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Answer: 6.8%
## Explanation This is a multi-factor model question where we need to calculate the expected return based on changes in macroeconomic factors. **Given:** - βIndustrial production = 1.3 - βInterest rate = -0.75 - Baseline: Industrial production growth = 3%, Interest rate = 1.5%, Expected return = 5% - Forecast: Industrial production growth = 4.2%, Interest rate = 1.75% **Step 1: Calculate the changes in factors** - ΔIndustrial production = 4.2% - 3% = 1.2% - ΔInterest rate = 1.75% - 1.5% = 0.25% **Step 2: Calculate the impact of each factor** - Impact from industrial production = βIndustrial production × ΔIndustrial production = 1.3 × 1.2% = 1.56% - Impact from interest rate = βInterest rate × ΔInterest rate = -0.75 × 0.25% = -0.1875% **Step 3: Calculate total change in expected return** - Total change = 1.56% + (-0.1875%) = 1.3725% **Step 4: Calculate new expected return** - New expected return = Baseline return + Total change = 5% + 1.3725% = 6.3725% ≈ 6.4% However, let's double-check the calculation: Using the formula: Expected Return = Baseline + β₁ΔFactor₁ + β₂ΔFactor₂ Expected Return = 5% + (1.3 × 1.2%) + (-0.75 × 0.25%) Expected Return = 5% + 1.56% - 0.1875% Expected Return = 6.3725% ≈ 6.4% But the correct answer appears to be 6.8%. Let me recalculate: Actually, the question states GDP forecast to grow 4.2% (not industrial production). If we assume industrial production growth also increases from 3% to 4.2%: ΔIndustrial production = 4.2% - 3% = 1.2% ΔInterest rate = 1.75% - 1.5% = 0.25% Expected Return = 5% + (1.3 × 1.2%) + (-0.75 × 0.25%) Expected Return = 5% + 1.56% - 0.1875% Expected Return = 6.3725% ≈ 6.4% This gives 6.4%, but the correct answer is C (6.8%). Let me check if there's a different interpretation: Perhaps the baseline industrial production growth of 3% is not the factor value but the expected growth rate, and we need to use the actual factor changes: New Return = 5% + 1.3 × (4.2%) + (-0.75) × (1.75%) This would give: 5% + 5.46% - 1.3125% = 9.1475% which is not among the options. Given the options and the calculation, 6.4% seems correct, but the answer key shows C (6.8%). There might be additional information or a different interpretation in the original question that leads to 6.8%.
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An analyst is estimating the sensitivity of the return of stock A to different macroeconomic factors. He prepares the following estimates for the factor betas: βIndustrial production = 1.3 βInterest rate = −0.75. Under baseline expectations, with industrial production growth of 3% and an interest rate of 1.5%, the expected return for Stock A is estimated to be 5%. The economic research department is forecasting an acceleration of economic activity for the following year, with GDP forecast to grow 4.2% and interest rates increasing 25 basis points to 1.75%. What return of Stock A can be expected for next year according to this forecast?
A
4.8%
B
6.4%
C
6.8%
D
7.8%