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Answer: IR for Fund 1 = 0.212, IR for Fund 2 = 0.155; Fund 1 performed better as it has a higher IR.
## Explanation The information ratio (IR) measures the excess return per unit of tracking error and is calculated as: \[ IR = \frac{E(R_p - R_b)}{\text{Tracking Error}} \] Where: - \(E(R_p - R_b)\) is the average excess return (portfolio return minus benchmark return) - Tracking Error is the standard deviation of the excess returns **Calculations:** **Fund 1:** - Average excess return = 0.073% = 0.00073 - Tracking error = 0.344% = 0.00344 - IR = 0.00073 / 0.00344 = 0.212 **Fund 2:** - Average excess return = 0.053% = 0.00053 - Tracking error = 0.341% = 0.00341 - IR = 0.00053 / 0.00341 = 0.155 **Interpretation:** - Fund 1 has an IR of 0.212 - Fund 2 has an IR of 0.155 - Since Fund 1 has a higher information ratio (0.212 > 0.155), it achieved higher returns more efficiently relative to its tracking error - A higher IR indicates better risk-adjusted performance and suggests the fund manager is more 'informed' in their investment decisions Therefore, Fund 1 performed better as it generated more excess return per unit of tracking risk.
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An analyst is analyzing the historical performance of two commodity funds tracking the Reuters/Jeffries-CRB® Index as benchmark. The analyst collated the data on the monthly returns and decided to use the information ratio (IR) to assess which fund achieved higher returns more efficiently, and presented the findings as shown below:
| Fund 1 | Fund 2 | Benchmark returns | |
|---|---|---|---|
| Average monthly return | 1.488% | 1.468% | 1.415% |
| Average excess return | 0.073% | 0.053% | 0.000% |
| Standard deviation of returns | 0.294% | 0.237% | 0.238% |
| Tracking error | 0.344% | 0.341% | 0.000% |
What is the information ratio for each fund, and what conclusion can be drawn?
A
IR for Fund 1 = 0.212, IR for Fund 2 = 0.155; Fund 1 performed better as it has a higher IR.
B
IR for Fund 1 = 0.212, IR for Fund 2 = 0.155; Fund 2 performed better as it has a lower IR.
C
IR for Fund 1 = 0.248, IR for Fund 2 = 0.224; Fund 1 performed better as it has a higher IR.
D
IR for Fund 1 = 0.248, IR for Fund 2 = 0.224; Fund 2 performed better as it has a lower IR.
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