chapter twenty l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
CHAPTER TWENTY PowerPoint Presentation
Download Presentation
CHAPTER TWENTY

Loading in 2 Seconds...

play fullscreen
1 / 49

CHAPTER TWENTY - PowerPoint PPT Presentation


  • 152 Views
  • Uploaded on

CHAPTER TWENTY. FUNDAMENTALS OF BOND VALUATION. YIELD TO MATURITY. CALCULATING YIELD TO MATURITY EXAMPLE Imagine three risk-free returns based on three Treasury bonds: Bond A,B are pure discount types; mature in one year . Bond C coupon pays $50/year;. matures in two years.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'CHAPTER TWENTY' - milton


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
chapter twenty

CHAPTER TWENTY

FUNDAMENTALS OF BOND VALUATION

yield to maturity
YIELD TO MATURITY
  • CALCULATING YIELD TO MATURITY EXAMPLE
    • Imagine three risk-free returns based on three Treasury bonds:

Bond A,B are pure discount types;

mature in one year

bond c coupon pays 50 year
Bond C coupon pays $50/year;

matures in two years

yield to maturity4
YIELD TO MATURITY

Bond Market Prices:

Bond A $934.58

Bond B $857.34

Bond C $946.93

WHAT IS THE YIELD-TO-MATURITY OF THE THREE BONDS?

yield to maturity5
YIELD TO MATURITY
  • YIELD-TO-MATURITY (YTM)
    • Definition: the single interest rate* that would enable investor to obtain all payments promised by the security.
    • very similar to the internal rate of return (IRR) measure

* with interest compounded at some specified interval

yield to maturity6
YIELD TO MATURITY
  • CALCULATING YTM:
    • BOND A
    • Solving for rA

(1 + rA) x $934.58 = $1000

rA = 7%

yield to maturity7
YIELD TO MATURITY
  • CALCULATING YTM:
    • BOND B
    • Solving for rB

(1 + rB) x $857.34 = $1000

rB = 8%

yield to maturity8
YIELD TO MATURITY
  • CALCULATING YTM:
    • BOND C
    • Solving for rC

(1 + rC)+{[(1+ rC)x$946.93]-$50 = $1000

rC = 7.975%

spot rate
SPOT RATE
  • DEFINITION: Measured at a given point in time as the YTM on a pure discount security
spot rate10
SPOT RATE
  • SPOT RATE EQUATION:

where Pt = the current market price of a

pure discount bond maturing in t years;

Mt = the maturity value

st = the spot rate

discount factors
DISCOUNT FACTORS
  • EQUATION:

Let dt = the discount factor

discount factors12
DISCOUNT FACTORS
  • EVALUATING A RISK FREE BOND:
    • EQUATION

where ct = the promised cash payments

n = the number of payments

forward rate
FORWARD RATE
  • DEFINITION: the interest rate today that will be paid on money to be
    • borrowed at some specific future date and
    • to be repaid at a specific more distant future date
forward rate14
FORWARD RATE
  • EXAMPLE OF A FORWARD RATE

Let us assume that $1 paid in one year at a spot rate of 7% has

forward rate15
FORWARD RATE
  • EXAMPLE OF A FORWARD RATE

Let us assume that $1 paid in two years at a spot rate of 7% has a

forward rate16
FORWARD RATE

f1,2 is the forward rate from year 1 to year 2

forward rate17
FORWARD RATE
  • To show the link between the spot rate in year 1 and the spot rate in year 2 and the forward rate from year 1 to year 2
forward rate18
FORWARD RATE

such that

or

forward rate19
FORWARD RATE
  • More generally for the link between years t-1 and t:
  • or
forward rates and discount factors
FORWARD RATES AND DISCOUNT FACTORS
  • ASSUMPTION:
    • given a set of spot rates, it is possible to determine a market discount function
    • equation
yield curves
YIELD CURVES
  • DEFINITION: a graph that shows the YTM for Treasury securities of various terms (maturities) on a particular date
yield curves22
YIELD CURVES
  • TREASURY SECURITIES PRICES
    • priced in accord with the existing set of spot rates and
    • associated discount factors
yield curves23
YIELD CURVES
  • SPOT RATES FOR TREASURIES
    • One year is less than two year;
    • Two year is less than three-year, etc.
yield curves24
YIELD CURVES
  • YIELD CURVES AND TERM STRUCTURE
    • yield curve provides an estimate of
      • the current TERM STRUCTURE OF INTEREST RATES
      • yields change daily as YTM changes
term structure theories
TERM STRUCTURE THEORIES
  • THE FOUR THEORIES

1. THE UNBIASED EXPECTATION THEORY

2. THE LIQUIDITY PREFERENCE THEORY

3. MARKET SEGMENTATION THEORY

4. PREFERRED HABITAT THEORY

term structure theories26
TERM STRUCTURE THEORIES
  • THEORY 1: UNBIASED EXPECTATIONS
    • Basic Theory: the forward rate represents the average opinion of the expected future spot rate for the period in question
    • in other words, the forward rate is an unbiased estimate of the future spot rate.
term structure theory unbiased expectations
TERM STRUCTURE THEORY: Unbiased Expectations
  • THEORY 1: UNBIASED EXPECTATIONS
    • A Set of Rising Spot Rates
      • the market believes spot rates will rise in the future
        • the expected future spot rate equals the forward rate
        • in equilibrium

es1,2 = f1,2

where es1,2 = the expected future spot

f1,2 = the forward rate

term structure theory unbiased expectations28
TERM STRUCTURE THEORY: Unbiased Expectations
  • THE THEORY STATES:
    • The longer the term, the higher the spot rate, and
    • If investors expect higher rates ,
      • then the yield curve is upward sloping
      • and vice-versa
term structure theory unbiased expectations29
TERM STRUCTURE THEORY: Unbiased Expectations
  • CHANGING SPOT RATES AND INFLATION
    • Why do investors expect rates to rise or fall in the future?
      • spot rates = nominal rates
        • because we know that the nominal rate is the real rate plus the expected rate of inflation
term structure theory unbiased expectations30
TERM STRUCTURE THEORY: Unbiased Expectations
  • CHANGING SPOT RATES AND INFLATION
    • Why do investors expect rates to rise or fall in the future?
      • if either the spot or the nominal rate is expected to change in the future, the spot rate will change
term structure theory unbiased expectations31
TERM STRUCTURE THEORY: Unbiased Expectations
  • CHANGING SPOT RATES AND INFLATION
    • Why do investors expect rates to rise or fall in the future?
      • if either the spot or the nominal rate is expected to change in the future, the spot rate will change
term structure theory unbiased expectations32
TERM STRUCTURE THEORY: Unbiased Expectations
  • Current conditions influence the shape of the yield curve, such that
    • if deflation expected, the term structure and yield curve are downward sloping
    • if inflation expected, the term structure and yield curve are upward sloping
term structure theory unbiased expectations33
TERM STRUCTURE THEORY: Unbiased Expectations
  • PROBLEMS WITH THIS THEORY:
    • upward-sloping yield curves occur more frequently
    • the majority of the time, investors expect spot rates to rise
    • not realistic position
term structure theory liquidity preference
TERM STRUCTURE THEORY: Liquidity Preference
  • BASIC NOTION OF THE THEORY
    • investors primarily interested in purchasing short-term securities to reduce interest rate risk
term structure theory liquidity preference35
TERM STRUCTURE THEORY: Liquidity Preference
  • BASIC NOTION OF THE THEORY
    • Price Risk
      • maturity strategy is more risky than a rollover strategy
      • to convince investors to buy longer-term securities, borrowers must pay a risk premium to the investor
term structure theory liquidity preference36
TERM STRUCTURE THEORY: Liquidity Preference
  • BASIC NOTION OF THE THEORY
    • Liquidity Premium
      • DEFINITION: the difference between the forward rate and the expected future rate
term structure theory liquidity preference37
TERM STRUCTURE THEORY: Liquidity Preference
  • BASIC NOTION OF THE THEORY
    • Liquidity Premium Equation

L = es1,2 -f1,2

where L is the liquidity premium

term structure theory liquidity preference38
TERM STRUCTURE THEORY: Liquidity Preference
  • How does this theory explain the shape of the yield curve?
    • rollover strategy
      • at the end of 2 years $1 has an expected value of

$1 x (1 + s1 ) (1 + es1,2 )

term structure theory liquidity preference39
TERM STRUCTURE THEORY: Liquidity Preference
  • How does this theory explain the shape of the yield curve?
    • whereas a maturity strategy holds that

$1 x (1 + s2 )2

    • which implies with a maturity strategy, you must have a higher rate of return
term structure theory liquidity preference40
TERM STRUCTURE THEORY: Liquidity Preference
  • How does this theory explain the shape of the yield curve?
    • Key Idea to the theory: The Inequality holds

$1(1+s1)(1 +es1,2)<$1(1 + s2)2

term structure theory liquidity preference41
TERM STRUCTURE THEORY: Liquidity Preference
  • SHAPES OF THE YIELD CURVE:
    • a downward-sloping curve
      • means the market believes interest rates are going to decline
term structure theory liquidity preference42
TERM STRUCTURE THEORY: Liquidity Preference
  • SHAPES OF THE YIELD CURVE:
    • a flat yield curve means the market expects interest rates to decline
term structure theory liquidity preference43
TERM STRUCTURE THEORY: Liquidity Preference
  • SHAPES OF THE YIELD CURVE:
    • an upward-sloping curve means rates are expected to increase
term structure theory market segmentation
TERM STRUCTURE THEORY: Market Segmentation
  • BASIC NOTION OF THE THEORY
    • various investors and borrowers are restricted by law, preference or custom to certain securities
term structure theory liquidity preference45
TERM STRUCTURE THEORY: Liquidity Preference
  • WHAT EXPLAINS THE SHAPE OF THE YIELD CURVE?
    • Upward-sloping curves mean that supply and demand intersect for short-term is at a lower rate than longer-term funds
    • cause: relatively greater demand for longer-term funds or a relative greater supply of shorter-term funds
term structure theory preferred habitat
TERM STRUCTURE THEORY: Preferred Habitat
  • BASIC NOTION OF THE THEORY:
    • Investors and borrowers have segments of the market in which they prefer to operate
term structure theory preferred habitat47
TERM STRUCTURE THEORY: Preferred Habitat
  • When significant differences in yields exist between market segments, investors are willing to leave their desired maturity segment
term structure theory preferred habitat48
TERM STRUCTURE THEORY: Preferred Habitat
  • Yield differences determined by the supply and demand conditions within the segment
term structure theory preferred habitat49
TERM STRUCTURE THEORY: Preferred Habitat
  • This theory reflects both
    • expectations of future spot rates
    • expectations of a liquidity premium