Explanation

To solve this regression problem, we need to calculate the beta coefficient (β) and the intercept (α) using the given data.

Step 1: Calculate Beta (β)

The formula for beta in a simple linear regression is:

$$\beta = \frac{\text{Cov}(R_{LMD}, R_{S\&P})}{\text{Var}(R_{S\&P})}$$

Given:

• Covariance = 6% = 0.06
• Variance of S&P 500 = (Volatility)^2 = (18%)^2 = 0.0324

$$\beta = \frac{0.06}{0.0324} = 1.85185 \approx 1.85$$

Step 2: Calculate Alpha (α)

The formula for the intercept is:

$$\alpha = \bar{R}_{LMD} - \beta \times \bar{R}_{S\&P}$$

Given:

• Mean return for LMD = 11% = 0.11
• Mean return for S&P 500 = 7% = 0.07

$$\alpha = 0.11 - 1.85 \times 0.07 = 0.11 - 0.1295 = -0.0195 \approx -0.02$$

Step 3: Construct the Regression Model

$$R_{LMD,t} = -0.02 + 1.85 R_{S\&P,t} + \varepsilon_t$$

This matches Option D.

Key Points:

• Beta represents the sensitivity of LMD returns to S&P 500 returns
• A beta of 1.85 indicates LMD is more volatile than the market
• The negative intercept suggests that when S&P 500 returns are zero, LMD tends to have slightly negative returns