Valuing swap as fixed and floating rate bonds

[afterworkguinness]

Hello,
In the example on valuing swap as fixed and floating rate bonds in the notes on Hull chapter 7, the future value of the floating leg is computed as: (6 month LIBOR /2)*Notional. The notes say the floating rate is halved because "it is a semi annual payment on 5.5%"

I understand that if a bond has a 4% per annum coupon paid semi annually it is $2 per coupon, I don't get why it's being done in this case though since the swap leg is 6 months and we have a 6 month LIBOR.

I have attached a screen shot of the question for reference.

Thanks in advance.

 

[David Harper CFA FRM]

Hi afterworkguiness,

The LIBOR rates are stated per annum (aka, nominal per annum), they are not "stated per six months." So, it's very much like your bond analogy: it just happens to be a six month instrument (tenor, i guess we could call it). It helps to keep in mind that interest rates are almost always (unless otherwise specified) expressed in the assumptions as per annum rates (and returned in the solution, too). So, if you just see 5.5% whatever, the best assumption is 5.5% stated (nominal) per annum, which is different than either the compound frequency ("with semi-annual compounding") and the underlying instrument's maturity/tenor (5.5% could apply to a 1-month LIBOR, 3-month LIBOR, or 1-year LIBOR ... )

So, the assumption here, to use phraseology typical in Hull, is "six-month LIBOR is 5.5% per annum with semi-annual compounding. Just like the fixed segment pays "4% per annum."
So every six months, they will net (4% - L)/2*notional. The fixed payer is not paying $4 = 4%*100 at each six month settlement; rather the six month fixed payer pays 4%/2*100 MM = $2 MM. I hope that explains, thanks,

 

[afterworkguinness]

Thank you for clearing that up.