Question

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

Answer 1

Outstanding Loan = $1,600,000

Probability of Default (P_D) = 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)