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 1978 - Feb 2023)
Note: The time period was constrained by the available data for Long Term Treasury [Jan 1978 - Feb 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 1978 to Feb 2023
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
12.03%
15.62%
0.498
0.00%
100.00%
2
Long Term Treasury
7.72%
11.40%
0.305
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
Long Term Treasury
US Stock Market
1.00
0.06
Long Term Treasury
0.06
1.00
Based on monthly returns from Jan 1978 to Feb 2023
Efficient Frontier Portfolios
Efficient Frontier Points
#
US Stock Market
Long Term Treasury
Expected Return *
Standard Deviation *
Sharpe Ratio *
1
0.00%
100.00%
7.72%
11.40%
0.305
2
1.01%
98.99%
7.76%
11.29%
0.311
3
2.02%
97.98%
7.81%
11.19%
0.318
4
3.03%
96.97%
7.85%
11.09%
0.325
5
4.04%
95.96%
7.89%
10.99%
0.332
6
5.05%
94.95%
7.94%
10.89%
0.339
7
6.06%
93.94%
7.98%
10.80%
0.346
8
7.07%
92.93%
8.02%
10.71%
0.353
9
8.08%
91.92%
8.07%
10.62%
0.360
10
9.09%
90.91%
8.11%
10.54%
0.367
11
10.10%
89.90%
8.16%
10.46%
0.374
12
11.11%
88.89%
8.20%
10.38%
0.381
13
12.12%
87.88%
8.24%
10.30%
0.388
14
13.13%
86.87%
8.29%
10.23%
0.395
15
14.14%
85.86%
8.33%
10.16%
0.402
16
15.15%
84.85%
8.37%
10.09%
0.409
17
16.16%
83.84%
8.42%
10.02%
0.416
18
17.17%
82.83%
8.46%
9.96%
0.423
19
18.18%
81.82%
8.50%
9.91%
0.430
20
19.19%
80.81%
8.55%
9.85%
0.436
21
20.20%
79.80%
8.59%
9.80%
0.443
22
21.21%
78.79%
8.63%
9.75%
0.450
23
22.22%
77.78%
8.68%
9.71%
0.456
24
23.23%
76.77%
8.72%
9.67%
0.463
25
24.24%
75.76%
8.76%
9.63%
0.469
26
25.25%
74.75%
8.81%
9.60%
0.475
27
26.26%
73.74%
8.85%
9.57%
0.481
28
27.27%
72.73%
8.89%
9.54%
0.487
29
28.28%
71.72%
8.94%
9.52%
0.493
30
29.29%
70.71%
8.98%
9.50%
0.498
31
30.30%
69.70%
9.03%
9.48%
0.504
32
31.31%
68.69%
9.07%
9.47%
0.509
33
32.32%
67.68%
9.11%
9.46%
0.514
34
33.33%
66.67%
9.16%
9.46%
0.519
35
34.34%
65.66%
9.20%
9.46%
0.523
36
35.35%
64.65%
9.24%
9.46%
0.528
37
36.36%
63.64%
9.29%
9.47%
0.532
38
37.37%
62.63%
9.33%
9.48%
0.536
39
38.38%
61.62%
9.37%
9.50%
0.540
40
39.39%
60.61%
9.42%
9.52%
0.543
41
40.40%
59.60%
9.46%
9.54%
0.546
42
41.41%
58.59%
9.50%
9.57%
0.549
43
42.42%
57.58%
9.55%
9.60%
0.552
44
43.43%
56.57%
9.59%
9.63%
0.555
45
44.44%
55.56%
9.63%
9.67%
0.557
46
45.45%
54.55%
9.68%
9.71%
0.559
47
46.46%
53.54%
9.72%
9.75%
0.561
48
47.47%
52.53%
9.77%
9.80%
0.563
49
48.48%
51.52%
9.81%
9.85%
0.564
50
49.49%
50.51%
9.85%
9.91%
0.566
51
50.51%
49.49%
9.90%
9.97%
0.567
52
51.52%
48.48%
9.94%
10.03%
0.568
53
52.53%
47.47%
9.98%
10.09%
0.568
54
53.54%
46.46%
10.03%
10.16%
0.569
55
54.55%
45.45%
10.07%
10.23%
0.569
56
55.56%
44.44%
10.11%
10.30%
0.569
57
56.57%
43.43%
10.16%
10.38%
0.569
58
57.58%
42.42%
10.20%
10.46%
0.569
59
58.59%
41.41%
10.24%
10.54%
0.569
60
59.60%
40.40%
10.29%
10.63%
0.568
61
60.61%
39.39%
10.33%
10.71%
0.568
62
61.62%
38.38%
10.37%
10.80%
0.567
63
62.63%
37.37%
10.42%
10.90%
0.566
64
63.64%
36.36%
10.46%
10.99%
0.565
65
64.65%
35.35%
10.51%
11.09%
0.564
66
65.66%
34.34%
10.55%
11.19%
0.563
67
66.67%
33.33%
10.59%
11.29%
0.562
68
67.68%
32.32%
10.64%
11.40%
0.560
69
68.69%
31.31%
10.68%
11.51%
0.559
70
69.70%
30.30%
10.72%
11.61%
0.557
71
70.71%
29.29%
10.77%
11.73%
0.556
72
71.72%
28.28%
10.81%
11.84%
0.554
73
72.73%
27.27%
10.85%
11.95%
0.553
74
73.74%
26.26%
10.90%
12.07%
0.551
75
74.75%
25.25%
10.94%
12.19%
0.549
76
75.76%
24.24%
10.98%
12.31%
0.547
77
76.77%
23.23%
11.03%
12.43%
0.545
78
77.78%
22.22%
11.07%
12.56%
0.543
79
78.79%
21.21%
11.11%
12.68%
0.541
80
79.80%
20.20%
11.16%
12.81%
0.539
81
80.81%
19.19%
11.20%
12.94%
0.537
82
81.82%
18.18%
11.24%
13.07%
0.535
83
82.83%
17.17%
11.29%
13.20%
0.533
84
83.84%
16.16%
11.33%
13.33%
0.531
85
84.85%
15.15%
11.38%
13.47%
0.529
86
85.86%
14.14%
11.42%
13.60%
0.527
87
86.87%
13.13%
11.46%
13.74%
0.525
88
87.88%
12.12%
11.51%
13.88%
0.523
89
88.89%
11.11%
11.55%
14.02%
0.521
90
89.90%
10.10%
11.59%
14.16%
0.519
91
90.91%
9.09%
11.64%
14.30%
0.517
92
91.92%
8.08%
11.68%
14.44%
0.515
93
92.93%
7.07%
11.72%
14.59%
0.513
94
93.94%
6.06%
11.77%
14.73%
0.510
95
94.95%
5.05%
11.81%
14.88%
0.508
96
95.96%
4.04%
11.85%
15.02%
0.506
97
96.97%
3.03%
11.90%
15.17%
0.504
98
97.98%
2.02%
11.94%
15.32%
0.502
99
98.99%
1.01%
11.98%
15.47%
0.500
100
100.00%
0.00%
12.03%
15.62%
0.498
*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.