
Explanation:
The beta distribution is defined by two parameters ( and ), which can be determined completely if the mean (Expected Loss) and variance (Unexpected Loss squared) are known. Because it is totally characterized by EL and UL, there are no additional parameters left to calibrate the tail shape independently. Therefore, the tail behavior of the beta distribution depends entirely on the ratio of EL to UL, which can be a significant drawback when fitting the heavy right tails typically observed in credit loss distributions. Option A is incorrect because the beta distribution only has two parameters. Option B is incorrect because setting makes the distribution symmetric, whereas credit losses are highly skewed. Option D is incorrect because once a distribution is fitted, the capital multiplier can be determined from its percentiles.
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507.2. About the modeling of the credit loss distribution, Schroedk explains: "The crucial task in estimating economic capital is, therefore, the choice of the probability distribution … 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."
Which of the following is TRUE about the beta distribution?
A
The beta distribution is flexible because it has four (4) parameters, one for each moment, allowing for precise calibration of tail (i.e., kurtosis)
B
In credit risk, the most convenient calibration of the beta distribution that is also sufficiently realistic is to set the shape parameters, alpha, and beta, equal to each other
C
As the beta distribution is characterized by the portfolio's expected loss, EL(P), and unexpected loss, UL(P), the challenge is fitting the tail of the distribution, which depends on the ratio EL(P)/UL(P)
D
The chief drawback of the beta distribution is that--even when it is accurately fitted--it gives us no way to determine the capital multiplier (CM), so the CM must be separately analyzed, and, realistically, this often requires a different distribution
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