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.
Efficient Frontier Configuration
Efficient Frontier Results (Jan 1977 - Dec 2021)
Note: The time period was constrained by the available data for Short Term Treasury [Jan 1977 - May 2023].
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 1977 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
12.33%
15.28%
0.524
0.00%
100.00%
2
Short Term Treasury
5.56%
3.06%
0.405
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
Short Term Treasury
US Stock Market
1.00
0.05
Short Term Treasury
0.05
1.00
Based on monthly returns from Jan 1977 to Dec 2021
Efficient Frontier Portfolios
Efficient Frontier Points
#
US Stock Market
Short Term Treasury
Expected Return *
Standard Deviation *
Sharpe Ratio *
1
3.00%
97.00%
5.77%
3.02%
0.477
2
3.98%
96.02%
5.83%
3.03%
0.498
3
4.96%
95.04%
5.90%
3.04%
0.518
4
5.94%
94.06%
5.96%
3.06%
0.537
5
6.92%
93.08%
6.03%
3.08%
0.554
6
7.90%
92.10%
6.10%
3.12%
0.569
7
8.88%
91.12%
6.16%
3.16%
0.583
8
9.86%
90.14%
6.23%
3.20%
0.595
9
10.84%
89.16%
6.30%
3.26%
0.606
10
11.82%
88.18%
6.36%
3.32%
0.615
11
12.80%
87.20%
6.43%
3.38%
0.623
12
13.78%
86.22%
6.50%
3.45%
0.629
13
14.76%
85.24%
6.56%
3.53%
0.635
14
15.74%
84.26%
6.63%
3.61%
0.639
15
16.71%
83.29%
6.69%
3.69%
0.642
16
17.69%
82.31%
6.76%
3.78%
0.645
17
18.67%
81.33%
6.83%
3.87%
0.646
18
19.65%
80.35%
6.89%
3.97%
0.647
19
20.63%
79.37%
6.96%
4.07%
0.648
20
21.61%
78.39%
7.03%
4.17%
0.648
21
22.59%
77.41%
7.09%
4.28%
0.647
22
23.57%
76.43%
7.16%
4.39%
0.647
23
24.55%
75.45%
7.22%
4.50%
0.645
24
25.53%
74.47%
7.29%
4.61%
0.644
25
26.51%
73.49%
7.36%
4.73%
0.642
26
27.49%
72.51%
7.42%
4.84%
0.640
27
28.47%
71.53%
7.49%
4.96%
0.638
28
29.45%
70.55%
7.56%
5.08%
0.636
29
30.43%
69.57%
7.62%
5.20%
0.634
30
31.41%
68.59%
7.69%
5.33%
0.632
31
32.39%
67.61%
7.76%
5.45%
0.629
32
33.37%
66.63%
7.82%
5.58%
0.627
33
34.35%
65.65%
7.89%
5.71%
0.625
34
35.33%
64.67%
7.95%
5.84%
0.622
35
36.31%
63.69%
8.02%
5.97%
0.620
36
37.29%
62.71%
8.09%
6.10%
0.617
37
38.27%
61.73%
8.15%
6.23%
0.615
38
39.25%
60.75%
8.22%
6.36%
0.613
39
40.23%
59.77%
8.29%
6.50%
0.610
40
41.21%
58.79%
8.35%
6.63%
0.608
41
42.19%
57.81%
8.42%
6.76%
0.605
42
43.17%
56.83%
8.48%
6.90%
0.603
43
44.15%
55.85%
8.55%
7.04%
0.601
44
45.13%
54.87%
8.62%
7.17%
0.599
45
46.11%
53.89%
8.68%
7.31%
0.597
46
47.09%
52.91%
8.75%
7.45%
0.594
47
48.07%
51.93%
8.82%
7.59%
0.592
48
49.05%
50.95%
8.88%
7.73%
0.590
49
50.03%
49.97%
8.95%
7.87%
0.588
50
51.01%
48.99%
9.02%
8.01%
0.586
51
51.99%
48.01%
9.08%
8.15%
0.584
52
52.97%
47.03%
9.15%
8.29%
0.582
53
53.95%
46.05%
9.21%
8.43%
0.580
54
54.93%
45.07%
9.28%
8.57%
0.579
55
55.91%
44.09%
9.35%
8.71%
0.577
56
56.89%
43.11%
9.41%
8.85%
0.575
57
57.87%
42.13%
9.48%
8.99%
0.573
58
58.85%
41.15%
9.55%
9.14%
0.572
59
59.83%
40.17%
9.61%
9.28%
0.570
60
60.81%
39.19%
9.68%
9.42%
0.568
61
61.79%
38.21%
9.74%
9.57%
0.567
62
62.77%
37.23%
9.81%
9.71%
0.565
63
63.75%
36.25%
9.88%
9.85%
0.564
64
64.73%
35.27%
9.94%
10.00%
0.562
65
65.71%
34.29%
10.01%
10.14%
0.561
66
66.69%
33.31%
10.08%
10.29%
0.559
67
67.67%
32.33%
10.14%
10.43%
0.558
68
68.65%
31.35%
10.21%
10.58%
0.557
69
69.63%
30.37%
10.28%
10.72%
0.555
70
70.61%
29.39%
10.34%
10.87%
0.554
71
71.58%
28.42%
10.41%
11.01%
0.553
72
72.56%
27.44%
10.47%
11.16%
0.551
73
73.54%
26.46%
10.54%
11.30%
0.550
74
74.52%
25.48%
10.61%
11.45%
0.549
75
75.50%
24.50%
10.67%
11.60%
0.548
76
76.48%
23.52%
10.74%
11.74%
0.546
77
77.46%
22.54%
10.81%
11.89%
0.545
78
78.44%
21.56%
10.87%
12.03%
0.544
79
79.42%
20.58%
10.94%
12.18%
0.543
80
80.40%
19.60%
11.00%
12.33%
0.542
81
81.38%
18.62%
11.07%
12.47%
0.541
82
82.36%
17.64%
11.14%
12.62%
0.540
83
83.34%
16.66%
11.20%
12.77%
0.539
84
84.32%
15.68%
11.27%
12.91%
0.538
85
85.30%
14.70%
11.34%
13.06%
0.537
86
86.28%
13.72%
11.40%
13.21%
0.536
87
87.26%
12.74%
11.47%
13.36%
0.535
88
88.24%
11.76%
11.54%
13.50%
0.534
89
89.22%
10.78%
11.60%
13.65%
0.533
90
90.20%
9.80%
11.67%
13.80%
0.532
91
91.18%
8.82%
11.73%
13.95%
0.531
92
92.16%
7.84%
11.80%
14.09%
0.531
93
93.14%
6.86%
11.87%
14.24%
0.530
94
94.12%
5.88%
11.93%
14.39%
0.529
95
95.10%
4.90%
12.00%
14.54%
0.528
96
96.08%
3.92%
12.07%
14.69%
0.527
97
97.06%
2.94%
12.13%
14.83%
0.526
98
98.04%
1.96%
12.20%
14.98%
0.526
99
99.02%
0.98%
12.26%
15.13%
0.525
100
100.00%
0.00%
12.33%
15.28%
0.524
*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.