Bond Pricing Theorem

This presentation describes various theorems of bond pricing. It also gives information about bond returns, bond risk and bond duration.

1. BOND PRICING THEOREM Presented by- Pallav Dodrajka 1

2. CONTENT Introduction Bond Returns coupon rate current yield spot interest rate yield to maturity Bond Risk Bond Duration Bond Prices Bond Pricing Theorems 2

3. INTRODUCTION Bonds are Long-term fixed income securities. Debentures are also long-term fixed income securities. Both of these are debt securities . The two major categories of bonds are G overnment bonds C orporate bonds . There are the two main features of bonds such as C allability and Convertibility. 3

4. BOND RETURNS 4

5. COUPON RATE It is the nominal rate of interest fixed and printed on the bond certificate. It is calculated on the face value of the bond. It is the rate at which interest is payable by the issuing company to the bondholder. 5

6. 2. CURRENT YIELD The current market price of a bond in the secondary market may differ from its face value. The current yield relates the annual interest receivable on a bond to its current market price. It can be expressed as follows:- Where I n = Annual Interest P o = Current market price current yield=I n /P o × 100 6

7. 3. SPOT INTEREST RATE Zero coupon bond is a special type of bond which does not pay annual interests. The return on this bond is in the form of a discount on issue of the bond . This type of bond is also called pure discount bond or deep discount bond . Spot interest rate is the annual rate of return on a bond that has only one cash inflow to the investor. 7

8. 4. YIELD TO MATURITY (YTM) This is the most widely used measure of return on bonds. It may be defined as the compounded rate of return an investor is expected to receive from a bond purchased at the current market price and held to maturity. It is really the internal rate of return earned from holding a bond till maturity. YTM depends upon the cash outflow for purchasing the bond, that is, the cost or Current market price of the bond as well as the cash inflows from the bond, namely the future interest payments and the terminal principal repayment. YTM is the discount rate that makes the present value of cash inflows from the bond equal to the cash outflow for purchasing the bond. 8

9. BOND RISKS Two types of risk are associated with investment in bonds are D efault risk I nterest rate risk Default risk refers to the possibility that a company may fail to pay the interest or principal on the stipulated dates. Poor financial performance of the company leads to such defaults. Interest rate risk affects the value of bonds more directly than stocks, and it is a major risk to all bondholders. As interest rates rise, bond prices fall and vice versa. 9

10. BOND DURATION Duration is the weighted average measure of a bond’s life. The various time periods in which the bond generates cash flows are weighted according to the relative size of the present value of those flows. The formula for computing duration d is:- D = bond's duration -- C = periodic coupon payment F = face value  at maturity -- T = number of periods until maturity r = periodic  yield to maturity -- t = period in which the coupon is received 10

11. 11 BOND PRICING THEOREMS

12. Theorem 1 If bond market price increases Then its yield must decrease Conversely if a bond market price decreases Then its yield must increase 12

13. Theorem 2 Bond Price Variability is directly related to the term to maturity For the given change in the level of market interest rate, the change in bond prices are greater for long term maturity 13

14. Theorem 3 I f the bond's yield does not change over its life T hen the size of its discount or premium will decrease A t an increasing rate as it life shortens 14

15. Theorem 4 The percentage change in a bond’s price owing to change in its yield W ill be smaller if the coupon rate is higher 15

16. Theorem 5 A decrease in a bonds yield will rise the bonds price by an amount that is Greater in size than the corresponding fall in the bonds price that would occur if there where an equal sized increase in the bonds yield The price-yield relation is convex 16

17. CONVEXITY Definition A measure of a curvedness of the price-yield relationship 17

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