Swaps

1. Swaps Part-II

2. Transactions Equivalent to a Swap • Consider the following swap. • Citibank has entered into a swap with a notional principal of 50 MM USD. • Today is 15 December 2003. • Citi will pay a fixed rate of 7.5% per annum on the 15th of March, June, September and December. • It will receive payments every quarter based on the 90 day LIBOR at the start of the period.

3. Equivalent (Cont…) • Interest will be computed based on the actual number of days in a given three month interval. • The year is assumed to consist of 360 days. • The ex-post payments made/received by Citibank are as described below.

4. Equivalent (Cont…)

5. Equivalent (Cont…) • Now instead of entering into this swap, assume that Citi had issued a one year fixed rate note with a principal of 50MM, on which it has to make quarterly payments at the fixed rate of 7.5%. • Assume that the money is used to purchase a one year floating rate note with a face value of 50 MM, and which pays coupons on a quarterly basis based on the LIBOR at the beginning of the quarter.

6. Equivalent (Cont…) • The net result is an interest rate swap. • Notice that at the outset there is an inflow of 50MM from the fixed rate note and an outflow of 50MM on account of the floating rate note. • Thus the net cash flow is zero. • This is equivalent to a swap where the principal is specified purely for computing the interest but is never exchanged.

7. Equivalent (Cont…) • Similarly at the end 50MM will come in when the floating note matures, and will be exactly the amount required to retire the fixed rate note. • Thus once again there is no exchange of principal. • As long as interest payments on both the fixed as well as floating notes are based on an ACT/360 basis, the net result is an interest rate swap.

8. Equivalent (Cont…) • A swap can also be viewed as a spot transaction combined with a series of FRAs. • On 15 December we know that Citi will receive a payment of 960,000 on 15 March and will have to make a payment of 937500 on that day. • This is equivalent to a spot transaction where the counterparty agrees to pay 22500 to Citi on March 15.

9. Equivalent (Cont…) • The second payment is equivalent to a FRA in which Citi agrees to pay fixed on 15 June and receive a payment on that day based on the LIBOR as of 15 March. • The remaining two exchanges of interest payments can also be viewed as FRAs with maturity dates on 15 September and 15 December respectively.

10. Pricing a Swap at the Outset. • We will now see how the fixed rate for a coupon swap is arrived at. • A swap can be viewed as a combination of a fixed rate and a floating rate bond. • Since it involves no initial exchange of cash it should have zero initial value. • Consider the following data for a swap.

11. Pricing (Cont…) • Quantum Electronics has entered into a swap with a notional principal of 20MM. • It promises to pay fixed and receive at LIBOR every six months for a period of two years. • Assume that every six monthly period consists of 180 days and that the year consists of 360 days. • The current interest rate structure is as follows.

12. Term Structure

13. Pricing (Cont…) • The floating rate note corresponding to the swap will have a value of 20MM. • The question is, what is the coupon rate that will make the fixed rate note have a value of 20MM. • If we denote the unknown semi-annual coupon by C, then:

14. Pricing (Cont…) C C C _______ + ______ + _______ (1.092).5 (1.099) (1.1046)1.5 C + 20,000,000 + _______________ = 20,000,000 (1.1078)2  C = 1,045,000  Annual coupon rate = 10.45%

15. Pricing (Cont…) • Thus if Quantum agrees to pay at a fixed rate of 10.45% every six months and receive at LIBOR, the swap will have zero initial value.

16. Pricing a Swap During Its Life. • At the outset a swap has zero initial value. • That is, it is neither an asset nor a liability. • Subsequently during its life it can attain a positive or a negative value. • Consider the swap from the perspective of the party that is paying fixed but receiving floating. • Obviously it stands to benefit if rates were to rise subsequently but will lose if rates were to fall.

17. Example • A company called Global Resources has entered into a swap where it agrees to pay fixed at 10.67% and receive LIBOR. • The notional principal is 20MM. • Payments are to be made every six months for two years. • Successive payment dates are exactly 180 days apart and the year consists of 360 days.

18. Example (Cont…) • This swap was initially priced at 10.67%. However 1.25 years have now elapsed and interest rates have changed. • The LIBOR on the last payment date was 9.42%. • So the next receipt is 942,000. • Each payment is of course 1,067,000.

19. Example (Cont…) • The best way to price this swap is by valuing the fixed as well as the floating rate notes that taken together are equivalent to the swap. • Assume that the discount rate for the payment to be made after .25 years is 9.12% and that for the payment after .75 years is 9.23%.

20. Example (Cont…) • The value of the fixed rate bond is: 1,067,000 21,067,000 _________+ __________ = 20761216 (1.0912).25 (1.0923).75 • The value of the floating rate bond is: 942,000 + 20,000,000 __________________ = 20490005 (1.0912).25

21. Example (Cont…) • The rationale is that the value of the floating rate bond will reset to par on the next payment date. • As far as the company is concerned, its fixed rate obligations have a value of 20761216 whereas its floating rate receipts have a value of 20490005. • Thus the swap has a value of -271,211 and is therefore currently a liability.

22. Currency Swaps • What is a currency swap? • It is a contract which commits two counterparties to an exchange, over an agreed period, two streams of payments in different currencies, each calculated using a different interest rate, and an exchange, at the end of the period, of the corresponding principal amounts, at an exchange rate agreed at the start of the contract.

23. Example • Barclays Bank London agrees to pay Citibank New York over a period of two years a stream of interest on 17MM USD. • The interest rate is fixed at the outset. • Citibank in return agrees to pay interest on 10MM GBP at a rate agreed upon at the outset. • They also commit to exchange at the end of the two-year period the principal amounts of 17MM USD and 10MM GBP.

24. Differences Between Currency Swaps and IRS • Currency swaps involve an exchange of payments in two currencies. • Not only is interest exchanged, there is also an exchange of principal. • In this case the exchange of principal takes place only at maturity. • Thus the impact on the balance sheet is only at maturity.

25. Differences (Cont…) • Thus this kind of a swap is termed an off balance sheet (OBS) transaction. • The interest payments being exchanged may be computed on a: • Fixed versus floating basis • Floating versus floating basis • Or a Fixed-Fixed basis

26. Motivation • Why may Barclays and Citibank want to enter into such a swap? • At maturity Barclays may have an amount in USD that it wishes to exchange for GBP. • Citibank on the contrary may have an amount in GBP that it wishes to exchange for USD.

27. Motivation (Cont…) • In a currency swap the rate for the exchange of principal will be fixed at the outset. • This rate is usually the spot exchange rate prevailing at that time. • But is subject to negotiations. • By fixing the exchange rate the two banks hedge each other against exchange rate risk.

28. Exchange of Principal at Inception? • By definition a currency swap only requires the exchange of principal at maturity. • However it can so be structured so that there is an exchange of currencies at the outset as well. • This kind of deal is also called a currency swap but is something more than just a swap.

29. Exchange (Cont…) • A swap with an initial exchange of principal is a combination of a risk and a hedge. • This is because to exchange currencies at the outset the two parties must have either borrowed or else accrued income in the respective currencies. • This is a source of risk. • The actual swap itself is a hedging device.

30. Mechanics • Let us assume that Citibank and Barclays were to exchange principal amounts at the outset. • Barclays would sell 10MM GBP to Citibank in exchange for 17MM USD. • The sterling sold by Barclays and the dollars sold by Citi would be borrowed by these banks specifically for the purpose of the swap.

31. Mechanics (Cont…) • At maturity this exchange of principal would be reversed. • The re-exchange of principals at maturity would be at the original exchange rate. • Such swaps are therefore termed as par swaps. • The sterling received by Barclays at expiration from Citi would be used to payoff its original borrowing.

32. Mechanics (Cont…) • The periodic interest payments received from Citi would be used by Barclays to service its sterling loan. • The dollars received by Citi at maturity would be used by it to retire its original borrowing. • The periodic interest payments received from Barclays would be used by Citi to service its dollar loan.

33. Mechanics (Cont…) • Thus, through a currency swap, each counterparty effectively services the debt of the other.

34. Important! • If there is an initial exchange of principal through a currency swap, the borrowings which are undertaken to fund this initial exchange are separate from the swap itself. • But the initial exchange would be a part of the currency swap documentation.

35. Terminology • The term currency swap is generally used to describe swaps involving two different currencies. • But strictly speaking the term applies only to those swaps in which both the interest streams are calculated using fixed rates. • A currency swap in which at least one of the interest streams is calculated using a floating rate is called a cross-currency swap.

36. Terminology (Cont…) • There are two types of cross-currency swaps. • Coupon swaps involve a fixed-floating swap. • Basis swaps involve a floating-floating swap. • Currency swaps where there is an initial exchange of principal are sometimes referred to as Cash Swaps.

37. Terminology (Cont…) • In practice, swapping directly between non-dollar currencies can be difficult, particularly when a floating rate is involved. • In such cases the desired swap can be achieved by going through a series of swaps involving an intermediate currency which is usually the dollar.

38. Terminology (Cont…) • The link in such swaps is typically the 6M USD LIBOR. • Thus is because while Eurodollar deposits are very liquid, eurodeposits in other currencies are relatively illiquid. • A cocktail swap may involve multiple legs. • Some legs could involve two currencies, while others may be interest rate swaps.

39. A Circus Swap • A circus swap is a very simple cocktail swap. • It consists of a cross-currency coupon swap (fixed versus floating) and a single-currency (coupon swap). • Both floating streams are calculated using the same LIBOR. • This can be used to replicate a fixed-fixed currency swap.

40. Illustration • An investment bank pays interest on Swiss Francs at a fixed rate to UBS and receives interest based on the 6M LIBOR in US dollars. • At maturity the bank will deliver Swiss Francs to UBS and will receive the equivalent from it in dollars. • The bank then enters into an interest rate swap with JP Morgan Chase where it pays interest in USD based on the 6M LIBOR and receives a fixed interest in dollars. • The net result is that it is paying a fixed rate in Swiss Francs and receiving a fixed rate in dollars.

41. Counterparties • In the case of single currency swaps, counterparties are distinguished on the basis of who pays fixed and who receives fixed. • However in the case of currency or cross-currency swaps the relationship is complicated by the exchange of currencies.

42. Counterparties (Cont…) • Thus there is a need to describe each counterparty in terms of the interest rate and the currency that it pays, and the interest rate and the currency that it receives.

43. Credit Risk • In the case of Interest Rate Swaps, the risk is with respect to interest only. • However in the case of currency swaps credit risk is with respect to both interest as well as principal.

44. Credit Risk and IRS • The credit risk on an interest rate swap is basically an issue on non-payment of interest. • The size of a loss due to non-payment is a function of how interest rates move. • Thus credit risk is often expressed in terms of a wider concept called default risk.

45. Default Risk • Default risk is defined as: credit risk x interest rate risk • In other words credit risk measures the probability of a default, whereas default risk measures the probable loss due to default.

46. Interest Rate Risk • While analyzing the interest rate risk component, we need to distinguish between Current Risk and Future Risk. • Current risk refers to the interest loss which would be suffered in the event of an immediate default. • Future risk is the interest loss which would be suffered in the event of a default in the future.

47. Interest Rate Risk (Cont…) • The impact of an immediate swap default can be estimated with certainty. • The impact of a future default is uncertain because the date of default is unknown.

48. Matched Books • Dealers who arrange swaps try and maintain matched books. • The way to run a matched book is by hedging it as soon as possible with an equal and opposite swap. • Matching a swap in this fashion is called a reversal.

49. Matched Books (Cont…) • A reversal will take care of the dealer’s interest rate risk. • But he is now exposed to default risk from both sides. • One way of avoiding this problem is by terminating or canceling the original swap. • Of course such termination requires the consent of the counterparty.

50. Termination • When a swap is terminated it is valued in terms of its profitability to the counterparties. • As discussed earlier the profitability is the NPV of the fixed rate stream versus that of the floating rate stream. • The future values of LIBOR used to value the floating rate streams are usually determined from futures contracts or from FRAs.