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.




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




(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.




(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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