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Which of the following statements are true:
1. A transition matrix is the probability of a security migrating from one rating class to another during its lifetime.
2. Marginal default probabilities refer to probabilities of default in a particular period, given survival at the beginning of that period.
3. Marginal default probabilities will always be greater than the corresponding cumulative default probability.
4. Loss given default is generally greater when recovery rates are low.
Statement I is incorrect. A transition matrix expresses the probabilities of moving to a given set of ratings at the end of a period (usually one year) conditional upon a given rating at the beginning of the period. It does not make a reference to an individual security and certainly not to the probability of migrating to other ratings during its entire lifetime.
Statement II is correct. Marginal default probabilities are the probability of default in a given year, conditional upon survival at the beginning of that year.
Statement III is incorrect. Cumulative probabilities of default will always be greater than the marginal probabilities of default - except in year 1 when they will be equal.
Statement IV is correct. LGD = 1 - Recovery Rate, therefore a low recovery rate implies higher LGD.