1. Interest Rates CHAPTER 4

2. Types of Rates  There are 3 types of rates that are used in the current derivative markets.  Treasury Rates  LIBOR Rates  REPO Rates

3. Treasury Rates  Treasury rates are the rates an investor earns on Treasury bills and Treasury bonds.  They are assumed to be risk-free which means that there is no possibility of government can default while paying the principal and the interest.  Students are advised to be not to be mistaken with the rates offered with the Eurodollar bonds which might be different from the treasury rates.  In order to be Treasury Rates, issued bonds and bills should be in local denomination

4. LIBOR RATES LIBOR stands for London Interbank Offer Rate. It is a reference interest rate, produced once a day, designed to reflect the rate of interest at which banks can obtain unsecured loans from other banks. A rate closely related to LIBOR is LIBID. This is the London Interbank Bid Rate and is the rate at which banks are prepared to borrow from (i.e., accept deposits from) other banks. LIBOR is more creditworthy rate in contrast with LIBID LIBOR rate can only be used by the banks who have a credit rating higher or equal to AA rating.

5. REPO Rates REPO rates stands for repurchase agreements. This is a contract where an investment dealer who owns securities agrees to sell them to another company now and buy them back later at a slightly higher price. Sometimes repurchase agreements are mistaken with the “Short Selling” Short selling seems to be similar but, there are some differences between repurchase agreements. ◦In short selling investment dealer does not own securities, he/she borrows securities ◦In short selling you have to buy back securities whatever the price is.

6. REPO Rates There are two types of Repo rates; ◦Overnight Repos ◦Term Repos

7. Measuring Interest Rates

8. Continuous Compounding What is continuous compounding? Continuous compounding is related with the compounding frequency. It assumes that compounding continuous until a limit is set. In this case our limit is how many times a principal is compounded. Until that limit is reached we compound principal daily with continuously compounding rate.

9. Continuous Compounding

10. Conversion Formulas Define R c : continuously compounded rate R m : same rate with compounding m times per year

11. Examples What is the continuously compounded rate equivalent to 10% with semi-annual compounding ? 2ln(1.05)=9.758% What is the rate equivalent to 8% with quarterly continuous compounding? 4(e 0.08/4 -1)=8.08% 11

12. Zero Rates A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T 12

13. Example (Table 4.2, page 87) 13

14. Bond Pricing To calculate the cash price of a bond we discount each cash flow at the appropriate zero rate In our example, the theoretical price of a two-year bond providing a 6% coupon semiannually is 14

15. Bond Yield The bond yield is the discount rate that makes the present value of the cash flows on the bond equal to the market price of the bond Suppose that the market price of the bond in our example equals its theoretical price of 98.39 The bond yield is given by solving to get y = 0.0676 or 6.76% with cont. comp. 15

16. Par Yield The par yield for a certain maturity is the coupon rate that causes the bond price to equal its face value. In our example we solve 16

17. Forward Rates The forward rate is the future zero rate implied by today’s term structure of interest rates 17

18. Formula for Forward Rates Suppose that the zero rates for time periods T 1 and T 2 are R 1 and R 2 with both rates continuously compounded. The forward rate for the period between times T 1 and T 2 is This formula is only approximately true when rates are not expressed with continuous compounding 18

19. Application of the Formula 19 Year ( n )Zero rate for n -year investment (% per annum) Forward rate for n th year (% per annum) 13.0 24.05.0 34.65.8 45.06.2 55.56.5

20. Upward vs Downward Sloping Yield Curve For an upward sloping yield curve: Fwd Rate > Zero Rate > Par Yield For a downward sloping yield curve Par Yield > Zero Rate > Fwd Rate 20