Lecture Presentation Software to accompany Investment Analysis and Portfolio Management Eighth Edition by Frank K. Reilly

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Lecture Presentation Software to
accompanyInvestment Analysis and Portfolio
ManagementEighth Editionby Frank K. Reilly
Keith C. Brown
Chapter 18

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Chapter 18 - The Analysis and Valuation of Bonds

• Questions to be answered
• How do you determine the value of a bond based on
  the present value formula?
• What are the alternative bond yields that are
  important to investors?

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Chapter 18 - The Analysis and Valuation of Bonds

• How do you compute the following yields on bonds
  current yield, yield to maturity, yield to call,
  and compound realized (horizon) yield?
• What are spot rates and forward rates and how do
  you calculate these rates from a yield to
  maturity curve?
• What is the spot rate yield curve and forward
  rate curve?

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Chapter 18 - The Analysis and Valuation of Bonds

• How and why do you use the spot rate curve to
  determine the value of a bond?
• What are the alternative theories that attempt to
  explain the shape of the term structure of
  interest rates?
• What factors affect the level of bond yields at a
  point in time?
• What economic forces cause changes in bond yields
  over time?

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Chapter 18 - The Analysis and Valuation of Bonds

• When yields change, what characteristics of a
  bond cause differential price changes for
  individual bonds?
• What is meant by the duration of a bond, how do
  you compute it, and what factors affect it?
• What is modified duration and what is the
  relationship between a bonds modified duration
  and its volatility?

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Chapter 18 - The Analysis and Valuation of Bonds

• What is effective duration and when is it useful?
• What is the convexity for a bond, how do you
  compute it, and what factors affect it?
• Under what conditions is it necessary to consider
  both modified duration and convexity when
  estimating a bonds price volatility?

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Chapter 18 - The Analysis and Valuation of Bonds

• What happens to the duration and convexity of
  bonds that have embedded call options?
• What are effective duration and effective
  convexity and when are they useful?
• What is empirical duration and how is it used
  with common stocks and other assets?
• What are the static yield spread and the
  option-adjusted spread?

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Chapter 18 - The Analysis and Valuation of Bonds

• What are effective duration and effective
  convexity and when are they useful?
• What is empirical duration and how is it used
  with common stocks and other assets?
• What are the static yield spread and the
  option-adjusted spread?

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The Fundamentals of Bond Valuation

• The present-value model

Where Pmthe current market price of the bond n
the number of years to maturity Ci the annual
coupon payment for bond i i the prevailing
yield to maturity for this bond issue Ppthe par
value of the bond
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The Fundamentals of Bond Valuation

• If yield lt coupon rate, bond will be priced at a
  premium to its par value
• If yield gt coupon rate, bond will be priced at a
  discount to its par value
• Price-yield relationship is convex (not a
  straight line)

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The Present Value Model

• The value of the bond equals the present value
  of its expected cash flows

where Pm the current market price of the
bond n the number of years to maturity Ci
the annual coupon payment for Bond I i the
prevailing yield to maturity for this bond
issue Pp the par value of the bond
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The Yield Model

• The expected yield on the bond may be computed
  from the market price

where i the discount rate that will discount
the cash flows to equal the current market price
of the bond
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Computing 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
Promised yield to call
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.
Realized (horizon) yield
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Nominal Yield

• Measures the coupon rate that a bond investor
  receives as a percent of the bonds par value

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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

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Promised Yield to Maturity

• Widely used bond yield figure
• Assumes
• Investor holds bond to maturity
• All the bonds cash flow is reinvested at the
  computed yield to maturity

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Computing the Promised Yield to Maturity

• Solve for i that will equate the current price to
  all cash flows from the bond to maturity, similar
  to IRR

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Computing Promised Yield to Call

• where
• Pm market price of the bond
• Ci annual coupon payment
• nc number of years to first call
• Pc call price of the bond

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Realized (Horizon) YieldPresent-Value Method
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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

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Yield Adjustments for Tax-Exempt Bonds

• Where
• FTEY fully taxable yield equivalent
• i the promised yield on the tax exempt bond
• T the amount and type of tax exemption (i.e.,
  the investors marginal tax rate)

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Bond Valuation Using Spot Rates

• where
• Pm the market price of the bond
• Ct the cash flow at time t
• n the number of years
• it the spot rate for Treasury securities
  at maturity t

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What Determines Interest Rates

• Inverse relationship with bond prices
• Forecasting interest rates
• Fundamental determinants of interest rates
• i RFR I RP
• where
• RFR real risk-free rate of interest
• I expected rate of inflation
• RP risk premium

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What Determines Interest Rates

• Effect of economic factors
• real growth rate
• tightness or ease of capital market
• expected inflation
• or supply and demand of loanable funds
• Impact of bond characteristics
• credit quality
• term to maturity
• indenture provisions
• foreign bond risk including exchange rate risk
  and country risk

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Term Structure of Interest Rates

• It is a static function that relates the term to
  maturity to the yield to maturity for a sample of
  bonds at a given point in time.
• Term Structure Theories
• Expectations hypothesis
• Liquidity preference hypothesis
• Segmented market hypothesis
• Trading implications of the term structure

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Spot Rates and Forward Rates

• Creating the Theoretical Spot Rate Curve
• Calculating Forward Rates from the Spot Rate Curve

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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

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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

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Segmented-Market Hypothesis

• Different institutional investors have different
  maturity needs that lead them to confine their
  security selections to specific maturity segments
  

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Trading Implications of the Term Structure

• Information on maturities can help you formulate
  yield expectations by simply observing the shape
  of the yield curve

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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

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Yield Spreads

• Magnitudes and direction of yield spreads can
  change over time

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What Determines the Price Volatility for Bonds

• Bond price change is measured as the percentage
  change in the price of the bond

Where EPB the ending price of the bond BPB
the beginning price of the bond
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What Determines the Price Volatility for Bonds

• Four Factors
• 1. Par value
• 2. Coupon
• 3. Years to maturity
• 4. Prevailing market interest rate

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What Determines the Price Volatility for Bonds

• Five observed behaviors
• 1. Bond prices move inversely to bond yields
  (interest rates)
• 2. For a given change in yields, longer maturity
  bonds post larger price changes, thus bond price
  volatility is directly related to maturity
• 3. Price volatility increases at a diminishing
  rate as term to maturity increases
• 4. Price movements resulting from equal absolute
  increases or decreases in yield are not
  symmetrical
• 5. Higher coupon issues show smaller percentage
  price fluctuation for a given change in yield,
  thus bond price volatility is inversely related
  to coupon

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What Determines the Price Volatility for Bonds

• The maturity effect
• The coupon effect
• The yield level effect
• Some trading strategies

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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

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The Duration Measure

• Developed by Frederick R. Macaulay, 1938
• Where
• t time period in which the coupon or
  principal payment occurs
• Ct interest or principal payment that occurs in
  period t
• i yield to maturity on the bond

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Characteristics of Macaulay Duration

• Duration of a bond with coupons is always less
  than its term to maturity because duration gives
  weight to these interim payments
• A zero-coupon bonds duration equals its maturity
• There is an inverse relationship between duration
  and coupon
• There is a positive relationship between term to
  maturity and duration, but duration increases at
  a decreasing rate with maturity
• There is an inverse relationship between YTM and
  duration
• Sinking funds and call provisions can have a
  dramatic effect on a bonds duration

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Modified Duration and Bond Price Volatility

• An adjusted measure of duration can be used to
  approximate the price volatility of an
  option-free (straight) bond

Where m number of payments a year YTM
nominal YTM
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Modified Duration and Bond Price Volatility

• Bond price movements will vary proportionally
  with modified duration for small changes in
  yields
• An estimate of the percentage change in bond
  prices equals the change in yield time modified
  duration

Where ?P change in price for the bond P
beginning price for the bond Dmod the modified
duration of the bond ?i yield change in basis
points divided by 100
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Trading Strategies Using Modified Duration

• Longest-duration security provides the maximum
  price variation
• If you expect a decline in interest rates,
  increase the average modified duration of your
  bond portfolio to experience maximum price
  volatility
• If you expect an increase in interest rates,
  reduce the average modified duration to minimize
  your price decline
• Note that the modified duration of your portfolio
  is the market-value-weighted average of the
  modified durations of the individual bonds in the
  portfolio

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Bond Duration in Years for Bonds Yielding 6
Percent Under Different Terms
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Bond Convexity

• Modified duration is a linear approximation of
  bond price change for small changes in market
  yields
• However, price changes are not linear, but a
  curvilinear (convex) function

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Price-Yield Relationship for Bonds

• The graph of prices relative to yields is not a
  straight line, but a curvilinear relationship
• This can be applied to a single bond, a portfolio
  of bonds, or any stream of future cash flows
• The convex price-yield relationship will differ
  among bonds or other cash flow streams depending
  on the coupon and maturity
• The convexity of the price-yield relationship
  declines slower as the yield increases
• Modified duration is the percentage change in
  price for a nominal change in yield

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Modified Duration

• For small changes this will give a good
  estimate, but this is a linear estimate on the
  tangent line

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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

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Determinants of Convexity

• Inverse relationship between coupon and convexity
• Direct relationship between maturity and
  convexity
• Inverse relationship between yield and convexity

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Modified Duration-Convexity Effects

• Changes in a bonds price resulting from a change
  in yield are due to
• Bonds modified duration
• Bonds convexity
• Relative effect of these two factors depends on
  the characteristics of the bond (its convexity)
  and the size of the yield change
• Convexity is desirable

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Duration and Convexity for Callable Bonds

• Issuer has option to call bond and pay off with
  proceeds from a new issue sold at a lower yield
• Embedded option
• Difference in duration to maturity and duration
  to first call
• Combination of a noncallable bond plus a call
  option that was sold to the issuer
• Any increase in value of the call option reduces
  the value of the callable bond

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Option Adjusted Duration

• Based on the probability that the issuing firm
  will exercise its call option
• Duration of the non-callable bond
• Duration of the call option

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Convexity of Callable Bonds

• Noncallable bond has positive convexity
• Callable bond has negative convexity

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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

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Effective Duration

• Measure of the interest rate sensitivity of an
  asset
• Use a pricing model to estimate the market prices
  surrounding a change in interest rates
• Effective Duration Effective Convexity

P- the estimated price after a downward shift
in interest rates P the estimated price after
a upward shift in interest rates P the
current price S the assumed shift in the term
structure
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Effective Duration

• Effective duration greater than maturity
• Negative effective duration
• Empirical duration

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Empirical Duration

• Actual percent change for an asset in response to
  a change in yield during a specified time period

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Yield Spreads With Embedded Options

• Static Yield Spreads
• Consider the total term structure
• Option-Adjusted Spreads
• Consider changes in the term structure and
  alternative estimates of the volatility of
  interest rates

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The InternetInvestments Online

• http//www.bondcalc.com
• http//www.bondmarkets.com
• http//www.pimco.com
• http//www.bonds-online.com

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• End of Chapter 18
• The Analysis and Valuation of Bonds

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Future topicsChapter 19

• Bond Portfolio Management Strategies