financial institutions & markets lecture 5

8/8/2019 Financial Institutions & Markets Lecture 5

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Financial Institutions & Markets

How do Risk and Term Structure

Affect Interest Rates?Lecture 5

1


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Chapter Preview

In the last chapter, we examined interest

rates, but made a big assumption there is

only one economy-wide interest rate. Of

course, that isnt really the case.

In this chapter, we will examine the different

rates that we observe for financial products.


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Chapter Preview

We will fist examine bonds that offer similar

payment streams but differ in price. The price

differences are due to the risk structure of

interest rates. We will examine in detail what

this risk structure looks like and ways to

examine it.


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Chapter Preview

Next, we will look at the different rates

required on bonds with different maturities.

That is, we typically observe higher rates on

longer-term bonds. This is known as the term

structure of interest rates. To study this, we

usually look at Treasury bonds to minimize the

impact of other risk factors.


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Chapter Preview

So, in sum, we will examine how the individual

risk of a bond affects its required rate. We

also explore how the general level of interest

rates varies with the maturity of the debt

instruments. Topics include:

Risk Structure of Interest Rates

Term Structure of Interest Rates


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Risk Structure of Interest Rates

To start this discussion, we first examine the

yields for several categories of long-term

bonds over the last 85 years.

You should note several aspects regarding

these rates, related to different bond

categories and how this has changed through

time.


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Risk Structure

of Long Bonds in the U.S.


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Risk Structure

of Long Bonds in the U.S.

The figure show two important features of

the interest-rate behavior of bonds.

Rates on different bond categories changefrom one year to the next.

Spreads on different bond categories change

from one year to the next.


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Factors Affecting Risk Structure

of Interest Rates

To further examine these features, we will

look at three specific risk factors.

Default Risk

Liquidity

Income Tax Considerations


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Default Risk Factor

One attribute of a bond that influences its interestrate is its risk of default, which occurs when theissuer of the bond is unable or unwilling to makeinterest payments when promised.

U.S. Treasury bonds have usually been considered tohave no default risk because the federal governmentcan always increase taxes to pay off its obligations (orjust print money). Bonds like these with no default

risk are called default-free bonds.


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Default Risk Factor (cont.)

The spread between the interest rates on bonds withdefault risk and default-free bonds, called the riskpremium, indicates how much additional interestpeople must earn in order to be willing to hold that

risky bond.

A bond with default risk will always have a positiverisk premium, and an increase in its default risk willraise the risk premium.


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Increase in Default Risk

on Corporate Bonds


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Analysis of Figure 5.2: Increase in Default on

Corporate Bonds

Corporate Bond Market

1. Re on corporate bonds q, Dc q, Dc shifts left

2. Risk of corporate bonds o, Dc q, Dc shifts left

3. Pc

q, ic

o Treasury Bond Market

4. Relative Re on Treasury bonds o, DT o, DT shifts right

5. Relative risk of Treasury bonds q, DT o, DT shifts right

6. PT

o, iT

q Outcome

Risk premium, ic - iT, rises


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Default Risk Factor (cont.)

Default risk is an important component of the size ofthe risk premium.

Because of this, bond investors would like to know asmuch as possible about the default probability of abond.

One way to do this is to use the measures providedby credit-rating agencies: Moodys and S&P areexamples.


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Bond Ratings


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Case: Enron and the Baa-Aaa spread

Enron filed for bankruptcy in December2001, amidst an accounting scandal.

Because of the questions raised about thequality of auditors, the demand for lower-credit bonds fell, and a flight- to-qualityfollowed (demand for T-securities

increased. Result: Baa-Aaa spread increased from 84

bps to 128 bps.


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Liquidity Factor

Another attribute of a bond that influences itsinterest rate is its liquidity; a liquid asset is onethat can be quickly and cheaply converted into

cash if the need arises. The more liquid anasset is, the more desirable it is (higherdemand), holding everything else constant.

Lets examine what happens if a corporatebond becomes less liquid (Figure 1 again).


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Decrease in Liquidity

of Corporate Bonds

Figure 5.2 Response to a Decrease in the Liquidity of Corporate Bonds


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Analysis of Figure 5.1: Corporate Bond Becomes

Less Liquid

Corporate Bond Market

1. Liquidity of corporate bonds q, Dc q, Dc shifts left

2. Pc q, ic o

Treasury Bond Market1. Relatively more liquid Treasury bonds, DT o, DT shifts right

2. PT o, iT q

Outcome

Risk premium, ic - iT, rises

Risk premium reflects not only corporate bonds' default risk

but also lower liquidity


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Liquidity Factor (cont.)

The differences between interest rates on

corporate bonds and Treasury bonds (that is,

the risk premiums) reflect not only the

corporate bonds default risk but its liquidity

too. This is why a risk premium is sometimes

called a risk and liquidity premium.


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Income Taxes Factor

An odd feature of Figure 1 is that municipal

bonds tend to have a lower rate the

Treasuries. Why?

Munis certainly can default. Orange County

(California) is a recent example from the early

1990s.

Munis are not as liquid a Treasuries.


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Income Taxes Factor

However, interest payments on municipal

bonds are exempt from federal income taxes,

a factor that has the same effect on the

demand for municipal bonds as an increase in

their expected return.

Treasury bonds are exempt from state and

local income taxes, while interest paymentsfrom corporate bonds are fully taxable.


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Income Taxes Factor

For example, suppose you are in the 35% tax

bracket. From a 10%-coupon Treasury bond,

you only net $65 of the coupon paymentbecause of taxes

However, from an 8%-coupon muni, you net

the full $80. For the higher return, you are

willing to hold a riskier muni (to a point).


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Tax Advantages of Municipal Bonds


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Analysis of Figure 5.3:

Tax Advantages of Municipal Bonds

Municipal Bond Market

1. Tax exemption raises relative Re on municipal bonds,Dm o, Dm shifts right

2. Pm o

Treasury Bond Market

1. Relative Re on Treasury bonds q, DT q, DT shifts left

2. PTq

Outcomeim < iT


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Term Structure of Interest Rates

Now that we understand risk, liquidity, and

taxes, we turn to another important influence

on interest rates maturity.Bonds with different maturities tend to have

different required rates, all else equal.


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Term Structure Facts to Be Explained

Besides explaining the shape of the yield curve,

a good theory must explain why:

Interest rates for different maturitiesmove together. We see this on the next slide.


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Interest Rates on Different Maturity Bonds Move

Together


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Term Structure Facts to Be Explained

Besides explaining the shape of the yield curve,a good theory must explain why:

Interest rates for different maturitiesmove together.

Yield curves tend to have steep upward slopewhen short rates are low and downward slopewhen short rates are high.

Yield curve is typically upward sloping.


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Three Theories of Term Structure

1. Expectations Theory Pure Expectations Theory explains 1 and 2,

but not 3

2. Market Segmentation Theory Market Segmentation Theory explains 3, but not 1 and 2

3. Liquidity Premium Theory

Solution: Combine features of both Pure ExpectationsTheory and Market Segmentation Theory to get LiquidityPremium Theory and explain all facts


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Expectations Theory

Key Assumption: Bonds of different

maturities are perfect substitutes

Implication: Re on bonds of differentmaturities are equal


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Expectations Theory

To illustrate what this means, consider two

alternative investment strategies for a two-

year time horizon.

1. Buy $1 of one-year bond, and when it

matures, buy another one-year bond with

your money.

2. Buy $1 of two-year bond and hold it.


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Expectations Theory

The important point of this theory is that if

the Expectations Theory is correct, your

expectedwealth is the same (a the start) for

both strategies. Of course, your actual wealth

may differ, if rates change unexpectedlyafter

a year.

We show the details of this in the next few

slides.


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(1 it)(1 it1e

) 1 ! 1 it it1e

it(it1e

) 1

Expectations Theory

Expected return from strategy 1

Since it(iet+1) is also extremely small, expected

return is approximatelyit+ i

et+1


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(1 i2t)(1 i2t) 1! 1 2(i2t) (i2t)2

1

Since (i2t)2 is extremely small, expected return is approximately

2(i2t)

Expectations Theory

Expected return from strategy 2


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i2t !it i

t1

e

2

Expectations Theory

From implication above expected returns of twostrategies are equal

Therefore

2 i2t

! it

it1

e

Solving fori2t

(1)


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Expectations Theory

To help see this, heres a picture that describes

the same information:


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int!

it i

t1 i

t 2 ... i

t n1

n

More generally for n-period bond

Dont let this seem complicated. Equation 2simply states that the interest rate on a long-term bond equals the average of short rates

expected to occur over life of the long-termbond.

(2)


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More generally for n-period bond

Numerical example

One-year interest rate over the next five years

are expected to be 5%, 6%, 7%, 8%, and 9%

Interest rate on two-year bond today:(5% + 6%)/2 = 5.5%

Interest rate for five-year bond today:

(5% + 6% + 7% + 8% + 9%)/5 = 7%

Interest rate for one- to five-year bonds today:

5%, 5.5%, 6%, 6.5% and 7%


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Expectations Theory

and Term Structure Facts

Explains why yield curve has different slopes

1. When short rates are expected to rise in future, averageof future short rates = intis above today's short rate;

therefore yield curve is upward sloping.2. When short rates expected to stay same in future,

average of future short rates same as today's, and yieldcurve is flat.

3. Only when short rates expected to fall will yield curve bedownward sloping.


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Expectations Theory


Pure expectations theory explains fact 1that

short and long rates move together

1. Short rate rises are persistent

2. If it o today, ie

t+1, ie

t+2 etc. o

average of future rates o into

3. Therefore: ito into(i.e., short and long rates move together)


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Expectations Theory


Explains fact 2that yield curves tend to have steep

slope when short rates are low and downward slope

when short rates are high

1. When short rates are low, they are expected to rise tonormal level, and long rate = average of future short

rates will be well above today's short rate; yield curve

will have steep upward slope.

2. When short rates are high, they will be expected to fallin future, and long rate will be below current short

rate; yield curve will have downward slope.


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Expectations Theory


Doesn't explain fact 3that yield curve

usually has upward slope

Short rates are as likely to fall in future as rise, so

average of expected future short rates will not

usually be higher than current short rate:

therefore, yield curve will not usually

slope upward.


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Market Segmentation Theory

Key Assumption: Bonds of different maturities arenot substitutes at all

Implication: Markets are completely segmented;

interest rate at each maturity aredetermined separately


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Market Segmentation Theory

Explains fact 3that yield curve is usually upwardsloping People typically prefer short holding periods and thus have

higher demand for short-term bonds, which have higher prices

and lower interest rates than long bonds

Does not explain fact 1or fact 2 because its assumeslong-term and short-term rates are determinedindependently.


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Liquidity Premium Theory

Key Assumption: Bonds of different maturities

are substitutes, but are not

perfect substitutes

Implication: Modifies Pure Expectations

Theory with features of Market

Segmentation Theory


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Investors prefer short-term rather than long-term

bonds. This implies that investors must be paid

positive liquidity premium, int, to hold long term

bonds.


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int!

it i

t1

e i

t 2

e ... i

t n1

e

n l

nt


Results in following modification of Expectations

Theory, where lntis the liquidity premium.

(3)

We can also see this graphically


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Numerical Example

1. One-year interest rate over the next five

years: 5%, 6%, 7%, 8%, and 9%

2. Investors' preferences for holding short-termbonds so liquidity premium for one- to five-

year bonds: 0%, 0.25%, 0.5%, 0.75%, and

1.0%


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Numerical Example

Interest rate on the two-year bond:

0.25% + (5% + 6%)/2 = 5.75%

Interest rate on the five-year bond:

1.0% + (5% + 6% + 7% + 8% + 9%)/5 = 8% Interest rates on one to five-year bonds:

5%, 5.75%, 6.5%, 7.25%, and 8%

Comparing with those for the pure expectationstheory, liquidity premium theory produces yield

curves more steeply upward sloped


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Liquidity Premium Theory:

Term Structure Facts

Explains All 3 Facts

Explains fact 3that usual upward sloped yield

curve by liquidity premium for

long-term bonds

Explains fact 1 and fact 2 using same explanations

as pure expectations theory because it has

average of future short rates as determinant oflong rate


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Market Predictions

of FutureShort Rates

53


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Evidence on the Term Structure

Initial research (early 1980s) found little useful

information in the yield curve for predicting

future interest rates.

Recently, more discriminating tests show that

the yield curve has a lot of information about

very short-term and long-term rates, but says

little about medium-term rates.


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The Practicing Manager: Forecasting Interest

Rates with the Term Structure

Pure Expectations Theory: Invest in 1-period bonds

or in two-period bond

1 it

1 it1

e 1 ! 1 i2t 1 i2t 1

Solve for forward rate, iet+1

it1

e

!1 i2t

2

1 it

1 (4)

Numerical example: i1t= 5%, i2t= 5.5%

it1

e

!1 0.055 2

1 0.051 ! 0.06 ! 6%


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Forecasting Interest Rates

with the Term Structure

Compare 3-year bond versus 3 one-year bonds

Using iet+1 derived in (4), solve for ie

t+2

1 it

1 it1

e 1 it2e 1 ! 1 i3t 1 i3t 1 i3t 1

it2e

!1 i

3t

3

1 i2t

2 1


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Generalize to:

Liquidity Premium Theory: int- = same as pure expectations

theory; replace intby int- in (5)

to get adjusted forward-rate forecast

itn

e

!1 i

n1t n 1

1 int n 1 (5)

itn

!

1 in1t

ln 1t

n1

1 int

lnt

n1 (6)


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Numerical Example

2t= 0.25%, 1t=0, i1t=5%, i2t= 5.75%

Example: 1-year loan next year

T-bond + 1%,2t= .4%, i1t= 6%, i2t= 7%

Loan rate must be > 8.2%

it1e

!1 0.0575 0.0025 2

1 0.05 1! 0.06 ! 6%

it1

e

!1 0.07 0.004 2

1 0.06 1 ! 0.072 ! 7.2%


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Chapter Summary

Risk Structure of Interest Rates: We examinethe key components of risk in debt: default,liquidity, and taxes.

Term Structure of Interest Rates: Weexamined the various shapes the yield curvecan take, theories to explain this, and

predictions of future interest rates based onthe theories.

financial institutions & markets lecture 5

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