Plain vanilla bond: semi-annual coupon Par value Coupon YTM Time to maturity, years Calculate Macaulay and modified duration, as well as convexity Calculate change in price if YTM moves up by 1% 1,000.00 3.00% 1.50% 10.5 Calculate the impact of 40bps rise in yields (parallel shift) for the $50 m active portfolio vs the benchmark Active weights BMK weightDuration Convexity 2 yr Treasures 20% 33% 1.99 5.00 5 yr Treasuries 20% 33% 4.88 26.50 10 yr Treasures 60% 33% 9.02 90.80 Portfolio size, Sm Change in YTM 50.00 0.40% You are analyzing a 3 year corporale bond with a 12% annual coupon with a 20% probability of default with 60% severity The par value is $1000. The risk free rates are 1% for 1 year, 1.5% for 2 years, and 2% for 3 years Calculate the fair value of the bond and the YTM. Par Interest payment Probability of default Severity of default Risk-free ratt year 1,000.00 120.00 20% 60% 1 2 1.00% 1.50% 2.00% 3 Year! 120 Cash flow Probability 80% 48 20% Expected CF Discounted No default Default 105.6 SUMPRODUCT(C17:C18,017:018) 104.554 F191(1+DILYCH Year 2 Cash flow Probability 120 64.00% 80% 80% 48 16.00% 80% 20% 48 20% 20% x 100% Expected CF 100.00% No default in year 2 given no default in year Default in year 2 given no default in year Default in your 2 given default in year! 94.08 Discounted 91.32 Year 3 Cash flow Probability 1120 31.20% 64% x 80% 448 12.800% 64% x 20% 448 16.000% 16% x 100% 448 20% 20% x 100% 100% No default in year 3 given no default in year 1 and 2 Default in year 3 given no default in year 1 and 2 Default in year 3 given default in year 2 and no default in year 1 Default in year 3 given default in year 1 and 2 792,064 Discounted 746.38 Sum of DCF 942.25 YTM 14.51% The Republic of Ireland bonds are currently rated AA-by Moody's. Following the global tax disput, Ireland came out as a winner, and Moody's upgraded it to AA. This resulted in a 25bps narrowing in its credit spread. What is the % price impact on its 10-year 3.5% coupon bond with modified duration of 8.5? Hint: assume that modified duration is equal to spread duration