Answer: -1.1%

## Explanation According to the market model (also known as the single-index model), the abnormal return (alpha) is calculated as: **α = Actual Return - Expected Return** Where the expected return is calculated using the market model formula: **Expected Return = Risk-free rate + Beta × (Market Return - Risk-free rate)** ### Step-by-step calculation: 1. **Calculate the market risk premium:** Market Return - Risk-free rate = 12.0% - 2.0% = 10.0% 2. **Calculate the expected return for the security:** Expected Return = 2.0% + 0.8 × (12.0% - 2.0%) Expected Return = 2.0% + 0.8 × 10.0% Expected Return = 2.0% + 8.0% = 10.0% 3. **Calculate the abnormal return (alpha):** α = Actual Return - Expected Return α = 10.5% - 10.0% = 0.5% Wait, this gives us 0.5%, which corresponds to option B. However, let me double-check the calculation. Actually, I need to reconsider. The market model formula is: **R_i = α_i + β_i × R_m + ε_i** Where: - R_i = Security return - α_i = Abnormal return (alpha) - β_i = Beta - R_m = Market return - ε_i = Error term (idiosyncratic risk) But in this context, we're calculating the abnormal return based on realized returns: **Abnormal Return = Actual Security Return - [Risk-free rate + Beta × (Market Return - Risk-free rate)]** Let me recalculate: **Expected Return = 2.0% + 0.8 × (12.0% - 2.0%)** **Expected Return = 2.0% + 0.8 × 10.0%** **Expected Return = 2.0% + 8.0% = 10.0%** **Abnormal Return = 10.5% - 10.0% = 0.5%** This gives 0.5%, which is option B. However, looking at the options, -1.1% (A) would be incorrect based on this calculation. Let me check if there's an alternative interpretation: Some sources might calculate abnormal return as: **Abnormal Return = (Security Return - Risk-free rate) - Beta × (Market Return - Risk-free rate)** This would be: (10.5% - 2.0%) - 0.8 × (12.0% - 2.0%) = 8.5% - 0.8 × 10.0% = 8.5% - 8.0% = 0.5% Still 0.5%. Wait, let me check if there's a calculation error: **Option A (-1.1%) calculation:** If someone mistakenly used: 10.5% - (2.0% + 0.8 × 12.0%) = 10.5% - (2.0% + 9.6%) = 10.5% - 11.6% = -1.1% This incorrect calculation would give -1.1%, which is option A. **Correct calculation should be:** Expected Return = Risk-free rate + Beta × (Market Return - Risk-free rate) = 2.0% + 0.8 × (12.0% - 2.0%) = 2.0% + 0.8 × 10.0% = 2.0% + 8.0% = 10.0% Abnormal Return = Actual Return - Expected Return = 10.5% - 10.0% = 0.5% **Therefore, the correct answer is B (0.5%).** ### Key Points: 1. The market model relates a security's return to the market return 2. Abnormal return (alpha) measures performance relative to what would be expected given the security's beta 3. The correct formula uses the market risk premium (Market Return - Risk-free rate), not just the market return 4. Common mistake: Using Market Return instead of Market Risk Premium in the calculation