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A portfolio consists of two (long) assets £100 million each. The probability of default over the next year is 10% for the first asset, 20% for the second asset, and the joint probability of default is 3%. Estimate the expected loss on this portfolio due to credit defaults over the next year, assuming 40% recovery rate for both assets.
answer:. £18 million
a) The three loss events are
(i) Default by the first alone, with probability 0.10 − 0.03 = 0.07
(ii) Default by the second, with probability 0.20 − 0.03 = 0.17
(iii) Default by both, with probability 0.03
The respective losses are £100×(1 − 0.4) × 0.07 = 4.2, £100×(1 − 0.4) ×
0.17 = 10.2, £200×(1 − 0.4) × 0.03 = 3.6, for a total expected loss of £18
million.
I cannot recall why you subtract the joint probability from the individual probabilities; the rest is totally clear. Please explain just that one concept. Thanks!
answer:. £18 million
a) The three loss events are
(i) Default by the first alone, with probability 0.10 − 0.03 = 0.07
(ii) Default by the second, with probability 0.20 − 0.03 = 0.17
(iii) Default by both, with probability 0.03
The respective losses are £100×(1 − 0.4) × 0.07 = 4.2, £100×(1 − 0.4) ×
0.17 = 10.2, £200×(1 − 0.4) × 0.03 = 3.6, for a total expected loss of £18
million.
I cannot recall why you subtract the joint probability from the individual probabilities; the rest is totally clear. Please explain just that one concept. Thanks!
