Question

A in perpetuity NOT correct

You are managing a portfolio of $1.0 million. Your target duration is 22 years and you can choose from two bonds: a zero-coupon bond with maturity five years, and a perpetuity, each currently yielding 2%. a. How much of () the zero-coupon bond and (i) the perpetuity will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Answer is complete but not entirely correct. Zero-coupon bond 63.04 39.96 (x% Perpetuity bond

Answer 1

The duration of zero coupon bonds are equals to its maturity period because zero-coupon bond has no cash flow until maturity.

Therefore duration of zero coupon bond = 5 years

The perpetual bonds have no maturity period; therefore duration of perpetuity bond is calculated in following manner

Duration of perpetuity bond = (1 + yield)/yield

= (1+2%)/2% = 1.02/0.02 = 51 years

Duration of portfolio is its weightage average.

Total investment amount of portfolio = $1.0 million

Assume that x is invested in zero coupon bonds

Therefore (1-x) will be invested in perpetuity bonds

The target duration = 22 years

Therefore,

The target duration of portfolio = weight of zero coupon bond in portfolio * duration of zero coupon bond + weight of perpetuity bond in portfolio * duration of perpetuity bond

Or 22 = x * 5 + (1-x) * 51

Or 22 = 5 x + 51 – 51 x

Or (51 -22) = 51 x – 5 x

Or x = (51 -22)/ (51 -5) = 29/46 = 0.6304 or 63.04%

Therefore 63.04% invested in zero coupon bonds

And 1 – x = 1 - 0.6304 = 0.3696 or 36.96% invested in perpetuity bond