Estimation of Market Risk measures
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It will underestimate the true VaR because, delta-normal method assumes that the return distribution is normal, that is, it assumes that large negative returns are less likely compared to a fat tailed distribution.
Hope this helps.
Hope this helps.
I agree with @Gyilmaz 's answer because the question specifically states "in the presence of fat tails," but I just want to point out that the "delta-normal method" contains two assumptions: 1. the returns that are jointly normal and 2. exposures can be approximated by delta.
That's two effects. Fat tails imply that (normal) VaR will understimate, but non-linearities exploit the second assumptions. Think about options or bonds (or marginal VaR, for that matter). For a long call option position, delta over-estimates the exposure (because it neglects gamma); for a long bond position, duration over-estimates the exposure (because it neglects convexity). Similarly, component VaR (based on marginal VaR, an essentially delta-type concept as it is a linear approximation) will tend to over-estimate the true portfolio exposure; i.e., will tend to be greater than incremental VaR. So, we could argue that the answer here is unclear. Thanks!
P.S. Append: Geez, I just noticed that the question says "for a linear portfolio" ... the intent of that is to nullify the second assumption (or to rule-out non-linear exposures is what I mean), so please ignore my caveat! I think @Gyilmaz answer does not require further clarification. Apologies ...
That's two effects. Fat tails imply that (normal) VaR will understimate, but non-linearities exploit the second assumptions. Think about options or bonds (or marginal VaR, for that matter). For a long call option position, delta over-estimates the exposure (because it neglects gamma); for a long bond position, duration over-estimates the exposure (because it neglects convexity). Similarly, component VaR (based on marginal VaR, an essentially delta-type concept as it is a linear approximation) will tend to over-estimate the true portfolio exposure; i.e., will tend to be greater than incremental VaR. So, we could argue that the answer here is unclear. Thanks!
P.S. Append: Geez, I just noticed that the question says "for a linear portfolio" ... the intent of that is to nullify the second assumption (or to rule-out non-linear exposures is what I mean), so please ignore my caveat! I think @Gyilmaz answer does not require further clarification. Apologies ...
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David's explanation for portfolios with nonlinear payoffs is more important than the linear case because an exam question on this topic is more likely to test the nonlinear case which requires a deeper understanding.
Thanks @David Harper CFA FRM CIPM @Gyilmaz
Explanation on Non linear exposure was very valuable even though question ruled out non linear exposures.
Thanks again!!!!
Explanation on Non linear exposure was very valuable even though question ruled out non linear exposures.
Thanks again!!!!
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