Notes
Page 1
Economics of Capital Markets
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Term Structure of Interest RatesTerm Structure of Interest Rates
Major Topics:– Introduction– Yield Curve Patterns– Term Structure Theories
Economics of Capital Markets
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IntroductionIntroduction
Notes
Page 2
Economics of Capital Markets
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Term Structure of Interest RatesIntroductionTerm Structure of Interest RatesIntroduction
Behavior of interest rates to explain
Economics of Capital Markets
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Term Structure of Interest RatesIntroduction (Continued)
Term Structure of Interest RatesIntroduction (Continued)
The structure of rates for a particular type of security where the only difference among them is maturity is called the term structureA plot of the rates vs. maturity is called the yield curve
Notes
Page 3
Economics of Capital Markets
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Yield Curve PatternsYield Curve Patterns
Economics of Capital Markets
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Term Structure of Interest RatesYield Curve PatternsTerm Structure of Interest RatesYield Curve Patterns
Three general patterns to yield curves
Problem: accounting for patternTypical pattern found in Wall Street Journal in Credit Market column
Notes
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Economics of Capital Markets
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Term Structure TheoriesTerm Structure Theories
Economics of Capital Markets
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Term Structure of Interest RatesTerm Structure TheoriesTerm Structure of Interest RatesTerm Structure Theories
Four theories dominate literature– Expectations Hypothesis– Liquidity Preference Theory– Segmented Markets Theory– Preferred Habitat Theory
Each theory will be examined in turn
Notes
Page 5
Economics of Capital Markets
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Term Structure of Interest RatesExpectations HypothesisTerm Structure of Interest RatesExpectations Hypothesis
Founded on concept that a rational economic agent is indifferent between equal returns from one investment possibility and the next best alternative
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Basic assumption– Buyers of bonds do not prefer one maturity to
another
Notes
Page 6
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Theory development– Investment problem: invest for two years– Two investment strategies
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Notationi01 = Nominal interest rate in period 0 for 1
yeari11
e = Nominal interest rate expected in period 1 for 1 year
i02 = Nominal interest rate in period 0 for 2years
Notes
Page 7
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Strategy 1
Strategy 2
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Conjecture
Focus is on interest rates, not dollar returns– What are the rate relationships?
Notes
Page 8
Economics of Capital Markets
Page 15Version 1.0 Outline
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
We require that
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Conclusion
– More generally, for an n-period security
rate forward theis iwhere
ni ... i i i
i
ej1
e1,1n
e21
e1101
0n−++++
=
Notes
Page 9
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Conclusions
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Properties of short-term rates
Notes
Page 10
Economics of Capital Markets
Page 19Version 1.0 Outline
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Properties of short-term rates (Continued)
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Policy implication– Short-term and long-term rates are perfect
substitutes in portfolios– FED cannot influence yield curve by buying
one maturity and selling another - can only influence expectations
Notes
Page 11
Economics of Capital Markets
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Term Structure of Interest RatesExpectations Hypothesis (Continued)
Term Structure of Interest RatesExpectations Hypothesis (Continued)
Problem with hypothesis– Implies any shape to yield curve– Yield curve almost always slopes upward
implying that short-term rates are expected to rise
Economics of Capital Markets
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Term Structure of Interest RatesLiquidity Preference TheoryTerm Structure of Interest RatesLiquidity Preference Theory
Recall that wealth can be held in form of money balances or bonds– W = M + B
» M is perfectly liquid and riskless» B is highly illiquid and risky
– Investors trade off liquid for illiquid assets
Notes
Page 12
Economics of Capital Markets
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Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Focus on B– B is a series of risky, illiquid assets– Not only do investors tradeoff between M and
B, but also between different Bs
Economics of Capital Markets
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Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Basic concept– Planning or investment horizon
» Expected amount of time you will be invested in the market
» Example: plan to close on a house in 6 months
Investor chooses a B matching or close to matching the planning horizon– Focus on risk over planning horizon
Notes
Page 13
Economics of Capital Markets
Page 25Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Two kinds of riskReinvestment riskReinvestment risk
Price riskPrice risk
Economics of Capital Markets
Page 26Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Two kinds of risk (Continued)
Rise
Fall
Change inRates
Risks
Reinvestment Price
Summary
Notes
Page 14
Economics of Capital Markets
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Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Gains and losses example for bondsBond prices and yields
Yield Price (5 Yrs)6.00% $112.79537.00% $108.31668.00% $104.05549.00% $100.00009.50% $98.045910.00% $96.1391
Economics of Capital Markets
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Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Slightly Non-LinearPattern
Plot
Price-Yield Curve
Yield (%)
Pric
e ($
)
6 7 8 9 10
100
105
110
Notes
Page 15
Economics of Capital Markets
Page 29Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Differences in price response– Current yield = 7.00%
Falls to 6.00% => Price rises to $112.7953Rises to 8.00% => Price falls to $104.0554» Percentage point change in yield is the same:
+/- 1% pt.» But note differences in price changes
% price increase: 4.135%%price decrease: -3.934%
From $108.3166
Economics of Capital Markets
Page 30Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Symmetry of gains/losses– Gains/losses not symmetric
» The gain from a rate decrease is larger in percentage terms than the loss from a rate increaseof the same amount
Conclusion
Notes
Page 16
Economics of Capital Markets
Page 31Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Additional fact about bonds– For given percentage change in yields, the
percentage change in bond prices will be greater the longer the bond’s maturity
PricesYield 5 Year 20 Year6.00% $112.7953 $134.67227.00% $108.3166 $121.35518.00% $104.0554 $109.8964
4.135%
-3.934%
10.974%
-9.442%
Economics of Capital Markets
Page 32Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
For previous case of a 6 month investment– Could avoid all risk by buying 1 6-month bond– If cannot buy 1 6-month bond
Notes
Page 17
Economics of Capital Markets
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Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Risk vs. planning horizonRisk
Maturity6 Months
Planning HorizonPlanning Horizon3 Months 12 Months
IncreasingReinvestment
Risk
IncreasingPriceRisk
Economics of Capital Markets
Page 34Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Liquidity Preference Theory assumes market dominated by investors with short horizons
Notes
Page 18
Economics of Capital Markets
Page 35Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
We know from CAPM that the market interest rate is sum of two components– Risk free rate– Risk premium
MarketInterest
Rate
Risk Premium
Risk Free Rate
Source of Rate
{Liquidity
PreferenceTheory Gives
This Part
Economics of Capital Markets
Page 36Version 1.0 Outline
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Term Structure of Interest RatesLiquidity Preference Theory (Continued)
Yield curve implication– Longer term bonds have more overall risk so
higher expected returns are demanded regardless of expectations of short-term rate movements
– Therefore, even if rates are expected to remain constant, long-term rates will still be higher
» Contrary to expectations hypothesis
Yield curve combination of both theories
Notes
Page 19
Economics of Capital Markets
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Term Structure of Interest RatesPreferred Habitat TheoryTerm Structure of Interest RatesPreferred Habitat Theory
Liquidity Preference has strong assumption
Economics of Capital Markets
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Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Long-term institutional investors
Preferred Habitat Theory sometimes called institutional demand theory
Notes
Page 20
Economics of Capital Markets
Page 39Version 1.0 Outline
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Different planning horizonsRisk
Planning Horizon
1 Year 10 Years 20 Years
Individual Investor
Commercial Bank
Insurance Cos.
Economics of Capital Markets
Page 40Version 1.0 Outline
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
“Preferred Habitat” name due to each type of investor having preferred - zero risk -investment maturity
Notes
Page 21
Economics of Capital Markets
Page 41Version 1.0 Outline
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Preferred Habitat does not preclude possibility that most funds come from investors with short horizons
Economics of Capital Markets
Page 42Version 1.0 Outline
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Preferred Habitat recognizes both types of risk
Notes
Page 22
Economics of Capital Markets
Page 43Version 1.0 Outline
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Assume Expectations Hypothesis is still correct– Add Preferred Habitat on top of equation
premium risk theis 0 kwhere
k n
i ... i i i i
0n
0n
e1,1n
e21
e1101
0n
>
+++++
= −
Economics of Capital Markets
Page 44Version 1.0 Outline
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Preferred Habitat is consistent with two empirical facts
Notes
Page 23
Economics of Capital Markets
Page 45Version 1.0 Outline
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Can account for downward sloping yield curve
Economics of Capital Markets
Page 46Version 1.0 Outline
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Term Structure of Interest RatesPreferred Habitat Theory (Continued)
Additional empirical fact about yield curves– Tend to have especially steep upward slope
when short-term rates are low and a downward slope when short-term rates are high
Notes
Page 24
Economics of Capital Markets
Page 47Version 1.0 Outline
Term Structure of Interest RatesSegmentation Theory
Term Structure of Interest RatesSegmentation Theory
Under Preferred Habitat, investors move from preferred maturity only if compensated by risk premium
Economics of Capital Markets
Page 48Version 1.0 Outline
Term Structure of Interest RatesSegmentation Theory (Continued)
Term Structure of Interest RatesSegmentation Theory (Continued)
Assume infinite risk aversion– Investors then do not move from preferred
habitat» Invest in securities matching preferred horizons
– Market is perfectly segmented» Extreme version of Preferred Habitat
Notes
Page 25
Economics of Capital Markets
Page 49Version 1.0 Outline
Term Structure of Interest RatesSegmentation Theory (Continued)
Term Structure of Interest RatesSegmentation Theory (Continued)
Implication– Long-term and short-term rates determined in
separate markets
Economics of Capital Markets
Page 50Version 1.0 Outline
Term Structure of Interest RatesReview Questions
Term Structure of Interest RatesReview Questions
State some empirical facts about interest rates.What is a yield curve?What is the term structure of the interest rate?What are the major theories of the term structure?What is a planning horizon?What risk is implied by the Liquidity Preference Theory?What is a major assumption of the Liquidity Preference Theory?What is a Preferred Habitat?
Notes
Page 26
Economics of Capital Markets
Page 51Version 1.0 Outline
Term Structure of Interest RatesKey Terms and Concepts
Term Structure of Interest RatesKey Terms and Concepts
Planning HorizonPreferred HabitatTerm StructureYield Curve
Economics of Capital Markets
Page 52Version 1.0 Outline
Term Structure of Interest RatesSuggested Readings
Term Structure of Interest RatesSuggested Readings
Fabozzi, F.J. and Modigliani, F. 1992. Capital Markets: Institutions and Instruments. Englewood Cliffs, NJ: Prentice Hall.Livingston, M. 1993. Money and Capital Markets, 2nd. ed. NY: New York Institute of Finance.Malkiel. B.G. 1987. “Term Structure of Interest Rates.” in The New Palgrave.
Notes
Page 27
Economics of Capital Markets
Page 53Version 1.0 Outline
Term Structure of Interest RatesTerm Structure of Interest Rates
Appendix
Economics of Capital Markets
Page 54Version 1.0 Outline
Term Structure of Interest RatesAutocorrelated StructuresTerm Structure of Interest RatesAutocorrelated Structures
For Any Time Series, Zt
Z Z u
u N(0to ensure a finite variance
t t -1 t
t u2
= +
=
<
φ
σ
φ
, )1
Notes
Page 28
Economics of Capital Markets
Page 55Version 1.0 Outline
Term Structure of Interest RatesExtended Bond Yield-Price RelationshipTerm Structure of Interest RatesExtended Bond Yield-Price Relationship
$40
$60
$80
$100
$120
$140
$160
$180 P
rice
4.006.25
8.5010.75
13.0015.25
17.50
Yield (%)
5 Yr Price
20 Yr. Price
Economics of Capital Markets
Page 56Version 1.0 Outline
Term Structure of Interest RatesIntroductionTerm Structure of Interest RatesIntroduction
Real Nominal
Riskless
Risky
Short-term
Long-termRis
k D
imen
sion
Value Dimension Matu
rity D
imen
sion