Question

You plan to form a portfolio by investing in a 6-year zero-coupon bond and a 3-year 6% annual coupon bond with a yield to maturity of 10%. The target duration of this portfolio is 4 years. Therefore, ________ of the portfolio value should be allocated to the zero-coupon bond. A) 37.1% B) 62.9% C) 83.33% D) 24%

Answer 1

Solution : -

Assume the Par value of Coupon Bond = $100

Coupon Amount = $100 * 6% = $6

- fx L10 A 1 Solution : B C D E F G H Years Pmt PVE @ 10% 0.909 0.826 0.751 PV $5.45 $4.96 $79.64 Weight 0.0606 0.0551 0.8844 PV * Years 5.4545455 9.9173554 238.9181067 $6 $106 Price = $90.053 $254.290 10 11 12 Now Duration of Bond = $254.29 / $90.053 = 2.824 Years 15 And Duration of Zero Coupon Bond = 6.0 Years 17 18

Now Assume weight of 3 Year Coupon Bond be X

Therefore Weight of Zero Coupon Bond be ( 1 - X )

Target Duration = 4 Years

Now

2.824 X + 6 * ( 1 - X ) = 4

2.824 X - 6 X = 4 - 6

3.176 X = 2

X = 0.629

( 1 - X ) = 1 - 0.629 = 0.371 = 37.1%

Therefore 37.1% of the portfolio value should be allocated to the zero-coupon bond.

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