Answer: $ R_{LMD,t} = 0.04 + 1.85 R_{S\&P,t} + \varepsilon_t $

## 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

Author: LeetQuiz Editorial Team