Collar Question

CFA Level III Derivatives
#1

Urgh, I just got through a collar question. Basically, the data was that a bank makes LIBOR +200 bps on its assets, & its liabilities were fixed at 5%. It described how it also bought a floor & a cap (collar). I understand the collar, and also understand how to calculate annual interest earned here, which is what the question asked for.

Maybe I am just confusing myself but the reason I got this wrong- was because it also mentioned quarterly payments (I assume on the floor & cap). My confusion is that the annual interest earned calculation was based on the given libor at the beginning of the period…why? Don’t we have to look at how libor changes quarterly, instead of just looking at what it was at the beginning of the period?

#2

sorry I want to add to this–

Also confusing me in the question above is the payoff of the floor & cap were determined at the beginnig of the period…shouldn’t there we 4 different quarterly payoffs for those options?

#3

Post the question… no idea what you’re asking!

Floors and caps are paid in arears. If its a series of 4 collars, then theres 4 payoffs. if its 1 collar, then theres 1 payoff.

#4

  1. Collar = Buy Floor and Sell Cap (correct me if needed)

  2. The periodic LIBOR rates determine the periodic cash flows. For example $100 loan - 4% LIBOR first quarter $1.50 cashflow. 8% second qtr, $2.50 etc…

However EAR has nothing to do with LIBOR. Just the timing of cashflows ie Loan, interest and principal cashflows. This will give you periodic yield from which you annualize using 365 day count basis.

#5

Correct if you’re the lender; incorrect (backwards) if you’re the borrower.

#6

mrb102189,

Maybe this will help (and correct me if I’M WRONG), but I always kinda talk to myself as I’m going through these problems as I set them up and also tend to write out what I have to do in bullet points which I’ve been told helps for getting partial credit. While collars and their effective interest sound similar to effective annual interest (EAR), whether you’re a borrower or a lender, they’re not the same…

First, a collar, whether we’re trading equities, FX, options, rates, etc. CAN EITHER BE:

  • Buying a Put (Floor) and Selling a Call (Cap)
  • Buying a Call (Cap) and Selling a Put (Floor)

For the purposes of your question, we’ll just talk interest rate collars from here.

  1. If we’re Buying a Put (Floor) and Selling a Call (Cap), where do we stand and what do we want?:

IF LIBOR IS ABOVE THE CAP, WE MAKE A PAYMENT (POSITIVE COST) #NOTSWEET :frowning_face:

Cap X: ____________________________________________________________

:slightly_smiling_face:

Floor X:_____________________________________________________________

BUT, IF LIBOR IS BELOW THE FLOOR, WE RECEIVE A PAYMENT (NEGATIVE COST) #SWEET :grin:

Why would we put on this type of collar? Answer: If we thought rates were going to FALL in the future aka we’re a lender and we won’t be able to lend at such nice, high, juicy lending rates…

2. If we’re Buying a Call (Cap) and Selling a Put (Floor):

IF LIBOR IS ABOVE THE CAP, WE RECEIVE A PAYMENT (NEGATIVE COST) #SWEET :grin:

Cap X: ____________________________________________________________

:slightly_smiling_face:

Floor X:_____________________________________________________________

BUT, IF LIBOR IS BELOW THE FLOOR, WE HAVE TO MAKE A PAYMENT (POSITIVE COST) #NOTSWEET :frowning_face:

Why would we put on this type of collar? Answer: If we thought rates were going to RISE in the future aka we’re a borrower and we won’t be able to borrow at such nice, low, screw you bank I don’t wanna pay high rates…rates.

Regardless of which collar you’re putting on, I always set up the Effective Interest Payment questions like so, and again, we’ll assume you’re buying a floor and selling a cap:

STEPS

  1. Determine payment dates (@ end of period using start-of-period LIBOR rates. Why??? Because payments are paid in arrears so we use the beginning of the period LIBOR rates. Dumb, I know…)
  2. Calculate payment on the floating rate liability for each payment date [NP x (LIBOR + SPREAD) x days/360)].
  3. Next calculate payments received/paid on cap/floor should either be in-the-money.
  4. Determine net payment on loan by combining Liability Payment + Payment Paid from Cap - Payment Received from Floor (if either are in-the-money).

SET UP:

So I always set it up like so, again for LONG A FLOOR; SHORT A CAP

  • Interest Payment : Notional Principal (NP) x (LIBOR FROM BEG. OF PERIOD + SPREAD) (DAYS/360)
    • CAP: If OTM, NO PAYMENT. If ITM: NP x (LIBOR FROM BEG. OF PERIOD - CAP STRIKE) (DAYS/360)
    • FLOOR: If OTM, NO RECEIPT. If ITM: NP x (FLOOR STRIKE - LIBOR FROM BEG. PERIOD) (DAYS/360)
    • Effective Interest Payment = Interest Payment + Cap Cost (if any) - Floor Payoff (if any)

I always try to ask myself at the beginning AND the end of the question, 'Who is Making Payments and does this make sense?'

IF A BANK ENTERS A COLLAR AND THE QUESTION ASKS TO CALCULATE ITS PAYMENTS, GO ABOUT IT THE NORMAL WAY, BUT IF THE QUESTION ASKS TO CALCULATE THE PAYMENTS TO THE BANK THEN REVERSE THE PREMIUM PAYOFFS!!!

Maybe this helps or maybe I made things worse… :confused: