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%
3
Intermediate Term Treasury
6.75%
5.83%
0.416
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
Intermediate Term Treasury
US Stock Market
1.00
0.05
0.05
Short Term Treasury
0.05
1.00
0.92
Intermediate Term Treasury
0.05
0.92
1.00
Based on monthly returns from Jan 1977 to Dec 2021
Efficient Frontier Portfolios
Efficient Frontier Points
#
US Stock Market
Short Term Treasury
Intermediate Term Treasury
Expected Return *
Standard Deviation *
Sharpe Ratio *
1
3.00%
97.00%
0.00%
5.77%
3.02%
0.477
2
3.98%
96.02%
0.00%
5.83%
3.03%
0.498
3
4.96%
95.04%
0.00%
5.90%
3.04%
0.518
4
5.94%
94.06%
0.00%
5.96%
3.06%
0.537
5
6.92%
93.08%
0.00%
6.03%
3.08%
0.554
6
7.90%
92.10%
0.00%
6.10%
3.12%
0.569
7
8.88%
91.12%
0.00%
6.16%
3.16%
0.583
8
9.86%
90.14%
0.00%
6.23%
3.20%
0.595
9
10.84%
89.16%
0.00%
6.30%
3.26%
0.606
10
11.82%
88.18%
0.00%
6.36%
3.32%
0.615
11
12.80%
87.20%
0.00%
6.43%
3.38%
0.623
12
13.78%
86.22%
0.00%
6.50%
3.45%
0.629
13
14.76%
85.24%
0.00%
6.56%
3.53%
0.635
14
15.74%
84.26%
0.00%
6.63%
3.61%
0.639
15
16.71%
83.29%
0.00%
6.69%
3.69%
0.642
16
17.69%
82.31%
0.00%
6.76%
3.78%
0.645
17
18.31%
79.59%
2.10%
6.83%
3.87%
0.647
18
18.88%
76.70%
4.41%
6.89%
3.96%
0.648
19
19.46%
73.81%
6.73%
6.96%
4.06%
0.650
20
20.03%
70.92%
9.05%
7.03%
4.15%
0.651
21
20.61%
68.03%
11.36%
7.09%
4.25%
0.652
22
21.18%
65.14%
13.68%
7.16%
4.34%
0.653
23
21.76%
62.25%
15.99%
7.22%
4.44%
0.653
24
22.33%
59.36%
18.31%
7.29%
4.54%
0.654
25
22.91%
56.46%
20.63%
7.36%
4.64%
0.655
26
23.48%
53.57%
22.94%
7.42%
4.73%
0.655
27
24.06%
50.68%
25.26%
7.49%
4.83%
0.655
28
24.63%
47.79%
27.57%
7.56%
4.93%
0.655
29
25.21%
44.90%
29.89%
7.62%
5.03%
0.656
30
25.78%
42.01%
32.21%
7.69%
5.13%
0.656
31
26.36%
39.12%
34.52%
7.76%
5.24%
0.656
32
26.93%
36.23%
36.84%
7.82%
5.34%
0.656
33
27.51%
33.33%
39.16%
7.89%
5.44%
0.656
34
28.08%
30.44%
41.47%
7.95%
5.54%
0.655
35
28.66%
27.55%
43.79%
8.02%
5.64%
0.655
36
29.24%
24.66%
46.10%
8.09%
5.75%
0.655
37
29.81%
21.77%
48.42%
8.15%
5.85%
0.655
38
30.39%
18.88%
50.74%
8.22%
5.95%
0.655
39
30.96%
15.99%
53.05%
8.29%
6.06%
0.654
40
31.54%
13.10%
55.37%
8.35%
6.16%
0.654
41
32.11%
10.20%
57.68%
8.42%
6.27%
0.654
42
32.69%
7.31%
60.00%
8.48%
6.37%
0.653
43
33.26%
4.42%
62.32%
8.55%
6.47%
0.653
44
33.84%
1.53%
64.63%
8.62%
6.58%
0.653
45
34.70%
0.00%
65.30%
8.68%
6.68%
0.652
46
35.89%
0.00%
64.11%
8.75%
6.79%
0.652
47
37.07%
0.00%
62.93%
8.82%
6.91%
0.651
48
38.26%
0.00%
61.74%
8.88%
7.02%
0.649
49
39.45%
0.00%
60.55%
8.95%
7.14%
0.648
50
40.64%
0.00%
59.36%
9.02%
7.26%
0.646
51
41.82%
0.00%
58.18%
9.08%
7.39%
0.644
52
43.01%
0.00%
56.99%
9.15%
7.52%
0.642
53
44.20%
0.00%
55.80%
9.21%
7.65%
0.640
54
45.38%
0.00%
54.62%
9.28%
7.78%
0.637
55
46.57%
0.00%
53.43%
9.35%
7.91%
0.635
56
47.76%
0.00%
52.24%
9.41%
8.05%
0.632
57
48.95%
0.00%
51.05%
9.48%
8.19%
0.630
58
50.13%
0.00%
49.87%
9.55%
8.33%
0.627
59
51.32%
0.00%
48.68%
9.61%
8.48%
0.624
60
52.51%
0.00%
47.49%
9.68%
8.62%
0.621
61
53.70%
0.00%
46.30%
9.74%
8.77%
0.618
62
54.88%
0.00%
45.12%
9.81%
8.92%
0.615
63
56.07%
0.00%
43.93%
9.88%
9.07%
0.613
64
57.26%
0.00%
42.74%
9.94%
9.22%
0.610
65
58.44%
0.00%
41.56%
10.01%
9.37%
0.607
66
59.63%
0.00%
40.37%
10.08%
9.53%
0.604
67
60.82%
0.00%
39.18%
10.14%
9.68%
0.601
68
62.01%
0.00%
37.99%
10.21%
9.84%
0.598
69
63.19%
0.00%
36.81%
10.28%
10.00%
0.595
70
64.38%
0.00%
35.62%
10.34%
10.16%
0.593
71
65.57%
0.00%
34.43%
10.41%
10.32%
0.590
72
66.76%
0.00%
33.24%
10.47%
10.48%
0.587
73
67.94%
0.00%
32.06%
10.54%
10.64%
0.584
74
69.13%
0.00%
30.87%
10.61%
10.81%
0.582
75
70.32%
0.00%
29.68%
10.67%
10.97%
0.579
76
71.50%
0.00%
28.50%
10.74%
11.14%
0.576
77
72.69%
0.00%
27.31%
10.81%
11.30%
0.574
78
73.88%
0.00%
26.12%
10.87%
11.47%
0.571
79
75.07%
0.00%
24.93%
10.94%
11.64%
0.569
80
76.25%
0.00%
23.75%
11.00%
11.80%
0.566
81
77.44%
0.00%
22.56%
11.07%
11.97%
0.564
82
78.63%
0.00%
21.37%
11.14%
12.14%
0.561
83
79.82%
0.00%
20.18%
11.20%
12.31%
0.559
84
81.00%
0.00%
19.00%
11.27%
12.48%
0.557
85
82.19%
0.00%
17.81%
11.34%
12.65%
0.554
86
83.38%
0.00%
16.62%
11.40%
12.83%
0.552
87
84.57%
0.00%
15.43%
11.47%
13.00%
0.550
88
85.75%
0.00%
14.25%
11.54%
13.17%
0.548
89
86.94%
0.00%
13.06%
11.60%
13.34%
0.545
90
88.13%
0.00%
11.87%
11.67%
13.52%
0.543
91
89.31%
0.00%
10.69%
11.73%
13.69%
0.541
92
90.50%
0.00%
9.50%
11.80%
13.87%
0.539
93
91.69%
0.00%
8.31%
11.87%
14.04%
0.537
94
92.88%
0.00%
7.12%
11.93%
14.22%
0.535
95
94.06%
0.00%
5.94%
12.00%
14.39%
0.533
96
95.25%
0.00%
4.75%
12.07%
14.57%
0.531
97
96.44%
0.00%
3.56%
12.13%
14.75%
0.530
98
97.63%
0.00%
2.37%
12.20%
14.92%
0.528
99
98.81%
0.00%
1.19%
12.26%
15.10%
0.526
100
100.00%
0.00%
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.