1.A five-year fixed-rate loan of $100 million carries a 7 per cent annual interest rate. The borrower is rated BB. Based on hypothetical historical data, the probability distribution given below has been determined for various ratings upgrades, downgrades, status quo and default possibilities over the next year. Information also is presented reflecting the forward rates of the current government bond yield curve and the annual credit spreads of the various maturities of BBB bonds over Treasuries.

What is the present value of the loan at the end of the one-year risk horizon for the case where the borrower has been upgraded from BB to BBB?
What is the mean (expected) value of the loan at the end of year one?
What is the volatility of the loan value at the end of year one?
Calculate the 5 per cent and 1 per cent VARs for this loan assuming a normal distribution of values.
Estimate the ‘approximate’ 5 per cent and 1 per cent VARs using the actual distribution of loan values and probabilities.
How do the capital requirements of the 1 per cent VARs calculated in parts

(d) and

(e) above compare with the capital requirements of the BIS?
Go to the JPMorgan Chase website (www.jpmorgan.com/RiskManagement/CreditMetrics ). What data set information is provided for use with CreditMetrics? LO 11.4

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Forward rate spreads at time t Rating Probability distribution (%) New loan value plus coupon $ t rt (% st (%) AAA 0.01 114.82 1 3.00 0.72 AA 0.31 114.60 2 3.40 0.96 A 1.45 114.03 3 3.75 1.16 BBB 6.05 4 4.00 1.30 BB 85.48 108.55 B 5.60 98.43 CCC 0.90 86.82 Default 0.20 54.12