Answer: IR for Fund I = 0.212, IR for Fund II = 0.155; Fund I performed better as it has a higher IR.

This question tests your understanding of the **Information Ratio (IR)**, a key performance measure used in portfolio management to assess how efficiently a fund manager generates excess returns relative to a benchmark. --- ## Understanding the Information Ratio The **Information Ratio** measures the risk-adjusted performance of an investment relative to its benchmark. It is calculated as: $$\text{IR} = \frac{\text{Average Excess Return}}{\text{Tracking Error}}$$ Where: - **Average Excess Return** = Fund's average return − Benchmark's average return - **Tracking Error** = Standard deviation of the excess returns (measures how consistently the fund deviates from the benchmark) **Interpretation**: A higher IR indicates better performance because it means the fund generated more excess return per unit of active risk taken. Generally: - IR > 0.5 is considered good - IR > 1.0 is considered excellent - A negative IR indicates underperformance relative to the benchmark --- ## Detailed Option Analysis ### Option A: IR for Fund I = 0.212, IR for Fund II = 0.155; Fund II performed better as it has a lower IR. | Aspect | Evaluation | |--------|------------| | IR Calculations | ✅ **Correct** - The values 0.212 and 0.155 are accurately computed | | Conclusion | ❌ **Incorrect** - The interpretation is wrong | **Why it's wrong**: This option makes a critical error in interpretation. A **lower** Information Ratio does **not** indicate better performance. The IR measures excess return per unit of tracking error, so a higher value means the manager is more efficient at generating alpha. Fund I with IR = 0.212 has outperformed Fund II with IR = 0.155, making Fund I the better performer. --- ### Option B: IR for Fund I = 0.212, IR for Fund II = 0.155; Fund I performed better as it has a higher IR. | Aspect | Evaluation | |--------|------------| | IR Calculations | ✅ **Correct** - Both values are accurately computed | | Conclusion | ✅ **Correct** - The interpretation is accurate | **Calculation verification**: **For Fund I:** $$\text{IR}_I = \frac{0.073\%}{0.344\%} = 0.212$$ **For Fund II:** $$\text{IR}_{II} = \frac{0.053\%}{0.341\%} = 0.155$$ **Why it's correct**: This option correctly calculates the IR for both funds using the appropriate formula (excess return divided by tracking error). The conclusion is also accurate—Fund I's higher IR of 0.212 indicates it generated more excess return per unit of active risk taken compared to Fund II's IR of 0.155. --- ### Option C: IR for Fund I = 0.248, IR for Fund II = 0.224; Fund I performed better as it has a higher IR. | Aspect | Evaluation | |--------|------------| | IR Calculations | ❌ **Incorrect** - Wrong values computed | | Conclusion | ⚠️ Technically correct logic, but based on wrong numbers | **Why it's wrong**: This option uses the **wrong denominator** in the calculation. Let's verify where these incorrect numbers come from: $$\frac{0.073\%}{0.294\%} = 0.248 \quad \text{and} \quad \frac{0.053\%}{0.237\%} = 0.224$$ Notice that 0.294% and 0.237% are the **standard deviations of returns**, not the **tracking errors**. This is a fundamental error because: - The Information Ratio uses **tracking error** (volatility of excess returns), not the standard deviation of total returns - Tracking error specifically measures the consistency of the fund's deviation from its benchmark - Standard deviation measures total volatility, which includes both systematic and idiosyncratic risk --- ### Option D: IR for Fund I = 0.248, IR for Fund II = 0.224; Fund II performed better as it has a lower IR. | Aspect | Evaluation | |--------|------------| | IR Calculations | ❌ **Incorrect** - Uses standard deviation instead of tracking error | | Conclusion | ❌ **Incorrect** - Both the calculation error and interpretation error | **Why it's wrong**: This option combines both errors from Options A and C: 1. Uses the wrong denominator (standard deviation of returns instead of tracking error) 2. Incorrectly interprets that a lower IR indicates better performance This represents a complete misunderstanding of both the calculation and interpretation of the Information Ratio. --- ## Summary Table | Option | IR Calculations | Interpretation | Verdict | |--------|----------------|----------------|---------| | A | ✅ Correct | ❌ Wrong (lower IR ≠ better) | Incorrect | | B | ✅ Correct | ✅ Correct | **Correct Answer** | | C | ❌ Wrong (uses std dev) | ✅ Correct logic | Incorrect | | D | ❌ Wrong (uses std dev) | ❌ Wrong (lower IR ≠ better) | Incorrect | --- ## Key Takeaways for FRM Exam 1. **Formula**: IR = Average Excess Return / Tracking Error (NOT standard deviation of returns) 2. **Interpretation**: Higher IR = Better risk-adjusted performance relative to benchmark 3. **Common traps to avoid**: - Confusing tracking error with standard deviation of returns - Misinterpreting the direction of the ratio (higher is better) - Not distinguishing between Sharpe Ratio (uses total risk) and Information Ratio (uses active risk) --- ## Reference Answer **The correct answer is B.** The Information Ratio for Fund I is 0.212 (0.073% / 0.344%) and for Fund II is 0.155 (0.053% / 0.341%). Fund I performed better because it achieved a higher IR, indicating it generated more excess return per unit of tracking error, demonstrating superior efficiency in active management relative to the benchmark.