Explanation:
We need to calculate β₂ using the formula: βᵢ = ρᵢ/σₚ
From the given information:
Step 1: Use the relationship between Marginal VaR and β
The marginal VaR is related to β by: Marginal VaRᵢ = βᵢ × (Portfolio VaR / Portfolio Value)
Step 2: Calculate β₂
Marginal VaR₂ = β₂ × (Portfolio VaR / Portfolio Value) 0.440 = β₂ × (61.6 / 200) 0.440 = β₂ × 0.308 β₂ = 0.440 / 0.308 = 1.429
Step 3: Verification
We can verify this makes sense:
Therefore, β₂ = 1.429
This matches option B.
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Let βᵢ = ρᵢ/σₚ, where ρ denotes the correlation between the return of asset i and the return of the portfolio, σᵢ is the volatility of the return of asset i and σₚ is the volatility of the return of the portfolio. What is β₂?
A
0.714
B
1.429
C
1.513
D
Cannot determine from information provided.