8010 Exam Dumps : Operational Risk Manager (ORM) Exam

Assuming timeinvariance and the Markov property, it is easy to calculate the transition matrix for any time period as P^n, where P is the given transition matrix for one period and n the number of time periods that we need to compute the new transition matrix for. ThusChoice 'b' is the correct answer.

The easiest way to answer this question is to ignore the joint probability of default as thatis irrelevant to expected losses. The joint probability of default impacts the volatility of the losses, but not the expected amount. One way to think about it is to think of asset portfolios, where diversification reduces risk (ie standard deviation) butthe expected returns are nothing but the average of the expected returns in the portfolio. Just as the expected returns of the portfolio are not affected by the volatility or correlations (these affect standard deviation), in the same way the joint probability of default does not affect the expected losses. Therefore the expected losses for this portfolio are simply $1m x 10% + $1m x 15% = $250,000.

This can also be seen from the lens of a joint probability distribution as follows:

There are four possibilities for this portfolio:

- Only loan A defaults: loss of $1m: 9% probability

- Only loan B defaults: loss of $1m: 14% probability

- Both loan A and B default: loss of $2m: 1% probability

- Neither A nor B default: loss of $0m: 76% probability

Therefore the expected losses on the portfolio are ($1m x 9%) + ($1m x 14%) + ($2m x 1%) + ($0m x 76%) = $250,000.

(Notes: How is the above table calculated? The totals (10%, 90%, 15% and 85%) are filled in first. The top left cell (both A & B default) is given as 1%. We can now calculate the rest of the cells as the totals are known.)

Choice 'a' is the correct answer. Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.