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Extreme Events – Specimen Question A.4.2

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You are an investor trying to understand better the joint behaviour of Indices A and B in Exercise A.2.1:

 

(a)    Identify the series corresponding to the principal components of Indices A and B.

 

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(b)   Given a linear combination of Index A and B what is the maximum possible kurtosis of a linear combination of A and B?

 

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(c)    More generally, can you identify two series where the linear combination of the series with the least variance is also the one with the maximum kurtosis? Hint: try identifying two series with very few terms in them as it simplifies the relevant mathematics.

 

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(d)   What lessons might you draw from (c) in terms of use of variance or variance-related risk statistics when used to estimate the likelihood of extreme events?

 

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