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.
Answer/Hints
(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)?
Answer/Hints
(c) Prepare a
standardised quantile-quantile plot for Index A. Does it appear to be fat-tailed?
Answer/Hints
(d) Does the
Cornish-Fisher 4th moment approximation appear to under or overstate the
fat-tailed behaviour of this series?
Answer/Hints
(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?
Answer/Hints
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