Our Portfolio currently contains two bonds: (Duration =5.71 years) And (Duration

Question

Our Portfolio currently contains two bonds:

(Duration =5.71 years)

And

(Duration = 0,40 years)

You want to arrange a classic immunization of a liability of PLN 10 million payable in 1,5 years. Please calculate the weights of the bonds in the immunized portfolio and the number of bonds which you need to purchase in order to put the strategy in place.

IDS1024 101,0 Nominal value (PLN) Interest in the current interest period (96) Accrued interest (in PLN) 1 000,00 100,5 4 100,0 9,5 99,17 25,97 99,0 98,5 99,0 Jul 2015 Jul 2016 Jul 2017 24 April Jul 2018 14D 1M 3M M 1R MAX Basic Information Bond profitabllity calculator BGK 2014-05-26 2014-05-26 2024-10-25 1 000,00 1 270 000 000,00 ssuer's name Date of authorization Date of first listing Date of redemption Nominal value (PLN) Issue value (PLN) Type of bond Interest in the current interest period (96) Accrued interest in PLNI ssuer's www Fixed interest-rate 25.97 www.bgk.com.pl

Explanation / Answer

Soln : Let w1 and w2 be the weights required of the 2 given bonds for immunizing the liability of 10 million, need to pay in 1.5 years.

w1 +w2 = 1 , as there would not be any other bond/

Also, we can say that w1* duration of bond1 + duration of bond 2* w2 = 1.5

w1*5.71 +w2*0.40 = 1.5

Take w1 = 1-w2 from above equation

(1-w2)*5.71 + w2*0.4 = 1.5

on solving we get , w2 = 0.793

w1 = 1-0.793 = 0.21

Number of bond1 should be = 10 million/1000 * 0.21 = 2072 (approx.)

For bond 2 = 10000* 0.793 = 7928

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