Explanation:
Statement A is false. The beta distribution's primary advantage is its flexibility; it can be symmetric (if ) or highly skewed (if ) solely based on its two shape parameters ( and ). It does not require a third parameter to be skewed.
Statements B, C, and D are all true aspects highlighted by Schroeck regarding the practical application and constraints of the beta distribution in modeling credit loss distributions.
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922.2. Schroeck writes that "[t]he crucial task in estimating economic capital is, therefore, the choice of the probability distribution, because we are only interested in the tail of this distribution. Credit risks are not normally distributed but highly skewed because, as mentioned previously, the upward potential is limited to receiving at maximum the promised payments and only in very rare events to losing a lot of money. One distribution often recommended and suitable for this practical purpose is the beta distribution. This kind of distribution is especially useful in modeling a random variable that varies between 0 and c (> 0). And, in modeling credit events, losses can vary between 0 and 100%, so that c = 1. The beta distribution is extremely flexible in the shapes of the distribution it can accommodate."
In regard to the beta distribution, each of the following statements is true EXCEPT, which is false?
A
The beta distribution is symmetric for all values of alpha and beta but can only be skewed if we add a third parameter
B
The beta distribution is a continuous approximation of a binomial distribution (the sum of independent two-point distributions)
C
For high-quality portfolios—i.e., when EL(portfolio) is greater than UL(portfolio)—the beta distribution has too fat a tail and is likely to overestimate economic capital
D
For low-quality portfolios—i.e., when EL(portfolio) is less than UL(portfolio)—the beta distribution has too thin a tail and is likely to underestimate economic capital
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