Explanation:
B is correct. The probability matrix is a tabular representation of a probability mass function (PMF) that relates the outcomes of a bond's return profile and its classification.
A is incorrect: The probability matrix represents a PMF, not a cumulative distribution function (CDF). A CDF shows cumulative probabilities up to certain values, while a PMF shows probabilities of specific outcomes.
C is incorrect: Each cell contains the probability that a combination of two outcomes is realized (return profile and classification), not three outcomes.
D is incorrect: The marginal distribution is computed by summing across rows or columns, not multiplying. For example, to get the marginal distribution of bond classifications, you would sum the probabilities across all return profiles for each classification type.
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A junior fixed-income analyst at an investment management firm is evaluating the credit quality of a diversified bond portfolio consisting of bonds classified as investment grade, high-yield, or unrated. Upon observing that the expected return profile of a bond appears to be related to its classification, the analyst constructs a probability matrix to assign probabilities to different combinations of a bond's return profile and its classification. Which of the following correctly describes this probability matrix?
A
The probability matrix is a multivariate representation of a cumulative density function (CDF) which relates the outcomes of a bond's return profile and its classification.
B
The probability matrix is a tabular representation of the probability mass function (PMF) which relates the outcomes of a bond's return profile and its classification.
C
Each cell in the probability matrix contains the probability that a combination of three outcomes is realized.
D
The marginal distribution of a random variable in the probability matrix can be computed by multiplying the probability of the three classification outcomes.
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