Financial Modelling Assignment -
1. Today is 1 January 2018. Jackson who is aged 80 has a portfolio which consists of three different types of financial instruments (henceforth referred to as instrument A, instrument B and instrument C.
- Instrument A is a zero-coupon bond with a face value of 100. This bond matures at par. The maturity date is 1 July 2023.
- Instrument B is a Treasury bond with a coupon rate of j2 = 3.45% 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 = 2.85% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2021.
a. i. What is the duration of a instrument A? Express your answer in terms of years and round your answer to three decimal places. Assume the yield rate is j2 = 5% p.a.
ii. 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 = 5% p.a.
iii. 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 = 5% p.a.
b. Jackson's portfolio is composed of 250 units of instrument A, 200 units of instrument B and 180 units of instrument C. Jackson decides to sell the whole portfolio today at a sale yield rate of j2 = 4.65% p.a.
i. Calculate the sale price of one instrument A. Round your answer to four decimal places.
ii. Calculate the sale price of one instrument B. Round your answer to four decimal places.
iii. Calculate the sale price of one instrument C. Round your answer to four decimal places.
iv. Calculate the total sale proceed. Round your answer to two decimal places.
v. Based on the duration values in part a and the price in part b (i)-(iv), calculate today's duration of Jackson's portfolio right before sale. Express your answer in terms of years and round your answer to two decimal places.
c. Jackson purchased all the instrument A on 1 July 2013, purchased all the instrument B on 1 January 2014 and purchased all the instrument C on 1 July 2011.
i. Calculate the purchase price of one instrument A, given that the purchase yield rate is j2 = 4.5% p.a. Round your answer to four decimal places.
ii. Calculate the purchase price of one instrument B, given that the purchase yield rate is j2 = 4.5% p.a. Round your answer to four decimal places.
iii. Calculate the purchase price of one instrument C, given that the purchase yield rate is j2 = 4.5% p.a. Round your answer to four decimal places.
d. Based on your part b and part c calculation, what is Jackson's holding period yield rate for instrument A, instrument B and instrument C? Assume the reinvestment rate is j2 = 4.35% p.a. Express your answers in terms of j2 as a percentage and round your answers to one decimal place.
Table 1: Survival probability
|
Year
|
Probability of surviving form start if year to end of year
|
|
1
|
0.75
|
|
2
|
0.58
|
|
3
|
0.37
|
|
4
|
0.23
|
|
5
|
0
|
e. Jackson will use $50,000 from the total sale proceed of instruments as a single premium to purchase an annuity today. This annuity pays X at the end of each year while Jackson is alive. The estimated probability of Jackson surviving for the next 5 years is stated in table 1. The yield rate is assumed to be j1 = 3.2% p.a. Calculate X value. Round your answers to three decimal places. Draw a detailed contingent cash flow diagram for instrument D, from the perspective of Jackson.