What is the intervals of $4,680?

Question

The following formula expresses the expected amount lost when a borrower defaults on a loan where PD is the probability of default on the loan, EAD is the exposure at default(the face value loan) and LGD is the loss given default(expressed as a decimal). For a certain class of mortgages 6% of the borrowers are expected to default the face value of these mortgages averages $260,000 on average, the bank recovers 70% of the mortgaged amount if the borrower defaults by sellingthe property. The expected loss becomes the interval {$_ and $_}  Somebody please help.

Answer 1

If the bank recovers 70% of the mortgaged amount then 30% (0.3) is lost, so LGD=0.3. No formula has been given to relate the PD of 6%, EAD of $260,000 and LGD. Therefore the best we can do is to multiply PD*LGD*EAD=0.06*0.3*260000=$4,680, which is the amount expressed in the title of this question. To put intervals to this we can calculate PD(1-PD)=0.06*0.94=0.0564 to derive a standard deviation and apply this to $4,680=$264 approx. therefore the interval is $4,416 to $4,944.