0.00%26.19%0.00%11.33%12.75%0.851
840.00%0.00%25.00%50.35%0.00%0.00%0.00%24.65%0.00%11.42%13.05%0.839
850.00%0.00%25.00%51.89%0.00%0.00%0.00%23.11%0.00%11.51%13.35%0.828
860.00%0.00%25.00%53.43%0.00%0.00%0.00%21.57%0.00%11.61%13.65%0.816
870.00%0.00%25.00%54.97%0.00%0.00%0.00%20.03%0.00%11.70%13.96%0.804
880.00%0.00%25.00%56.51%0.00%0.00%0.00%18.49%0.00%11.80%14.28%0.793
890.00%0.00%25.00%58.05%0.00%0.00%0.00%16.95%0.00%11.89%14.60%0.782
900.00%0.00%25.00%59.59%0.00%0.00%0.00%15.41%0.00%11.99%14.93%0.771
910.00%0.00%25.00%61.13%0.00%0.00%0.00%13.87%0.00%12.08%15.26%0.761
920.00%0.00%25.00%62.67%0.00%0.00%0.00%12.33%0.00%12.17%15.59%0.751
930.00%0.00%25.00%64.21%0.00%0.00%0.00%10.79%0.00%12.27%15.93%0.741
940.00%0.00%25.00%65.76%0.00%0.00%0.00%9.24%0.00%12.36%16.27%0.731
950.00%0.00%25.00%67.30%0.00%0.00%0.00%7.70%0.00%12.46%16.61%0.722
960.00%0.00%25.00%68.84%0.00%0.00%0.00%6.16%0.00%12.55%16.96%0.712
970.00%0.00%25.00%70.38%0.00%0.00%0.00%4.62%0.00%12.65%17.31%0.703
980.00%0.00%25.00%71.92%0.00%0.00%0.00%3.08%0.00%12.74%17.67%0.695
990.00%0.00%25.00%73.46%0.00%0.00%0.00%1.54%0.00%12.84%18.02%0.686
1000.00%0.00%25.00%75.00%0.00%0.00%0.00%0.00%0.00%12.93%18.38%0.678
*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 (0.47% annualized).
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 2008 to Dec 2018
  • The efficient frontier is based on the monthly returns, volatilities, and correlations of the specified assets
  • 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