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.
Two stocks, X and Y, have a correlation of 0.50. Stock Y's return has a standard deviation of 0.26. Given that the covariance between X and Y is 0.005, determine the variance of returns for stock X.
Other
Community
NNikitesh
A
0.13
B
0.00148
C
0.0385
D
0.0148
Explanation:
Step-by-step solution:
-
Given values:
- Correlation between X and Y, ρ(X,Y) = 0.50
- Standard deviation of Y, σᵧ = 0.26
- Covariance between X and Y, Cov(X,Y) = 0.005
- We need to find variance of X, Var(X) = σₓ²
-
Correlation formula: ρ(X,Y) = Cov(X,Y) / (σₓ × σᵧ)
-
Substitute known values: 0.50 = 0.005 / (σₓ × 0.26)
-
Solve for σₓ: σₓ × 0.26 = 0.005 / 0.50 σₓ × 0.26 = 0.01 σₓ = 0.01 / 0.26 σₓ = 0.0384615 ≈ 0.0385
-
Calculate variance of X: Var(X) = σₓ² = (0.0385)² = 0.00148225 ≈ 0.00148
Key points:
- Correlation is the standardized covariance
- Variance is the square of standard deviation
- The calculation requires solving for the unknown standard deviation first, then squaring it to get variance
- Option C (0.0385) is the standard deviation, not the variance
- Option D (0.0148) is off by a factor of 10
- Option A (0.13) is incorrect
Comments
Loading comments...