Answer-first summary for fast verification
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 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.
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Samantha Xiao is trying to get some insight into the relationship between the return on stock LMD () and the return on the S&P 500 index (). Using historical data she estimates the following:
Assuming she uses the same data to estimate the regression model given by:
Using the ordinary least squares technique, which of the following models will she obtain?
A
B
C
D
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