Extreme Events – Specimen Question A.2.1
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Question and Answer Summary
You are an investor seeking to understand the behaviour of Index A:
(a) Calculate the
mean, (sample) standard deviation, skew and (excess) kurtosis of its log
returns over the period covered by the above table.
(b) Do the statistics
calculated in (a) appear to characterise a fat-tailed distribution if we adopt
the null hypothesis that the log returns would otherwise be coming from a
normal distribution and we use the limiting form of the distributions for these
test statistics (i.e. the form ruling when , where is the
number of observations)?
(c) Prepare a
standardised quantile-quantile plot for Index A. Does it appear to be fat-tailed?
(d) Does the
Cornish-Fisher 4th moment approximation appear to under or overstate the
fat-tailed behaviour of this series?
(e) What other
methodologies could you use to formulate a view about how fat-tailed this
return series might be if your focus was principally on fat-tailed behaviour
around or below the lower 10th percentile quantile level?
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