Explanation:
In a quantile regression framework for VaR validation, a well-specified model implies that the VaR estimates accurately reflect the corresponding quantiles of the portfolio return distribution. This translates to an intercept of zero (no bias in the VaR estimates) and a slope of one (a one-to-one relationship between the VaR and the portfolio return quantile). Any deviation from these values suggests model misspecification.
A is incorrect. These values would imply a constant VaR equal to 1, regardless of portfolio returns.
B is incorrect. These values would imply a VaR of zero, regardless of portfolio returns.
D is incorrect. While a slope of 1 is correct, an intercept of 1 would imply a consistent upward bias in the VaR estimates.
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Q.6472 When evaluating a VaR model using quantile regression, we regress the VaR estimate on the observed change in portfolio value. Under the null hypothesis of a well-specified VaR model, what are the expected values of the intercept (α₀) and the slope (α₁) in this regression?
A
α₀ = 1, α₁ = 0
B
α₀ = 0, α₁ = 0
C
α₀ = 0, α₁ = 1
D
α₀ = 1, α₁ = 1
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