Answer-first summary for fast verification
Answer: Binomial
The correct answer is C, Binomial distribution. This is because the scenario involves a fixed number of bonds (random variables), each with the same annualized probability of default. The binomial distribution is used to model the number of successes (in this case, defaults) in a fixed number of independent trials (bonds), where each trial has the same probability of success (default probability). The Bernoulli distribution, option A, describes the outcome of a single trial, not the aggregate outcome of multiple trials. The lognormal distribution, option B, is typically used for modeling asset prices and is not suitable for counting events like defaults. The exponential distribution, option D, models the time until an event occurs, rather than the count of events. Therefore, the binomial distribution is the most appropriate for describing the number of defaults in the portfolio over the next year.
Author: LeetQuiz Editorial Team
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A fixed-income portfolio manager oversees a diverse portfolio consisting of bonds issued by several corporations. It is assumed that each bond within this portfolio has the same annual probability of default. Additionally, the manager believes that the default events of these bonds are mutually independent, meaning the occurrence of a default in one bond does not affect the probability of default in any other bond. Given these conditions, which statistical distribution would be the most appropriate to model the number of bond defaults in this portfolio over the course of the next year?
A
Lognormal
B
Bernoulli
C
Binomial
D
Exponential
