Powerpoint file

1. Fixed-Income Securities

2. Pricing of Bonds
The price of any financial security is equal to the total
present value of the expected cash flows from the
security. Therefore, determining the price requires:
● an estimate of the expected cash flows
● an estimate of the appropriate required yield or
rate of return
The required yield reflects the yield for financial
instruments with comparable risk or alternative
substitute investment.
The term comparable indicates option-free bonds with
the same credit quality and maturity.

3. Pricing of Bonds
The cash flows of an option-free straight bond consist
of all the periodic coupon payments till maturity and par
or face (or maturity) value at maturity.
The bond pricing process is based on the following
three assumptions:
● the coupon payments are made every six
months
● the coupon rate is fixed for the entire term of
the bond
● one rate is used to discount all cash flows
Pricing Zero-Coupon Bond
Pricing process of deep discount or zero-coupon bond.

4. Pricing of Bonds
Price-Yield Relationship: There exists inverse
relationship between price of bond and the required
yield or market interest rate. The graphical presentation
of the price-yield relationship of an option-free bond
shows a convex shape curve. The point at which the
curve intersects the vertical axis indicates the
maximum price of a bond.
Relationship Among Coupon Rate, Required
Yield or Market Interest Rate and Price:
When CR = YTM, price = par value.
When CR > YTM, price > par value (premium bond)
When CR < YTM, price < par value (discount bond)

5. Pricing of Bonds
You are reviewing a price sheet for bonds and see the following
prices (per $100 par value) reported. You observe what seem to
be several errors. Without calculating the price of each bond,
indicate which bonds seem to be reported incorrectly, and explain
why?
Bond Price Coupon Rate (%) Required Yield (%)
U 90 6 9
V 96 9 8
W 110 8 6
X 105 0 5
Y 107 7 9
Z 100 6 6

6. Pricing of Bonds
Relationship Between Bond Price and Time (If the
Required Yield or Market Interest Rate is
Unchanged):
If the required yield does not change between the time
the bond is purchased and the maturity date, in case of a
bond selling at par, its coupon will be equal to the
required yield and its price will remain constant as the
bond moves toward the maturity date.
However, the price of a premium or discount bond
will not remain the same as the bond approaches
maturity. The price of a discount bond increases while
the price of a premium bond decreases as it approaches
maturity and the price of both the bonds will be equal
to par at the maturity date.

7. Pricing of Bonds
Reasons For Change in the Price of a Bond
The price of a bond will change for one or more of the
following reasons:
 There is a change in required yield owing to changes
in credit quality of the issuer
 There is a change in the price of a discount or premium
bond without any change in the required yield simply
because the bond is moving toward maturity.
 There is a change in the required yield due to a change
in the yield of comparable bonds i.e. a change in
the yield required by the market.

8. Pricing of Bonds
Bond Pricing Assumptions
The framework for pricing a bond is based on the
following assumptions:
♦ The next coupon payment is exactly 6 months from now
♦ The cash flows are known
♦ The appropriate required yield can be determined
♦ One rate is used to discount all the cash flows
Changes in the Assumptions:
If Next Coupon is Paid Less Than Six Months:
In this case the price of the bond should be determined
according to the equation given in Example XLS

9. Pricing of Bonds
Cash Flows May Not Be Certain:
For most of the bonds, other than the option-free bonds,
the cash flows are not known with certainty. However,
the cash flows of callable bonds depend on the level of
current interest rates relative to the coupon rate. These
bonds will be called if the market interest rate goes
substantially below the coupon rate. As such, the cash
flows of bonds that may be called prior to maturity are
dependent on current interest rates in the market.
One Discount Rate Applicable To All Cash Flows:
Instead of applying one discount rate throughout the
life of the bond more appropriate discount rates should
be used in different stages of the term to maturity.
Example XLS

10. Pricing of Bonds
Pricing of Floating Rate Securities
Pricing of Inverse Floating Rate Securities

11. Arbitrage-Free Valuation
Under traditional approach of bond valuation, it is typical
to view the security as the same package of cash flows,
and to discount all the cash flows with one discount rate.
Under the arbitrage-free valuation approach, the issue is
viewed as various zero-coupon bonds that should be
valued individually and added together to determine the
value of the security. This approach of bond valuation
does not allow a risk-free profit to be generated by
"stripping" coupons of the security and selling them
at a higher price than purchasing the security in the
market. The discount rate used in valuation is the
treasury spot rate applicable in different time periods.

12. Arbitrage-Free Valuation
A dealer has the ability to strip a security or to take apart
the cash flows that make up the bond. These Treasury
strips can be sold to investors in the treasury strip market.
So if the market price of a Treasury security is less than
the value using the arbitrage-free valuation, a dealer will
buy the security, strip the bond and then sell the Treasury
strips at a higher amount than the purchase price for the
whole bond.
On the other hand, if the market price is more than the
value using the arbitrage-free valuation, the dealer will
buy the strips, make the bond "whole" and sell it at a
higher price than that of the purchased strips.

13. Arbitrage-Free Valuation
Credit Spreads and the Valuation of Non-
Treasury Securities: The Treasury spot rates can be
used to value any default free securities. The value of
non-Treasury security is determined by discounting the
cash flows with the Treasury spot rates plus a yield
spread to reflect the additional risk. The limitation of this
approach is that it assumes the yield or credit spread to
be constant which is not true in reality. In fact credit
spread increases with the maturity of the bond. This
implies, there exists a term structure of credit spreads.
The term structure of credit spreads vary on the basis of
credit rating and market sector. Typically, the lower the
credit rating, the steeper the term structure of credit
spreads .

14. Arbitrage-Free Valuation
When the credit spread for a given credit rating and
market sector are added to the Treasury spot rates the
resulting term structure is used to value the bond with that
credit rating in that market sector. This term structure is
referred to as the benchmark spot rate curve or bench
mark zero-coupon rate curve.

15. Valuation Models
A valuation model provides the fair value of a security.
Thus far, the two valuation approaches have been presented
that deal with valuing simple securities i.e. the securities
that do not have an embedded option. A Treasury security
and an option-free non-Treasury security can be valued
using the arbitrage-free valuation approach.
In the fixed income area, two common models i.e. the
binomial model and the Monte Carlo simulation model are
used to value securities with embedded options. The former
model is used to value callable bonds, putable bonds,
floating rate notes, etc. in which the coupon formula is
based on an interest rate. The Monte Carlo simulation
model is used to value mortgage-backed securities and
certain types of asset-backed securities.