
Explanation:
The Information Ratio (IR) is calculated as the expected active return divided by the tracking error (which is the standard deviation of the active returns).
First, let's calculate the active return for each year (Portfolio Return - Benchmark Return): Year 1: 0.072 - 0.070 = 0.002 Year 2: 0.052 - 0.054 = -0.002 Year 3: 0.052 - 0.047 = 0.005 Year 4: 0.060 - 0.060 = 0.000 Year 5: 0.048 - 0.033 = 0.015
Next, we find the mean (average) active return: Mean Active Return = (0.002 - 0.002 + 0.005 + 0.000 + 0.015) / 5 = 0.020 / 5 = 0.004 (or 0.4%)
Then, we calculate the standard deviation (tracking error) of these active returns: Squared deviations from the mean: Year 1: (0.002 - 0.004)^2 = (-0.002)^2 = 0.000004 Year 2: (-0.002 - 0.004)^2 = (-0.006)^2 = 0.000036 Year 3: (0.005 - 0.004)^2 = (0.001)^2 = 0.000001 Year 4: (0.000 - 0.004)^2 = (-0.004)^2 = 0.000016 Year 5: (0.015 - 0.004)^2 = (0.011)^2 = 0.000121
Sum of squared deviations = 0.000004 + 0.000036 + 0.000001 + 0.000016 + 0.000121 = 0.000178 Sample variance = 0.000178 / (5 - 1) = 0.000178 / 4 = 0.0000445 Sample standard deviation (Tracking Error) =
Finally, Information Ratio = Mean Active Return / Tracking Error IR = 0.004 / 0.00667 0.59`96, which rounds to 0.60.
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| Year | Portfolio rate of return | Benchmark rate of return | Portfolio beta with respect to the benchmark |
|---|---|---|---|
| 1 | 0.072 | 0.070 | 0.92 |
| 2 | 0.052 | 0.054 | 0.88 |
| 3 | 0.052 | 0.047 | 0.90 |
| 4 | 0.060 | 0.060 | 0.84 |
| 5 | 0.048 | 0.033 | 0.89 |
What is the approximate value of the manager’s information ratio?
A
1.08
B
0.60
C
0.90
D
0.20
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