Question on Skewness and Kurtosis calculations

edupristine
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Question on Skewness and Kurtosis calculations

Postby edupristine » Thu Jul 24, 2014 8:44 am

Hi nripraj.2001

First of all, we should be clear with the fact the distribution implied in the given question is Bernoulli distribution.

This is because the bonds can go in only one of the two states. Either the bond will default with 5% probability or it will survive with a 95% probability.

Keeping this distribution in mind,

Skewness = third central moment/ (cube of std deviation)
Kurtosis = fourth central moment/ (fourth power of std deviation)

In the above two formulas, to calculate denominator i.e. standard deviation, first find out the variance of Bernoulli distribution as follows:
Variance = n*p*(1-p)

Variance = 1*95%*5%

Hence standard deviation = sqr root (variance) . Here the value of n=1 because we have a single bond only.

For numerator, please note the below formulas:

Third cross moment for a binomial dist.: p*(1-p)^3 + (1-p)*p^3 where p = 0.95

Similarly, Fourth cross moment for a binomial dist.: p*(1-p)^4 + (1-p)*p^4 where again, p= 0.95

After substituting the values, the answer would be option (c).

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