This tool uses mean-variance optimization to calculate and plot the efficient frontier for the specified asset classes, mutual funds, ETFs, or stocks based on historical returns or forward-looking capital market assumptions
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.
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
Short Term Treasury
4.43%
2.07%
0.669
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
-0.11
Short Term Treasury
-0.11
1.00
Based on monthly returns from Jan 1986 to Dec 2021
Efficient Frontier Portfolios
Efficient Frontier Points
#
US Stock Market
Short Term Treasury
Expected Return *
Standard Deviation *
Sharpe Ratio *
1
3.15%
96.85%
4.66%
2.01%
0.805
2
4.13%
95.87%
4.73%
2.02%
0.838
3
5.11%
94.89%
4.80%
2.04%
0.867
4
6.09%
93.91%
4.87%
2.07%
0.889
5
7.07%
92.93%
4.95%
2.10%
0.907
6
8.04%
91.96%
5.02%
2.15%
0.920
7
9.02%
90.98%
5.09%
2.21%
0.927
8
10.00%
90.00%
5.16%
2.28%
0.931
9
10.98%
89.02%
5.23%
2.36%
0.932
10
11.96%
88.04%
5.31%
2.44%
0.930
11
12.94%
87.06%
5.38%
2.53%
0.925
12
13.91%
86.09%
5.45%
2.63%
0.919
13
14.89%
85.11%
5.52%
2.73%
0.911
14
15.87%
84.13%
5.60%
2.83%
0.903
15
16.85%
83.15%
5.67%
2.94%
0.893
16
17.83%
82.17%
5.74%
3.06%
0.884
17
18.80%
81.20%
5.81%
3.18%
0.874
18
19.78%
80.22%
5.88%
3.30%
0.864
19
20.76%
79.24%
5.96%
3.42%
0.854
20
21.74%
78.26%
6.03%
3.54%
0.844
21
22.72%
77.28%
6.10%
3.67%
0.835
22
23.70%
76.30%
6.17%
3.80%
0.825
23
24.67%
75.33%
6.25%
3.93%
0.816
24
25.65%
74.35%
6.32%
4.06%
0.807
25
26.63%
73.37%
6.39%
4.20%
0.799
26
27.61%
72.39%
6.46%
4.33%
0.790
27
28.59%
71.41%
6.53%
4.47%
0.782
28
29.57%
70.43%
6.61%
4.61%
0.775
29
30.54%
69.46%
6.68%
4.75%
0.767
30
31.52%
68.48%
6.75%
4.89%
0.760
31
32.50%
67.50%
6.82%
5.03%
0.753
32
33.48%
66.52%
6.89%
5.17%
0.747
33
34.46%
65.54%
6.97%
5.31%
0.740
34
35.43%
64.57%
7.04%
5.45%
0.734
35
36.41%
63.59%
7.11%
5.59%
0.728
36
37.39%
62.61%
7.18%
5.74%
0.723
37
38.37%
61.63%
7.26%
5.88%
0.717
38
39.35%
60.65%
7.33%
6.03%
0.712
39
40.33%
59.67%
7.40%
6.17%
0.707
40
41.30%
58.70%
7.47%
6.32%
0.702
41
42.28%
57.72%
7.54%
6.46%
0.698
42
43.26%
56.74%
7.62%
6.61%
0.693
43
44.24%
55.76%
7.69%
6.75%
0.689
44
45.22%
54.78%
7.76%
6.90%
0.685
45
46.20%
53.80%
7.83%
7.05%
0.680
46
47.17%
52.83%
7.90%
7.19%
0.677
47
48.15%
51.85%
7.98%
7.34%
0.673
48
49.13%
50.87%
8.05%
7.49%
0.669
49
50.11%
49.89%
8.12%
7.64%
0.666
50
51.09%
48.91%
8.19%
7.79%
0.662
51
52.07%
47.93%
8.27%
7.93%
0.659
52
53.04%
46.96%
8.34%
8.08%
0.656
53
54.02%
45.98%
8.41%
8.23%
0.653
54
55.00%
45.00%
8.48%
8.38%
0.650
55
55.98%
44.02%
8.55%
8.53%
0.647
56
56.96%
43.04%
8.63%
8.68%
0.644
57
57.93%
42.07%
8.70%
8.83%
0.641
58
58.91%
41.09%
8.77%
8.98%
0.639
59
59.89%
40.11%
8.84%
9.13%
0.636
60
60.87%
39.13%
8.92%
9.28%
0.634
61
61.85%
38.15%
8.99%
9.43%
0.631
62
62.83%
37.17%
9.06%
9.58%
0.629
63
63.80%
36.20%
9.13%
9.73%
0.627
64
64.78%
35.22%
9.20%
9.88%
0.624
65
65.76%
34.24%
9.28%
10.03%
0.622
66
66.74%
33.26%
9.35%
10.18%
0.620
67
67.72%
32.28%
9.42%
10.33%
0.618
68
68.70%
31.30%
9.49%
10.48%
0.616
69
69.67%
30.33%
9.56%
10.63%
0.614
70
70.65%
29.35%
9.64%
10.78%
0.612
71
71.63%
28.37%
9.71%
10.93%
0.610
72
72.61%
27.39%
9.78%
11.08%
0.609
73
73.59%
26.41%
9.85%
11.23%
0.607
74
74.57%
25.43%
9.93%
11.38%
0.605
75
75.54%
24.46%
10.00%
11.54%
0.603
76
76.52%
23.48%
10.07%
11.69%
0.602
77
77.50%
22.50%
10.14%
11.84%
0.600
78
78.48%
21.52%
10.21%
11.99%
0.599
79
79.46%
20.54%
10.29%
12.14%
0.597
80
80.43%
19.57%
10.36%
12.29%
0.596
81
81.41%
18.59%
10.43%
12.44%
0.594
82
82.39%
17.61%
10.50%
12.59%
0.593
83
83.37%
16.63%
10.57%
12.75%
0.591
84
84.35%
15.65%
10.65%
12.90%
0.590
85
85.33%
14.67%
10.72%
13.05%
0.589
86
86.30%
13.70%
10.79%
13.20%
0.587
87
87.28%
12.72%
10.86%
13.35%
0.586
88
88.26%
11.74%
10.94%
13.50%
0.585
89
89.24%
10.76%
11.01%
13.66%
0.584
90
90.22%
9.78%
11.08%
13.81%
0.582
91
91.20%
8.80%
11.15%
13.96%
0.581
92
92.17%
7.83%
11.22%
14.11%
0.580
93
93.15%
6.85%
11.30%
14.26%
0.579
94
94.13%
5.87%
11.37%
14.42%
0.578
95
95.11%
4.89%
11.44%
14.57%
0.577
96
96.09%
3.91%
11.51%
14.72%
0.576
97
97.07%
2.93%
11.59%
14.87%
0.575
98
98.04%
1.96%
11.66%
15.02%
0.574
99
99.02%
0.98%
11.73%
15.18%
0.573
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.