You are managing a portfolio of $1 million. Your target duration is 10 years, and you...

You are managing a portfolio of $1 million. Your target duration is 10 years, and you can invest in two bonds, a zero-coupon bond with maturity of five years and a perpetuity, each currently yielding 5.2%.

a. What weight of each bond will you hold to immunize your portfolio? (Round your answers to 2 decimal places.)


Zero-coupon bond		%
Perpetuity bond		%

b. How will these weights change next year if target duration is now nine years? (Round your answers to 2 decimal places.)


Zero-coupon bond		%
Perpetuity bond		%

Expert Solution

Duration of portfolio	Duration of zero coupon bondw+Duration of perpetuity bond(1-w)

Duration of zero-coupon bond is equal to its maturity period of 5 years
Duration of perpetuity bond	1.052/0.052
Duration of perpetuity bond	20.23	years

Duration of portfolio	Duration of zero coupon bondw+Duration of perpetuity bond(1-w)
10	(5w)+(20.23*(1-w))
10	5w+20.23-20.23w
20.23-10	15.23w
w	(20.23-10)/15.23
w	0.6717

Perpetuity bond	1-0.6717
Perpetuity bond	0.3283

Zero coupon bond	67.17%
Perpetuity bond	32.83%

b.
Duration of portfolio	Duration of zero coupon bondw+Duration of perpetuity bond(1-w)
9	(5w)+(20.23*(1-w))
9	5w+20.23-20.23w
20.23-9	15.23w
w	(20.23-9)/15.23
w	0.7374

Perpetuity bond	1-0.7374
Perpetuity bond	0.2626

Zero coupon bond	73.74%
Perpetuity bond	26.26%

jeff jeffy answered 1 year ago

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