Lecture Presentation Software
to accompany
Investment Analysis and
Portfolio Management
Seventh Edition
by
Frank K. Reilly & Keith C. Brown
Chapter 19
The Analysis and Valuation
of Bonds
Additional Comments
Types of Bond Yields
Yield Measure
Purpose
Nominal Yield
Measures the coupon rate
Current yield
Measures current income rate
Promised yield to maturity
Measures expected rate of return for bond held
to maturity
Measures expected rate of return for bond held
to first call date
Measures expected rate of return for a bond
likely to be sold prior to maturity. It considers
specified reinvestment assumptions and an
estimated sales price. It can also measure the
actual rate of return on a bond during some past
period of time.
Promised yield to call
Realized (horizon) yield
Nominal Yield
Measures the coupon rate that a bond
investor receives as a percent of the bond’s
par value
Current Yield
Similar to dividend yield for stocks
Important to income oriented investors
CY = Ci/Pm
where:
CY = the current yield on a bond
Ci = the annual coupon payment of bond i
Pm = the current market price of the bond
Promised Yield to Maturity
• Widely used bond yield figure
• Assumes
– Investor holds bond to maturity
– All the bond’s cash flow is reinvested at the
computed yield to maturity
Pp
Ci 2
Pm  

t
2n
(1  i 2)
t 1 (1  i 2)
2n
Solve for i that will
equate the current price
to all cash flows from
the bond to maturity,
similar to IRR
Promised Yield to Call
Present-Value Method
2 nc
Ci / 2
Pc
Pm  

t
2 nc
(1  i )
t 1 (1  i )
Where:
Pm = market price of the bond
Ci = annual coupon payment
nc = number of years to first call
Pc = call price of the bond
Realized Yield
Present-Value Method
2 hp
Pf
Ct / 2
Pm  

t
2 hp
(1  i 2)
t 1 (1  i 2)
Calculating Future Bond Prices
Pf 
2 n  2 hp

t 1
Pp
Ci / 2

t
2 n  2 hp
(1  i 2) (1  i 2)
Where:
Pf = estimated future price of the bond
Ci = annual coupon payment
n = number of years to maturity
hp = holding period of the bond in years
i = expected semiannual rate at the end of the holding period
What Determines Interest Rates
•
•
•
•
•
Term structure of interest rates
Expectations hypothesis
Liquidity preference hypothesis
Segmented market hypothesis
Trading implications of the term structure
Expectations Hypothesis
• Any long-term interest rate simply
represents the geometric mean of current
and future one-year interest rates expected
to prevail over the maturity of the issue
Liquidity Preference Theory
• Long-term securities should provide higher
returns than short-term obligations because
investors are willing to sacrifice some
yields to invest in short-maturity obligations
to avoid the higher price volatility of longmaturity bonds
Segmented-Market Hypothesis
• Different institutional investors have
different maturity needs that lead them to
confine their security selections to specific
maturity segments
Trading Implications of the Term
Structure
• Information on maturities can help you
formulate yield expectations by simply
observing the shape of the yield curve
Yield Spreads
• Segments: government bonds, agency
bonds, and corporate bonds
• Sectors: prime-grade municipal bonds
versus good-grade municipal bonds, AA
utilities versus BBB utilities
• Coupons or seasoning within a segment or
sector
• Maturities within a given market segment or
sector
Yield Spreads
Magnitudes and direction of yield spreads
can change over time
The Duration Measure
• Since price volatility of a bond varies inversely with
its coupon and directly with its term to maturity, it is
necessary to determine the best combination of these
two variables to achieve your objective
• A composite measure considering both coupon and
maturity would be beneficial
• Such a measure is provided by duration, discussed
previously
• The duration of a portfolio is the dollar-weighted
average of the duration of the bonds in the portfolio.
Bond Convexity
• Modified duration provides a linear approximation
of bond price change for small changes in market
yields
P
100   Dmod  i
P
• However, price changes are not linear, but instead
follow a curvilinear (convex) function
Determinants of Convexity
The convexity is the measure of the curvature
and is the second derivative of price with
resect to yield (d2P/di2) divided by price
Convexity is the percentage change in dP/di
for a given change in yield
2
d P
2
di
Convexity 
P
Determinants of Convexity
• Inverse relationship between coupon and convexity
• Direct relationship between maturity and convexity
• Inverse relationship between yield and convexity
Modified Duration-Convexity Effects
• Changes in a bond’s price resulting from a
change in yield are due to:
– Bond’s modified duration
– Bond’s convexity
• Relative effect of these two factors depends
on the characteristics of the bond (its
convexity) and the size of the yield change
• (Positive) convexity is desirable
Convexity of Callable Bonds
• Noncallable bond has positive convexity
• Callable bond has negative convexity
Limitations of Macaulay and
Modified Duration
• Percentage change estimates using modified
duration only are good for small-yield
changes
• Difficult to determine the interest-rate
sensitivity of a portfolio of bonds when
there is a change in interest rates and the
yield curve experiences a nonparallel shift
• Initial assumption that cash flows from the
bond are not affected by yield changes
Future topics
Chapter 20
• Bond Portfolio Management
Strategies