Extreme Events – Specimen Question A.4.2
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Question and Answer Summary
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.
Answer/Hints
(b) Given a linear
combination of Index A and B what is the maximum possible kurtosis of a linear
combination of A and B?
Answer/Hints
(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.
Answer/Hints
(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?
Answer/Hints
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