Explanation

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

Step 1: Calculate Beta (β)

The beta coefficient in a simple linear regression is calculated as:

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

Given:

• Covariance = 6%
• 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 alpha intercept is calculated as:

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

Given:

• Mean return for LMD = 11%
• Mean return for S&P 500 = 7%
• β = 1.85

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

Step 3: Final Regression Equation

The regression model is:

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

This matches Option D.

Note: Option B has the correct beta (1.85) but the wrong alpha (-0.02 instead of 0.04). Option D has both the correct beta and alpha values.