Floating Leg Of Swap Valuations

[PaulGrey]

Hi David,

Great site - very pleased with my purchase.

I'm a little stuck on putting together the floating leg part of the swap w.r.t. for screencast LO 31.6.
I think I understand the fixed rate side no probs.

1. The last cash flow is 1.25 years with a LIBOR of 6.5%. But isn't this is for the 12 Months? Should there be an entry for the 15 months in the table of LIBOR rates.

2. I think the 1st float rate is 2.75%, since were using a 6 month LIBOR for 3 months. What I can't work out, what happens to the other floating rates. How do they get simplified or 'shortcutted' into one cash flow.

Thanks a lot,
Paul

 

[David Harper CFA FRM]

Hi Paul,

Thanks for saying that, great to hear.

1. Yes, correct, I think the example is *flawed* b/c of this (I'll start an 2008 errata here on the forum soon). Either the table should say 6.5% @ 15 months, or better, 7% at 15 months.

2. (I imagine you realize this refers to Hull Chapter 7, although it's a rare example of where Hull wasn't clear for me). In this case, the receiver of the floater is going to get the next coupon in +3 months. So the coupon is a "given" cash flow. Now, at the moment that next coupon in paid, the key idea is that the value of the floating bond must be its par ($100 here) because its future coupons float at the same rate we use to discount. An analogy: for a fixed coupon bond, if coupon rate = YTM, then bond prices at par. Similarly, you'll pay par for a bond that floats coupons because variations in your discount rate are "negated" by fluctuating coupons. So that single cash flow, in three months, is the coupon the receiver knows to be getting plus the FV (+ 3 months) of a bond that must be worth its par. (The other tricky thing about this, IMO, is that three months forward, that first coupon is paying a SIX MONTH rate; rates are determined at the start of each six month leg and paid at then end.)

Here is the link to the EditGrid that underlies this slide example, in case it's helpful.

Please note: I just now changed the 15 month rate, to per your point (1), so the 15-month is 7% - i.e., an unrealistically steep, straight line

Below the example you will notice, I also have an example to show why the floater must = par. To your point (2), you'll see if you change coupon rates, it doesn't matter, the bond is always worth par.

David