Question

1. Assume that i₁ = 11% and i₂ = 12%, and that k₁ = 14.50% and k₂ = 16.50%. What is the expected probability of repayment on the one-year corporate bonds in one year's time (round to two decimals)?

2. Assume a $500 000 loan has a duration of 2.5 years. The current interest rate level is 10% and a sudden change in the credit premium of 1% is expected. Further assume that the one-year income on the loan is $2500. What is the loan's RAROC (round to two decimals)?

3. Assume that B = $200 000, r = 1 year, i = 7%, d = 0.9, N(h₁) = 0.174120 and N(h₂) = 0.793323. Using Moody's KMV Credit Monitor model, what is the current market value of the loan (round to two decimals)?

Answer 1

1. The probability of repayment in year 1 is:

p 1 = (1.11) / 1.1450 = 0.9694 , or probability of default = 1 – 0.9694 = 3.06%

The marginal probability of repayment in year 2 is:

p 2 = (1.12) / 1.1650 = 0.9614 , or probability of default = 1 – 0.9614 = 3.86%

2. Loan (asset) at risk or capital at risk = DLN = -D x LN x (DR/(1+R))

= -2.5*500,000*(-0.01/1.10) = 11,363.64

RAROC = one year income on a loan / loan (asset) at risk or capital at risk

= 2,500/11,363.64= 22%

3.  Current market value of the loan = [Be^(–i*r)] * [{(1/d)N(h 1 )} + N(h 2 )]

= [200,000* e^( - 0.07*1)] * [{(1/0.9) * 0.174120} + 0.793323]

= 186,478.76 * 0.98689 = $184,015.32