Lecture Presentation Software to accompany
Investment Analysis and Portfolio Management
Seventh Editionby
Frank K. Reilly & Keith C. Brown
Chapter 19
The Analysis and Valuation of Bonds
Additional Comments
Types of Bond YieldsYield Measure PurposeNominal 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
Promised yield to call Measures expected rate of return for bond held to first call date
Realized (horizon) yield 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.
Nominal Yield
Measures the coupon rate that a bond investor receives as a percent of the bond’s par value
Current YieldSimilar to dividend yield for stocksImportant 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 maturitySolve for i that will equate the current price to all cash flows from the bond to maturity, similar to IRR
n
tn
p
ti
m i
P
i
CP
2
12)21()21(
2
Promised Yield to CallPresent-Value Method
Where:
Pm = market price of the bond
Ci = annual coupon payment
nc = number of years to first call
Pc = call price of the bond
ncc
nc
tt
im i
P
i
CP
2
2
1 )1()1(
2/
Realized YieldPresent-Value Method
hp
fhp
tt
tm i
P
i
CP
2
2
1 )21()21(
2/
Calculating Future Bond Prices
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
hpn
phpn
tt
if i
P
i
CP
22
22
1 )21()21(
2/
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 long-maturity 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
• However, price changes are not linear, but instead follow a curvilinear (convex) function
iDP
P
mod100
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
Pdi
Pd2
2
Convexity
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 topicsChapter 20
• Bond Portfolio Management Strategies