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.
Note: You can hover over any of the data points on the chart for more information.
Efficient Frontier Assets
Efficient Frontier Assets
#
Asset
CAGR
Expected Return*
Standard Deviation
Sharpe Ratio*
Min. Weight
Max. Weight
1
SPDR S&P 500 ETF Trust (SPY)
6.46%
7.91%
16.39%
0.466
0.00%
100.00%
2
iShares Core US Aggregate Bond ETF (AGG)
4.10%
4.18%
4.06%
0.964
0.00%
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 (0.26% annualized).
Asset Correlations
Asset Correlations
Name
Ticker
SPY
AGG
SPDR S&P 500 ETF Trust
SPY
1.00
0.09
iShares Core US Aggregate Bond ETF
AGG
0.09
1.00
Based on monthly returns from Jan 2008 to Dec 2015
Efficient Frontier Points
#
SPY
AGG
Expected Return*
Standard Deviation*
Sharpe Ratio*
1
3.92%
96.08%
4.32%
4.01%
1.013
2
4.89%
95.11%
4.36%
4.01%
1.021
3
5.86%
94.14%
4.40%
4.02%
1.027
4
6.83%
93.17%
4.43%
4.04%
1.032
5
7.80%
92.20%
4.47%
4.06%
1.035
6
8.77%
91.23%
4.50%
4.09%
1.037
7
9.74%
90.26%
4.54%
4.12%
1.037
8
10.71%
89.29%
4.57%
4.16%
1.035
9
11.68%
88.32%
4.61%
4.21%
1.032
10
12.65%
87.35%
4.65%
4.26%
1.028
11
13.62%
86.38%
4.68%
4.32%
1.023
12
14.59%
85.41%
4.72%
4.38%
1.016
13
15.56%
84.44%
4.75%
4.45%
1.009
14
16.53%
83.47%
4.79%
4.52%
1.001
15
17.50%
82.50%
4.82%
4.60%
0.992
16
18.47%
81.53%
4.86%
4.68%
0.983
17
19.44%
80.56%
4.90%
4.76%
0.973
18
20.41%
79.59%
4.93%
4.85%
0.962
19
21.39%
78.61%
4.97%
4.94%
0.952
20
22.36%
77.64%
5.00%
5.04%
0.941
21
23.33%
76.67%
5.04%
5.14%
0.930
22
24.30%
75.70%
5.07%
5.24%
0.918
23
25.27%
74.73%
5.11%
5.34%
0.907
24
26.24%
73.76%
5.15%
5.45%
0.896
25
27.21%
72.79%
5.18%
5.56%
0.885
26
28.18%
71.82%
5.22%
5.67%
0.873
27
29.15%
70.85%
5.25%
5.79%
0.862
28
30.12%
69.88%
5.29%
5.90%
0.851
29
31.09%
68.91%
5.33%
6.02%
0.840
30
32.06%
67.94%
5.36%
6.14%
0.830
31
33.03%
66.97%
5.40%
6.27%
0.819
32
34.00%
66.00%
5.43%
6.39%
0.809
33
34.97%
65.03%
5.47%
6.52%
0.799
34
35.94%
64.06%
5.51%
6.64%
0.789
35
36.91%
63.09%
5.54%
6.77%
0.779
36
37.88%
62.12%
5.58%
6.90%
0.770
37
38.86%
61.14%
5.61%
7.03%
0.761
38
39.83%
60.17%
5.65%
7.17%
0.752
39
40.80%
59.20%
5.69%
7.30%
0.743
40
41.77%
58.23%
5.72%
7.43%
0.734
41
42.74%
57.26%
5.76%
7.57%
0.726
42
43.71%
56.29%
5.79%
7.71%
0.718
43
44.68%
55.32%
5.83%
7.84%
0.710
44
45.65%
54.35%
5.87%
7.98%
0.702
45
46.62%
53.38%
5.90%
8.12%
0.694
46
47.59%
52.41%
5.94%
8.26%
0.687
47
48.56%
51.44%
5.97%
8.40%
0.680
48
49.53%
50.47%
6.01%
8.54%
0.673
49
50.50%
49.50%
6.05%
8.69%
0.666
50
51.47%
48.53%
6.08%
8.83%
0.659
51
52.44%
47.56%
6.12%
8.97%
0.653
52
53.41%
46.59%
6.16%
9.12%
0.646
53
54.38%
45.62%
6.19%
9.26%
0.640
54
55.35%
44.65%
6.23%
9.41%
0.634
55
56.33%
43.67%
6.26%
9.55%
0.628
56
57.30%
42.70%
6.30%
9.70%
0.623
57
58.27%
41.73%
6.34%
9.84%
0.617
58
59.24%
40.76%
6.37%
9.99%
0.612
59
60.21%
39.79%
6.41%
10.14%
0.606
60
61.18%
38.82%
6.45%
10.29%
0.601
61
62.15%
37.85%
6.48%
10.43%
0.596
62
63.12%
36.88%
6.52%
10.58%
0.591
63
64.09%
35.91%
6.55%
10.73%
0.586
64
65.06%
34.94%
6.59%
10.88%
0.582
65
66.03%
33.97%
6.63%
11.03%
0.577
66
67.00%
33.00%
6.66%
11.18%
0.573
67
67.97%
32.03%
6.70%
11.33%
0.568
68
68.94%
31.06%
6.74%
11.48%
0.564
69
69.91%
30.09%
6.77%
11.63%
0.560
70
70.88%
29.12%
6.81%
11.78%
0.556
71
71.85%
28.15%
6.85%
11.93%
0.552
72
72.82%
27.18%
6.88%
12.08%
0.548
73
73.79%
26.21%
6.92%
12.23%
0.544
74
74.77%
25.23%
6.95%
12.39%
0.540
75
75.74%
24.26%
6.99%
12.54%
0.537
76
76.71%
23.29%
7.03%
12.69%
0.533
77
77.68%
22.32%
7.06%
12.84%
0.530
78
78.65%
21.35%
7.10%
13.00%
0.526
79
79.62%
20.38%
7.14%
13.15%
0.523
80
80.59%
19.41%
7.17%
13.30%
0.520
81
81.56%
18.44%
7.21%
13.45%
0.516
82
82.53%
17.47%
7.25%
13.61%
0.513
83
83.50%
16.50%
7.28%
13.76%
0.510
84
84.47%
15.53%
7.32%
13.91%
0.507
85
85.44%
14.56%
7.36%
14.07%
0.504
86
86.41%
13.59%
7.39%
14.22%
0.501
87
87.38%
12.62%
7.43%
14.38%
0.498
88
88.35%
11.65%
7.47%
14.53%
0.496
89
89.32%
10.68%
7.50%
14.68%
0.493
90
90.29%
9.71%
7.54%
14.84%
0.490
91
91.26%
8.74%
7.58%
14.99%
0.488
92
92.24%
7.76%
7.61%
15.15%
0.485
93
93.21%
6.79%
7.65%
15.30%
0.483
94
94.18%
5.82%
7.69%
15.46%
0.480
95
95.15%
4.85%
7.72%
15.61%
0.478
96
96.12%
3.88%
7.76%
15.77%
0.475
97
97.09%
2.91%
7.80%
15.92%
0.473
98
98.06%
1.94%
7.83%
16.08%
0.471
99
99.03%
0.97%
7.87%
16.24%
0.469
100
100.00%
0.00%
7.91%
16.39%
0.466
*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 (0.26% 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 2015
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