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Extreme Events – Specimen Question A.2.1

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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.

 

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(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)?

 

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(c)    Prepare a standardised quantile-quantile plot for Index A. Does it appear to be fat-tailed?

 

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(d)   Does the Cornish-Fisher 4th moment approximation appear to under or overstate the fat-tailed behaviour of this series?

 

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(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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