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 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%
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Tangency Portfolio
Ticker Name Allocation
VTSAX Vanguard Total Stock Mkt Idx Adm 11.67%
VBTLX Vanguard Total Bond Market Index Adm 88.33%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Provided Portfolio7.92%10.12%0.72
Tangency Portfolio4.79%3.42%1.22

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1Vanguard Total Stock Mkt Idx Adm (VTSAX)9.15%10.47%15.43%0.6390.00%100.00%
2Vanguard Total Bond Market Index Adm (VBTLX)4.00%4.05%3.34%1.0310.00%100.00%
3iShares Preferred&Income Securities ETF (PFF)5.87%7.52%17.37%0.3980.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (0.61% annualized).

Asset Correlations

Asset Correlations
NameTickerVTSAXVBTLXPFF
Vanguard Total Stock Mkt Idx AdmVTSAX1.00-0.030.53
Vanguard Total Bond Market Index AdmVBTLX-0.031.000.24
iShares Preferred&Income Securities ETFPFF0.530.241.00
Based on monthly returns from Jan 2008 to Dec 2019
Efficient Frontier Points
#VTSAXVBTLXPFFExpected Return*Standard Deviation*Sharpe Ratio*
14.95%95.05%0.00%4.36%3.25%1.156
25.91%94.09%0.00%4.42%3.25%1.173
36.87%93.13%0.00%4.48%3.26%1.188
47.83%92.17%0.00%4.54%3.28%1.200
58.79%91.21%0.00%4.60%3.31%1.209
69.75%90.25%0.00%4.66%3.34%1.216
710.71%89.29%0.00%4.72%3.38%1.220
811.67%88.33%0.00%4.79%3.42%1.222
912.63%87.37%0.00%4.85%3.47%1.221
1013.59%86.41%0.00%4.91%3.53%1.219
1114.55%85.45%0.00%4.97%3.59%1.214
1215.51%84.49%0.00%5.03%3.66%1.209
1316.47%83.53%0.00%5.09%3.73%1.201
1417.43%82.57%0.00%5.15%3.81%1.193
1518.39%81.61%0.00%5.21%3.89%1.183
1619.35%80.65%0.00%5.27%3.97%1.173
1720.31%79.69%0.00%5.33%4.06%1.162
1821.27%78.73%0.00%5.39%4.16%1.151
1922.23%77.77%0.00%5.45%4.25%1.139
2023.19%76.81%0.00%5.51%4.35%1.127
2124.15%75.85%0.00%5.57%4.46%1.114
2225.11%74.89%0.00%5.63%4.56%1.102
2326.07%73.93%0.00%5.69%4.67%1.089
2427.03%72.97%0.00%5.75%4.78%1.077
2527.99%72.01%0.00%5.81%4.89%1.064
2628.95%71.05%0.00%5.88%5.01%1.052
2729.91%70.09%0.00%5.94%5.12%1.040
2830.87%69.13%0.00%6.00%5.24%1.028
2931.83%68.17%0.00%6.06%5.36%1.016
3032.79%67.21%0.00%6.12%5.49%1.005
3133.75%66.25%0.00%6.18%5.61%0.993
3234.71%65.29%0.00%6.24%5.73%0.982
3335.67%64.33%0.00%6.30%5.86%0.972
3436.63%63.37%0.00%6.36%5.99%0.961
3537.59%62.41%0.00%6.42%6.12%0.951
3638.55%61.45%0.00%6.49%6.25%0.941
3739.51%60.49%0.00%6.55%6.38%0.931
3840.47%59.53%0.00%6.61%6.51%0.922
3941.43%58.57%0.00%6.67%6.64%0.913
4042.39%57.61%0.00%6.73%6.77%0.904
4143.35%56.65%0.00%6.79%6.91%0.895
4244.31%55.69%0.00%6.85%7.04%0.887
4345.27%54.73%0.00%6.91%7.18%0.879
4446.23%53.77%0.00%6.98%7.32%0.871
4547.19%52.81%0.00%7.04%7.45%0.863
4648.15%51.85%0.00%7.10%7.59%0.855
4749.11%50.89%0.00%7.16%7.73%0.848
4850.07%49.93%0.00%7.22%7.87%0.841
4951.03%48.97%0.00%7.28%8.00%0.834
5051.99%48.01%0.00%7.35%8.14%0.827
5152.95%47.05%0.00%7.41%8.28%0.821
5253.91%46.09%0.00%7.47%8.42%0.814
5354.87%45.13%0.00%7.53%8.57%0.808
5455.83%44.17%0.00%7.59%8.71%0.802
5556.79%43.21%0.00%7.65%8.85%0.796
5657.75%42.25%0.00%7.72%8.99%0.791
5758.71%41.29%0.00%7.78%9.13%0.785
5859.67%40.33%0.00%7.84%9.28%0.780
5960.63%39.37%0.00%7.90%9.42%0.774
6061.60%38.40%0.00%7.96%9.56%0.769
6162.56%37.44%0.00%8.03%9.70%0.764
6263.52%36.48%0.00%8.09%9.85%0.759
6364.48%35.52%0.00%8.15%9.99%0.755
6465.44%34.56%0.00%8.21%10.14%0.750
6566.40%33.60%0.00%8.27%10.28%0.746
6667.36%32.64%0.00%8.34%10.43%0.741
6768.32%31.68%0.00%8.40%10.57%0.737
6869.28%30.72%0.00%8.46%10.72%0.733
6970.24%29.76%0.00%8.52%10.86%0.729
7071.20%28.80%0.00%8.58%11.01%0.725
7172.16%27.84%0.00%8.65%11.15%0.721
7273.12%26.88%0.00%8.71%11.30%0.717
7374.08%25.92%0.00%8.77%11.44%0.713
7475.04%24.96%0.00%8.83%11.59%0.710
7576.00%24.00%0.00%8.90%11.74%0.706
7676.96%23.04%0.00%8.96%11.88%0.703
7777.92%22.08%0.00%9.02%12.03%0.699
7878.88%21.12%0.00%9.08%12.18%0.696
7979.84%20.16%0.00%9.15%12.32%0.693
8080.80%19.20%0.00%9.21%12.47%0.690
8181.76%18.24%0.00%9.27%12.62%0.687
8282.72%17.28%0.00%9.33%12.77%0.684
8383.68%16.32%0.00%9.40%12.91%0.681
8484.64%15.36%0.00%9.46%13.06%0.678
8585.60%14.40%0.00%9.52%13.21%0.675
8686.56%13.44%0.00%9.58%13.36%0.672
8787.52%12.48%0.00%9.65%13.50%0.669
8888.48%11.52%0.00%9.71%13.65%0.667
8989.44%10.56%0.00%9.77%13.80%0.664
9090.40%9.60%0.00%9.84%13.95%0.662
9191.36%8.64%0.00%9.90%14.10%0.659
9292.32%7.68%0.00%9.96%14.24%0.657
9393.28%6.72%0.00%10.03%14.39%0.654
9494.24%5.76%0.00%10.09%14.54%0.652
9595.20%4.80%0.00%10.15%14.69%0.650
9696.16%3.84%0.00%10.21%14.84%0.647
9797.12%2.88%0.00%10.28%14.99%0.645
9898.08%1.92%0.00%10.34%15.14%0.643
9999.04%0.96%0.00%10.40%15.29%0.641
100100.00%0.00%0.00%10.47%15.43%0.639
*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 (0.61% 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 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 3-month treasury bill returns as the risk free rate