Immunization with IRS (floater)

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TRAXX
Posts: 5
Joined: Wed Jul 18, 2012 10:35 pm

Immunization with IRS (floater)

Postby TRAXX » Mon Jan 13, 2014 11:35 pm

Dear professor,
I have a question from the polish version of CFA exam. There was one strange question about immunization strategy. There was a 10-year zerocoupon bond, with flat spot rate curve which equals 5,5%. Face value of the bond has been given, and in exercise we ought to immunize this bond, but when bond will be 7 years to maturity (so immunize in three years). The only instrument which we can use is Interest Rate Swap of WIBOR 3m (Warsaw Interbank Offered Rate 3 months). The question in exercise was 'WHAT AMOUNT OF FACE VALUE SHOULD THIS IRS HAVE?' How can I properly solve this exercise?

I executed present value of 7-year bond, and then I assumed that swap can be valuated as bond, so IRS can be valued as a floater. Floater after interests payment has present value equal to his face value and the duration of floater is equal to maturity to next interest payment (which equals to 3 months = 0,25 of year). Duration of the zerocoupon bond equals to their time to maturity, which was 7 years in three years. So... I just divided present value of the 7-year zerocoupon bond by 0,25 (which was duration of floater) and then I assumed it is equal to the face IRS value (it was my answer). What are you thoughts about this?

Thank you vey much in advance.

Best regards
TRAXX

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