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 1972 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
11.64%
15.57%
0.459
0.00%
100.00%
2
Intermediate Term Treasury
6.74%
5.73%
0.392
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
0.05
Intermediate Term Treasury
0.05
1.00
Based on monthly returns from Jan 1972 to Dec 2021
Efficient Frontier Portfolios
Efficient Frontier Points
#
US Stock Market
Intermediate Term Treasury
Expected Return *
Standard Deviation *
Sharpe Ratio *
1
10.68%
89.32%
7.26%
5.46%
0.508
2
11.59%
88.41%
7.30%
5.46%
0.516
3
12.49%
87.51%
7.35%
5.46%
0.523
4
13.39%
86.61%
7.39%
5.47%
0.531
5
14.29%
85.71%
7.44%
5.49%
0.537
6
15.19%
84.81%
7.48%
5.51%
0.544
7
16.10%
83.90%
7.52%
5.53%
0.549
8
17.00%
83.00%
7.57%
5.55%
0.555
9
17.90%
82.10%
7.61%
5.58%
0.560
10
18.80%
81.20%
7.66%
5.62%
0.564
11
19.71%
80.29%
7.70%
5.65%
0.569
12
20.61%
79.39%
7.75%
5.69%
0.572
13
21.51%
78.49%
7.79%
5.74%
0.576
14
22.41%
77.59%
7.83%
5.78%
0.579
15
23.31%
76.69%
7.88%
5.83%
0.581
16
24.22%
75.78%
7.92%
5.89%
0.584
17
25.12%
74.88%
7.97%
5.94%
0.585
18
26.02%
73.98%
8.01%
6.00%
0.587
19
26.92%
73.08%
8.06%
6.07%
0.588
20
27.82%
72.18%
8.10%
6.13%
0.589
21
28.73%
71.27%
8.14%
6.20%
0.590
22
29.63%
70.37%
8.19%
6.27%
0.590
23
30.53%
69.47%
8.23%
6.35%
0.590
24
31.43%
68.57%
8.28%
6.42%
0.590
25
32.34%
67.66%
8.32%
6.50%
0.590
26
33.24%
66.76%
8.37%
6.58%
0.589
27
34.14%
65.86%
8.41%
6.67%
0.588
28
35.04%
64.96%
8.45%
6.75%
0.587
29
35.94%
64.06%
8.50%
6.84%
0.586
30
36.85%
63.15%
8.54%
6.93%
0.585
31
37.75%
62.25%
8.59%
7.02%
0.584
32
38.65%
61.35%
8.63%
7.12%
0.582
33
39.55%
60.45%
8.67%
7.21%
0.581
34
40.46%
59.54%
8.72%
7.31%
0.579
35
41.36%
58.64%
8.76%
7.41%
0.577
36
42.26%
57.74%
8.81%
7.51%
0.575
37
43.16%
56.84%
8.85%
7.61%
0.574
38
44.06%
55.94%
8.90%
7.71%
0.572
39
44.97%
55.03%
8.94%
7.82%
0.570
40
45.87%
54.13%
8.98%
7.92%
0.568
41
46.77%
53.23%
9.03%
8.03%
0.565
42
47.67%
52.33%
9.07%
8.14%
0.563
43
48.58%
51.42%
9.12%
8.25%
0.561
44
49.48%
50.52%
9.16%
8.36%
0.559
45
50.38%
49.62%
9.21%
8.47%
0.557
46
51.28%
48.72%
9.25%
8.59%
0.555
47
52.18%
47.82%
9.29%
8.70%
0.552
48
53.09%
46.91%
9.34%
8.81%
0.550
49
53.99%
46.01%
9.38%
8.93%
0.548
50
54.89%
45.11%
9.43%
9.05%
0.546
51
55.79%
44.21%
9.47%
9.17%
0.544
52
56.69%
43.31%
9.52%
9.28%
0.542
53
57.60%
42.40%
9.56%
9.40%
0.539
54
58.50%
41.50%
9.60%
9.52%
0.537
55
59.40%
40.60%
9.65%
9.65%
0.535
56
60.30%
39.70%
9.69%
9.77%
0.533
57
61.21%
38.79%
9.74%
9.89%
0.531
58
62.11%
37.89%
9.78%
10.01%
0.529
59
63.01%
36.99%
9.82%
10.14%
0.527
60
63.91%
36.09%
9.87%
10.26%
0.524
61
64.81%
35.19%
9.91%
10.39%
0.522
62
65.72%
34.28%
9.96%
10.51%
0.520
63
66.62%
33.38%
10.00%
10.64%
0.518
64
67.52%
32.48%
10.05%
10.76%
0.516
65
68.42%
31.58%
10.09%
10.89%
0.514
66
69.33%
30.67%
10.13%
11.02%
0.512
67
70.23%
29.77%
10.18%
11.15%
0.511
68
71.13%
28.87%
10.22%
11.28%
0.509
69
72.03%
27.97%
10.27%
11.41%
0.507
70
72.93%
27.07%
10.31%
11.54%
0.505
71
73.84%
26.16%
10.36%
11.67%
0.503
72
74.74%
25.26%
10.40%
11.80%
0.501
73
75.64%
24.36%
10.44%
11.93%
0.499
74
76.54%
23.46%
10.49%
12.06%
0.498
75
77.45%
22.55%
10.53%
12.19%
0.496
76
78.35%
21.65%
10.58%
12.32%
0.494
77
79.25%
20.75%
10.62%
12.45%
0.493
78
80.15%
19.85%
10.67%
12.59%
0.491
79
81.05%
18.95%
10.71%
12.72%
0.489
80
81.96%
18.04%
10.75%
12.85%
0.488
81
82.86%
17.14%
10.80%
12.99%
0.486
82
83.76%
16.24%
10.84%
13.12%
0.484
83
84.66%
15.34%
10.89%
13.25%
0.483
84
85.56%
14.44%
10.93%
13.39%
0.481
85
86.47%
13.53%
10.97%
13.52%
0.480
86
87.37%
12.63%
11.02%
13.66%
0.478
87
88.27%
11.73%
11.06%
13.79%
0.477
88
89.17%
10.83%
11.11%
13.93%
0.475
89
90.08%
9.92%
11.15%
14.06%
0.474
90
90.98%
9.02%
11.20%
14.20%
0.472
91
91.88%
8.12%
11.24%
14.34%
0.471
92
92.78%
7.22%
11.28%
14.47%
0.470
93
93.68%
6.32%
11.33%
14.61%
0.468
94
94.59%
5.41%
11.37%
14.74%
0.467
95
95.49%
4.51%
11.42%
14.88%
0.466
96
96.39%
3.61%
11.46%
15.02%
0.464
97
97.29%
2.71%
11.51%
15.16%
0.463
98
98.20%
1.80%
11.55%
15.29%
0.462
99
99.10%
0.90%
11.59%
15.43%
0.461
100
100.00%
0.00%
11.64%
15.57%
0.459
*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.