Reference no: EM132465376
You hold an initial A-rated bond with current value $112 and an initial B-rated bond valued at $108. Each bond can be in 3 possible states at the end of the year namely, A-rated, B-rated or D-rated (i.e. in default). The value of both bonds in the default state is $51. If the A-rated bond moves to B-rated, its value at the end of the year is $109. If the B-rated bond moves to A-rated its value rises to $110. For simplicity assume that if either bond stays in its current rating, its value is unchanged at end year. The transition probabilities for the initial-A and B-rated bonds are: Pa = [0.92, 0.07, 0.01] and Pb = [0.03, 0.90, 0.07]
Calculate:
(i.) the mean value of the 2 bonds
(ii.) the standard deviation in value, for each of the bonds taken separately
(iii.) the value of the 'two-bond' portfolio in each future state and the migration probability matrix, assuming independence between the movements of bonds A and
(iv.) the mean and standard deviation of the 'two-bond' portfolio
(v.) the marginal risk of adding bond-B to bond-A
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