06.the Risk and Term Structure of Interest Rates

7/30/2019 06.the Risk and Term Structure of Interest Rates

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Copyright 2011 Pearson Canada Inc. 6 - 1

Chapter 6

The Risk and Term Structure ofInterest Rates


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Risk and Term Structure of Interest Rates

The risk structure of interest rates looks atbonds with the same term to maturity anddifferent interest rates.

The term structure of interest rates looks atthe relationship among interest rates onbonds with different terms to maturity.


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Default Risk

Default risk - occurs when the issuer of the

bond is unable or unwilling to make interest

payments or pay off the face value

Canadian government bonds are considered

default free.

Risk premium - the spread between the

interest rates on bonds with default risk and

bonds without default risk


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Response to an Increase in Default Risk

on Corporate Bonds


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Credit Ratings Agencies


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Corporate-Canada Bond Spread 1978 - 2005


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Other Factors influencing the Risk

Structure

Liquidity how quickly and cheaply a bond

can be converted to cash

Income tax considerations in some countries

certain government bonds are not taxable.

In Canada coupon payments on fixed-income

securities are taxed as ordinary income.

In the U.S. interest payments on municipal bonds

are exempt from federal income tax



Term Structure of Interest Rates

Bonds with identical risk, liquidity, and tax

characteristics may have different interest rates

because the time remaining to maturity is different.

Yield curve - a plot of the yield on bonds withdiffering terms to maturity but the same risk,

liquidity and tax considerations

Upward-sloping

long-term rates are aboveshort-term rates

Flat short- and long-term rates are the same

Inverted long-term rates are below short-term rates



Empirical Facts To Be Explained by the Term

Structure

1. Interest rates on bonds of differentmaturities move together over time.

2. When short-term interest rates are low,yield curves are more likely to have anupward slope; when short-term rates arehigh, yield curves are more likely to slope

downward and be inverted.

3. Yield curves almost always slope upward.



Three Theories to Explain the Three Facts

1. Expectations theory explains the first two

facts but not the third.

2. Segmented markets theory explains factthree but not the first two.

3. Liquidity premium theory combines the two

theories to explain all three facts.



Term Structure of Interest Rates Fact 1



Expectations Theory

The interest rate on a long-term bond will equal anaverage of the short-term interest rates that people

expect to occur over the life of the long-term bond.

Buyers of bonds do not prefer bonds of one maturity

over another; they will not hold any quantity of a bond if

its expected return is less than that of another bond

with a different maturity.

Bonds like these are said to be perfect substitutes.



Expectations TheoryExample

Let the current rate on one-year bond be 6%.

You expect the interest rate on a one-year

bond to be 8% next year. Then the expected return for buying two one-

year bonds averages (6% + 8%)/2 = 7%.

The interest rate on a two-year bond must be7% for you to be willing to purchase it.



Expectations TheoryIn General I

For an investment of $1

it= todays interest rate on a one-period bond

iet+1 = interest rate on a one-period bondexpected for next period

i2t

= todays interest rate on the two-period

bond



Expectations TheoryIn General II

Expected return over the two periods frominvesting $1 in the two-period bond and holding it

for the two periods

2t

22t

2

22

2

22

22

2iisperidstwoforperiod-twotheholdingfor

returnexpectedthesmallveryis)(iSince

)(2

1)(21

1)1)(1(

tt

tt

tt

ii

ii

ii


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Expectations TheoryIn General III

e

t

e

tt

e

tt

e

tt

e

tt

e

tt

e

t

i

ii

iiii

iiii

i

1t

1

11

11

1t

igetwegSimplifyin

smallextremelyis)(

)(1)(1

1)1)(i(1

investment$1thewithboughtarebondsperiod-onetwoIf


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Expectations TheoryIn General IV

Both bond will be held only if the expected returns are equal.

2

2

12

12

e

tt

t

e

ttt

iii

iii

The two-period rate must equal the average of the two one-periodrates. For bonds with longer maturities:

n

iiiii

e

nt

e

t

e

tt

nt

)1(21 ...

The n-period interest rate equals the average of the one-period

interest rates expected to occur over the n-period life of the

bond


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Expectations Theory

Explains why the term structure of interest rateschanges at different times.

Explains why interest rates on bonds with different

maturities move together over time (fact 1). Explains why yield curves tend to slope up when short-

term rates are low and slope down when short-term

rates are high (fact 2).

Cannot explain why yield curves usually slope upward

(fact 3).


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Segmented Markets Theory

Bonds of different maturities are not substitutes.

The interest rate for each bond with a different maturity

is determined by the demand for and supply of that

bond.

Investors have preferences for bonds of one maturity

over another.

If investors have short desired holding periods andgenerally prefer bonds with shorter maturities that have

less interest-rate risk, then this explains why yield curves

usually slope upward (fact 3).


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Liquidity Premium & Preferred Habitat Theories

The interest rate on a long-term bond will

equal an average of short-term interest rates

expected to occur over the life of the long-

term bond plus a liquidity premium thatresponds to supply and demand conditions for

that bond.

Bonds of different maturities are substitutesbut not perfect substitutes.


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Liquidity Premium Theory

nt

e

nt

e

t

e

tt

ntl

n

iiiii

)1(21 ...

where lnt is the liquidity premium for the n-period

bond at time t

lnt

is always positive and increases with the term to

maturity


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Preferred Habitat Theory

Investors have a preference for bonds of one

maturity over another.

They will be willing to buy bonds of different

maturities only if they earn a somewhat

higher expected return.

Investors are likely to prefer short-term bondsover longer-term bonds.


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The Relationship Between Theories


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Liquidity Premium & Preferred Habitat Theories II

Interest rates on different maturity bonds movetogether over time; explained by the first term in

the equation.

Yield curves tend to slope upward when short-termrates are low and to be inverted when short-term rates

are high; explained by the liquidity premium term in the

first case and by a low expected average in the second

case.

Yield curves typically slope upward; explained

by a larger liquidity premium as the term to

maturity lengthens.


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Predictive Power of the Yield Curve

Can use theories to make predictions about short-term rates.

Steeply rising yield curveshort term rates areexpected to rise

Moderately steep yield curveshort-term rates arenot expected to rise or fall substantially in the future

A flat yield curve short-term rates are expected to

fall moderately in the future. Inverted yield curve short-term rates are expectedto fall sharply in the future.


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Predictive Power of the Yield Curve


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Interpreting Yield Curves 1996 -2006

Inverted yield curves Jan 1990short-term

rates were expected to decrease in the future.

By March 1991, 3 month Treasury bills rates

had fallen from 12% to less than 9%.

Upward sloping yield curve in Jan 2009

indicated short term rates would increase.


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Interpreting Yield Curves

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06.the Risk and Term Structure of Interest Rates