Answer-first summary for fast verification
Answer: $ E(R_x) = 0.11 + 0.40 \times E(R_s) $
## Explanation For the linear regression model: $$ R_x = a + b \times R_s + \epsilon_t $$ The expected value equation becomes: $$ E(R_x) = a + b \times E(R_s) $$ To find the coefficients using ordinary least squares: ### Step 1: Calculate the slope coefficient (b) $$ b = \frac{\text{Cov}(R_s, R_x)}{\text{Var}(R_s)} = \frac{[\text{Corr}(R_s, R_x) \times SD(R_s) \times SD(R_x)]}{\text{Var}(R_s)} = \text{Corr}(R_s, R_x) \times \frac{SD(R_x)}{SD(R_s)} $$ Given: - Correlation = 0.3 - SD(R_x) = 20% = 0.20 - SD(R_s) = 15% = 0.15 $$ b = 0.3 \times \frac{0.20}{0.15} = 0.3 \times 1.333 = 0.40 $$ ### Step 2: Calculate the intercept (a) $$ a = \bar{R_x} - b \times \bar{R_s} = 0.15 - 0.40 \times 0.10 = 0.15 - 0.04 = 0.11 $$ ### Step 3: Final Model $$ E(R_x) = 0.11 + 0.40 \times E(R_s) $$ This matches option B exactly.
Author: Tanishq Prabhu
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An analyst is trying to establish the relationship between the return on stock X(Rx) and the return on stock S(Rs). Stock X is listed on the Bombay Stock Exchange (BSE). The analyst has assumed a linear relationship as follows.
Furthermore, the analyst has gathered the following historical data.
| Expected return on stock X | 15% |
|---|---|
| Expected return on S | 10% |
| Standard deviation of return on stock X | 20% |
| Standard deviation of return on stock S | 15% |
| Correlation between returns on stock X and S | 0.3 |
Which of the following is the correct model that can be deduced using the ordinary least squares technique?
A
B
C
D
None of the above
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