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.
Asset Class | Allocation |
---|---|
US Stock Market | 52.53% |
Long Term Treasury | 47.47% |
Save portfolio » |
Portfolio | Expected Return | Standard Deviation | Sharpe Ratio |
---|---|---|---|
Max Sharpe Ratio Portfolio | 10.61% | 9.88% | 0.59 |
# | Asset | Expected Return | Standard Deviation | Sharpe Ratio | Min. Weight | Max. Weight |
---|---|---|---|---|---|---|
1 | US Stock Market | 12.70% | 15.48% | 0.501 | 0.00% | 100.00% |
2 | Long Term Treasury | 8.33% | 11.22% | 0.335 | 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 | US Stock Market | Long Term Treasury |
---|---|---|
US Stock Market | 1.00 | 0.04 |
Long Term Treasury | 0.04 | 1.00 |
Based on monthly returns from Jan 1978 to Jun 2022 |
# | US Stock Market | Long Term Treasury | Expected Return* | Standard Deviation* | Sharpe Ratio* |
---|---|---|---|---|---|
1 | 0.00% | 100.00% | 8.33% | 11.22% | 0.335 |
2 | 1.01% | 98.99% | 8.37% | 11.12% | 0.342 |
3 | 2.02% | 97.98% | 8.41% | 11.01% | 0.349 |
4 | 3.03% | 96.97% | 8.46% | 10.91% | 0.356 |
5 | 4.04% | 95.96% | 8.50% | 10.81% | 0.363 |
6 | 5.05% | 94.95% | 8.54% | 10.71% | 0.370 |
7 | 6.06% | 93.94% | 8.59% | 10.62% | 0.377 |
8 | 7.07% | 92.93% | 8.63% | 10.53% | 0.384 |
9 | 8.08% | 91.92% | 8.67% | 10.44% | 0.391 |
10 | 9.09% | 90.91% | 8.72% | 10.35% | 0.399 |
11 | 10.10% | 89.90% | 8.76% | 10.27% | 0.406 |
12 | 11.11% | 88.89% | 8.80% | 10.19% | 0.413 |
13 | 12.12% | 87.88% | 8.85% | 10.11% | 0.420 |
14 | 13.13% | 86.87% | 8.89% | 10.03% | 0.427 |
15 | 14.14% | 85.86% | 8.93% | 9.96% | 0.435 |
16 | 15.15% | 84.85% | 8.98% | 9.89% | 0.442 |
17 | 16.16% | 83.84% | 9.02% | 9.83% | 0.449 |
18 | 17.17% | 82.83% | 9.07% | 9.76% | 0.456 |
19 | 18.18% | 81.82% | 9.11% | 9.70% | 0.463 |
20 | 19.19% | 80.81% | 9.15% | 9.65% | 0.470 |
21 | 20.20% | 79.80% | 9.20% | 9.60% | 0.476 |
22 | 21.21% | 78.79% | 9.24% | 9.55% | 0.483 |
23 | 22.22% | 77.78% | 9.28% | 9.50% | 0.490 |
24 | 23.23% | 76.77% | 9.33% | 9.46% | 0.496 |
25 | 24.24% | 75.76% | 9.37% | 9.42% | 0.502 |
26 | 25.25% | 74.75% | 9.42% | 9.39% | 0.508 |
27 | 26.26% | 73.74% | 9.46% | 9.36% | 0.514 |
28 | 27.27% | 72.73% | 9.50% | 9.33% | 0.520 |
29 | 28.28% | 71.72% | 9.55% | 9.30% | 0.526 |
30 | 29.29% | 70.71% | 9.59% | 9.29% | 0.531 |
31 | 30.30% | 69.70% | 9.64% | 9.27% | 0.537 |
32 | 31.31% | 68.69% | 9.68% | 9.26% | 0.542 |
33 | 32.32% | 67.68% | 9.72% | 9.25% | 0.547 |
34 | 33.33% | 66.67% | 9.77% | 9.25% | 0.551 |
35 | 34.34% | 65.66% | 9.81% | 9.25% | 0.556 |
36 | 35.35% | 64.65% | 9.86% | 9.25% | 0.560 |
37 | 36.36% | 63.64% | 9.90% | 9.26% | 0.564 |
38 | 37.37% | 62.63% | 9.94% | 9.27% | 0.567 |
39 | 38.38% | 61.62% | 9.99% | 9.28% | 0.571 |
40 | 39.39% | 60.61% | 10.03% | 9.30% | 0.574 |
41 | 40.40% | 59.60% | 10.08% | 9.33% | 0.577 |
42 | 41.41% | 58.59% | 10.12% | 9.35% | 0.579 |
43 | 42.42% | 57.58% | 10.16% | 9.38% | 0.582 |
44 | 43.43% | 56.57% | 10.21% | 9.42% | 0.584 |
45 | 44.44% | 55.56% | 10.25% | 9.45% | 0.586 |
46 | 45.45% | 54.55% | 10.30% | 9.50% | 0.588 |
47 | 46.46% | 53.54% | 10.34% | 9.54% | 0.589 |
48 | 47.47% | 52.53% | 10.38% | 9.59% | 0.590 |
49 | 48.48% | 51.52% | 10.43% | 9.64% | 0.591 |
50 | 49.49% | 50.51% | 10.47% | 9.70% | 0.592 |
51 | 50.51% | 49.49% | 10.52% | 9.76% | 0.593 |
52 | 51.52% | 48.48% | 10.56% | 9.82% | 0.593 |
53 | 52.53% | 47.47% | 10.61% | 9.88% | 0.593 |
54 | 53.54% | 46.46% | 10.65% | 9.95% | 0.593 |
55 | 54.55% | 45.45% | 10.69% | 10.03% | 0.593 |
56 | 55.56% | 44.44% | 10.74% | 10.10% | 0.592 |
57 | 56.57% | 43.43% | 10.78% | 10.18% | 0.592 |
58 | 57.58% | 42.42% | 10.83% | 10.26% | 0.591 |
59 | 58.59% | 41.41% | 10.87% | 10.34% | 0.590 |
60 | 59.60% | 40.40% | 10.92% | 10.43% | 0.589 |
61 | 60.61% | 39.39% | 10.96% | 10.52% | 0.588 |
62 | 61.62% | 38.38% | 11.00% | 10.61% | 0.587 |
63 | 62.63% | 37.37% | 11.05% | 10.70% | 0.585 |
64 | 63.64% | 36.36% | 11.09% | 10.80% | 0.584 |
65 | 64.65% | 35.35% | 11.14% | 10.90% | 0.582 |
66 | 65.66% | 34.34% | 11.18% | 11.00% | 0.581 |
67 | 66.67% | 33.33% | 11.23% | 11.11% | 0.579 |
68 | 67.68% | 32.32% | 11.27% | 11.21% | 0.577 |
69 | 68.69% | 31.31% | 11.32% | 11.32% | 0.575 |
70 | 69.70% | 30.30% | 11.36% | 11.43% | 0.573 |
71 | 70.71% | 29.29% | 11.40% | 11.54% | 0.571 |
72 | 71.72% | 28.28% | 11.45% | 11.66% | 0.569 |
73 | 72.73% | 27.27% | 11.49% | 11.77% | 0.566 |
74 | 73.74% | 26.26% | 11.54% | 11.89% | 0.564 |
75 | 74.75% | 25.25% | 11.58% | 12.01% | 0.562 |
76 | 75.76% | 24.24% | 11.63% | 12.13% | 0.560 |
77 | 76.77% | 23.23% | 11.67% | 12.26% | 0.557 |
78 | 77.78% | 22.22% | 11.72% | 12.38% | 0.555 |
79 | 78.79% | 21.21% | 11.76% | 12.51% | 0.552 |
80 | 79.80% | 20.20% | 11.81% | 12.64% | 0.550 |
81 | 80.81% | 19.19% | 11.85% | 12.77% | 0.548 |
82 | 81.82% | 18.18% | 11.90% | 12.90% | 0.545 |
83 | 82.83% | 17.17% | 11.94% | 13.03% | 0.543 |
84 | 83.84% | 16.16% | 11.99% | 13.17% | 0.540 |
85 | 84.85% | 15.15% | 12.03% | 13.30% | 0.538 |
86 | 85.86% | 14.14% | 12.08% | 13.44% | 0.535 |
87 | 86.87% | 13.13% | 12.12% | 13.58% | 0.533 |
88 | 87.88% | 12.12% | 12.16% | 13.72% | 0.530 |
89 | 88.89% | 11.11% | 12.21% | 13.86% | 0.528 |
90 | 89.90% | 10.10% | 12.25% | 14.00% | 0.525 |
91 | 90.91% | 9.09% | 12.30% | 14.14% | 0.523 |
92 | 91.92% | 8.08% | 12.34% | 14.29% | 0.520 |
93 | 92.93% | 7.07% | 12.39% | 14.43% | 0.518 |
94 | 93.94% | 6.06% | 12.43% | 14.58% | 0.516 |
95 | 94.95% | 5.05% | 12.48% | 14.73% | 0.513 |
96 | 95.96% | 4.04% | 12.52% | 14.87% | 0.511 |
97 | 96.97% | 3.03% | 12.57% | 15.02% | 0.508 |
98 | 97.98% | 2.02% | 12.61% | 15.17% | 0.506 |
99 | 98.99% | 1.01% | 12.66% | 15.32% | 0.504 |
100 | 100.00% | 0.00% | 12.70% | 15.48% | 0.501 |
*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. |