1. [Expected and unexpected loss] Sometimes the unexpected loss is defined as the standard deviation of the portfolio loss. Let us consider this denition in this question. Consider a portfolio containing m : 1000 equally rated credit risks. Assume that for every obligor the exposure is EADI- 2 $1M , and the default probability pi = 1%. Calculate the expected loss and unexpected loss of the portfolio in the following situations: (a) LGDs are modelled as deterministic and in all cases L-GDI- = 0.4. Defaults are assumed to occur independently. (b) LGDs are modelled as deterministic as in (a) but defaults are assumed to be de- pendent. Assume that in all cases the default correlation between pairs of default indicators is given by PM = 0.005 for 'i # j. (c) Defaults are dependent as in (b) but LGDs are modelled as random variables LGDi : Az- satisfying Ai ~ Beta(a, b) where a : 9.2 and b : 13.8. Assume that LGDs are mutually independent across the portfolio and independent of the default indicator variables