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