1. Fall-02 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html EMBAF Zvi Wiener Based on Chapter 2 in Fabozzi Bond Markets, Analysis and Strategies Pricing of Bonds

2. Zvi WienerFabozzi Ch 2 slide 2 Time value of money How to calculate price of a bond Why the price of a bond changes Relation between yield and price Relation between coupon and price Price changes when approaching maturity Floaters and inverse floaters Accrued interest and price quotes

3. Zvi WienerFabozzi Ch 2 slide 3 Time Value of Money present value PV = CF t /(1+r) t Future value FV = CF t (1+r) t Net present value NPV = sum of all PV -PV5555105

4. Zvi WienerFabozzi Ch 2 slide 4 Time Value You have $100 now and are going to deposit it for 5 years with 6% interest. What will be the final amount? It depends on calculation method! Yearly compounding: $100*1.06 5 Semiannual compounding: $100*1.03 12 Monthly compounding: $100*1.005 60

5. Zvi WienerFabozzi Ch 2 slide 5 Periodic Rate r = Annual interest rate Number of periods in a year Effective Rate = A n

6. Zvi WienerFabozzi Ch 2 slide 6 Zero coupon bond Pricing of Bonds

7. Zvi WienerFabozzi Ch 2 slide 7 Term structure of interest rates Pricing of Bonds

8. Zvi WienerFabozzi Ch 2 slide 8 Yield = IRR = Internal Rate of Return How do we know that there is a solution? Yield

9. Zvi WienerFabozzi Ch 2 slide 9 Example Price calculation: Yield calculation:

10. Zvi WienerFabozzi Ch 2 slide 10 Price-Yield Relationship Price and yield (of a straight bond) move in opposite directions. yield price

11. Zvi WienerFabozzi Ch 2 slide 11 General pricing formula

12. Zvi WienerFabozzi Ch 2 slide 12 Accrued Interest Accrued interest = interest due in full period* (number of days since last coupon)/ (number of days in period between coupon payments)

13. Zvi WienerFabozzi Ch 2 slide 13 Day Count Convention Actual/Actual - true number of days 30/360 - assume that there are 30 days in each month and 360 days in a year. Actual/360

14. Zvi WienerFabozzi Ch 2 slide 14 Floater The coupon rate of a floater is equal to a reference rate plus a spread. For example LIBOR + 50 bp. Sometimes it has a cap or a floor.

15. Zvi WienerFabozzi Ch 2 slide 15 Inverse Floater Is usually created from a fixed rate security. Floater coupon = LIBOR + 1% Inverse Floater coupon = 10% - LIBOR Note that the sum is a fixed rate security. If LIBOR>10% there is typically a floor.

16. Zvi WienerFabozzi Ch 2 slide 16 Price Quotes and Accrued Interest Assume that the par value of a bond is $1,000. Price quote is in % of par + accrued interest the accrued interest must compensate the seller for the next coupon.

17. Zvi WienerFabozzi Ch 2 slide 17 Questions 2, 3, 7, 8, 11 Home Assignment Chapter 2

18. Zvi WienerFabozzi Ch 2 slide 18 FRM-99, Question 17 Assume a semi-annual compounded rate of 8% per annum. What is the equivalent annually compounded rate? A. 9.2% B. 8.16% C. 7.45% D. 8%

19. Zvi WienerFabozzi Ch 2 slide 19 FRM-99, Question 17 (1 + y s /2) 2 = 1 + y (1 + 0.08/2) 2 = 1.0816 ==> 8.16%

20. Zvi WienerFabozzi Ch 2 slide 20 FRM-99, Question 28 Assume a continuously compounded interest rate is 10% per annum. What is the equivalent semi-annual compounded rate? A. 10.25% per annum. B. 9.88% per annum. C. 9.76% per annum. D. 10.52% per annum.

21. Zvi WienerFabozzi Ch 2 slide 21 FRM-99, Question 28 (1 + y s /2) 2 = e y (1 + y s /2) 2 = e 0.1 1 + y s /2 = e 0.05 y s = 2 (e 0.05 - 1) = 10.25%

22. Zvi WienerFabozzi Ch 2 slide 22 Mortgage example You take a mortgage $100,000 for 10 years with yearly payments and 7% interest. What is the size of each payment?

23. Zvi WienerFabozzi Ch 2 slide 23 Mortgage example How much do you own bank after 3 first payments? What is the fair value of your debt if interest rates are 5%?