Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
An analyst is trying to establish the relationship between the return on stock (X) (R_X) and the return on stock (S)(R_s). 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?
Other
Community
NNikitesh
A
B
C
D
None of the above
Explanation:
The correct answer is B:
Explanation:
- Model Setup: The linear regression model is given as:
Taking expectations (since ):
E(R_X) = a + b \times E(R_S) $`$2`. **Calculating Slope Coefficient (b):**
The slope coefficient in OLS regression is calculated as: b = \frac{\text{Cov}(R_S, R_X)}{\text{Var}(R_S)} Since correlation $\rho = \frac{\text{Cov}(R_S, R_X)}{\sigma_S \sigma_X}$, we can write: \text{Cov}(R_S, R_X) = \rho \times \sigma_S \times \sigma_X b = \frac{\rho \times \sigma_S \times \sigma_X}{\sigma_S^2} = \rho \times \frac{\sigma_X}{\sigma_S} b = 0.3 \times \frac{0.20}{0.15} = 0.3 \times 1.3333 = 0.40 3
. **Calculating Intercept (a):** The intercept is calculated using the means: $$ a = \bar{R}_X - b \times \bar{R}_S $$ Substituting the given values: $$ a = 0.15 - 0.40 \times 0.10 = 0.15 - 0.04 = 0.11 $$4`. Final Model:
Verification of Other Options:
- Option A:
$0.40+ 0.40 \times E(R_S)$ - Incorrect intercept - Option C:
$0.40+ 0.11 \times E(R_S)$ - Incorrect intercept and slope - Option D: None of the above - Incorrect since Option B is correct
Comments
Loading comments...