Explanation:
B is correct. The probability matrix relates realizations to probabilities; that is, it is a tabular representation of a PMF.
A is incorrect. The probability matrix is a tabular representation of a PMF, not a CDF.
C is incorrect. Each cell contains the probability that the combination of two outcomes (the realization of the first component/column variable, which is the return, and the realization of the second component/row variable, which is the classification) is realized.
D is incorrect. When a PMF is represented as a probability matrix, the marginal distribution of a random variable can be computed from the joint distribution by summing across columns (which constructs the marginal distributions of the row variables) or summing down rows (which constructs the marginal PMF for the column variables).
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Q-89. 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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