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 2013 to create this portfolio and this portfolio is composed of 35 units of instrument A and 32 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 = 3.06% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023. (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 = 3.69% p.a.

Select one: a. 2.425

b. 2.888

c. 4.850

d. 5.776

Answer 1

=(0.5*1.53%/(1+3.69%/2)^1+1*1.53%/(1+3.69%/2)^2+1.5*1.53%/(1+3.69%/2)^3+2*1.53%/(1+3.69%/2)^4+2.5*1.53%/(1+3.69%/2)^5+2.5*100%/(1+3.69%/2)^5)/(1.53%/(1+3.69%/2)^1+1.53%/(1+3.69%/2)^2+1.53%/(1+3.69%/2)^3+1.53%/(1+3.69%/2)^4+1.53%/(1+3.69%/2)^5+100%/(1+3.69%/2)^5)

=2.4251