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.

1
%
%
%
2
%
%
%
3
%
%
%
4
%
%
%
5
%
%
%
6
%
%
%
7
%
%
%
8
%
%
%
9
%
%
%
10
%
%
%
Total
%

Asset Groups
Min. Weight
Max. Weight
A
%
%
B
%
%
C
%
%
D
%
%
E
%
%
F
%
%

Efficient Frontier Results (Jan 1987 - Dec 2018)

Portfolio Allocations

EF #1 Tangency Portfolio
Asset Class Allocation
US Stock Market 40.97%
Long Term Treasury 59.03%
Save portfolio »
EF #2 Tangency Portfolio
Asset Class Allocation
US Stock Market 15.26%
Total US Bond Market 84.74%
Save portfolio »

Efficient Frontier #1 Assets

Efficient Frontier #1 Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market9.76%11.02%14.99%0.5220.00%100.00%
2Long Term Treasury7.26%7.75%9.64%0.4730.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (3.19% annualized).

Efficient Frontier #1 Asset Correlations

Efficient Frontier #1 Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.00-0.12
Long Term Treasury-0.121.00
Based on provided custom correlation matrix

Efficient Frontier #2 Assets

Efficient Frontier #2 Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market9.76%11.02%14.99%0.5220.00%100.00%
2Total US Bond Market5.78%5.85%3.81%0.6980.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (3.19% annualized).

Efficient Frontier #2 Asset Correlations

Efficient Frontier #2 Asset Correlations
AssetUS Stock MarketTotal US Bond Market
US Stock Market1.000.07
Total US Bond Market0.071.00
Based on provided custom correlation matrix
Efficient Frontier #1 Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
131.25%68.75%8.76%7.66%0.727
231.95%68.05%8.79%7.66%0.730
332.64%67.36%8.81%7.67%0.733
433.33%66.67%8.83%7.67%0.735
534.03%65.97%8.85%7.68%0.737
634.72%65.28%8.88%7.69%0.739
735.42%64.58%8.90%7.70%0.741
836.11%63.89%8.92%7.72%0.743
936.81%63.19%8.94%7.73%0.744
1037.50%62.50%8.97%7.75%0.745
1138.20%61.80%8.99%7.77%0.746
1238.89%61.11%9.01%7.80%0.747
1339.58%60.42%9.04%7.82%0.747
1440.28%59.72%9.06%7.85%0.748
1540.97%59.03%9.08%7.88%0.748
1641.67%58.33%9.10%7.91%0.748
1742.36%57.64%9.13%7.94%0.747
1843.06%56.94%9.15%7.98%0.747
1943.75%56.25%9.17%8.01%0.746
2044.45%55.55%9.19%8.05%0.746
2145.14%54.86%9.22%8.09%0.745
2245.83%54.17%9.24%8.14%0.743
2346.53%53.47%9.26%8.18%0.742
2447.22%52.78%9.28%8.23%0.741
2547.92%52.08%9.31%8.27%0.739
2648.61%51.39%9.33%8.32%0.737
2749.31%50.69%9.35%8.38%0.736
2850.00%50.00%9.37%8.43%0.734
2950.69%49.31%9.40%8.48%0.731
3051.39%48.61%9.42%8.54%0.729
3152.08%47.92%9.44%8.60%0.727
3252.78%47.22%9.47%8.66%0.725
3353.47%46.53%9.49%8.72%0.722
3454.17%45.83%9.51%8.78%0.719
3554.86%45.14%9.53%8.85%0.717
3655.56%44.44%9.56%8.91%0.714
3756.25%43.75%9.58%8.98%0.711
3856.94%43.06%9.60%9.05%0.708
3957.64%42.36%9.62%9.12%0.705
4058.33%41.67%9.65%9.19%0.702
4159.03%40.97%9.67%9.26%0.699
4259.72%40.28%9.69%9.34%0.696
4360.42%39.58%9.71%9.41%0.693
4461.11%38.89%9.74%9.49%0.690
4561.81%38.19%9.76%9.56%0.687
4662.50%37.50%9.78%9.64%0.684
4763.19%36.81%9.81%9.72%0.680
4863.89%36.11%9.83%9.80%0.677
4964.58%35.42%9.85%9.88%0.674
5065.28%34.72%9.87%9.97%0.670
5165.97%34.03%9.90%10.05%0.667
5266.67%33.33%9.92%10.14%0.664
5367.36%32.64%9.94%10.22%0.661
5468.06%31.94%9.96%10.31%0.657
5568.75%31.25%9.99%10.40%0.654
5669.44%30.56%10.01%10.48%0.650
5770.14%29.86%10.03%10.57%0.647
5870.83%29.17%10.06%10.66%0.644
5971.53%28.47%10.08%10.75%0.641
6072.22%27.78%10.10%10.85%0.637
6172.92%27.08%10.12%10.94%0.634
6273.61%26.39%10.15%11.03%0.631
6374.31%25.69%10.17%11.12%0.627
6475.00%25.00%10.19%11.22%0.624
6575.69%24.31%10.22%11.31%0.621
6676.39%23.61%10.24%11.41%0.618
6777.08%22.92%10.26%11.51%0.614
6877.78%22.22%10.28%11.60%0.611
6978.47%21.53%10.31%11.70%0.608
7079.17%20.83%10.33%11.80%0.605
7179.86%20.14%10.35%11.90%0.602
7280.56%19.44%10.38%12.00%0.599
7381.25%18.75%10.40%12.10%0.596
7481.94%18.06%10.42%12.20%0.593
7582.64%17.36%10.44%12.30%0.590
7683.33%16.67%10.47%12.41%0.586
7784.03%15.97%10.49%12.51%0.584
7884.72%15.28%10.51%12.61%0.581
7985.42%14.58%10.54%12.71%0.578
8086.11%13.89%10.56%12.82%0.575
8186.81%13.19%10.58%12.92%0.572
8287.50%12.50%10.60%13.03%0.569
8388.19%11.81%10.63%13.13%0.566
8488.89%11.11%10.65%13.24%0.563
8589.58%10.42%10.67%13.35%0.561
8690.28%9.72%10.70%13.45%0.558
8790.97%9.03%10.72%13.56%0.555
8891.67%8.33%10.74%13.67%0.552
8992.36%7.64%10.76%13.77%0.550
9093.06%6.94%10.79%13.88%0.547
9193.75%6.25%10.81%13.99%0.545
9294.44%5.56%10.83%14.10%0.542
9395.14%4.86%10.86%14.21%0.539
9495.83%4.17%10.88%14.32%0.537
9596.53%3.47%10.90%14.43%0.534
9697.22%2.78%10.92%14.54%0.532
9797.92%2.08%10.95%14.65%0.529
9898.61%1.39%10.97%14.76%0.527
9999.31%0.69%10.99%14.87%0.525
100100.00%0.00%11.02%14.99%0.522
*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 (3.19% annualized).
Efficient Frontier #2 Points
#US Stock MarketTotal US Bond MarketExpected Return*Standard Deviation*Sharpe Ratio*
14.67%95.33%6.09%3.75%0.773
25.63%94.37%6.14%3.75%0.786
36.59%93.41%6.19%3.76%0.797
47.56%92.44%6.23%3.77%0.807
58.52%91.48%6.28%3.79%0.815
69.48%90.52%6.33%3.82%0.823
710.45%89.55%6.38%3.85%0.829
811.41%88.59%6.43%3.88%0.834
912.37%87.63%6.48%3.93%0.837
1013.33%86.67%6.53%3.97%0.840
1114.30%85.70%6.58%4.02%0.841
1215.26%84.74%6.63%4.08%0.842
1316.22%83.78%6.67%4.14%0.842
1417.19%82.81%6.72%4.20%0.840
1518.15%81.85%6.77%4.27%0.838
1619.11%80.89%6.82%4.34%0.836
1720.08%79.92%6.87%4.42%0.832
1821.04%78.96%6.92%4.50%0.829
1922.00%78.00%6.97%4.58%0.824
2022.96%77.04%7.02%4.67%0.820
2123.93%76.07%7.07%4.76%0.815
2224.89%75.11%7.12%4.85%0.810
2325.85%74.15%7.17%4.94%0.804
2426.82%73.18%7.21%5.04%0.798
2527.78%72.22%7.26%5.14%0.793
2628.74%71.26%7.31%5.24%0.787
2729.70%70.30%7.36%5.34%0.781
2830.67%69.33%7.41%5.45%0.775
2931.63%68.37%7.46%5.56%0.768
3032.59%67.41%7.51%5.67%0.762
3133.56%66.44%7.56%5.78%0.756
3234.52%65.48%7.61%5.89%0.750
3335.48%64.52%7.66%6.00%0.744
3436.45%63.55%7.71%6.12%0.738
3537.41%62.59%7.76%6.23%0.732
3638.37%61.63%7.81%6.35%0.727
3739.33%60.67%7.86%6.47%0.721
3840.30%59.70%7.91%6.59%0.715
3941.26%58.74%7.96%6.71%0.710
4042.22%57.78%8.00%6.83%0.704
4143.19%56.81%8.05%6.96%0.699
4244.15%55.85%8.10%7.08%0.694
4345.11%54.89%8.15%7.21%0.689
4446.07%53.93%8.20%7.33%0.684
4547.04%52.96%8.25%7.46%0.679
4648.00%52.00%8.30%7.59%0.674
4748.96%51.04%8.35%7.71%0.669
4849.93%50.07%8.40%7.84%0.665
4950.89%49.11%8.45%7.97%0.660
5051.85%48.15%8.50%8.10%0.656
5152.82%47.18%8.55%8.23%0.651
5253.78%46.22%8.60%8.36%0.647
5354.74%45.26%8.65%8.49%0.643
5455.70%44.30%8.70%8.62%0.639
5556.67%43.33%8.75%8.76%0.635
5657.63%42.37%8.80%8.89%0.631
5758.59%41.41%8.85%9.02%0.627
5859.56%40.44%8.90%9.16%0.624
5960.52%39.48%8.95%9.29%0.620
6061.48%38.52%9.00%9.42%0.616
6162.44%37.56%9.05%9.56%0.613
6263.41%36.59%9.10%9.69%0.610
6364.37%35.63%9.15%9.83%0.606
6465.33%34.67%9.20%9.96%0.603
6566.30%33.70%9.25%10.10%0.600
6667.26%32.74%9.30%10.24%0.597
6768.22%31.78%9.35%10.37%0.594
6869.19%30.81%9.40%10.51%0.591
6970.15%29.85%9.45%10.65%0.588
7071.11%28.89%9.50%10.78%0.585
7172.07%27.93%9.55%10.92%0.582
7273.04%26.96%9.60%11.06%0.580
7374.00%26.00%9.65%11.20%0.577
7474.96%25.04%9.70%11.34%0.574
7575.93%24.07%9.75%11.47%0.572
7676.89%23.11%9.80%11.61%0.569
7777.85%22.15%9.85%11.75%0.567
7878.81%21.19%9.90%11.89%0.565
7979.78%20.22%9.95%12.03%0.562
8080.74%19.26%10.00%12.17%0.560
8181.70%18.30%10.05%12.31%0.558
8282.67%17.33%10.11%12.45%0.555
8383.63%16.37%10.16%12.59%0.553
8484.59%15.41%10.21%12.73%0.551
8585.56%14.44%10.26%12.87%0.549
8686.52%13.48%10.31%13.01%0.547
8787.48%12.52%10.36%13.15%0.545
8888.44%11.56%10.41%13.29%0.543
8989.41%10.59%10.46%13.43%0.541
9090.37%9.63%10.51%13.57%0.539
9191.33%8.67%10.56%13.71%0.537
9292.30%7.70%10.61%13.85%0.536
9393.26%6.74%10.66%13.99%0.534
9494.22%5.78%10.71%14.14%0.532
9595.19%4.81%10.76%14.28%0.530
9696.15%3.85%10.81%14.42%0.529
9797.11%2.89%10.86%14.56%0.527
9898.07%1.93%10.91%14.70%0.525
9999.04%0.96%10.97%14.84%0.524
100100.00%0.00%11.02%14.99%0.522
*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 (3.19% 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 1987 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