Financial Risk Manager Part 1

Explanation

The correlation coefficient is calculated using the formula:

$\text{Corr}(R_x, R_y) = \frac{\text{Cov}(R_x, R_y)}{\sigma(R_x) \cdot \sigma(R_y)}$

Given:

• Covariance: Cov(Rₓ, Rᵧ) = 0.093
• Variance of Rₓ = 0.69
• Variance of Rᵧ = 0.36

First, we need to calculate the standard deviations:

• σ(Rₓ) = √(Variance of Rₓ) = √0.69 = 0.8306
• σ(Rᵧ) = √(Variance of Rᵧ) = √0.36 = 0.6

Now, plug into the correlation formula:

$\text{Corr}(R_x, R_y) = \frac{0.093}{0.8306 \times 0.6} = \frac{0.093}{0.49836} = 0.1865$

Therefore, the correlation coefficient is 0.1865, which corresponds to option B.

Key points:

1. Correlation is the standardized version of covariance
2. Standard deviation is the square root of variance
3. The correlation coefficient ranges from -1 to +1
4. This positive correlation (0.1865) indicates that when Stock X's returns increase, Stock Y's returns tend to increase slightly as well, though the relationship is relatively weak.