Question

URGENT!!

You plan to form a portfolio by investing in a 6-year zero-coupon bond and a 3-year 6% annual coupon bond with a yield to maturity of 11%. The target duration of this portfolio is 5 years. Therefore, ________ of the portfolio value should be allocated to the zero-coupon bond.

		A) 68.55%
		B) 31.45%
		C) 83.33%
		D) 24%

Answer 1

Given that a portfolio is formed by investing in a 6-year zero-coupon bond and a 3-year 6% annual coupon bond with a yield to maturity of 11%.

First calculating duration of 6% annual bond as follow:

Assuming face value = $1000

Annual coupon = 6% of 1000 = $1060

Coupon in final year includes FV = C+FV = 60 + 1000 = $1060

PV of coupon is calculated using Coupn/(1+YTM)^year

Price = sum of all coupons = $877.71

Weight = PV of coupon/Price

Duration of each coupon = weight*year

Duration of bond = sum of duration of coupon = 2.82 years

Year	Coupon	PV of coupon = coupon/(1+YTM)^year	weight=PV of coupon/Price	Duration = weight*year
1	$                 60.00	$                 54.05	0.06158	0.06158
2	$                 60.00	$                 48.70	0.05548	0.11095
3	$           1,060.00	$               775.06	0.88295	2.64884
	Price	$               877.81	Duration	2.82

Duration of zero coupon bond = years to maturity = 6 year

So, duration of portfolio is weighted average duration of its bonds.

let weight of zero coupon bond be w

then weight of coupon bond = 1-w

=> Duration of portfolio = w*6 + (1-w)*2.82

=> 5 = 6w + 2.82 - 2.82w

=> w = 0.6855

Therefore, 68.55% of the portfolio value should be allocated to the zero-coupon bond.

Option A is correct.