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 make(Create) this portfolio and this portfolio is composed of 26 units of instrument A and 41 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 = 3.27% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023.

(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 =2.59% p.a.

Select one:

a. 64.5666

b. 78.3119

c. 61.5183

d. 65.4027

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 = 2.59% p.a. and Joan has just received the coupon payment.

Select one:

a. 101.6359

b. 103.2709

c. 105.6942

d. 101.9506

(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 = 2.59% p.a.

Select one:

a. 2.422

b. 5.767

c. 4.843

d. 2.883

(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:

a. 6.79

b. 4.74

c. 4.73

d. 6.19

Answer 1

(a) Calculation the current price of instrument A per $100 face value

Current price of Zero Coupon Bond will be present value of cashflow at YTM rate.

Maturity Value = 100

YTM = 2.59% p.a.

N = 9.5 remaining years

so,

100 *1/(1+0.0259)^9.5 = 78.4336

b) Calculation the current price of instrument B per $100 face value

Remaining Years = july 2020 - dec 2022

Year	Cash Flow	PVF @  2.59%	PV of Cash Flow
1	3.27(100*3.27%)	0.9747	3.1874
2	3.27	0.9501	3.1070
2.5	1.635(100*3.27%*6/12)	0.9381	1.5337
2.5	100	0.9381	93.8075
	Current Market Price	101.6356

(c) duration of instrument B

Year	PV of Cash Flow	PV/Total Price	Duration(PV/Price*Year)
1	3.1874	0.0314	0.0314
2	3.1070	0.0306	0.0612
2.5	1.5337	0.0151	0.0378
2.5	93.8075	0.9230	2.3075
	101.6356	1	2.4379

(d) calculation the current duration of Joan's portfolio

Duration Of PF = Duration Of ZCB* W + Duration of Treasury Bond* W

Value of

Total Value Of PF =78.4336*26 + 101.6356*41

=2039.2736+4167.0596

= 6206.332

Duration = 9.5*2039.2736/6206.332 + 2.4379*4167.0596/6206.332

=3.1215+1.6368

=4.75