The Level and Structure of Interest Rates

1
Chapter 3

• The Level and Structure of Interest Rates

2
Historical Interest Rate Patterns

• Over the last three decades interest rates have
  often followed patterns of persistent increases
  or persistent decreases with fluctuations around
  these trends.
• In the 1970s and early 1980s the U.S.s inflation
  led to increasing interest rates during that
  period. This period of increasing rates was
  particularly acute from the late 1970s through
  early 1980s when the U.S. Federal Reserve changed
  the direction of monetary policy by raising
  discount rates, increasing reserve requirements,
  and lowering monetary growth.

3
Historical Interest Rate Patterns

• This period of increasing rates was followed by a
  period of declining rates from the early 1980s to
  the late 1980s, then a period of gradually
  increasing rates for most of the 1990s, and
  finally a period of decreasing rates from 2000
  through 2003.
• The different interest rates levels observed
  since the 1970s can be explained by such factors
  as economic growth, monetary and fiscal policy,
  and inflation.

4
Historical Interest Rate Patterns
TREASURY BILL RATES, 1970-2003
5
Historical Interest Rate Spreads

• In addition to the observed fluctuations in
  interest rate levels, there have also been
  observed spreads between the interest rates on
  bonds of different categories and terms to
  maturity over this same period.
• For example, the spread between yields on Baa and
  AAA bonds is greater in the late 1980s and early
  1990s when the U.S. economy was in recession
  compared to the differences in the mid to late
  1990s when the U.S. economy was growing.
• In general, spreads can be explained by
  differences in each bonds characteristics risk,
  liquidity, and taxability.

6
Historical Interest Rate Spreads
TREASURY BOND, Aaa CORPORATE, Baa CORPORATE, AND
MORTAGE RATES, 1970-2002
7
Historical Interest Rate Spreads

• Interest rate differences can be observed between
  similar bonds with different maturities. The
  figures on the next slide shows two plots of the
  YTM on U.S. government bonds with different
  maturities for early 2002 and early 1981.
• The graphs are known as yield curves and they
  illustrate what is referred to as the term
  structure of interest rates.
• The lower graph shows a positively-sloped yield
  curve in early 2002 with rates on short-term
  government securities lower than
  intermediate-term and long-term ones.
• In contrast, the upper graph shows a negatively
  sloped curve in early 1981 with short-term rates
  higher than intermediate- and long-term ones.

8
Historical Interest Rate SpreadsYield Curves
9
Objective

• Understanding what determines both the overall
  level and structure of interest rates is an
  important subject in financial economics. Here,
  we examine the factors that are important in
  explaining the level and differences in interest
  rates.
• Examining the behavior of overall interest rates
  using basic supply and demand analysis
• Looking at how risk, liquidity, and taxes explain
  the differences in the rates on bonds of
  different categories.
• Looking at four well-known theories that explain
  the term structure on interest rates.

10
Supply and Demand Analysis

• One of the best ways to understand how market
  forces determine interest rates is to use
  fundamental supply and demand analysis.
• In determining the supply and demand for bonds,
  let us treat different bonds as being alike and
  simply assume the bond in question is a
  one-period, zero-coupon bond paying a principal
  of F equal to 100 at maturity and priced at P0 to
  yield a rate i.
• Given this type of bond, we want to determine the
  important factors that determine its supply and
  demand.

11
Bond Demand and Supply Analysis

• Bond Demand Curve
• Bond Demand Curve The curve shows an inverse
  relationship between, bond demand, BD, and its
  price, P0, and a direct relation between BD
  interest rate, i, given other factors are
  constant.
• Bond demand curve is also called the supply of
  loanable funds curve.

12
Bond Demand and Supply Analysis

• Bond Demand Curve
• The factors held constant include the overall
  wealth or economic state of the economy, as
  measured by real output, gdp, the bonds risk
  relative to other assets, its liquidity relative
  to other assets, expected future interest rates,
  E(i) and inflation, and government policies

13
Bond Demand and Supply Analysis

• Bond Demand Curve
• Bond demand is inversely related to its price and
  directly related to interest rate.
• The bond demand curve showing bond demand and
  price relation is negatively-sloped.
• This reflects the fundamental assumption that
  investors will demand more bonds the lower the
  price or equivalently the greater the interest
  rate.
• Changes in the economy, futures interest rate and
  inflation expectations, risk, liquidity, and
  government policies lead to either rightward or
  leftward shifts in the demand curve, reflecting
  greater or less bond demand at each price or
  interest rate.

14

• Bond Demand Curve

15
Bond Demand and Supply Analysis

• Bond Supply Curve
• The bond supply curve shows the quantity supplied
  of bonds, BS, by corporations, governments, and
  intermediaries is directly related to the bonds
  price and inversely related interest rate, given
  other factors such as the state of the economy,
  government policy, and expected future inflation
  are constant
• Bond supply curve is also called the demand of
  loanable funds curve.

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Bond Demand and Supply Analysis

• Bond Supply Curve
• The bond supply curve is positively sloped.
• The positively sloped curve reflects the
  fundamental assumption that corporations,
  governments, and financial intermediaries will
  sell more bonds the greater the bonds price or
  equivalently the lower the interest rate.
• The bond supply curve will shift in response to
  changes in the state of the economy, government
  policy, and expected inflation.

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• Supply Curve for Bonds

18
Bond Demand and Supply Analysis

• Equilibrium
• The equilibrium rate, i and price, P0, are
  graphically defined by the intersection of the
  bond supply and bond demand curves.

19

• Supply and Demand for Bonds

20
Bond Demand and Supply Analysis

• Proof of Equilibrium
• If the bond price were below this equilibrium
  price (or equivalently the interest rate were
  above the equilibrium rate), then investors would
  want more bonds than issuers were willing to
  sell.
• This excess demand would drive the price of the
  bonds up, decreasing the demand and increasing
  the supply until the excess was eliminated.

21
Bond Demand and Supply Analysis

• Proof of Equilibrium
• If the price on bonds were higher than its
  equilibrium (or interest rates lower that the
  equilibrium rate), then bondholders would want
  fewer bonds, while issuers would want to sell
  more bonds.
• This excess supply in the market would lead to
  lower prices and higher interest rates,
  increasing bond demand and reducing bond supply
  until the excess supply was eliminated.

22
Bond Demand and Supply Analysis
23
Bond Demand and Supply Analysis
24
Bond Demand and Supply Analysis
25
Bond Demand and Supply Analysis
26
Cases Using Demand and Supply Analysis

• Expansionary Open Market Operation
• Central Bank buys bonds, decreasing the bond
  supply and shifting the bond supply curve to the
  left.
• The impact would be an increase in bond prices
  and a decrease in interest rates. Intuitively, as
  the central bank buys bonds, they will push the
  price of bond up and interest rate down.

27
Expansionary Open Market Operation
28
Cases Using Demand and Supply Analysis

• Economic Recession
• In an economic recession, there is less capital
  formation and therefore fewer bonds are sold.
• This leads to a decrease in bond supply and a
  leftward shift in the bond supply curve.
• The recession also lowers bond demand, shifting
  the bond demand curve to the left.
• If the supply effect dominates the demand effect,
  then there will be an increase in bond prices and
  a decrease in interest rates.

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Economic Recession
30
Cases Using Demand and Supply Analysis

• Treasury Financing of a Deficit
• With a government deficit, the Treasury will have
  to sell more bonds to finance the shortfall.
• Their sale of bonds will increase the supply of
  bonds, shifting the bond supply curve to the
  right, initially creating an excess supply of
  bonds.
• This excess supply will force bond prices down
  and interest rates up.

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Treasury Financing of Deficit
32
Cases Using Demand and Supply Analysis

• Economic Expansion
• In a period of economic expansion, there is an
  increase in capital formation and therefore more
  bonds are being sold to finance the capital
  expansion.
• This leads to an increase in bond supply and a
  rightward shift in the bond supply curve.
• The expansion also increases bond demand,
  shifting the bond demand curve to the right.
• If the supply effect dominates the demand
  effects, then there will be a decrease in bond
  prices and an increase in interest rates.

33
Economic Expansion
34
Risk and Risk Premium

• Investment risk is the uncertainty that the
  actual rate of return realized from a security
  will differ from the expected rate.
• In general, a riskier bond will trade in the
  market at a price that yields a greater YTM than
  a less risky bond.
• The difference in the YTM of a risky bond and the
  YTM of less risky or risk-free bond is referred
  to as a risk spread or risk premium.

35
Risk and Risk Premium

• The risk premium, RP, indicates how much
  additional return investors must earn in order to
  induce them to buy the riskier bond
• We can use the supply and demand model to show
  how the risk premium is positive.

RP YTM on Risky Bond - YTM on Risk-Free Bond
36
Risk and Risk Premium

• Consider the equilibrium adjustment that would
  occur for two identical bonds (C and T) that are
  priced with the same yields, but events occur
  that make one of the bonds more risky.

37
Risk and Risk Premium

• The increased riskiness on the one bond (Bond C)
  would cause its demand to decrease, shifting its
  bond demand curve to the left. That bonds
  riskiness would also make the other bond (Bond T)
  more attractive, increasing its demand and
  shifting its demand curve to the right.
• At the new equilibriums, the riskier bonds price
  is lower and its rate greater than the other.
• The different risk associated with bonds leads to
  a market adjustment in which at the new
  equilibrium there is a positive risk premium.

38
Risk Premium
The riskiness of Bond C increases the demand for
Bond T, shifting its bond demand curve to the
right. Impact A Lower Interest Rate on Bond T
The riskiness of Bond C decreases its demand,
shifting its bond demand curve to the left.
Impact A Higher Interest Rate on Bond C
39
Risk Premiums and Investors Return-Risk Premiums

• The size of the risk premium depends on
  investors attitudes toward risk.
• To see this relation, suppose there are only two
  bonds available in the market a risk-free bond
  and a risky bond.

40
Risk Premiums and Investors Return-Risk Premiums

• Suppose the risk-free bond is a zero-coupon bond
  promising to pay 1,000 at the end of one year
  and currently is trading for 909.09 to yield a
  one-year risk-free rate, Rf, of 10

41
Risk Premiums and Investors Return-Risk Premiums

• Suppose the risky bond is a one-year zero coupon
  bond with a principal of 1,000.
• Suppose there is a .8 probability the bond would
  pay its principal of 1,000 and a .2 probability
  it would pay nothing.
• The expected dollar return from the risky bond is
  therefore 800

E(Return) .8(1,000) .2(0) 800
42
Risk Premiums and Investors Return-Risk Premiums

• Given the choice of two securities, suppose that
  the market were characterized by investors who
  were willing to pay 727.27 for the risky bond,
  in turn yielding them an expected rate of return
  of 10
• In this case, investors would be willing to
  receive an expected return from the risky
  investment that is equal to the risk-free rate of
  10, and the risk premium, E(R) - Rf, would be
  equal to zero.
• In finance terminology, such a market is
  described as risk neutral.

RP 0 ? Risk-Neutral Market
43
Risk Premiums and Investors Return-Risk Premiums

• Instead of paying 727.27, suppose investors like
  the chance of obtaining returns greater than 10
  (even though there is a chance of losing their
  investment), and as a result are willing to pay
  750 for the risky bond. In this case, the
  expected return on the bond would be 6.67 and
  the risk premium would be negative
• By definition, markets in which the risk premium
  is negative are called risk loving.

RP lt 0 ? Risk-Loving Market
44
Risk Premiums and Investors Return-Risk Premiums

• Risk loving markets can be described as ones in
  which investors enjoy the excitement of the
  gamble and are willing to pay for it by accepting
  an expected return from the risky investment that
  is less than the risk-free rate.
• Even though there are some investors who are risk
  loving, a risk loving market is an aberration,
  with the exceptions being casinos, sports
  gambling markets, lotteries, and racetracks.

45
Risk Premiums and Investors Return-Risk Premiums

• Suppose most of the investors making up our
  market were unwilling to pay 727.27 or more for
  the risky bond.
• In this case, if the price of the risky bond were
  727.27 and the price of the risk-free were
  909.09, then there would be little demand for
  the risky bond and a high demand for the
  risk-free one.
• Holders of the risky bonds who wanted to sell
  would therefore have to lower their price,
  increasing the expected return. On the other
  hand, the high demand for the risk-free bond
  would tend to increase its price and lower its
  rate.

46
Risk Premiums and Investors Return-Risk Premiums

• Suppose the markets cleared when the price of the
  risky bond dropped to 701.75 to yield 14, and
  the price of the risk-free bond increased to
  917.43 to yield 9
• In this case, the risk premium would be 5

47
Risk Premiums and Investors Return-Risk Premiums

• By definition, markets in which the risk premium
  is positive are called risk-averse markets.
• In a risk-averse market, investors require
  compensation in the form of a positive risk
  premium to pay them for the risk they are
  assuming.
• Risk-averse investors view risk as a disutility,
  not a utility as risk-loving investors do.

RP gt 0 ? Risk-Averse Market
48
Risk Premiums and Investors Return-Risk Premiums

• Historically, security markets such as the stock
  and corporate bond markets have generated rates
  of return that, on average, have exceeded the
  rates on Treasury securities.
• This would suggest that such markets are risk
  averse.
• Since most markets are risk averse, a relevant
  question is the degree of risk aversion.
• The degree of risk aversion can be measured in
  terms of the size of the risk premium. The
  greater investors risk aversion, the greater the
  demand for risk-free securities and the lower the
  demand for risky ones, and thus the larger the
  risk premium.

49
Liquidity and Liquidity Premium

• Liquid securities are those that can be easily
  traded and in the short-run are absent of risk.
• In general, we can say that a less liquid bond
  will trade in the market at a price that yields a
  greater YTM than a more liquid one.

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Liquidity and Liquidity Premium

• The difference in the YTM of a less liquid bond
  and the YTM of a more liquid one is defined as
  the liquidity premium, LP

LP YTM on Less Liquid Bond - YTM on
More-Liquid Bond
51
Liquidity and Liquidity Premium

• Consider the equilibrium adjustment that would
  occur for two identical bonds that are priced
  with the same yields, but events occur that make
  one of the bonds less liquid.
• The decrease in liquidity on one of the bonds
  would cause its demand to decrease, shifting its
  bond demand curve to the left. The decrease in
  that bonds liquidity would also make the other
  bond relatively more liquid, increasing its
  demand and shifting its demand curve to the
  right.
• Once the markets adjust to the liquidity
  difference between the bonds, then the less
  liquid bonds price would be lower and its yield
  greater than the relative more liquid bond.
• Thus, the difference in liquidity between the
  bonds leads to a market adjustment in which there
  is a difference between rates due to their
  different liquidity features.

52
Liquidity Premium
The decrease in liquidity of Bond C increases
the demand for Bond T, shifting its bond demand
curve to the right. Impact A Lower Interest
Rate on Bond T
The decrease in liquidity of Bond C decreases
its demand, shifting its bond demand curve to
the left. Impact A Higher Interest Rate on Bond
C
53
Taxability

• An investor in a 40 income tax bracket who
  purchased a fully-taxable 10 corporate bond at
  par, would earn an after-tax yield, ATY, of 6
  ATY 10(1-.4).
• In general, the ATY can be found by solving for
  that yield, ATY, that equates the bonds price to
  the present value of its after-tax cash flows

54
Taxability and Pre-Tax Yield Spread

• Bonds that have different tax treatments but
  otherwise are identical will trade at different
  pre-tax YTM.
• That is, the investor in the 40 tax bracket
  would be indifferent between the 10
  fully-taxable corporate bond and a 6 tax-exempt
  municipal bond selling at par, if the two bond
  were identical in all other respects.
• The two bonds would therefore trade at equivalent
  after-tax yields of 6, but with a pre-tax yield
  spread of 4

55
Taxability and Pre-Tax Yield Spread

• In general, bonds whose cash flows are subject to
  less taxes trade at a lower YTM than bonds that
  are subject to more taxes.
• Historically, taxability explains why U.S.
  municipal bonds whose coupon interest is exempt
  from federal income taxes, have traded at yields
  below default-free U.S. Treasury securities even
  though many municipals are subject to default
  risk.

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Term Structure of Interest Rates

• Term Structure examines the relationship between
  YTM and maturity, M.
• Yield Curve Plot of YTM against M for bonds that
  are otherwise alike.

57
Term Structure of Interest Rates

• A yield curve can be constructed from current
  observations. For example, one could take all
  outstanding corporate bonds from a group in which
  the bonds are almost identical in all respects
  except their maturities, then generate the
  current yield curve.
• For investors who are more interested in long-run
  average yields instead of current ones, the yield
  curve could be generated by taking the average
  yields over a sample period (e.g., 5-year
  averages) and plotting these averages against
  their maturities.
• Finally, a widely-used approach is to generate a
  spot yield curve from spot rates.

58
Term Structure of Interest Rates

• Shapes Yield curves have tended to take on one
  of the three shapes
• They can be positively-sloped with long-term
  rates being greater than shorter-term ones.
• Such yield curves are called normal or upward
  sloping curves. They are usually convex from
  below, with the YTM flattening out at higher
  maturities.
• Yield curves can also be negatively-sloped, with
  short-term rates greater than long-term ones.
• These curves are known as inverted or downward
  sloping yield curves. Like normal curves, these
  curves also tend to be convex, with the yields
  flattening out at the higher maturities.
• Yield curves can be relatively flat, with YTM
  being invariant to maturity.

59
Term Structure of Interest Rates
60
Theories of the Term Structure of Interest Rates

• The actual shape of the yield curve depends on
• The types of bonds under consideration (e.g., AAA
  bond versus B bond)
• Economic conditions (e.g., economic growth or
  recession, tight monetary conditions, etc.)
• The maturity preferences of investors and
  borrowers
• Investors' and borrowers' expectations about
  future rates, inflation, and the state of
  economy.

61
Theories of the Term Structure of Interest Rates

• Four theories have evolved over the years to try
  to explain the shapes of yield curves
• Market Segmentation Theory (MST)
• Preferred Habitat Theory (PHT)
• Liquidity Premium Theory (LPT)
• Pure Expectation Theory (PET)

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Market Segmentation Theory

• MST Yield curve is determined by supply and
  demand conditions unique to each maturity
  segment.
• MST assumes that markets are segmented by
  maturity.

63
Market Segmentation Theory

• Example The yield curve for high quality
  corporate bonds could be segmented into two
  markets
• short-term
• long-term

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Market Segmentation Theory

• Short-Term Market
• The supply of short-term corporate bonds, such as
  commercial paper would depend on business demand
  for short-term assets such as inventories,
  accounts receivables, and the like
• The demand for short-term corporate bonds would
  emanate from investors looking to invest their
  excess cash for short periods.
• The demand for short-term bonds by investors and
  the supply of such bonds by corporations would
  ultimately determine the rate on short-term
  corporate bonds.

65
Market Segmentation Theory

• Long-Term Market
• The supply of long-term bonds would come from
  corporations trying to finance their long-term
  assets (plant expansion, equipment purchases,
  acquisitions, etc.).
• The demand for such bonds would come from
  investors, either directly or indirectly through
  institutions (e.g., pension funds, mutual funds,
  insurance companies, etc.), who have long-term
  liabilities and horizon dates.
• The demand for long-term bonds by investors and
  the supply of such bonds by corporations would
  ultimately determine the rate on long-term
  corporate bonds.

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Market Segmentation Theory Illustration

• Short-Term Market

Yield Curve for corporate bonds with two maturity
segments ST and LT
67
Market Segmentation Theory Illustration

• Long-Term Market

68
Market Segmentation Theory

• Important to MST is the idea of unique or
  independent markets.
• According to MST, the short-term bond market is
  unaffected by rates determined in the
  intermediate or long-term markets, and vice
  versa.
• This independence assumption is based on the
  premise that investors and borrowers have a
  strong need to match the maturities of their
  assets and liabilities.

69
MST Supply and Demand Model

• One way to examine how market forces determine
  the shape of yield curves is to examine MST using
  our supply and demand analysis.
• Consider a simple world in which there are two
  types of corporate and government treasury bonds
• Corporate bonds long-term (BcLT) and short-term
  (BcST)
• Treasury bonds long-term (BTLT) and short-term
  (BTLT).
• Assumptions The supplies and demands for each
  sector and segment are based on the following
  assumptions

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MST Supply and Demand Model

• Assumption 1 Short-Term Bond Demand for
  Corporate and Treasury
• The most important factors determining the demand
  for short-term bonds (both corporate and
  Treasury) are the bonds own price or interest
  rate, government policy, liquidity, and risk.
• Short-term bond demand is assumed to be inversely
  related to its price and directly related to its
  own rate (negatively sloped bond demand curves)
  government actions that affect the supply of
  loanable funds also can change bond demand (e.g.,
  monetary policy changing bank reserve
  requirements).
• The demand for the short-term bond in one sector
  is also assumed to be an inverse function of the
  short-term rate in the other sector, but not the
  long-term rate in either its sector or the other
  sector given the assumption of segmented markets.

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MST Supply and Demand Model

• Assumption 1 Short-Term Bond Demand for
  Corporate and Treasury

72
MST Supply and Demand Model

• Assumption 2 Long-Term Bond Demand for
  Corporate and Treasury
• The most important factors determining the demand
  for long-term bonds (both corporate and Treasury)
  are the bonds own price or interest rate,
  government policy such as monetary actions (e.g.,
  change in bank reserve requirements), liquidity,
  and risk.
• Demand is assumed to be inversely related to its
  own price and directly related to its own rate
  (negatively sloped bond demand curves).
• In addition, the demand for the long-term bond in
  one sector is an inverse function of the
  long-term rate in the other sector, but not a
  function of short-term rates given the market
  segmentation assumption.

73
MST Supply and Demand Model

• Assumption 2 Long-Term Bond Demand for Corporate
  and Treasury

74
MST Supply and Demand Model

• Assumption 3 Long-Term and Short-Term Bond
  Supplies for Corporate
• The supplies of short-term and long-term
  corporate bonds are directly related to their own
  prices and inversely to their own interest rates
  (positively sloped corporate bond supply curve)
  and directly related to general economic
  conditions, increasing in economic expansion and
  decreasing in recession.

75
MST Supply and Demand Model

• Assumption 4 Long-Term and Short-Term Bond
  Supplies for Treasury
• The supplies of Treasury bonds depend only on
  government actions (monetary and fiscal policy),
  and not on the economic state or interest rates.
• This assumption says that the sale or purchase of
  Treasury securities by the central bank or the
  Treasury is a policy decision. The assumption
  that the supply of Treasury securities depends on
  government actions and not interest rates means
  that the bond supply curve is vertical.

76
MST Supply and Demand Model

• In the exhibit, the two equilibrium rates for
  short-term and long-term corporate bonds are
  plotted against their corresponding maturities to
  generate the yield curve for corporate bonds.
• Similarly, the equilibrium rates for short-term
  and long-term Treasury bonds are plotted against
  their corresponding maturities to generate the
  yield curve for Treasury bonds.

77
Market Segmentation Theory Model
78
MST Supply and Demand Model

• These yield curves, in turn, capture an MST world
  in which interest rates for each segment are
  determined by the supply and demand for that
  bond, with the rates on bonds in the other
  maturity segments having no effect.
• In general, the positions and the shapes of the
  yield curves depend on the factors that determine
  the supply and demand for short-term and
  long-term bonds.

79
MST Cases Using SD Model

• Economic Expansion
• When an economy moves into a period of economic
  growth, business demand for short-term and
  long-term assets increases.
• As a result, many companies issue more short-term
  bonds to finance their larger inventories and
  accounts receivables. They also issue more
  long-term bonds to finance their increase in
  investments in plants, equipment, and other
  long-term assets.
• In the bond market, these actions cause the
  short-term and the long-term supplies of bonds to
  increase as the economy grows.

80
MST Cases Using SD Model

• Economic Expansion
• At the initial interest rates, the increase in
  bonds outstanding creates an excess supply. This
  drives bond prices down and the YTM up.
• Using the supply and demand model, the economic
  expansion shifts the corporate short-term and
  long-term bond supply curves to the right,
  creating an excess supply for short-term bonds at
  icST and an excess supply for long-term bonds at
  icLT.
• The excess causes corporate bond prices to fall
  and rates to rise until a new equilibrium is
  reached (icST and icLT).

81
MST Cases Using SD Model

• Economic Expansion
• As the rates on short-term and long-term
  corporate bonds increase, short-term and
  long-term Treasury securities become relatively
  less attractive.
• As a result, the demands for short-term and
  long-term Treasuries decrease, shifting the
  short-term and long-term Treasury bond demand
  curves to the left and creating an excess supply
  in both Treasury markets at their initial rates.
• Like the corporate bond markets, the excess
  supply in the Treasury security markets will
  cause their prices to decrease and their rates to
  rise until a new equilibrium is attained.

82
MST Cases Using SD Model

• Economic Expansion
• Thus, the supply and demand analysis shows that a
  recession has a tendency to increase both
  short-term and long-term rates for corporate
  bonds, and by a substitution effect, increase
  short-term and long-term Treasury rates.
• Hence, an economic expansion causes the yield
  curves for both sectors to shift up.

83
Economic Expansion
84
MST Cases Using SD Model

• Government surplus in which the Treasury buys
  existing long-term Treasury bonds
• When the Treasury uses a surplus to buy long-term
  Treasury securities there is a decrease in the
  supply of long-term Treasuries (leftward shift in
  the Treasury LT bond supply curve).
• The decrease in supply would push the price of
  the long-term government securities up, resulting
  in a lower long-term Treasury yield.

85
MST Cases Using SD Model

• Government surplus in which the Treasury buys
  existing long-term Treasury bonds
• In the corporate bond market, the lower rates on
  long-term government securities would lead to an
  increase in the demand for long-term corporate
  securities (rightward shift in the corporate LT
  bond demand curve), which, in turn, would lead to
  an excess demand in that market.
• As bondholders try to buy long-term corporate
  bonds, the prices on such bonds would increase,
  causing the yields on long-term corporate bonds
  to fall until a new equilibrium is reached.

86
MST Cases Using SD Model

• Government surplus in which the Treasury buys
  existing long-term Treasury bonds
• Thus, the purchase of the long-term Treasury
  securities decreases both long-term government
  and long-term corporate rates.
• Since the long-term market is assumed to be
  independent of short-term rates, the total
  adjustment to the Treasurys purchase of
  long-term securities would occur through the
  decrease in long-term corporate and Treasury
  rates.
• If corporate and Treasury yield curves were
  initially flat, the Treasurys action would cause
  the yield curves to become negatively sloped.

87
Government surplus in which the
Treasury buys existing long-term Treasury bonds
88
MST Cases Using SD Model

• Contractionary open market operation in which
  the Central Bank sells some of it short-term
  Treasury securities
• A contractionary OMO in which the Fed sells
  short-term Treasury securities would cause the
  price on short-term Treasury securities to
  decrease and their yield to increase. This would
  be reflected by a rightward shift in the
  short-term Treasury bond supply curve, as the
  Central Bank sells it securities to the public.
• As the yield on short-term Treasuries increases,
  the demand for short-term corporate would
  decrease (demand curve shifting left), leading to
  lower prices and higher yields on short-term
  corporate bonds.

89
MST Cases Using SD Model

• Contractionary open market operation in which
  the Central Bank sells some of it short-term
  Treasury securities
• Since the long-term market is assumed to be
  independent of short-term rates, the total
  adjustment to the Central banks sale of
  short-term securities to the public would be in
  the short-term corporate and Treasury markets
  with no impact on the long-term markets.
• If both the Treasury and corporate yield curves
  were initially flat, then the contractionary OMO
  would result in new negatively sloped yield
  curves.

90
Contractionary Open Market
Operation Central Bank sells short-term
Treasuries
91
MST Outline of Cases Using SD Model

• Recession
• Outline Decrease in capital formation (S-T and
  L-T) ? Fewer bonds sold (S-T and L-T) ? Excess
  demand for bonds (S-T and L-T) ? Bond prices
  increase and rates decrease. ? Downward shift in
  YC

92
MST Outline of Cases Using SD Model

• Expansionary open market operation in which the
  central bank buys short-term Treasury securities
• Outline Central bank buys S-T Treasuries
  (T-bills) ? T-bill prices increase and rates
  decrease ? Substitution effect in which the
  demand for S-T corporate securities increase,
  causing their prices to increase and their yields
  to decrease. ? Tendency for YC to become
  positively sloped.

93
MST Outline of Cases Using SD Model

• Treasury Sale of long-term Treasury bonds
• Outline Treasury sells L-T Treasuries (T-Bonds)
  ? T-Bond prices decrease and yields increase ?
  Substitution effect in which the demand for L-T
  corporate securities decrease, causing their
  prices to decrease and their rates to increase. ?
  Tendency for YC to become positively sloped.

94
Preferred Habitat Theory (PHT)

• PHT assumes that investors and borrowers are
  willing to give up their desired maturity segment
  and assume market risk if rates are attractive.
• PHT asserts that investors and borrowers will be
  induced to forego their perfect hedges and shift
  out of their preferred maturity segments when
  supply and demand conditions in different
  maturity markets do not match.

95
Preferred Habitat Theory (PHT)

• PHT is a necessary extension of the MST
• If an economy is poorly hedged (e.g., more
  investors want ST investments and more borrowers
  want to borrow LT), then the market will not be
  in equilibrium.
• In such cases, ST and LT rates will change and
  the markets will clear as investors and borrowers
  give up their hedge.

96
Preferred Habitat Theory (PHT)

• To illustrate PHT, consider an economic world in
  which, on the demand side, investors in corporate
  securities, on average, prefer short-term to
  long-term instruments, while on the supply side,
  corporations have a greater need to finance
  long-term assets than short-term, and therefore
  prefer to issue more long-term bonds than
  short-term.
• Combined, these relative preferences would cause
  an excess demand for short-term bonds and an
  excess supply for long-term claims and an
  equilibrium adjustment would have to occur.

97
Preferred Habitat Theory (PHT)

• In the long-term market, the excess supply would
  force issuers to lower their bond prices, thus
  increasing bond yields and inducing some
  investors to change their short-term investment
  demands.
• In the short-term market, the excess demand would
  cause bond prices to increase and rates to fall,
  inducing some corporations to finance their
  long-term assets by selling short-term claims.
• Ultimately, equilibriums in both markets would be
  reached with long-term rates higher than
  short-term rates, a premium necessary to
  compensate investors and borrowers/issuers for
  the market risk they've assumed.

98
Preferred Habitat Theory

• Poorly Hedged Economy Investors, on average,
  prefer ST investments corporate borrowers, on
  average, prefer to borrow LT (sell LT corporate
  bonds)

99
Liquidity Preference Theory

• Long-term bonds are more price sensitive to
  interest rate changes than short-term bonds. As
  a result, the prices of long-term securities tend
  to be more volatile and therefore more risky than
  short-term securities.
• The Liquidity Premium Theory (LPT), also referred
  to as the Risk Premium Theory (RPT), posits that
  there is a liquidity premium for long-term bonds
  over short-term bonds.

100
Liquidity Preference Theory

• According to LPT, if investors were risk averse,
  then they would require some additional return
  (liquidity premium, LP) in order to hold
  long-term bonds instead of short-term ones.

101
Liquidity Preference Theory

• Thus, if the yield curve were initially flat, but
  had no risk premium factored in to compensate
  investors for the additional volatility they
  assumed from buying long-term bonds, then the
  demand for long-term bonds would decrease and
  their rates increase until risk-averse investors
  were compensated.
• In this case, the yield curve would become
  positively sloped.

102
Pure Expectations Theory

• Expectation theories address the question of what
  impact expectations have on the current yield
  curve.
• One of these theories is the Pure Expectations
  Theory (PET) also referred to as the unbiased
  expectations theory (UET).
• PET posits that the yield curve is governed by
  the condition that the implied forward rate is
  equal to the expected sport rate.

103
Pure Expectations Theory

• To illustrate PET
• Consider a market consisting of only two bonds a
  risk-free one-year zero-coupon bond and a
  risk-free two-year zero-coupon bond, both with
  principals of 100.
• Suppose that supply and demand conditions are
  such that both the one-year and two-year bonds
  are trading at an 8 YTM.
• Suppose that the market expects the yield curve
  to shift up to 10 next year, but, as yet, has
  not factored that expectation into its current
  investment decisions.
• Finally, assume the market is risk-neutral, such
  that investors do not require a risk premium for
  investing in risky securities (i.e., they will
  accept an expected rate on a risky investment
  that is equal to the risk-free rate).

104
Pure Expectations Theory

• Question
• What is the impact of the expectation on the
  current yield curve?

105
Pure Expectations Theory

• Consider investors with HD 2 years
• Alternatives
• Buy 2-year bond at 8
• Buy a series of 1-year bonds 1-year bond today
  at 8 and 1-year bond one year later at E(r11)
  10. The expected return from
  the series would be 9
• In a risk-neutral world, investors with HD 2
  years would prefer the series of 1-year bonds
  over the 2-year bond.

106
Pure Expectations Theory

• Consider investors with HD 1 year.
• Alternatives
• Buy 1-year bond at 8.
• Buy a 2-year bonds at 8 for P2 100/(1.08)2
  85.734, then sell it one year later at an
  expected price of E(P11) 100/(1.10) 90.91.
  The expected rate of return would be 6
• In a risk-neutral world, investors with HD 1
  year would prefer the 1-year bond over the 2-year
  bond.

107
Pure Expectations Theory

• Thus, in a risk-neutral market with an
  expectation of higher rates next year, both
  investors with one-year horizon dates and
  investors with two-year horizon dates would
  purchase one-year instead of two-year bonds
• If enough investors do this, an increase in the
  demand for one-year bonds and a decrease in the
  demand for two-year bonds would occur until the
  average annual rate on the two-year bond is equal
  to the equivalent annual rate from the series of
  one-year investments (or the one-year bond's rate
  is equal to the rate expected on the two-year
  bond held one year).

108
Pure Expectations Theory

• Investors with HD of 2 years and those with HD of
  1 year would prefer one-year bonds over two- year
  bonds.
• Market Response

109
Pure Expectations Theory

• In the example, if the price on a two-year bond
  fell such that it traded at a YTM of 9 and the
  rate on a one-year bond stayed at 8, then
  investors with two-year horizon dates would be
  indifferent between a two-year bond yielding a
  certain 9 and a series of one-year bonds
  yielding 10 and 8, for an expected rate of 9.
  
• Investors with one-year horizon dates would
  likewise be indifferent between a one-year bond
  yielding 8 and a two-year bond purchased at 9
  and sold one year later at 10, for an expected
  one-year rate of 8.

110
Pure Expectations Theory

• Thus in this case, the impact of the market's
  expectation of higher rates would be to push
  2-year rates up to 9.
• Note With YTM2 9 and YTM1 8, the implied
  forward rate is f11 10 -- the same rate as the
  expected rate E(r11).

111
Pure Expectations Theory

• Assume that the market response is one in which
  only the demand for 2-year bonds is affected by
  the expectations.

112
Pure Expectations Theory

• In the above example, the yield curve is
  positively sloped, reflecting expectations of
  higher rates.
• By contrast, if the yield curve were currently
  flat at 10 and there was a market expectation
  that it would shift down to 8 next year, then
  the expectation of lower rates would cause the
  yield curve to become negatively sloped.

113
Pure Expectations Theory

• That is, given a yield curve currently flat at
  10 and a market expectation that it would shift
  down to 8 next year, an investor with a two-year
  horizon date would prefer the two-year bond at
  10 to a series of one-year bonds yielding an
  expected rate of only 9 (E(R)
  (1.10)(1.08)1/2 -1 .09).
• Similarly, an investor with a one-year horizon
  would also prefer buying a two-year bond that has
  an expected rate of return of 12 (P2
  100/(1.10)2 82.6446, E(P11) 100/1.08
  92.5926, E(R) 92.5926-82.6446/82.6446
  .12) to the one-year bond that yields only 10.

114
Pure Expectations Theory

• In markets for both one-year and two-year bonds,
  the expectations of lower rates would cause the
  demand and price of the two-year bond to
  increase, lowering its rate, and the demand and
  price for the one-year bond to decrease,
  increasing its rate.

115
Pure Expectations Theory
Market expects the yield curve to shift down
from 10 to 8.
Investor with a one-year horizon would prefer
buying a two-year bond that has an expected rate
of return of 12 to the one-year bond that
yields only 10 P2 100/(1.10)2 82.6446
E(P11) 100/1.08 92.5926 E(R)
92.5926-82.6446/82.6446 .12
Investors with two-year horizon dates would
prefer the two-year bond at 10 to a series of
one-year bonds yielding an expected rate of only
9 (E(R) (1.10)(1.08)1/2 -1 .09)
YC become negatively sloped
116
Pure Expectations Theory

• The adjustments would continue until the rate on
  the two-year bond equaled the average rate from
  the series of one-year investments, or until the
  rate on the one-year bond equaled the expected
  rate from holding a two-year bond one year (or
  when the implied forward rate is equal to
  expected spot rates).
• In this case, if one-year rates stayed at 8,
  then the demand for the two-year bond would
  increase until it was priced to yield 9 - the
  expected rate from the series (1.10)(1.08)1/2
  -1 .09

117
Pure Expectations Theory

• Assume that the market response is one in which
  only the demand for 2-year bonds is affected by
  the expectations.

118
Features of PET

• One of the features of the PET is that in
  equilibrium the yield curve reflects current
  expectations about future rates. From our
  preceding examples
• When the equilibrium yield curve was positively
  sloped, the market expected higher rates in the
  future
• When the curve was negatively sloped, the market
  expected lower rates.

119
Features of PET

• 2. PET intuitively captures what should be
  considered as normal market behavior.
• For example, if long-term rates were expected to
  be higher in the future, long-term investors
  would not want to purchase long-term bonds now,
  given that next period they would be expecting
  higher yields and lower prices on such bonds.
  Instead, such investors would invest in
  short-term securities now, reinvesting later at
  the expected higher long-term rates.
• In contrast, borrowers/issuers wishing to borrow
  long-term would want to sell long-term bonds now
  instead of later at possibly higher rates.
• Combined, the decrease in demand for long-term
  bonds by investors and the increase in the supply
  of long-term bonds by borrowers would serve to
  lower long-term bond prices and increase yields,
  leading to a positively-sloped yield curve.

120
Features of PET

• 3. If PET strictly holds (i.e., we can accept all
  of the model's assumptions), then the expected
  future rates would be equal to the implied
  forward rates. As a result, one could forecast
  futures rates and future yield curves by simply
  calculating implied forward rates from current
  rates.

121
Features of PET

• The last feature suggests that given a spot yield
  curve, one could use PET to estimate next
  period's spot yield curve by determining the
  implied forward rates.
• The exhibit on the next slide shows spot rates on
  bonds with maturities ranging from one year to
  five years (Column 2). From these rates,
  expected spot rates (St) are generated for bonds
  one year from the present (Column 3) and two
  years from the present (Column 4). The expected
  spot rates shown are equal to their corresponding
  implied forward rates.

122
Features of PET
123
Features of PET
124
Features of PET

• According to PET, if the market is risk-neutral,
  then the implied forward rate is equal to the
  expected spot rate, and in equilibrium, the
  expected rate of return for holding any bond for
  one year would be equal to the current spot rate
  on one-year bonds.

125
Features of PET

• For example, the expected rate of return from
  purchasing a two-year zero-coupon bond at the
  spot rate of 10.5 and selling it one year later
  at an expected one-year spot rate equal to the
  implied forward rate of f11 11 is 10. This
  is the same rate obtained from investing in a
  one-year bond

126
Features of PET

• Similarly, the expected rate of return from
  holding a three-year bond for one year, then
  selling it at the implied forward rate of f21 is
  also 10. That is
• Any of the bonds with spot rates shown in the
  exhibit would have expected rates for one year
  of 10 if the implied forward rate were used as
  the estimated expected rate.

127
Features of PET

• Similarly, any bond held for two years and sold
  at its forward rate would earn the two-year spot
  rate of 10.5. For example, a four-year bond
  purchased at the spot rate of 11.5 and expected
  to be sold two years later at f22 12.5, would
  trade at an expected rate of 10.5 - the same as
  the current two-year spot.

128
Features of PET

• Analysts often refer to forward rates as hedgable
  rates.
• The most practical use of forward rates or
  expected spot yield curves generated from forward
  rates is that they provide cut-off rates, useful
  in evaluating investment decisions.
• For example, an investor with a one-year horizon
  date should only consider investing in the
  two-year bond in our above example, if she
  expected one-year rates one year later to be less
  than f11 11 that is, assuming she is
  risk-averse and wants an expected rate greater
  than 10.
• Thus, forward rates serve as a good cut-off rate
  for evaluating investments.

129
Websites

• Historical interest rate data on different bonds
  can be found at the Federal Reserve site
  www.federalreserve.gov/releases/h15/data.htm
• and www.research.stlouisfed.org/fred2
• For information on Federal Reserve policies go to
• www.federalreserve.gov/policy.htm
• For information on European Central Banks go to
• www.ecb.int

130
Websites

• Current and historical data on U.S. government
  expenditures and revenues can be found at
  www.gpo.gov/usbudget.
• Yield curves can be found at a number of
  siteswww.ratecurve.com and www.bloomberg.com