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 32 units of instrument A and 39 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 = 4.82% 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 = 4.09% p.a

Answer 1

		Bond Duration = Present value of (cash flows multiplied by length of time to receipt) / (the  current market value)
		BOND B
		Par value	$100
		Semi Annual Coupon =(100*4.82%)/2	$2.41
		SeminAnnual Yield to maturity =(4.09/2)%	2.045%
		Present Value (PV)=(Cash flow)/(1.02045^N)
		N=Semi annual Period of cash flow
		Terminal Cash Flow =100+2.41	$102.41
			N	CF	A=CF/(1.02045^N)	B=N*CF	C=B/(1.02045^N)
		Date	Semi annual Period	Cash Flow	Present Value of Cash Flow	Year*Cash Flow	Present Value of( Year*Cash flow)
		Janury,1,2021	1	$2.41	$2.36	$2.41	$2.36
		July,1,2021	2	$2.41	$2.31	$4.82	$4.63
		Janury,1,2022	3	$2.41	$2.27	$7.23	$6.80
		July,1,2022	4	$2.41	$2.22	$9.64	$8.89
		Janury,1,2023	5	$102.41	$92.55	$512.05	$462.76
				SUM	$101.72		$485.44
	D	Current Market Price	$101.72
	E	Present Value (Cashflow*time of receipt)	$485.44
	F=E/F	Semi annual Bond Duration	4.7724
	G=F/2	Bond duration in years=4.77/2	2.386	Years