4. a) Cumulative average default rates calculated by Moody's over the 19702012 period are given in the table below (in percentages): 1 2 3 4 5 7 10 0.503 0.000 0.013 0.013 0.037 0.106 0.247 Aa 0.022 0.069 0.139 0.256 0.383 0.621 0.922 A 0.063 0.203 0.414 0.625 0.870 1.441 2.480 Baa 0.177 0.495 0.894 1.369 1.877 2.927 4.740 Ba 1.112 3.083 5.424 7.934 10.189 14.117 19.708 B 4.051 9.608 15.216 20.134 24.613 32.747 41.947 Caa 16.448 27.867 36.908 44.128 50.366 58.302 69.483 al) What is the unconditional default probability for Caa-rated bond during the fifth year? a2) What is the corresponding default intensity during the third year? a3) If the average recovery rate in case of default for B-rated bonds was 35%, what would be the fair yield spread (over and above risk-free rate) for the corresponding 4-year bonds on the basis of historical average default rates given in the table above? 4. a) Cumulative average default rates calculated by Moody's over the 19702012 period are given in the table below (in percentages): 1 2 3 4 5 7 10 0.503 0.000 0.013 0.013 0.037 0.106 0.247 Aa 0.022 0.069 0.139 0.256 0.383 0.621 0.922 A 0.063 0.203 0.414 0.625 0.870 1.441 2.480 Baa 0.177 0.495 0.894 1.369 1.877 2.927 4.740 Ba 1.112 3.083 5.424 7.934 10.189 14.117 19.708 B 4.051 9.608 15.216 20.134 24.613 32.747 41.947 Caa 16.448 27.867 36.908 44.128 50.366 58.302 69.483 al) What is the unconditional default probability for Caa-rated bond during the fifth year? a2) What is the corresponding default intensity during the third year? a3) If the average recovery rate in case of default for B-rated bonds was 35%, what would be the fair yield spread (over and above risk-free rate) for the corresponding 4-year bonds on the basis of historical average default rates given in the table above