Question

In: Finance

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 %

Solutions

Expert Solution

Duration of portfolio Duration of zero coupon bond*w+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 bond*w+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 bond*w+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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