Bond Pricing Theorem

BOND PRICING THEOREM
Presented by-
Pallav Dodrajka
1

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

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
– Government bonds
– Corporate bonds.
• There are the two main features of bonds such as
Callability and Convertibility.
3

1. 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

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
In = Annual Interest
Po = Current market price
current yield=In/Po × 100
6

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

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

BOND RISKS
• Two types of risk are associated with investment in bonds are
– Default risk
– Interest 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

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

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

Theorem 3
If the bond's yield does not change over its life
Then the size of its discount or premium will
decrease
At an increasing rate as it life shortens
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Theorem 4
The percentage change in a bond’s price owing
to change in its yield
Will be smaller if the coupon rate is higher
15

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

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

Bond Pricing Theorem

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Bond Pricing Theorem