Question

A 4% annual coupon bond has 5 years remaining until maturity and is priced to yield 6%.

(a) What is the price per 100 of par?

(b) For this bond, estimate the price value of a basis point by first considering an increase in yield and then a decrease in yield.  

(c) Now show that for very small price changes, the absolute value of a bond’s price change does not differ much conditional on whether the yield change is a rise or a fall in yield.

Thanks   

Answer 1

a)

given,

- coupon 4%   annual,

                coupon amount   (PMT)    = 1000X4%   = $40

               time to mature    (n)         = 5

                YTM      (rate)                =6%  

             par Vale     (FV)                =100$

bond prices are found by using PV formula

excel formula

b)   Price value Change of a basis point is $0.04

for 1 basis points increase in ytm

only the YTM is changed from 6% to 6.01% all others same values

for 1 basis points fall in ytm

only the YTM is changed from 6% to 5,99%% all others same values

as seen above the Price value Change of a basis point is $0.04

c)

lets compute the bond prices for a 1% increase and 1 % decrease in YTM.

as seen above, when the interest rates rises by 1 % the bond prices of a 4% coupon falls by 4.23%  

similarly when the interest rates fell by 1 % the bond prices of a 4% coupon increased by 4.47%  

bonds with lower coupon rates are more prone to the interest rate risk. that is they fluctuate more than a high coupon bond - when interest rates fluctuates.