Question

Assume a four-year maturity float-rate bond. Par value is $1,000. Its discount rate is LIBOR+3%. The discount rate for fixed cash flows is 5%. Its coupon rate is LIBOR+1%. a. What is the price of this floater? b. What is the modified duration of this floater? c. What is the convexity of this floater?

Answer 1

a.) Firstly we calculate price of the floter :

par value = $1000

LIBOR = 5%

DISCOUNT RATE = LIBOR + 3%

EFFECTIVE DISCOUNT RATE = 5% + 3% i.e. = 8%, i.e. = .08

COUPON RATE = LIBOR + 1%

EFFECTIVE COUPON RATE = 5% + 1% i.e.= 6%

NOW PRICE OF THE FLOTER

= PAR VALUE * (1-effective discount rate)

=$1000 * (1-.08)

=$920 /-

b) MODIFIED DURATION OF THIS FLOTER

FORMULA :

Modified Duration=(1+nYTM​)Macauley Duration​

MODIFIED DURATION = MACAULEY DURATION / ( 1 + YTM / n)

MODIFIED DURATION = 4 / ( 1 + .06/4)

MODIFIED DURATION = 4 / 1.015

MODIFIED DURATION = 3.9408867 /-

c) CONVEXITY OF THIS FLOATER

no any any changes in the convexity of this floater