Question

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 1

Firstly, we consider three loss events;

Event 1 Default by the first alone, with probability  0.1 - 0.03 = 0.07

Event 2 Default by the second, with probability  0.20 - 0.03 = 0.17

Event 3 Default by both, with probability  0.03

Secondly, we considered their respective losses

Event 1 £100 × (1 - 0.4) × 0.07=£4.2

Event 2 £100 × (1 - 0.4) × 0.17=£10.2

Event 3 £200 × (1 - 0.4) × 0.03=£3.6 , £200 is cummulative sum of two assets each worth £100

The expected loss amount is obtained by adding these three loss events.

£4.2+£10.2+£3.6=£18.0 Millions.

The total expected loss of this portfolio is £18 millions.