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
Notes and Disclosures
IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
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. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
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.
Portfolio optimization is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. 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 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 1986 to Dec 2021
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
Efficient Frontier Assets
Efficient Frontier Assets
#
Asset
Expected Return
Standard Deviation
Sharpe Ratio
Min. Weight
Max. Weight
1
US Stock Market
11.80%
15.33%
0.572
0.00%
100.00%
2
Intermediate Term Treasury
5.95%
4.77%
0.611
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
Asset
US Stock Market
Intermediate Term Treasury
US Stock Market
1.00
-0.09
Intermediate Term Treasury
-0.09
1.00
Based on monthly returns from Jan 1986 to Dec 2021
Efficient Frontier Portfolios
Efficient Frontier Points
#
US Stock Market
Intermediate Term Treasury
Expected Return *
Standard Deviation *
Sharpe Ratio *
1
10.81%
89.19%
6.58%
4.42%
0.802
2
11.71%
88.29%
6.64%
4.43%
0.813
3
12.62%
87.38%
6.69%
4.43%
0.824
4
13.52%
86.48%
6.74%
4.45%
0.834
5
14.42%
85.58%
6.80%
4.46%
0.842
6
15.32%
84.68%
6.85%
4.48%
0.850
7
16.22%
83.78%
6.90%
4.51%
0.856
8
17.12%
82.88%
6.95%
4.54%
0.862
9
18.02%
81.98%
7.01%
4.58%
0.867
10
18.92%
81.08%
7.06%
4.62%
0.871
11
19.82%
80.18%
7.11%
4.66%
0.873
12
20.72%
79.28%
7.16%
4.71%
0.875
13
21.62%
78.38%
7.22%
4.77%
0.877
14
22.53%
77.47%
7.27%
4.82%
0.877
15
23.43%
76.57%
7.32%
4.89%
0.877
16
24.33%
75.67%
7.37%
4.95%
0.876
17
25.23%
74.77%
7.43%
5.02%
0.875
18
26.13%
73.87%
7.48%
5.09%
0.873
19
27.03%
72.97%
7.53%
5.17%
0.870
20
27.93%
72.07%
7.59%
5.24%
0.867
21
28.83%
71.17%
7.64%
5.32%
0.864
22
29.73%
70.27%
7.69%
5.41%
0.860
23
30.63%
69.37%
7.74%
5.50%
0.856
24
31.53%
68.47%
7.80%
5.58%
0.852
25
32.43%
67.57%
7.85%
5.68%
0.848
26
33.34%
66.66%
7.90%
5.77%
0.843
27
34.24%
65.76%
7.95%
5.87%
0.838
28
35.14%
64.86%
8.01%
5.97%
0.833
29
36.04%
63.96%
8.06%
6.07%
0.828
30
36.94%
63.06%
8.11%
6.17%
0.823
31
37.84%
62.16%
8.17%
6.27%
0.818
32
38.74%
61.26%
8.22%
6.38%
0.812
33
39.64%
60.36%
8.27%
6.49%
0.807
34
40.54%
59.46%
8.32%
6.59%
0.802
35
41.44%
58.56%
8.38%
6.71%
0.796
36
42.34%
57.66%
8.43%
6.82%
0.791
37
43.25%
56.75%
8.48%
6.93%
0.785
38
44.15%
55.85%
8.53%
7.05%
0.780
39
45.05%
54.95%
8.59%
7.16%
0.775
40
45.95%
54.05%
8.64%
7.28%
0.770
41
46.85%
53.15%
8.69%
7.40%
0.764
42
47.75%
52.25%
8.75%
7.52%
0.759
43
48.65%
51.35%
8.80%
7.64%
0.754
44
49.55%
50.45%
8.85%
7.76%
0.749
45
50.45%
49.55%
8.90%
7.88%
0.744
46
51.35%
48.65%
8.96%
8.00%
0.739
47
52.25%
47.75%
9.01%
8.13%
0.735
48
53.15%
46.85%
9.06%
8.25%
0.730
49
54.06%
45.94%
9.11%
8.38%
0.725
50
54.96%
45.04%
9.17%
8.50%
0.721
51
55.86%
44.14%
9.22%
8.63%
0.716
52
56.76%
43.24%
9.27%
8.76%
0.712
53
57.66%
42.34%
9.32%
8.89%
0.707
54
58.56%
41.44%
9.38%
9.02%
0.703
55
59.46%
40.54%
9.43%
9.15%
0.699
56
60.36%
39.64%
9.48%
9.28%
0.695
57
61.26%
38.74%
9.54%
9.41%
0.691
58
62.16%
37.84%
9.59%
9.54%
0.687
59
63.06%
36.94%
9.64%
9.67%
0.683
60
63.97%
36.03%
9.69%
9.80%
0.679
61
64.87%
35.13%
9.75%
9.93%
0.675
62
65.77%
34.23%
9.80%
10.07%
0.672
63
66.67%
33.33%
9.85%
10.20%
0.668
64
67.57%
32.43%
9.90%
10.33%
0.665
65
68.47%
31.53%
9.96%
10.47%
0.661
66
69.37%
30.63%
10.01%
10.60%
0.658
67
70.27%
29.73%
10.06%
10.74%
0.654
68
71.17%
28.83%
10.12%
10.87%
0.651
69
72.07%
27.93%
10.17%
11.01%
0.648
70
72.97%
27.03%
10.22%
11.14%
0.645
71
73.87%
26.13%
10.27%
11.28%
0.641
72
74.78%
25.22%
10.33%
11.42%
0.638
73
75.68%
24.32%
10.38%
11.55%
0.635
74
76.58%
23.42%
10.43%
11.69%
0.632
75
77.48%
22.52%
10.48%
11.83%
0.630
76
78.38%
21.62%
10.54%
11.97%
0.627
77
79.28%
20.72%
10.59%
12.10%
0.624
78
80.18%
19.82%
10.64%
12.24%
0.621
79
81.08%
18.92%
10.69%
12.38%
0.619
80
81.98%
18.02%
10.75%
12.52%
0.616
81
82.88%
17.12%
10.80%
12.66%
0.613
82
83.78%
16.22%
10.85%
12.80%
0.611
83
84.69%
15.31%
10.91%
12.94%
0.608
84
85.59%
14.41%
10.96%
13.08%
0.606
85
86.49%
13.51%
11.01%
13.21%
0.603
86
87.39%
12.61%
11.06%
13.35%
0.601
87
88.29%
11.71%
11.12%
13.49%
0.599
88
89.19%
10.81%
11.17%
13.63%
0.596
89
90.09%
9.91%
11.22%
13.78%
0.594
90
90.99%
9.01%
11.27%
13.92%
0.592
91
91.89%
8.11%
11.33%
14.06%
0.590
92
92.79%
7.21%
11.38%
14.20%
0.588
93
93.69%
6.31%
11.43%
14.34%
0.586
94
94.59%
5.41%
11.49%
14.48%
0.583
95
95.50%
4.50%
11.54%
14.62%
0.581
96
96.40%
3.60%
11.59%
14.76%
0.579
97
97.30%
2.70%
11.64%
14.90%
0.577
98
98.20%
1.80%
11.70%
15.04%
0.576
99
99.10%
0.90%
11.75%
15.19%
0.574
100
100.00%
0.00%
11.80%
15.33%
0.572
*Annualized 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.