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%
0.468
0.00%
100.00%
2
iShares Core US Aggregate Bond ETF (AGG)
4.10%
4.18%
4.06%
0.971
0.00%
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 (0.24% 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%
1.020
2
4.89%
95.11%
4.36%
4.01%
1.028
3
5.86%
94.14%
4.40%
4.02%
1.034
4
6.83%
93.17%
4.43%
4.04%
1.039
5
7.80%
92.20%
4.47%
4.06%
1.042
6
8.77%
91.23%
4.50%
4.09%
1.043
7
9.74%
90.26%
4.54%
4.12%
1.043
8
10.71%
89.29%
4.57%
4.16%
1.042
9
11.68%
88.32%
4.61%
4.21%
1.039
10
12.65%
87.35%
4.65%
4.26%
1.035
11
13.62%
86.38%
4.68%
4.32%
1.029
12
14.59%
85.41%
4.72%
4.38%
1.023
13
15.56%
84.44%
4.75%
4.45%
1.015
14
16.53%
83.47%
4.79%
4.52%
1.007
15
17.50%
82.50%
4.82%
4.60%
0.998
16
18.47%
81.53%
4.86%
4.68%
0.989
17
19.44%
80.56%
4.90%
4.76%
0.979
18
20.41%
79.59%
4.93%
4.85%
0.968
19
21.39%
78.61%
4.97%
4.94%
0.957
20
22.36%
77.64%
5.00%
5.04%
0.946
21
23.33%
76.67%
5.04%
5.14%
0.935
22
24.30%
75.70%
5.07%
5.24%
0.924
23
25.27%
74.73%
5.11%
5.34%
0.912
24
26.24%
73.76%
5.15%
5.45%
0.901
25
27.21%
72.79%
5.18%
5.56%
0.890
26
28.18%
71.82%
5.22%
5.67%
0.878
27
29.15%
70.85%
5.25%
5.79%
0.867
28
30.12%
69.88%
5.29%
5.90%
0.856
29
31.09%
68.91%
5.33%
6.02%
0.845
30
32.06%
67.94%
5.36%
6.14%
0.834
31
33.03%
66.97%
5.40%
6.27%
0.824
32
34.00%
66.00%
5.43%
6.39%
0.813
33
34.97%
65.03%
5.47%
6.52%
0.803
34
35.94%
64.06%
5.51%
6.64%
0.793
35
36.91%
63.09%
5.54%
6.77%
0.783
36
37.88%
62.12%
5.58%
6.90%
0.774
37
38.86%
61.14%
5.61%
7.03%
0.765
38
39.83%
60.17%
5.65%
7.17%
0.756
39
40.80%
59.20%
5.69%
7.30%
0.747
40
41.77%
58.23%
5.72%
7.43%
0.738
41
42.74%
57.26%
5.76%
7.57%
0.730
42
43.71%
56.29%
5.79%
7.71%
0.721
43
44.68%
55.32%
5.83%
7.84%
0.713
44
45.65%
54.35%
5.87%
7.98%
0.705
45
46.62%
53.38%
5.90%
8.12%
0.698
46
47.59%
52.41%
5.94%
8.26%
0.690
47
48.56%
51.44%
5.97%
8.40%
0.683
48
49.53%
50.47%
6.01%
8.54%
0.676
49
50.50%
49.50%
6.05%
8.69%
0.669
50
51.47%
48.53%
6.08%
8.83%
0.662
51
52.44%
47.56%
6.12%
8.97%
0.656
52
53.41%
46.59%
6.16%
9.12%
0.649
53
54.38%
45.62%
6.19%
9.26%
0.643
54
55.35%
44.65%
6.23%
9.41%
0.637
55
56.33%
43.67%
6.26%
9.55%
0.631
56
57.30%
42.70%
6.30%
9.70%
0.625
57
58.27%
41.73%
6.34%
9.84%
0.620
58
59.24%
40.76%
6.37%
9.99%
0.614
59
60.21%
39.79%
6.41%
10.14%
0.609
60
61.18%
38.82%
6.45%
10.29%
0.604
61
62.15%
37.85%
6.48%
10.43%
0.599
62
63.12%
36.88%
6.52%
10.58%
0.594
63
64.09%
35.91%
6.55%
10.73%
0.589
64
65.06%
34.94%
6.59%
10.88%
0.584
65
66.03%
33.97%
6.63%
11.03%
0.580
66
67.00%
33.00%
6.66%
11.18%
0.575
67
67.97%
32.03%
6.70%
11.33%
0.571
68
68.94%
31.06%
6.74%
11.48%
0.566
69
69.91%
30.09%
6.77%
11.63%
0.562
70
70.88%
29.12%
6.81%
11.78%
0.558
71
71.85%
28.15%
6.85%
11.93%
0.554
72
72.82%
27.18%
6.88%
12.08%
0.550
73
73.79%
26.21%
6.92%
12.23%
0.546
74
74.77%
25.23%
6.95%
12.39%
0.543
75
75.74%
24.26%
6.99%
12.54%
0.539
76
76.71%
23.29%
7.03%
12.69%
0.535
77
77.68%
22.32%
7.06%
12.84%
0.532
78
78.65%
21.35%
7.10%
13.00%
0.528
79
79.62%
20.38%
7.14%
13.15%
0.525
80
80.59%
19.41%
7.17%
13.30%
0.522
81
81.56%
18.44%
7.21%
13.45%
0.518
82
82.53%
17.47%
7.25%
13.61%
0.515
83
83.50%
16.50%
7.28%
13.76%
0.512
84
84.47%
15.53%
7.32%
13.91%
0.509
85
85.44%
14.56%
7.36%
14.07%
0.506
86
86.41%
13.59%
7.39%
14.22%
0.503
87
87.38%
12.62%
7.43%
14.38%
0.500
88
88.35%
11.65%
7.47%
14.53%
0.498
89
89.32%
10.68%
7.50%
14.68%
0.495
90
90.29%
9.71%
7.54%
14.84%
0.492
91
91.26%
8.74%
7.58%
14.99%
0.490
92
92.24%
7.76%
7.61%
15.15%
0.487
93
93.21%
6.79%
7.65%
15.30%
0.484
94
94.18%
5.82%
7.69%
15.46%
0.482
95
95.15%
4.85%
7.72%
15.61%
0.480
96
96.12%
3.88%
7.76%
15.77%
0.477
97
97.09%
2.91%
7.80%
15.92%
0.475
98
98.06%
1.94%
7.83%
16.08%
0.472
99
99.03%
0.97%
7.87%
16.24%
0.470
100
100.00%
0.00%
7.91%
16.39%
0.468
*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 (0.24% 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 1-month treasury bill returns as the risk free rate