In: Finance
QUESTION 19 Manning Bank recently disbursed a $2 million loan, of which $1.6 million is currently outstanding. The probability of default over the next year is 1%, and the recovery rate is 70%. The standard deviation of loss given default (LGD) is 20%. The expected and unexpected losses (standard deviation) for the bank are Expected loss = $4,800; unexpected loss = $57,489 Expected loss = $11,200; unexpected loss = $57,489 Expected loss = $4,800; unexpected loss = $115,942 Expected loss = $11,200; unexpected loss = $115,942
Outstanding Loan = $1,600,000
Probability of Default (PD) = 0.01
Recovery rate = 70%
Loss Rate = 30% (100 - 70)
Expected Loss can be calculated by the following formula:
Outstanding Loan * Probability of Default * Loss Rate
= 1,600,000 * 0.01 * 0.30
= $4800
Expected loss = $4800
For Unexpected Loss,
Variance of Probability of default is required to be calculated by the following formula:
= Probability of Default * (1 - Probability of Default)
= 0.01 * ( 1- 0.01)
= 0.0099
Now, For Unexpected Loss, the following formula can be used:
Note carefully, 0.0099 is actually the variance. This means that (standard deviation of loss rate)2 = 0.0099
Unexpected loss = $57,489 (after rounding off)
First Option is the answer. (Expected loss $4800, Unexpected loss $57,489)