Question

 

Problem 2 : Evaluate the following pure-yield pickup swap: You currently hold a 20-yearm AA-rated, 9% coupon rate bond with yield to maturity of 11.0%. As a swap candidate, you are considering a 20-yearm AA-rated, 11% coupon rate bond with yield to maturity of 11.5%, assume reinvestment rate is 11.5% and coupon are paid semi-annually, please fill out the table below and you must show (explain) clearly how numbers in the table are obtained.

	Current Bond	Candidate bond
Dollar investment
Coupon
i on one coupon
Principal value at year end
Total accrued
Realized compound yield
Value of swap:		basis point in one year

You must show (explain) clearly how numbers in the table are obtained. explain how?

Answer 1

Answer :

Available information :

Currently hold 20 - year, 9% coupon price, 11% yield rate

Swap candidate 20 - year, 11% coupon priced , 11.5% yield rate

Calculate the price of the current bond :

Current bond price = [$90 PVIF(11% , 20)] + [$1,000 PVF(11% , 20)]

= [$45 PVIF(5.5% , 40)] + [$1,000 PVF(5.5% , 40)]

= [$4516.04612] + [$1,000 0.11746]

= $722.07 + $117.46

Current bond price = $839.53

Calculate the price of the candidate bond :

Current bond price = [$110 PVIF(11.5%, 20)] + [$1,000 PVF(11.5% , 20)]

= [$55 PVIF(5.75% , 40)] + [$1,000 PVF(5.75% , 40)]

= [$5515.5330] + [$1,000 0.10685]

= $854.31 + $106.85

Current bond price = $961.61

Calculate the principal vlaue at the year end of current bond

Current bond price = [$90 PVIF(1% , 19)] + [$1,000 PVF(11% , 19)]

= [$45PVIF(5.5% , 38)] + [$1,000PVF(5.5% , 38)]

= [ $4515.80474] + [$1,000 0.13074]

= $711.21 + $130.74

Current bond price = $841.95

Calculation of principal value at year end of candidate bond

Current bond price = [$110PVIF(11.5% , 19)] + [$1,000 PVF(11.5% ,19)]

= [$55PVIF(5.75% , 38)] + [$1,000PVF(5.75% , 38)]

= [$5515.3131] + [$1,0000.11949]

= $711.21 + $130.74

= $842.22 + $119.49

Current bond price is $961.71

#	Current Bond	Candidate
Dollar Investment	$839.53	$961.61
Coupon	$90	$110
i on one coupon	2.59	3.16
Principal value at year end	$841.95	$961.71
Total accrued	$934.54	$1,074.87
Realized compound yield	11.0125	11.4988

Value of Swap : 48.6 basis points in one year (Assuming a 11.5% reinvestment rate)