Question

A 25-year semiannual bond has 10% coupon rate and par value $1,000. The current YTM of the bond is 10%. Its Macaulay duration is 9.58 years and convexity is 141.03.

(1) What is the bond’s modified duration? (2 points)

(2) What is the percentage price change if interest rate were to fall 125 basis points considering both duration and convexity? (4 points)

(3) What is the estimated price with 125 basis points decrease in yield? (4 points)

Answer 1

Given about abond,

years to maturity = 25 years

face value = $1000

coupon rate = 10%

YTM of the bond = 10%

Since coupon rate = YTM, bond is priced at par.

=> Price of the bond = face value = $1000

Macaulay duration = 9.58 years

Convexity C = 141.03

1). Bond's modified duration D= Macaulay duration/(1+YTM) = 9.58/1.1 = 8.71 years

2). percentage change in price can be calculated using formula

dP/P = -D*dy + (1/2)*C*dy^2

where dy = change in yield = -1.25%

So, percentage change in price = dP/P = -8.71*(-0.0215) + (1/2)*141.03*(-0.0125)^2 = 19.83%

3). New estimated price = P + dp

Where dp = P*percentage change = 19.83*1000 = $198.26

=> New estimated price = 1000 + 198.26 = $1198.26