Question

A financial firm, AAB limited, holds a loan portfolio of $280m. The portfolio comprises three loans issued to group companies such that holding company AAA rates gets $130m, company BBB rated receives $80 m and BB rated gets $70 m. Its is assumed that subsidiaries will default if the parent company defaults but the parent company will not necessarily default if any of its subsidiaries defaults. On the other hand, also assume that the one year probabilities of default for AAA rated for AAA rated loans in the event of default is 50%, the recovery value for BBB rated loans is 40% and the recovery value for BB rated loans is 30%.

Required

a) determine the one year expected credit and portfolio standard deviation from the portfolio above. Show all your workings.

Answer 1

Particulars. Loan amount. Probability. Expected. AAA. 130. .50. 65

BBB. 80. .60. 48

CCC. 70.    .70. 49

Expected credit.      $ 162

Standard deviation

Sum of probability (given return - expected return )²

^{= .50 *( 130 - 65) + .60*(80 -48) + .70(70 - 49)}

^{= 32.50 + 19.2 + 14.7}

^{= 66.4}