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

Question

You are managing a portfolio of $1 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity of 5 years, and a perpetuity, each currently yielding 7.5%.

What weight of each bond will you hold to immunize your portfolio? (Round your answers to 2 decimal places. Omit the "%" sign in your response.)

How will these weights change next year if target duration is now 9 years? (Round your answers to 2 decimal places. Omit the "%" sign in your response.)

You are managing a portfolio of $1 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity of 5 years, and a perpetuity, each currently yielding 7.5%.

Explanation / Answer

lets assume weight of zero coupon bond = X and weight of perpetuties = (1-x)

Duration of perpeturity = (1+Y) / Y =(1.075)/.075 =14.33 years

duration of portfolio = (duration of zero coupon bond*weight of zero coupon)+ (duration of perpetuity*weight of perpeturity in portfolio)

10 = (5*X)+(1-X)*14.33

10 = 5X+ 14.33 -14.33X

-4.33 = -9.33X

X= 4.33/9.33 = .464

weight of zero coupon bond = .464 =46.4%

weight of perpetuity =1-.464 = .536 = 53.6%

2-

duration of portfolio = (duration of zero coupon bond*weight of zero coupon)+ (duration of perpetuity*weight of perpeturity in portfolio)

9 = (4*X)+(1-X)*14.33

9 = 4X+ 14.33 -14.33X

-5.33 = -10.33X

X= 5.33/10.33 = .5159

weight of zero coupon bond = .5159 =51.59%

weight of perpetuity =1-.5159 = .4841 = 48.41%

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