Products and Markets

1. Products and Markets Financial Innovations and Product Design II Financial Innovations and Product Design II

2. Measuring Interest Rates • Compounding m-times per annum (annual, semiannual, quarterly etc.): • Continuous compounding: mn R m A 1 + eRn Financial Innovations and Product Design II

3. Measuring Interest Rates • Conversion formulas: • Rc : continuously compounded rate • Rm: same rate with compounding m times per year Financial Innovations and Product Design II

4. Interest Rate Markets • Types of rates • Treasury Rate • Applicable to borrowing by a government in its own currency • LIBOR • London InterBank Offer Rate • Interest rates charged in trading between banks • Repo Rate • Sale and repurchase at a slightly higher price • Most common: overnight repos Financial Innovations and Product Design II

5. Interest Rate Markets • Zero Rates: • Zero-coupon rate • The n-year ZR is the rate of interest earned on an investment that starts today and lasts for n years with no cash flows in between • Also referred to as the n-year spot rate Financial Innovations and Product Design II

6. Interest Rate Markets • Bond pricing: Financial Innovations and Product Design II

7. Interest Rate Markets • Bond pricing: • Using zero rates: • Using bond yields: • Bond yields are bond specific! Financial Innovations and Product Design II

8. Interest Rate Markets • Par Yield: • The par yield for a certain maturity is the coupon rate that causes the bond price to equal its face value • Example using zero rates from the previous example solves Financial Innovations and Product Design II

9. Interest Rate Markets • Bootstrap Method: • A method to extract the zero rates from prices of instruments that trade Bond Time to Annual Bond Principal Maturity Coupon Price (dollars) (years) (dollars) (dollars) Zero rates Three-month: Six-month: 1 year: 10,127% 10,469% 10,536% 100 0.25 0 97.5 100 0.50 0 94.9 100 1.00 0 90.0 100 1.50 8 96.0 100 2.00 12 101.6 Financial Innovations and Product Design II

10. Interest Rate Markets • Bootstrap Method: • 1,5 year zero rate? Solution yields R = 10,681% • Calculation of the 2 year zero rate is similar, R = 10,808% Financial Innovations and Product Design II

11. Interest Rate Markets • Forward rates: • Future zero rates implied by the current term structure of interest rates Financial Innovations and Product Design II

12. Interest Rate Markets • Forward rates: • Future zero rates implied by the current term structure of interest rates Financial Innovations and Product Design II

13. Interest Rate Markets • Forward rate agreement: • OTC agreement that a certain interest rate will apply to a certain principal during a specified future period of time Financial Innovations and Product Design II

14. Interest Rate Markets • Term structure theories: • What determines the shape of the zero curve? • Expectations theory: long-term interest rates reflect expected future short-term interest rates • Segmentation theory: no relationship between short-, medium- and long-term interest rates • Liquidity preference theory: forward rates should always be higher than expected future zero rates Financial Innovations and Product Design II

15. Interest Rate Markets • Day count conventions: • Define the way interest accrues over time • Interest earned between two dates: • Actual/actual: used for Treasury bonds • 30/360: used for corporate and municipal bonds • Actual/360: used for T-bills and other money market instruments Number of days between dates Number of days in reference period x Interest earned in reference period Financial Innovations and Product Design II

16. Interest Rate Markets • Quotations: • Bonds: • Quoted price is for a bond with a face value of 100 • Quoted in dollars and thirty-seconds of a dollar: • Example: • quoted price: 90-05 90 + 5/32 = 90,15625 • The price paid by the purchaser: cash price: Cash price = Quoted price + Accrued interest since last coupon date Financial Innovations and Product Design II

17. Interest Rate Markets • Quotations: • Treasury Bills: • If Y is the cash price of a T-Bill that has n days to maturity, the quoted price (discount rate) is: • This discount rate is not the same as the rate of return earned on the T-Bill – dollar return/cost Financial Innovations and Product Design II

18. Interest Rate Markets • Treasury bond futures: • Long-term interest rate futures contract • Any government bond that has more than 15 years to maturity on the first day of the delivery month and that is not callable within 15 years from that day can be delivered. • Because any bond that satisfies the conditions can be delivered, a parameter called „conversion factor“ is applied to obtain the price received by the party with the short position. Financial Innovations and Product Design II

19. Interest Rate Markets • Treasury bond futures: • The cash received then equals: • Conversion factor: • It is approximately equal to the value of the bond on the assumption that the yield curve is flat at 6% with semiannual compounding • Cheapest-to-deliver bond: • Since many bonds can be delivered, the CTD bond will be the one that ensured that following quation is minimized: (Quoted futures price x Conversion factor) + Accrued interest Quoted price – (Quoted futures price x Conversion factor) Financial Innovations and Product Design II

20. Interest Rate Markets • Treasury bond futures: • Wild card play: • Taking advantage of different trading times in the T-bond futures market and the T-bond spot market. Financial Innovations and Product Design II

21. Interest Rate Markets • Eurodollar futures: • Eurodollar: a dollar deposited in a U.S. or foreign bank outside the U.S. • Eurodollar interest rate: the rate earned on Eurodollars deposited by one bank with another bank • Three-month ED futures contracts are futures on the three-month ED interest rate, they have maturities in March, June, Sept., Dec. For up to 10 years in the future. Financial Innovations and Product Design II

22. Interest Rate Markets • Eurodollar futures: • If Q is the quoted price for a EDF contract, the value of the contract is given by: • Q is set so that on delivery day Q = 1 – R, where R is the 3 month ED interest rate on that day. 10.000[100 – 0,25(100 – Q)] Financial Innovations and Product Design II

23. Interest Rate Markets • Duration: • A measure of how long on average the holder of a bond has to wait before receiving cash payments. • The duration can be used to estimate bond price changes as a result of yield changes: B – bond price y – yield Financial Innovations and Product Design II

24. Interest Rate Markets • Duration: • When y is expressed with compounding m times per year, the Modified duration should be used: • Duration of a portfolio: weighted average of the durations of the individual bonds in the portfolio, with the weights being proportional to the bond prices Financial Innovations and Product Design II

25. Interest Rate Markets • Duration: • Hedging using duration: • Hedging against interest rate risk by matching the durations of assets and liabilities Financial Innovations and Product Design II

26. Interest Rate Markets • Duration: • Problems: • Hedging works only when there are parallel shifts in the yield curve • Unaccurate for larger yield changes Financial Innovations and Product Design II

27. Interest Rate Markets • Convexity: • Eliminates some of the unaccuracy caused by the duration when estimating price changes resulting from larger yield changes Financial Innovations and Product Design II

28. Swaps • Swap: • An agreement between two companies to exchange cash flows at specified future times according to specified rules Financial Innovations and Product Design II

29. Swaps • Interest rate swap: • One company agrees to pay cash flows equal to interest at a predetermined fixed rate on a notional principal and in return receives interest at a floating rate on the same notional principal • The notional principal itself is not exchanged • „Plain vanilla“ swap Financial Innovations and Product Design II

30. Swaps • Interest rate swap: • Assets and liabilities can be converted from fixed rate to floating rate & vice versa • Trasforming a liability (example): • Microsoft borrows at LIBOR + 10 bps • Intel borrows at 5,2% fixed • Microsoft & Intel enter into a swap: • Microsoft pays 5% and receives LIBOR • Intel pays LIBOR and receives 5% Financial Innovations and Product Design II

31. Swaps • Interest rate swap: • Trasforming a liability: • Result: • Intel pays LIBOR + 20bps • Microsoft pays 5,1% fixed 5% 5.2% Intel MS LIBOR+0.1% LIBOR Financial Innovations and Product Design II

32. Swaps • Interest rate swap: • Financial intermediary: • Usually two nonfinancial companies do not get in touch directly to arrange a swap – deal each deal with a financial intermediary (FI) • The FI enters into two offsetting swap transactions with the two companies and earns about 3-4bps • Because the FI has two separate contracts, it bears the default risk of one of the companies in the swap and still has to honor the remaining contract Financial Innovations and Product Design II

33. Swaps • Interest rate swap: • Financial intermediary: • Large FIs act as market makers, i.e. they are prepared to enter into a swap without an offsetting swap with another counterparty • Result: • Microsoft pays 5,115% • Intel pays LIBOR + 21,5bps • The FI earns 3bps 4.985% 5.015% 5.2% Intel F.I. MS LIBOR+0.1% LIBOR LIBOR Financial Innovations and Product Design II

34. Fixed Floating AAACorp 10.00% 6-month LIBOR + 0.30% BBBCorp 11.20% 6-month LIBOR + 1.00% Swaps • Interest rate swap: • Why are swaps so popular? • Comparative advantage argument: some companies have a comparative advantage in floating rate markets whereas others have a comparative advantage in fixed rate markets Financial Innovations and Product Design II

35. Swaps • Interest rate swap: • Why are swaps so popular? • Result: • AAA now pays LIBOR + 5bps (compared to LIBOR + 30bps) • BBB now pays 10,95% fixed (compared to 11,2%) 9.95% 10% AAA BBB LIBOR+1% LIBOR Financial Innovations and Product Design II

36. Swaps • Interest rate swap: • Criticism of the comparative advantage argument: • The fixed rate remains the same throughout the life of the swap whereas the floating rate is reset at constant intervals • This creates a problem to the company that transforms its floating rate obligation into a fixed rate • The amount fixed rate interest paid depends on the way the original floating rate is reset, i.e. if BBB was downgraded to a lower credit rating this would be reflected in a higher floating rate and thus increasing the amount of interest BBB has to pay Financial Innovations and Product Design II

37. Swaps • Interest rate swap: • Valuation using bonds: • The value of a swap can be characterized as the difference between two bonds – one paying a fixed coupon and one paying a floating rate coupon • The value of a swap to a company receiving floating and paying fixed is then: Vswap = Bfl - Bfix Financial Innovations and Product Design II

38. Swaps • Interest rate swap: • Valuation using bonds: • Value of a floating-rate bond? • Immediately after payment date, Bfl = principal • Between payments: • k*: floating-rate payment that will be made on the next payment date • L: notional principal • t1: time until the next payment date -r1t1 Bfl = (L+k*)e Financial Innovations and Product Design II

39. Swaps • Interest rate swap: • Swap rates: the average of Bid and Offer rates quoted by market makers in the swap market • Bid rate: the fixed rate in a contract where the market maker will pay fixed and receive floating • Offer rate: the fixed rate in a contract where the market maker will pay floating and receive fixed • Swap rates can be used to determine zero rates: • Consider a new swap where the fixed rate equals the swap rate, then we have: Bfl = Bfix Financial Innovations and Product Design II

40. Swaps • Interest rate swap: • Swap rates can be used to determine zero rates: • The floating-rate bond will be worth par • Thus, the fixed-rate bond will be worth par as well – the swap rate is the par yield of the fixed-rate bond • As a result, zero rates can be extracted using the bootstrap method • Swap rates are used to calculate the zero curve for longer maturities Financial Innovations and Product Design II

41. Swaps • Currency swap: • In its simplest form it involves exchanging principal and interest payments in one currency for principal and interest payments in another currency • The principal amounts are usually exchanged at the beginning and at the end of the swap‘s life Financial Innovations and Product Design II

42. Swaps • Currency swap: • Example: • Swap between IBM and BP • IBM pays a fixed rate of interest 11% in Pounds and receives a fixed rate of interest of 8% in dollars IBM‘s cash flows Dollars Pounds $ £ Year ------millions------ 2001 –15.00 +10.00 +1.20 2002 –1.10 +1.20 –1.10 2003 2004 +1.20 –1.10 +1.20 –1.10 2005 2006 +16.20 -11.10 Financial Innovations and Product Design II

43. Swaps • Currency swaps: • Valuation: • Using bonds: if S0 is the exchange rate (number of domestic currency per unit of foreign currency), BD the value of the domestic bond, BF the value of the foreign bond (in foreign currency units), the value to the party receiving domestic currency and paying foreign currency is: • Using forwards: the swap is decomposed into a series of forward contracts Vswap = BD – S0BF Financial Innovations and Product Design II

44. Swaps • Credit risk: • A swap is worth zero to a company initially • At a future time its value is liable to be either positive or negative • The company has credit risk exposure only when its value is positive • While market risks can be hedged by entering into offsetting contracts, credit risks are less easy to hedge Financial Innovations and Product Design II

45. Thank You for Your Attention! Financial Innovations and Product Design II