# Interest Rate Collar - Options

I read this and got messed up … “An Interest rate collar combines a cap and a floor. A borrower with a floating-rate loan may buy a cap for protection against rates above the cap and see a floor in order to defray some of the cost of the cap”. I don’t get the notion behind the latter half of the statement… Background ---------------- Present Interest Rate (S) = 7% CAP Strike Rate (X1) = 10% FLOOR Strike Rate (X2) = 3% Case 1: Interest Rate rises to 13% Case 2: Interest Rate falls to 1% Let’s say we have a borrower and a lender on a floating rate contract (with LIBOR being the floating rate) and the current-period floating rate at 7%. The borrower is a bit worried about the Interest Rates rising in the near future and purchases a Cap with a strike rate of 10% (i.e. LONG on the caplet), so if by chance, the interest rates rise above 10%, the cap is going be in-the-money cap and will compensate for the rising rates (Case-1: 13%-10%)*notional amount = CAP compensation. Understood till this… but then… Why does a borrower needs to go SHORT on a floor (sell a Floorlet with say a interest rate of 3%) simultaneously?? Why does a borrower always need an INTEREST RATE COLLAR. Because if he is short on an interest rates and Interest rates go below 3%, he will have to make additional payments to the counterparty?? Had he not entered into a SHORT position he would have not needed to pay the additional (3% - 1%)*notional amount to the LONG position (Case2)? How is the 3% FLOOR SHORT position helping him defray the cost of the cap??? Hope I am clear enough to expect a response - Dinesh S

He is RECEIVING a premium for selling the floor. These REC premiums can be used to PAY premiums for the cap he is buying (long).

He wouldn’t really need to go short on the floor, but by doing so he can seriously cut down on the cost of the cap. As you know, options are free. In some cases you can construct the collar for nothing or very little…the premiums recieved for selling the floor equal the premiums you must pay to be long on the cap. Hope this helps.

Wondeful!! Thanks so much mwvt9!! I am now pretty clear on what a IR-collar looks like. On a separate note… The losses for being in a SHORT-PUT position are limited to the Strike-Price (-X Max), but the losses for holding a SHORT-CALL position are unbounded, so why would a rational investor take such a position/risk for just a few pennies he receives at the beginning in the form of option call premium? - Dinesh S

Think about what the underlyer is here. It is interest rates. So the furthest that they can drop is to 0% and your floor is set at 3%. Also remember that if they did you would be happy because you would be paying that on the money you borrowed. The whole idea behind this was to hedge your risk of interest rates rising. You are putting in floor to make it cheaper. If interest rates went to zero you would lose money on the floor, but it would pale in comparision to the amount of money you would save on the debt payments.

I think I was not clear on what I wanted to ask, so I re-iterate “Being in a SHORT-CALL position is the riskiest position to be in (due to it’s unlimited-potential-losses), so why would one like to take such a position just for a little premium?” The example you gave is applicable for SHORT-PUT position, which is perfectly correct!! - Dinesh S

So how about this - for virtually any security realzed volatility at nearly all strikes at option expiration is less than implied volatility on options, say, 2 months prior to expiration. As you say, people don’t like the idea of taking on large risk for small gain. Because of that, it is systematically mispriced. If it’s systematically mispriced, why not buy all of it and diverse away your risk?

… true, and If the owner of the stock is confirmed that the price of the stock (current price \$50) he owns is not going to go anyway beyond \$60, under any circumstances. So he could write an out-of-the-money SHORT-CALL and create a COVERED-CALL option strategy and profit by getting that extra bit of income as a call-option-premium, even with no real-capital-appreciation of the stock!! But effectively what he has done is this “He has traded-off the stocks upsite potential for a call premium” … Am I in the right direction or did I loose my way? - Dinesh S

That is true to a certain extent. But you have to remember that the price of the option will take volatility into account. So you would not get much of a premium for a historically stable stock, but if you are selling a call for a very volatile stock you will receive a large premium. So it is not really the case you are describing where you are getting pennies for trading all your future upside on the stock. The market will price this for you. Someone will more knowledge in this area could help you better than I could.

If the owner of a stock @ \$50 is certain that the stock price will not go above \$60 he should be selling all the 60 calls his credit will allow him to sell regardless of whether he owns the stock at all as long as those calls are valuable to someone else. Certainty is really hard to come by when other people are uncertain.

Thanks all and one last question… Do we expect any of such questions in the exam… After reading the LOS’s, I initially thought that we just had 2 option strategies, ‘covered call’ and ‘protective put’ ******** Which of the following combinations of options and underlying investments have similarly shaped P&L diagrams? A. Covered Call and Protective Put B. Covered Call and short stock/long call C. Short put option/long call option and protective put D. Long call option/ short put options and long stock position ******** I drew all kinds of P&L diagrams, Payoff diagrams for this and found nothing matching. - Dinesh S

Try doing the payoff diagram on D) with the strikes on the put and the call being the same.

dinesh, Look back at the put/call parity equation. Rearrange it so that are just long the stock on one side of the equation and then see what you have on the other side. C+X/(1+r)^t=P+S S=C+X/(1+r)^t-P You can ignore the bond (X) for now. Because you have a positive sign on the call you are long. The negative sign on the put means you are short. This means that you can create a synthetic long stock position by buying a call and selling a put (and then you are also long the bond which we are ignoring right now). EDIT: Joey beat me to the punch

Perfect!! Got it, initially I took different strike prices for both options Here’s the workout (P&L diagrams) ----------------------------------------------- S=\$50 X1 = 40 Call Premium (CP) = \$4 LONG CALL (purchased a right to buy) X2 = 40 Put Premium (PP) = \$4 SHORT PUT (sold the right to sell) (Assumption: strikes considered the same…) LONG CALL -------------- Max(loss) = -\$4 (call premium) Max(Gain) = Unlimited Breakeven Point = X + CP = 4 + 40 = \$44 SHORT PUT -------------- Max(loss) = -(X - PP) = - (40 - 4) = -\$36 Max(Gain) = \$4 (put premium) Breakeven Point = X + CP = 4 + 40 = \$44 So we have a straight line from Max(loss) (i.e. -36) for short-put to Max(gain) (i.e. unlimited) for long-call (merging into a single line at Breakeven (i.e. at \$44)) which is exactly the same as a LONG-STOCK But do we expect such kinds on the exam? - Dinesh S

Yes, but you don’t have to figure out the numbers really. Just use the put/call parity formula. They will test the concept at level 1.

mwvt9 Wrote: ------------------------------------------------------- > dinesh, > > Look back at the put/call parity equation. > Rearrange it so that are just long the stock on > one side of the equation and then see what you > have on the other side. > > C+X/(1+r)^t=P+S > > S=C+X/(1+r)^t-P > > You can ignore the bond (X) for now. > Because you have a positive sign on the call you > are long. The negative sign on the put means you > are short. This means that you can create a > synthetic long stock position by buying a call and > selling a put (and then you are also long the bond > which we are ignoring right now). > > EDIT: Joey beat me to the punch WoW mwvt9!! I missed to read this before… that’s simply great, It takes no more than 10-secs to re-arrange the terms and Bingo! Actually I have not yet covered the Put-Call Party relation, so thought of putting in the actual numbers. - Dinesh S

Right.^ Once you get to put/call parity this will make much more sense. You were doing it the hard way for sure. After awhile you won’t even need the equation anymore. You will be able to do the concepts in your head. Good luck.

Pretty rewarding to watch people learn stuff you teach them isn’t it, mwvt9?

Yes, it really is. I like to try to give back because I have learned so much from the everybody here. The people on this forum will never know how much I appreciate their help.

Thanks mwvt9 and JoeyD!! The learning curve would have been much much steeper for me without your help and this forum. Will always remember and cherish these initial transitioning days. - Dinesh S