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Explanation:
To estimate a transition matrix for a three-month period from a one-year matrix, the fourth root of the one-year matrix should be taken. This reflects a shorter time fraction of a year and provides an estimate for the quarterly transition probabilities.
A is incorrect. Dividing the matrix probabilities by four does not accurately translate annual probabilities into quarterly ones.
B is incorrect. While empirical data is important, recalculating the matrix is not necessary when mathematical transformations like taking roots can be applied.
D is incorrect. Assuming that one-year probabilities are constant for all time periods does not adjust for the lower likelihood of transitions occurring over shorter timeframes.
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Q.6034 A risk manager needs to calculate the Credit VaR for a bond portfolio, which includes only 'A' rated bonds, using a rating transition matrix. If the manager wants to adjust this one-year transition matrix to estimate Credit VaR over a three-month period, what approach should be taken?
A
The original one-year transition matrix should be divided by four to approximate the transitions for a three-month period.
B
The transition probabilities in the matrix should be recalculated based on empirical data specific to three-month intervals.
C
The fourth root of the one-year transition matrix should be taken to estimate the transition matrix for a three-month period.
D
A new matrix should be created by assuming that the one-year probabilities remain constant over any shorter period.