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 28 units of instrument A and 50 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.

(a) Calculate the current price of instrument A per $100 face value. Round your answer to four decimal places. Assume the yield rate is j₂ =2.96% p.a.

(b) Calculate the current price of instrument B per $100 face value. Round your answer to four decimal places. Assume the yield rate is j₂ = 2.96% p.a. and Joan has just received the coupon payment.

Instrument B is a Treasury bond with a coupon rate of j₂ = 3.93% 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 = 2.96% p.a.

(d) Based on the price in part a and part b, and the duration value in part c, calculate the current duration of Joan’s portfolio. Express your answer in terms of years and round your answer to two decimal places.

Select one for question d)

a. 6.61

b. 4.48

c. 5.97

d. 4.41

Answer 1

So given in question today date 1/7/2020 and 28 units of instrument A, and 50 units of instrument b.

For A

zero coupon bond, face value 100, yield =2.96 P.a., time = 9.5 year

current price of instrument A

PV= Face value * (1/(1+0.0296)^9.5

PV_a = 75.796

For B

3.93% coupon rate, face value 100, yield =2.96%, Maturity Time = 2.5 years

Price today

Present value_b= Coupons*PVAF_{(2.96%,2.5yrs)}+ 100_{(2.96%,2.5yrs)}

Calculated this equation in excel using PRICE function.

So price is 102.29.

Duration for instrument A is same as its maturity becuase it is zero coupon bond.

Duration of instrument B is calculated using Macaulay duration formula.

It took weight of each cash flow and represent a time in which investor will get its price back. same time it also measures the senstivity.

It is solved using Excel, DURATION function used for the same.

Instrumen b duration is 2.38

In last portfolio duration is asked, it can be calculated as weighted average of durations of indvidual portfolio.

portfolio duration = (individual bonds total value / portfolio value)* Respective duration)+(individual bonds total value / portfolio value)* Respective duration

4.48 is portfolio duration

In snip of excel all answers are provided.