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heducation.com/hm.tpx shows what is correct and incorrect for the work you have completed so far the work you have done so far is correct, you may not have completed everything value: 10.00 points You are managing a portfolio of $2.1 million. Your target duration is 20 years, and you can choose from two bonds: a zero-coupon bond with maturity 10 years, and a perpetuity, each currently yielding 4%. a. How much of each bond will you hold in your portfolio? (Do not round Intermediate calculations. Round your answers to 2 decimal places.) Zero-coupon bond Perpetuity bond b. How will these fractions change next year if target duration is now nineteen years? (Do not round latermediate calculations. Round your answers to 2 decimal places.) Zero-coupon bond Perpetuity bond

Explanation / Answer

When the yield = 4%, we have duration of perpectuity = 1.04/0.04 = 26 years

If we take w = weight of zero coupon bond then 1 - w shall represent weight of perpectuity, such that

w * 10 years + (1-w) * 26 = 20 ( target duration)

10w + 26 - 26w = 20

16w = 6

w = 6/16 or 37.50 %

(1 - w) = 1 - 6/16 = 62.50 %

Question - b

After one year, zero coupon will have a remaining 10 - 1 = 9 years. But life of perpetuity remains at 26 years.

9 * w + 26 ( 1 - w ) = 19

17w = 7

w = 7/17 ............ or 41.18 %

(1-w) = 10/17 .... or 58.82 %

Zeo - coupon bond 37.5 % Perpetuity 62.5 %

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