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 - Oct 2019)

Portfolio Allocations

Provided Portfolio
Ticker Name Allocation
VTSAX Vanguard Total Stock Mkt Idx Adm 50.00%
VBTLX Vanguard Total Bond Market Index Adm 30.00%
PFF iShares Preferred&Income Securities ETF 20.00%
Save portfolio »
Tangency Portfolio
Ticker Name Allocation
VTSAX Vanguard Total Stock Mkt Idx Adm 11.62%
VBTLX Vanguard Total Bond Market Index Adm 88.38%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio7.71%10.18%0.70
Tangency Portfolio4.80%3.44%1.23

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1Vanguard Total Stock Mkt Idx Adm (VTSAX)8.69%10.01%15.51%0.6090.00%100.00%
2Vanguard Total Bond Market Index Adm (VBTLX)4.07%4.13%3.36%1.0630.00%100.00%
3iShares Preferred&Income Securities ETF (PFF)5.83%7.50%17.49%0.3970.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (0.56% annualized).

Asset Correlations

Asset Correlations
NameTickerVTSAXVBTLXPFF
Vanguard Total Stock Mkt Idx AdmVTSAX1.00-0.020.53
Vanguard Total Bond Market Index AdmVBTLX-0.021.000.24
iShares Preferred&Income Securities ETFPFF0.530.241.00
Based on monthly returns from Jan 2008 to Oct 2019
Efficient Frontier Points
#VTSAXVBTLXPFFExpected Return*Standard Deviation*Sharpe Ratio*
14.89%95.11%0.00%4.41%3.27%1.179
25.85%94.15%0.00%4.47%3.27%1.194
36.81%93.19%0.00%4.52%3.28%1.207
47.78%92.22%0.00%4.58%3.30%1.218
58.74%91.26%0.00%4.63%3.33%1.225
69.70%90.30%0.00%4.69%3.36%1.230
710.66%89.34%0.00%4.74%3.40%1.233
811.62%88.38%0.00%4.80%3.44%1.233
912.58%87.42%0.00%4.85%3.49%1.231
1013.54%86.46%0.00%4.91%3.55%1.227
1114.50%85.50%0.00%4.96%3.61%1.221
1215.46%84.54%0.00%5.02%3.68%1.213
1316.42%83.58%0.00%5.07%3.75%1.205
1417.38%82.62%0.00%5.13%3.83%1.195
1518.34%81.66%0.00%5.19%3.91%1.184
1619.30%80.70%0.00%5.24%4.00%1.173
1720.26%79.74%0.00%5.30%4.09%1.160
1821.22%78.78%0.00%5.35%4.18%1.148
1922.19%77.81%0.00%5.41%4.28%1.135
2023.15%76.85%0.00%5.46%4.38%1.121
2124.11%75.89%0.00%5.52%4.48%1.108
2225.07%74.93%0.00%5.58%4.59%1.095
2326.03%73.97%0.00%5.63%4.69%1.081
2426.99%73.01%0.00%5.69%4.81%1.068
2527.95%72.05%0.00%5.74%4.92%1.054
2628.91%71.09%0.00%5.80%5.03%1.041
2729.87%70.13%0.00%5.85%5.15%1.028
2830.83%69.17%0.00%5.91%5.27%1.016
2931.79%68.21%0.00%5.97%5.39%1.003
3032.75%67.25%0.00%6.02%5.51%0.991
3133.71%66.29%0.00%6.08%5.64%0.979
3234.67%65.33%0.00%6.13%5.76%0.968
3335.63%64.37%0.00%6.19%5.89%0.956
3436.60%63.40%0.00%6.25%6.02%0.945
3537.56%62.44%0.00%6.30%6.15%0.935
3638.52%61.48%0.00%6.36%6.28%0.924
3739.48%60.52%0.00%6.41%6.41%0.914
3840.44%59.56%0.00%6.47%6.54%0.904
3941.40%58.60%0.00%6.53%6.67%0.895
4042.36%57.64%0.00%6.58%6.81%0.885
4143.32%56.68%0.00%6.64%6.94%0.876
4244.28%55.72%0.00%6.70%7.08%0.867
4345.24%54.76%0.00%6.75%7.21%0.859
4446.20%53.80%0.00%6.81%7.35%0.851
4547.16%52.84%0.00%6.87%7.49%0.842
4648.12%51.88%0.00%6.92%7.63%0.835
4749.08%50.92%0.00%6.98%7.77%0.827
4850.04%49.96%0.00%7.03%7.90%0.820
4951.01%48.99%0.00%7.09%8.04%0.812
5051.97%48.03%0.00%7.15%8.18%0.805
5152.93%47.07%0.00%7.20%8.33%0.799
5253.89%46.11%0.00%7.26%8.47%0.792
5354.85%45.15%0.00%7.32%8.61%0.785
5455.81%44.19%0.00%7.37%8.75%0.779
5556.77%43.23%0.00%7.43%8.89%0.773
5657.73%42.27%0.00%7.49%9.03%0.767
5758.69%41.31%0.00%7.54%9.18%0.761
5859.65%40.35%0.00%7.60%9.32%0.756
5960.61%39.39%0.00%7.66%9.46%0.750
6061.57%38.43%0.00%7.71%9.61%0.745
6162.53%37.47%0.00%7.77%9.75%0.740
6263.49%36.51%0.00%7.83%9.90%0.735
6364.46%35.54%0.00%7.88%10.04%0.730
6465.42%34.58%0.00%7.94%10.19%0.725
6566.38%33.62%0.00%8.00%10.33%0.720
6667.34%32.66%0.00%8.05%10.48%0.716
6768.30%31.70%0.00%8.11%10.62%0.711
6869.26%30.74%0.00%8.17%10.77%0.707
6970.22%29.78%0.00%8.23%10.91%0.703
7071.18%28.82%0.00%8.28%11.06%0.699
7172.14%27.86%0.00%8.34%11.21%0.695
7273.10%26.90%0.00%8.40%11.35%0.691
7374.06%25.94%0.00%8.45%11.50%0.687
7475.02%24.98%0.00%8.51%11.65%0.683
7575.98%24.02%0.00%8.57%11.79%0.679
7676.94%23.06%0.00%8.63%11.94%0.676
7777.90%22.10%0.00%8.68%12.09%0.672
7878.87%21.13%0.00%8.74%12.24%0.669
7979.83%20.17%0.00%8.80%12.38%0.666
8080.79%19.21%0.00%8.85%12.53%0.662
8181.75%18.25%0.00%8.91%12.68%0.659
8282.71%17.29%0.00%8.97%12.83%0.656
8383.67%16.33%0.00%9.03%12.98%0.653
8484.63%15.37%0.00%9.08%13.12%0.650
8585.59%14.41%0.00%9.14%13.27%0.647
8686.55%13.45%0.00%9.20%13.42%0.644
8787.51%12.49%0.00%9.26%13.57%0.641
8888.47%11.53%0.00%9.31%13.72%0.639
8989.43%10.57%0.00%9.37%13.87%0.636
9090.39%9.61%0.00%9.43%14.01%0.633
9191.35%8.65%0.00%9.49%14.16%0.631
9292.31%7.69%0.00%9.55%14.31%0.628
9393.28%6.72%0.00%9.60%14.46%0.626
9494.24%5.76%0.00%9.66%14.61%0.623
9595.20%4.80%0.00%9.72%14.76%0.621
9696.16%3.84%0.00%9.78%14.91%0.618
9797.12%2.88%0.00%9.83%15.06%0.616
9898.08%1.92%0.00%9.89%15.21%0.614
9999.04%0.96%0.00%9.95%15.36%0.612
100100.00%0.00%0.00%10.01%15.51%0.609
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (0.56% annualized).
Notes on results:
  • Past performance is not a guarantee of future returns
  • Historical asset statistics are based on monthly returns from Jan 2008 to Oct 2019
  • 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 1-month treasury bill returns as the risk free rate