Bond is maturing in 10.25 years and has annual coupon rate 4.25% coupon paid sem
ID: 2807083 • Letter: B
Question
Bond is maturing in 10.25 years and has annual coupon rate 4.25% coupon paid semiannually and price 92-11+
a)Calculate its Yield to Maturity. (You can use Excel and try several Yields until you get required price.)
b) Suppose you have 9.5 Million market value of this bond. What is the Modified Duration, Macaulay Duration, DV01 and convexity of this portfolio.
c) Using Duration and Convexity formula approximation calculate bond price if the Yield to Maturity is increased 10 Basis Points.
d) Calculate the exact Bond price for 10 Basis points increased yield using full discount formula. Compare the two results c) and d)
Explanation / Answer
As per the given details, the yield to maturity would be as below"
face Value - 92
Market Value (Current Bond Price) - 103 & 81
Annual Coupon Rate - 4.25% (Paid Semi Annually)
Year to maturity - 10.25
Formula - Annual Interest Payment + ( (Face Value – Current Price) / (Years to Maturity)
Yield to maturity (at Market Value $103) = 2.89%
Yield to maturity (at market value $81) = 5.81%
b) Basis the given details, the Macaulay Duration of the bond would be Duration D (PV*T) / Present Value of the Bond
= 0.198011706