Hull, Swaps (Apple & Citi example)

[JanaRad]

Hi everyone,
Can someone please explain why the floating rate portion in Hull’s Apple-Citibank example is multiplied by 0.5?

(See page161) Apple pays fixed rate (3% pa on a notional principal of $100m) while Citi pays fixed (6m Libor rate prevailing prior to the pmt day * $100m * 0.5). What’s with the 0.5?

Thanks in advance,

Jana

 

[David Harper CFA FRM]

Hi @JanaRad The 0.5 is because the swap is exchanging cash flows every six months (twice per year) while the rates are expressed in per annum terms (i.e., 3.0% per annum). A helpful thing to keep in mind is that interest rate inputs are generally given in per annum terms, and should always be given in per annum terms (Hull is really disciplined about this, as you'd expect). In the long-run, this avoid confusion (the confusion of wondering if you are looking at a six-month rate or an annualized rate! it is resolved: you should always be looking at an annualized rate when you get the input). Similarly, final outputs/answer should also be translated back to per annum terms. If this swap exchanged only once per year, then there would be no multiplier; if it exchanged quarterly (four times per year), then Citi would pay (6m Libor rate prevailing prior to the pmt day * $100m * 0.20). Btw, I think you mean "Citi pays floating ..." I hope that helps!