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Interest Rate Collars

Download ACCA P4 Interest Rate Collars

This is a short article to explain what an interest rate collar is, and how interest rate options may be used to create one.
If we are borrowing money, then we can fix a maximum interest rate by buying a put option.

So, for example, if we buy a put option at a strike price of 92.00 then we will be fixing a maximum interest rate of 8%.
So….if the actual interest rate turns out to be only 5% we do not exercise the option and we just pay 5%. But if the actual interest rate turns out to be 10% then we pay the interest at 10% but exercise the option and effectively ‘claim back’ 2% from the seller of the option. (For details of how exactly this works see the Course Notes and lectures on options).

The benefit of buying the option is obvious – we fix a maximum rate but we get the benefit if rates are lower. However the downside is that we have to pay a premium for the option – whether or not we end up exercising it.
Similarly, there are people who are depositing money and therefore will be wanting to fix a minimum interest rate. They will buy a call option. If the interest rate falls then they will ‘claim’ from the seller of the option, but if the interest rate rises then they will get the benefit of the higher rates and will not exercise the option.

 

Back to the borrower!
They fix a maximum rate, but the downside is they have to pay the premium.

What they can do to reduce the cost is to also sell a call option (effectively becoming a dealer) and will therefore receive a premium from the person buying it.
This means they still have the benefit of fixing a maximum rate (a ‘cap’) but the net cost of it is reduced because although they still pay the premium for the put option, they will also be receiving a premium from selling the call option.
However, selling a call option will mean that they are accepting a minimum interest rate (a ‘floor’).

To illustrate with a very simple example.

Suppose we buy a put option with a strike price of 92.00 (fixing a maximum interest rate of 8%).
Suppose we also sell a call option with a strike price of 96.00 (fixing a minimum interest rate for the buyer of 4%).

Let us see what happens for different actual interest rates that might apply when they actually start
the loan.

Suppose the actual interest rate turns out to be:
10%; b) 6%; and c) 3%

 

a) If the actual interest is 10% then we will ‘claim’ on the put option and get 2% back from the seller. The person who bought the call option will not ‘claim’ because they are getting higher interest on their deposit. So the net cost to us is 8% – this is the most we will ever end up paying.

b) If the actual interest is 6% then we will not ‘claim’ on the put option. Also the person who bought the call option will not ‘claim’ from us. So we will end up paying 6% – we have got the benefit of the lower rate.

c) If the actual interest is 3% then we will not ‘claim’ on the put option. However, the person who bought the call option from us (because they wanted to fix a minimum interest rate on their deposit of 4%) will ‘claim’ 1% on us because we sold it to them. So we will end up paying 4% in total (3% on the loan, and 1% to the buyer of the call option).
The end result means that whatever the interest rate turns out to be, the maximum that we will end up paying will be 8% (fixed by buying the put option of 92.00), but it will also mean that the minimum we will end up paying is 4% (fixed by selling the call option at 96.00).

The reason that we might wish to do this is that we are still able to fix the maximum interest we will pay, but by accepting a minimum interest the net cost of the premium will be reduced (we pay for the put option, but receive a premium from selling the call option).
Having a maximum rate is a ‘cap’. Having a minimum rate is a ‘floor’.
Having a maximum and a minimum is a ‘collar’.

 

 

Reader Interactions

Comments

  2. Sir, in June 2015 paper, there was a question on interest rate collar, I’m confused at sell call option, and the examiner said call option is not exercised, the option holder can buy the instrument at a lower price of 95.44 instead of higher option exercise price of 96.00. this line confused me. what exactly mean by this. Thanks

    • If they have sold an option then it is up to the person who bought it to decide whether or not to exercise it. Since it is a call option then they buyer has the right to buy futures at 96.00, but if the price of the futures is 95.44 there is no point in the buyer exercising the option because they will end up paying more for the futures.

      • But sir, as buyer like i buy a call option, and exercise price is 96 and market price is 95.44 means market is receiveing a high interest and why i will not excersie.

      • That is correct, and that is what I said in my last reply.

        The buyer will not exercise, but if we are the seller (we have sold a call option) then it is the buyer that will decide not to exercise (which is what the examiner has said “the call option is not exercised”)

      • If the futures price is lower than the exercise price, then the buyer will not exercise.
        If the futures price is higher than the exercise price then the buyer will exercise.

        Therefore the effect of selling a call option is to limit the minimum interest.

        (It will help you to watch all of the lectures on interest rate options – collars are just one example of how options can be used)

      • sir, one more question,that is related to interest rate futures. if we want to borrow then we open by selling and close by buying. for instance; the future we sell has 5% means 95 but when we close by buying it is 96% or 6%. then it is gain of 1%. whatever we are buying a higher interest rate.waiting for reply. Thanks

      • But we are not buying. We are selling a call option as part of the collar.
        The buyer of the call option has the right to exercise the option and buy futures at 94. If the price of the future is 96, then he will exercise the option and buy futures at 94 and immediately sell at 96 and make a profit. So the buyer would exercise the option.

      • Hello sir,
        the market interest rate is at transaction date is 4.4% and the put options interest rate is 4.5% (100-95.5). So if we excercise it we will be making a loss of 0.1% right. But still the examiner has excersiced it, why has he don’t it.

      • I have no idea which exam question you are referring to.
        Ask in the Ask the Tutor Forum (not as a comment on an article) and say which question you mean.

    • Please post questions like this in the P4 Forum, and not as a comment on a lecture about interest rate collars!!

      If you are taking the Global variant of the P4 exam then you should practice those questions – Global is the exam in all countries except those that have their own special exam.

      Yes there are pilot papers – they are called specimen papers.

  5. Hi John,

    Just seeing this after the exam yesterday. I attempted the interest rate options question but left out the collar part. One thing that confused me though was the ticks given. I remember in one of your lectures you state that you usually ignore ticks. I answered the questions they was you solve them but inadvertently multiplied the ticks per contract again. Is that a problem – would the examiner ignore this error of judgement? How many marks can one get for correctly getting the number of contracts and the basis & expected futures price?

    Thanks.

    • I really cannot say how many marks you will get – I am not the marker, and I obviously cannot see what you wrote.
      However most of the marks are for proving you understand (rather than getting the exact figures) and so assuming your workings were clear enough I would not think that you would lose very many marks.
      Don’t worry about it now – I am sure it will not be many marks lost 🙂

      • Thanks John,

        I really want to appreciate your revision of the December 2013 Q1. It really made a difference as Q1 this diet was a prototype.

        GOD bless you.

        Although it has to be said that the variables that are included in Q1 need to be reassessed as students cant really finish such questions in the alloted time frame.

        Regards,

  8. Dear Tutor,

    Can I clarify this please, I am little bit confused.

    ACCA Dec 2011 , Question 2. Alecto Co. (To Borrow a Loan)

    Current LIBOR 3.3%
    Using Strike Price (Put option) 96.00
    Using Strike Price (Call Option Sold) 96.50

    DATE OF TRANSACTION (EXPECTED OUTCOME) – Using Interest Rate decrease
    Interest Rate (LIBOR) decreased by 0.5% , so LIBOR becomes 2.8%

    Of Course LIBOR has gone below our ‘CAP’ of 4% (Strike of 96.00) , so Don’t exercise option. At the same time LIBOR has also gone below minimum interest receivable on Call (of 3.5%), So they need to claim back difference between 3.5% and 2.8% – We will pay them this difference. Translated to futures, this will be difference between 96.50 (call Strike) and 97.20 (LIBOR on date of Loan).

    BUT the examiner Solution was :

    Difference Between the Strike Price of Call Options sold 96.50 (3.5%) and 97.02 (2.98%), which was the futures prices estimated on the date of Loan (May 1). This has confused me .

    I have gone through your explanation on Collars here again and the example you provided, so I think my solution above should be correct?

    Please let me know.

    Thanks

    • Traded options are not directly on interest rates. The option is the right to buy/sell futures at a fixed price on a future dates. So the profit or loss is the difference between the strike price and the futures price on that date.

      It may help to watch my lecture on interest rate options. (It’s not in itself a collar problem – it’s they way that interest rate options always work)

  10. Thanks a lot for this, I have been rushing over questions on collars (didn’t fully understand before now).

    One final thing please;

    CASE 1
    (As a borrower and assuming Interest rate goes up on date of loan)

    Effective Interest paid will be ?

    Net Premium paid (Difference btw Put premium and Call premium)
    Add Whatever the Interest is on the date of transaction
    Less Profit on Put Option

    That will then be used to determine the effective Interest rate.

    CASE 2
    (As a borrower and assuming Interest rate went down on date of loan)

    Effective Interest paid will be ?

    Net Premium paid (Difference btw Put premium and Call premium)
    Add Whatever the Interest is on the date of transaction
    Add what the call option buyer claims from us (assuming interest was lower than call option rate)

    That will then be used to determine the effective Interest rate.

    Hope this is correct?

    Thanks

  12. Thanks for the clarification. However I’m still unsure about fixing a “floor”. I understand that we hedge, so at least if everything goes wrong, we’ll still get a premium from the call option… but I don’t understand how practically that works.

    Would be great if you explain that floor part again. Thx

    • Remember two things:
      First, that we are borrowing money and so the interest we way on the borrowing will be whatever the rate turns out to be.
      Secondly, by selling a call option, we are being the dealer and if interest rates drop below the strike then we will have to pay out to the person who bought it.

      So….suppose we sold a call option at a strike of 95 (which is equivalent to 5%).

      If interest rates fall to 4% the we will pay 4% on the borrowing. But the person who bought the call option will ‘claim’ from us 1% (5% strike – 4%). So we will end up effectively paying out 4% + 1% = 5%.
      If interest falls to 3% then we will pay 3% on the borrowing. But the person who bought the call option will claim from is 2% (5% strike – 3%). So we will end up effectively paying out 3% + 2% = 5%

      So whatever happens, we will always end up paying out at least 5% – it cannot end up being any lower. So we have fixed a ‘floor’ – a minimum rate.

      (If interest rates are 6%, then we pay 6% on the borrowing but the person who bought the call option will not claim from us, so we then pay 6%. We limit the maximum we pay by buying a put option, but that is a separate thing and I think you are happy with that side of it.)

      • Dear Mr. Moffat

        From the above explanation, it becomes evident that there is sort of contractual agreement that makes it imperative to pay the buyer of the call option when the interest rate falls below the exercise price.

        Please advise if there is a rational explanation to this obligation to reimburse the call option buyer. It seems that there is something more to this than a simple contractual obligation.

        Please elaborate.

        Thank you

      • Of course there is an obligation and it is perfectly rational!
        If I sell you a call option then you have the right to buy from me an interest rate future at a fixed price. If you choose to exercise that right then I have to sell you the future at a fixed price.

  13. Thanks so much for this article.However i have a question on determining the period when to start claiming capital allowances,I have noticed that whenever it is mentioned that tax is claimable in arrears,capital allowances is claimed in year 1 but if it is mentioned that tax is claimed in the year when cash flow is generated

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