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
Expected Return
Standard Deviation
Sharpe Ratio
Min. Weight
Max. Weight
1
SPDR S&P 500 ETF Trust (SPY)
7.91%
16.39%
0.450
0.00%
100.00%
2
iShares Core US Aggregate Bond ETF (AGG)
4.18%
4.06%
0.945
0.00%
100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.
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%
0.992
2
4.89%
95.11%
4.36%
4.01%
1.000
3
5.86%
94.14%
4.40%
4.02%
1.006
4
6.83%
93.17%
4.43%
4.04%
1.010
5
7.80%
92.20%
4.47%
4.06%
1.013
6
8.77%
91.23%
4.50%
4.09%
1.015
7
9.74%
90.26%
4.54%
4.12%
1.014
8
10.71%
89.29%
4.57%
4.16%
1.013
9
11.68%
88.32%
4.61%
4.21%
1.010
10
12.65%
87.35%
4.65%
4.26%
1.006
11
13.62%
86.38%
4.68%
4.32%
1.000
12
14.59%
85.41%
4.72%
4.38%
0.994
13
15.56%
84.44%
4.75%
4.45%
0.987
14
16.53%
83.47%
4.79%
4.52%
0.978
15
17.50%
82.50%
4.82%
4.60%
0.970
16
18.47%
81.53%
4.86%
4.68%
0.960
17
19.44%
80.56%
4.90%
4.76%
0.950
18
20.41%
79.59%
4.93%
4.85%
0.940
19
21.39%
78.61%
4.97%
4.94%
0.930
20
22.36%
77.64%
5.00%
5.04%
0.919
21
23.33%
76.67%
5.04%
5.14%
0.908
22
24.30%
75.70%
5.07%
5.24%
0.897
23
25.27%
74.73%
5.11%
5.34%
0.886
24
26.24%
73.76%
5.15%
5.45%
0.874
25
27.21%
72.79%
5.18%
5.56%
0.863
26
28.18%
71.82%
5.22%
5.67%
0.852
27
29.15%
70.85%
5.25%
5.79%
0.841
28
30.12%
69.88%
5.29%
5.90%
0.830
29
31.09%
68.91%
5.33%
6.02%
0.820
30
32.06%
67.94%
5.36%
6.14%
0.809
31
33.03%
66.97%
5.40%
6.27%
0.799
32
34.00%
66.00%
5.43%
6.39%
0.789
33
34.97%
65.03%
5.47%
6.52%
0.779
34
35.94%
64.06%
5.51%
6.64%
0.769
35
36.91%
63.09%
5.54%
6.77%
0.759
36
37.88%
62.12%
5.58%
6.90%
0.750
37
38.86%
61.14%
5.61%
7.03%
0.741
38
39.83%
60.17%
5.65%
7.17%
0.732
39
40.80%
59.20%
5.69%
7.30%
0.723
40
41.77%
58.23%
5.72%
7.43%
0.715
41
42.74%
57.26%
5.76%
7.57%
0.707
42
43.71%
56.29%
5.79%
7.71%
0.698
43
44.68%
55.32%
5.83%
7.84%
0.691
44
45.65%
54.35%
5.87%
7.98%
0.683
45
46.62%
53.38%
5.90%
8.12%
0.675
46
47.59%
52.41%
5.94%
8.26%
0.668
47
48.56%
51.44%
5.97%
8.40%
0.661
48
49.53%
50.47%
6.01%
8.54%
0.654
49
50.50%
49.50%
6.05%
8.69%
0.647
50
51.47%
48.53%
6.08%
8.83%
0.641
51
52.44%
47.56%
6.12%
8.97%
0.634
52
53.41%
46.59%
6.16%
9.12%
0.628
53
54.38%
45.62%
6.19%
9.26%
0.622
54
55.35%
44.65%
6.23%
9.41%
0.616
55
56.33%
43.67%
6.26%
9.55%
0.610
56
57.30%
42.70%
6.30%
9.70%
0.605
57
58.27%
41.73%
6.34%
9.84%
0.599
58
59.24%
40.76%
6.37%
9.99%
0.594
59
60.21%
39.79%
6.41%
10.14%
0.588
60
61.18%
38.82%
6.45%
10.29%
0.583
61
62.15%
37.85%
6.48%
10.43%
0.578
62
63.12%
36.88%
6.52%
10.58%
0.573
63
64.09%
35.91%
6.55%
10.73%
0.569
64
65.06%
34.94%
6.59%
10.88%
0.564
65
66.03%
33.97%
6.63%
11.03%
0.560
66
67.00%
33.00%
6.66%
11.18%
0.555
67
67.97%
32.03%
6.70%
11.33%
0.551
68
68.94%
31.06%
6.74%
11.48%
0.547
69
69.91%
30.09%
6.77%
11.63%
0.542
70
70.88%
29.12%
6.81%
11.78%
0.538
71
71.85%
28.15%
6.85%
11.93%
0.534
72
72.82%
27.18%
6.88%
12.08%
0.531
73
73.79%
26.21%
6.92%
12.23%
0.527
74
74.77%
25.23%
6.95%
12.39%
0.523
75
75.74%
24.26%
6.99%
12.54%
0.520
76
76.71%
23.29%
7.03%
12.69%
0.516
77
77.68%
22.32%
7.06%
12.84%
0.513
78
78.65%
21.35%
7.10%
13.00%
0.509
79
79.62%
20.38%
7.14%
13.15%
0.506
80
80.59%
19.41%
7.17%
13.30%
0.503
81
81.56%
18.44%
7.21%
13.45%
0.499
82
82.53%
17.47%
7.25%
13.61%
0.496
83
83.50%
16.50%
7.28%
13.76%
0.493
84
84.47%
15.53%
7.32%
13.91%
0.490
85
85.44%
14.56%
7.36%
14.07%
0.487
86
86.41%
13.59%
7.39%
14.22%
0.485
87
87.38%
12.62%
7.43%
14.38%
0.482
88
88.35%
11.65%
7.47%
14.53%
0.479
89
89.32%
10.68%
7.50%
14.68%
0.476
90
90.29%
9.71%
7.54%
14.84%
0.474
91
91.26%
8.74%
7.58%
14.99%
0.471
92
92.24%
7.76%
7.61%
15.15%
0.468
93
93.21%
6.79%
7.65%
15.30%
0.466
94
94.18%
5.82%
7.69%
15.46%
0.464
95
95.15%
4.85%
7.72%
15.61%
0.461
96
96.12%
3.88%
7.76%
15.77%
0.459
97
97.09%
2.91%
7.80%
15.92%
0.456
98
98.06%
1.94%
7.83%
16.08%
0.454
99
99.03%
0.97%
7.87%
16.24%
0.452
100
100.00%
0.00%
7.91%
16.39%
0.450
*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.
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