19 - term structure - rutgers universityeconweb.rutgers.edu/paczkows/market/termstructure.pdf ·...

Notes

Economics of Capital Markets

Page 1Version 1.0 Outline

Term Structure of Interest RatesTerm Structure of Interest Rates

Major Topics:– Introduction– Yield Curve Patterns– Term Structure Theories



IntroductionIntroduction

Notes



Term Structure of Interest RatesIntroductionTerm Structure of Interest RatesIntroduction

Behavior of interest rates to explain



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



Yield Curve PatternsYield Curve Patterns



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



Term Structure TheoriesTerm Structure Theories



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



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



Term Structure of Interest RatesExpectations Hypothesis (Continued)


Basic assumption– Buyers of bonds do not prefer one maturity to

another

Notes





Theory development– Investment problem: invest for two years– Two investment strategies





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





Strategy 1

Strategy 2





Conjecture

Focus is on interest rates, not dollar returns– What are the rate relationships?

Notes





We require that





Conclusion

– More generally, for an n-period security

rate forward theis iwhere

ni ... i i i

i

ej1

e1,1n

e21

e1101

0n−++++

=

Notes





Conclusions





Properties of short-term rates

Notes





Properties of short-term rates (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





Problem with hypothesis– Implies any shape to yield curve– Yield curve almost always slopes upward

implying that short-term rates are expected to rise



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



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





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





Two kinds of riskReinvestment riskReinvestment risk

Price riskPrice risk





Two kinds of risk (Continued)

Rise

Fall

Change inRates

Risks

Reinvestment Price

Summary

Notes





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





Slightly Non-LinearPattern

Plot

Price-Yield Curve

Yield (%)

Pric

e ($

)

6 7 8 9 10

100

105

110

Notes





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





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





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%





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





Risk vs. planning horizonRisk

Maturity6 Months

Planning HorizonPlanning Horizon3 Months 12 Months

IncreasingReinvestment

Risk

IncreasingPriceRisk





Liquidity Preference Theory assumes market dominated by investors with short horizons

Notes





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





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



Term Structure of Interest RatesPreferred Habitat TheoryTerm Structure of Interest RatesPreferred Habitat Theory

Liquidity Preference has strong assumption



Term Structure of Interest RatesPreferred Habitat Theory (Continued)


Long-term institutional investors

Preferred Habitat Theory sometimes called institutional demand theory

Notes





Different planning horizonsRisk

Planning Horizon

1 Year 10 Years 20 Years

Individual Investor

Commercial Bank

Insurance Cos.





“Preferred Habitat” name due to each type of investor having preferred - zero risk -investment maturity

Notes





Preferred Habitat does not preclude possibility that most funds come from investors with short horizons





Preferred Habitat recognizes both types of risk

Notes





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

>

+++++

= −





Preferred Habitat is consistent with two empirical facts

Notes





Can account for downward sloping yield curve





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



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



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





Implication– Long-term and short-term rates determined in

separate markets



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



Term Structure of Interest RatesKey Terms and Concepts

Term Structure of Interest RatesKey Terms and Concepts

Planning HorizonPreferred HabitatTerm StructureYield Curve



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



Term Structure of Interest RatesTerm Structure of Interest Rates

Appendix



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



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



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

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