Chapter 6
Pricing Fixed-Income Securities
Chapter Objectives
1. Introduce the mathematics of interest rates for fixed-income securities.
2. Demonstrate the impact of compounding.
3. Describe the relationship between the interest rate on a security and the security’s market price.
4. Introduce the concept of duration as a measure of a security’s price sensitivity to changing interest
rates.
5. Explain how interest rates on di&erent money market instruments are quoted.
6. Introduce total return analysis and its use in valuing investments.
Key Concepts
1. Interest rate mathematics are based on the simple recognition that cash in your possession
today is worth more than the same amount of cash to be received at any time in the future.
2. Simple interest is interest paid only on the initial principal. Compound interest is interest paid on
the outstanding principal plus any interest that has been previously earned, but not paid out.
3. Interest may be compounded over di&erent intervals. The shorter is the interval, the greater is
the compounding frequency, and the greater is compound interest, ceteris paribus.
4. There are four basic price and interest rate relationships:
a. Market interest rates and bond prices vary inversely.
b. For a specific absolute change in interest rates, the proportionate increase in price when
rates fall exceeds the proportionate decrease in price when rates rise.
c. Long-term bonds change proportionately more in price than short-term bonds for a
given change in interest rates.
d. Low-coupon bonds change proportionately more in price than high-coupon bonds for a
given change in interest rates.
5. A security’s duration is a measure of its price sensitivity to changes in interest rates. The longer is
duration, the greater is the relative price sensitivity.
6. Many investors do not hold securities until final maturity and they cannot invest interim coupon
payments at the yield to maturity so yield to maturity is not that meaningful a return measure.
Similarly, many securities carry embedded options, such as the borrower’s option to prepay a
mortgage or the issuer’s option to call a bond. Total return analysis is useful because it allows an
investor to vary assumptions regarding cash 3ows and reinvestment rates and provides a
meaningful estimate of the realized return over a target holding period.
7. Interest rates on securities are quoted and calculated di&erently. Some instruments trade only
on a discount basis, while others are interest bearing. Some yields are quoted assuming a
360-day year, while other quoted yields assume a 365-day year. Basic interest rate calculations
must recognize these di&erences.
8. Money market yields can be best compared by calculating an e&ective annual yield.
Teaching Suggestions
This chapter provides background information for students who are unfamiliar with basic present value
or future value concepts and the mathematics of interest rates. It can be conveniently assigned as
background reading with students required to answer the end-of-chapter questions to demonstrate
proficiency.
Special attention should be paid to the four price and yield relationships which will be emphasized later
in the discussion of interest rate risk and the pricing of taxable and tax-exempt securities. Students
should also be comfortable with how Macaulay’s duration of a security without options is calculated, per
Exhibit 6.6, and what this figure means in terms of the security’s price sensitivity. In addition, it is
important to note the di&erence between yield to maturity and total return analysis. Comment on the
fact that the yield to maturity calculation assumes that all cash 3ows will be received as scheduled, will
be reinvested at the yield to maturity, and that the holder of the security will hold it until final maturity.
If any of these assumptions is violated (as they always are), yield to maturity is an incorrect measure of
return. For this reason, many analysts today focus on total return as a measure of yield. Investors can
vary their assumptions about the length of holding period, reinvestment rate, and when cash 3ows will
be generated (when embedded options will be exercised).
Students should be familiar with how yields are quoted. Refer them to The Wall Street Journal’s daily
publication of money market yields, and ask them to compare e&ective yields. They should also review
graphs that plot di&erent yields, ether from The Wall Street Journal or from Federal Reserve publications.
The Wall Street Journal’s Money and Investing Section has excellent data on the Treasury and LIBOR
swap curves and corporate bond data.