Question

Today is 1 July 2020. Joan has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Joan purchased all instruments on 1 July 2012 to create this portfolio and this portfolio is composed of 40 units of instrument A and 35 units of instrument B.

• Instrument A is a zero-coupon bond with a face value of 100. This bond matures at par. The maturity date is 1 January 2030.
• Instrument B is a Treasury bond with a coupon rate of j₂ = 4.01% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023.
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(c) What is the duration of instrument B? Express your answer in terms of years and round your answer to three decimal places. Assume the yield rate is j₂ = 3.92% p.a. Please provide working out.

a. 2.404

b. 5.713

c. 2.857

d. 4.808

Answer 1

(c)

Given semi annual compounding

So coupon = 100*4.01%/2 = 2.005

YTM = 3.92% / 2 = 1.96%

option a is correct

Present value = payments * PV factor

Weights = present value / bond price

Duration = weights * period

Duration = 4.808 periods (semi annual periods)

Since question requires in years = 4.808 / 2 = 2.404 years

(In case of any further explanation please comment.kindly rate the answer if it's helpful thank you)