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%.