Question

AF335: Final Exam Practice 1. A 3-year bond has a coupon rate of 2% and sells at par. What is the bond's duration? a. If interest rates fall by.5%, what will be the approximate percentage change in price? b. What is the approximate new price? C. What is the actual new price? Bond A pays a $40 semi-annual coupon. Bond B has a coupon rate of 7%. Which bond has the higher duration? Rand Aharviold to maturity of 9% Bond B has a vield to 2.

Answer 1

1. Duration of a bond = (Present value of Cashflow of year 1 * 1 + Present value of Cash flow of year 2 * 2 + .......+ Present value of Cashflow of year n * n)/ Price of bond

Where Present values are calculated at YTM

Here , Price of bond = Face value = P (say)

YTM = 2% (as the bond is selling at par)

Cash flow of year 1 = Cash flow of year 2 = P*0.02

Cash flow of year 3 = P*0.02 + P

So, Duration = (0.02P*1/.02 + 0.02P *2/1.02² + 1.02P *3/1.02³ ) / P

= 0.02/1.02+0.04/1.02²+3.06/1.02³

= 2.94 years

a) If interest rates fall by 0.5%, the price should increase by approximately duration (2.94) times change (0.5%) i.e. 1.47% increase.

b) The approximate new price is 1.0147* P (where P is the original price)

c) If interest rates fall by 0.5%, the required rate will become 1.5%, So by the bond pricing formula

New Price = present value of all future cashflows of bond

= 0.02P/1.015 + 0.02P/1.015² + 1.02P/1.015³

= 1.01456* P (where P is the original price)