Current information on Treasury bonds (risk-free, coupon distributed annually, face value = 1000) Term to Maturity Coupon rate 1 6% 2 8.5% Price 1000 1000 Default spreads over risk-free rate (p.a., stay constant for 2 years) Rating Default spreads AAA 0.75% AA 1% 1.8% BBB 2.25% BB 3.5% B 6.5% 10% Default Recovery rate: 40% Based on the information above, what should be the price of a 2-year risk-free zero-coupon bond? (Assume face value is 1000.) (b) Suppose you would like to examine the riskiness of a 2-year bond with a credit rating of A. The coupons are distributed annually at a rate of 10%. (Assume face value is 1000.) You have collected the following information: Ratings at the end of year 1 Ratings at the beginning of year 1 AAA AAA 98.40% AA A BBB BB B CCC Default 1.23% 0.12% 0.10% 0.08% 0.04% 0.02% 0.01% AA 1.40% 97.50% 0.72% 0.15% 0.10% 0.06% 0.04% 0.03% . 0.80% 1.10% 96.60% 1.16% 0.12% 0.09% 0.07% 0.06% BBB 0.72% 1.01% 1.87% 95.70% 0.29% 0.18% 0.13% 0.10% BB 0.55% 0.789 1.20% 2.10% 94.80% 0.24% 0.18% 0.15% B 0.54% 0.68% 1.08% 1.12% 2.22% 93.90% 0.25% 0.21% CCC 2.56% 92.0096 0.28% 0.46% 0.65% 0.98% 1.10% 1.97% Expected bond value 1 year later: 1072 Standard deviation of the bond value 1 year later: 16.7 i. Using the credit metrics approach, estimate the 1% value at risk for the bond value 1 year later. ii. Using the normal distribution assumption, estimate the 1% value at risk for the bond value 1 year later. iii. Are the two VaRs the same? Explain