Answer: 5.5%

## Understanding the 2-Factor Model Before analyzing the options, let me explain the framework. In a **multi-factor model**, the actual return of an asset can be decomposed into: $$R = E(R) + \beta_1 \cdot F_1 + \beta_2 \cdot F_2 + \varepsilon$$ Where: - **E(R)** = Initial expected return (based on consensus forecasts) - **β** = Factor sensitivities (betas) - **F** = Factor surprises (actual value minus expected value) - **ε** = Firm-specific (idiosyncratic) return --- ## Step-by-Step Calculation ### Step 1: Calculate Factor Surprises **GDP Surprise:** $$F_{GDP} = \text{Actual GDP} - \text{Consensus GDP} = 5\% - 6\% = -1\%$$ **Interest Rate Surprise:** $$F_{Interest} = \text{Actual Rate} - \text{Consensus Rate} = 4\% - 3\% = 1\%$$ ### Step 2: Apply the 2-Factor Model The revised return is calculated as: $$R_{revised} = E(R) + \beta_{GDP} \times F_{GDP} + \beta_{Interest} \times F_{Interest} + \varepsilon$$ Substituting the values: $$R_{revised} = 10\% + (1.5 \times -1\%) + (-1.00 \times 1\%) + (-2\%)$$ $$R_{revised} = 10\% - 1.5\% - 1\% - 2\%$$ $$R_{revised} = 10\% - 4.5\% = \mathbf{5.5\%}$$ --- ## Analysis of Each Option ### Option A: 1.5% ❌ **Incorrect** This would imply a total adjustment of -8.5% from the initial 10% expected return. There is no standard interpretation of the 2-factor model that would yield this result given the provided data. This answer appears to be incorrectly stated as the correct answer in the question key. ### Option B: 3.5% ❌ **Incorrect** This would require a total adjustment of -6.5%. While closer than Option A, this still does not match the correct factor model calculation. One possible error that could lead to this answer is forgetting to include the GDP surprise (-1%) or miscalculating the interest rate effect. ### Option C: 5.5% ✅ **Correct** This is the correct answer based on the standard 2-factor model calculation: - Initial expected return: 10% - GDP factor contribution: 1.5 × (-1%) = -1.5% - Interest rate factor contribution: -1.00 × 1% = -1% - Firm-specific return: -2% - **Total: 10% - 1.5% - 1% - 2% = 5.5%** ### Option D: 6.5% ❌ **Incorrect** This would result from a total adjustment of only -3.5%, which would occur if one of the negative components were omitted. A common error leading to this answer is forgetting to include the firm-specific return (-2%). --- ## Key Concept Summary | Component | Calculation | Impact | |-----------|-------------|--------| | Initial Expected Return | Given | +10.0% | | GDP Factor Effect | 1.5 × (-1%) | -1.5% | | Interest Rate Factor Effect | -1.0 × 1% | -1.0% | | Firm-Specific Return | Given | -2.0% | | **Revised Expected Return** | Sum | **5.5%** | --- ## Reference Answer **Based on the standard 2-factor model calculation, the correct answer is Option C: 5.5%.**