Explanation:
The information ratio (IR) is calculated as:
IR = Average excess returns / Standard deviation of excess returns
First, we need to calculate the excess returns for each year:
| Year | Portfolio Return | Benchmark Return | Beta | Excess Return |
|---|---|---|---|---|
| 1 | 0.072 | 0.070 | 0.92 | 0.072 - 0.070 = 0.002 |
| 2 | 0.052 | 0.054 | 0.88 | 0.052 - 0.054 = -0.002 |
| 3 | 0.052 | 0.047 | 0.90 | 0.052 - 0.047 = 0.005 |
| 4 | 0.060 | 0.060 | 0.84 | 0.060 - 0.060 = 0.000 |
| 5 | 0.048 | 0.033 | 0.89 | 0.048 - 0.033 = 0.015 |
Step 1: Calculate Average Excess Return Average = (0.002 + (-0.002) + 0.005 + 0.000 + 0.015) / 5 = 0.020 / 5 = 0.004
Step 2: Calculate Standard Deviation of Excess Returns Variance = [(0.002-0.004)² + (-0.002-0.004)² + (0.005-0.004)² + (0.000-0.004)² + (0.015-0.004)²] / 4 = [( -0.002)² + (-0.006)² + (0.001)² + (-0.004)² + (0.011)²] / 4 = [0.000004 + 0.000036 + 0.000001 + 0.000016 + 0.000121] / 4 = 0.000178 / 4 = 0.0000445
Standard deviation = √0.0000445 = 0.00667
Step 3: Calculate Information Ratio IR = 0.004 / 0.00667 = 0.599 ≈ 0.60
Why other options are incorrect:
Ultimate access to all questions.
A portfolio manager at a hedge fund manages an equity portfolio that is benchmarked to an index. The information on the performance of the portfolio and the benchmark over the last 5 years is provided below:
| 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
0.20
B
0.60
C
0.90
D
1.08
No comments yet.