ACST201 Financial Modelling Take Home Quiz 2 S2 2018

1. Today is 1 July 2018. Janet has a portfolio which consists of three differ- ent types of financial instruments (henceforth referred to as instrument A, instrument B and instrument C. Janets portfolio is composed of 100 units of instrument A, 150 units of instrument B and 250 units of instrument C). (35 marks)

Instrument A is a zero-coupon bond with a face value of 100. This bond matures at par. The maturity date is 1 January 2025.

Instrument B is a Treasury bond with a coupon rate of j2 = 3.55% p.a. and face value of 100. This bond matures at par. The maturity date is 1 July 2020.

Instrument C is a Treasury bond with a coupon rate of j2 = 3.25% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2020.

a. i. [2 marks] Calculate the current price of instrument A per $100 face value. Round your answer to four decimal places. Assume the yield rate isj2 = 3.5% p.a.

ii. [2 marks] Calculate the current price of instrument B per $100 face value. Round your answer to four decimal places. Assume the yield rate isj2 = 3.5% p.a. and Janet has just received the coupon payment.

iii. [2 marks] Calculate the current price of instrument C per $100 face value. Round your answer to four decimal places. Assume the yield rate isj2 = 3.5% p.a. and Janet has just received the coupon payment.

b. i. [1 marks] What is the duration of instrument A? Express your answer in terms of years and round your answer to three decimal places. Assume the yield rate is j2 = 3.5% p.a.

ii. [2 marks] 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 = 3.5% p.a.

iii. [2 marks] What is the duration of instrument C? Express your answer in terms of years and round your answer to three decimal places. Assume the yield rate is j2 = 3.5% p.a.

c.

i. [2 marks] Without actually calculating the new price, use the price in part a and the duration values in part b to estimate (use the price sen- sitivity formula) the change in price of instrument B that would result from an increase in yield rate of 10 basis points. Round your answer to two decimal places.

ii. [2 marks] Based on the price in part a and the duration values in part b, calculate the current duration of Janets portfolio. Express your answer in terms of years and round your answer to two decimal places.

d. Janet plans to sell the whole portfolio on 1 January 2019 at a sale yield rate ofj2 = 3.65% p.a. Assume that Janet will receive the coupon payments before the sale.

[2 marks] Calculate the sale price of instrument A per $100 face value. Round your answer to four decimal places.

[2 marks] Calculate the sale price of instrument B per $100 face value. Round your answer to four decimal places.

[2 marks] Calculate the sale price of instrument C per $100 face value. Round your answer to four decimal places.

[6 marks] Janet purchased the instrument C on 1 January 2014 at a price of $98.9244 per $100 face value. Calculate the holding period yield rate of one instrument C. Assume the reinvestment rate is j2 = 4.15% p.a. from the start of 2014 to the end of 2015 and j2 = 3.95% p.a. from the start of 2016 to the end of 2018. Express your answers as a j2 percentage rate and round your answers to one decimal place.

e. [8 marks] Janet will use part of the sale proceeds of these instruments to purchase a corporate bond with a coupon rate of j2 = 3.6% p.a. and face value of 100 on 1 January 2019. This corporate bond matures at par. The maturity date is 1 July 2024. The yield rate is assumed to be j2 = 3.7% p.a. Assume that this corporate bond has a 4% chance of default in any six-month period during the term of the bond. Assume also that, if default occurs, Janet will receive no further payments at all. Calculate the purchase price for 1 unit of this corporate bond. Round your answer to three decimal places. Draw the detailed contingent cash flow diagram associated with this corporate bond, from the perspective of Janet.