PRMIA Exam 8010 Topic 1 Question 10 Discussion

Unexpected losses (UEL) for individual loans in a portfolio will always sum to greater than the total unexpected loss for the portfolio (unless all the loans are correlated in such a way that they default together). This is akin to the 'diversification effect' in market risk, in other words, not all the obligors would default together. So the UEL for the portfolio will always be less than the sum of the UELs for individual loans. Therefore statement III is true. This 'diversification effect' will be affected by the default correlations between the obligors, in cases where the probability of various obligors defaulting together is low, the UEL for the portfolio would be much less than the UEL for the individual loans. Hence statement IV is true. I and II are false for the reasons explained above.