ch03 hein

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Chapter 3

The Level and Structure of

Interest Rates

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Loanable funds theory states that short-runinterest rates are determined by the supply anddemand of loanable funds. (see Figure 3-2)

The theory states that the equilibrium interest rateis a combination of a long-run base rate plus

short-run supply/demand factors and currentfinancial market risks.

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The Level of Rates

� Long-run base rate

� Inflation (expected)

The Structure of Rates

� Time to maturity

� Default risk

� Taxes

� Marketability

� Embedded options

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The long-run base rate is referred to as the realrate of interest.

Assuming individuals either consume or invest(delay consumption) and that individualsprefer consumption today, the real rate of

interest is the rate necessary to get individualsto delay consumption. (see Figure 3-4)

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When we lend our money, we are delayingconsumption. So, when we get our moneyback we want to be able to buy the same goods

that our money would have bought before.

Thus, we need to include expected inflation in allinterest rates.

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The Fisher Effect combines the real rate of interestand expected inflation to create a (risk-free)nominal interest rate.

The nominal interest rate is a market interest rate.That is, it is the rate you either pay or earn.

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( ) ( )( ( )) ! r R E i

r R E i R E i! ( ) ( * ( ))

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r = nominal interest rate

R = real rate of interest

E(i) = expected annual rate of inflation

solving for r,

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13.42%or 0.13420.070.060.070.06 !!r

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If borrower and lender agree that R = 6% and E i = 7%,

then what would be the contract interest rate for a one-year loan?

Using the Fisher Equation, the contract rate is:

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r R E i! ( )

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This equation is used as a ³rule of thumb´

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� Starting in 1997 the US Treasury has beenissuing securities, called TIPS, that compensateinvestors for inflation, as is occurs.

� Over the last year in the US, through July 2008,the annual rate of inflation based on the CPIwas 5.6%.

� This means an investor in a TIPS one year ago

would get a real interest plus 5.6%compensation of inflation.

� In other words, the stated interest rate on TIPScan be thought of as a real interest rate.

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� Quotes for ´conventionalµ or nominal Treasurysecurities can be found at:� http://online.wsj.com/mdc/public/page/2_3020-

treasury.html?mod=topnav_2_3000

� What is the interest rate on a five year to mature Treasurysecurity today, then? Is this a real interest rate or anominal interest rate?Why?

� What is its coupon rate?What is its price?

� Quotes for TIPS securities can be found at:� http://online.wsj.com/mdc/public/page/2_3020-tips.html?mod=topnav_2_3020

� What is the interest rate on a five year TIPS today? Is thisa real interest rate, or a nominal interest rate?Why?

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� Take the two different five year interest rateson Treasuries found for conventional and TIPSsecurities. Based on these yields, find what the

market is expecting inflation to be given thesetwo rates and the Fisher Effect.

� Do you think this is a good estimate of inflationover the next five years or not?Why?

� Which do you think would be a better five yearinvestment today: a conventional Treasury or aTIPS?Why?

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-1 0 - 5 0 5

1 0

1 5

2 0

Jan-69

Jan-72

Jan-75

Jan-78

Jan-81

Jan-84

Jan-87

Jan-90

Jan-93

Jan-96

Jan-99

M on t h-Y e ar

Percentage R

R

e al i z e dR e al R a t e s

A c t u al R a t e

of I nf l a t i o

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- 5 0 5 1 0

1 5

2 0

Jan-69

Jan-72

Jan-75

Jan-78

Jan-81

Jan-84

Jan-87

Jan-90

Jan-93

Jan-96

Jan-99

Jan-02

M on t h -Y e ar

Percentage Rate

I nf l a t i on

3 m t h T - b i l l

1 0 y r T -n o t e

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Debt Security Yield May 2000 April 2004

3-month Treasury bill 5.99% 0.91%6-month Treasury bill 6.39 1.17

1-year Treasury bill 6.33 1.53

2-year Treasury note 6.81 2.21





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Time to Maturity Impacts Relation between Rates

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Aaa Municipal bonds 20 years 4.89% 4.46%

Aaa Corporate bonds 20 years and above 7.64 5.80

Aa Corporate bonds 7.82 6.04

A Corporate bonds 8.07 6.13

Baa Corporate bonds 8.40 6.51

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Impact of Taxes and Default Risk

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The relationship between interest rates on similarsecurities with different times to maturity isreferred to as the

Term Structure of Interest Rates

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1. Expectations Theory

2. Liquidity Preference Theory

3. Preferred Habitat Theory

Each theory will be discussed in some detail in thefollowing slides.

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Current long-term interest rates are based oninvestors expectations of future interest rates«

which means that

Current long-term rates are combinations ofcurrent and expected future short-term rates.

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The yield curve plots yield against time tomaturity for default-free securities

Expectations theory can explain three shapes ofthe yield curve: upward-sloping, downward-sloping, and flat.

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1. Rates expected to rise in the future, then yieldcurve is upward sloping.

2. Rates expected to fall in the future, then yield

curve is downward sloping.

3. Rates expected to remain constant in thefuture, then the yield curve is flat.

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Under expectations theory, a long-term rate is

the geometric average of current andexpected future short-term rates.

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1 1 1 1 10 0 1 1 2 2 3 1

! r r f f f t

t

t t .

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wherer = spot rate

f = one-period expected future short-term rate

t = number of time periods in the long-term rate

and

prescript is beginning of time period covered by the rate postscript is ending of the time period

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1 1 1 10 3

3

0 1 1 2 2 3 ! r r f f

000 1 2 3

0r 3

0r 1 1f 2 2f 3

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Timeline of thr ee-year r ate

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Using data from May 2000 term structure(Figure 3.7 (Slide 17)), the expected one-

year rate maturing at the end of Year 2 is:

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1

1 0681

1 0633107291 2

0 22

0 11

2

2 !

!

! f r

r f

.

.. so is 7.29 .1

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Simply put, investors prefer liquidity.

This theory extends expectations theory by

assuming that investors are risk-averse andprefer short-term investments.

If investors are asked to extend beyond theirpreferred short-term time to maturity, theydemand a premium for the price riskcreated by going beyond their preferredtime horizon.

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1 1 1 1 10 0 1 1 2 1 2 2 3 2 3 1 1 !

r r f l f l f l t

t

t t t t .

0 1 2 2 3 3 4e e e el l l .

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wherel = risk premium for increasing time to maturity

and

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Liquidity Preference Theory explains why theyield curve slopes upward most of the time.

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6

6.2

6.4

6.6

6.8

0 5 10 15 20 25 30

Years a uri y

I

e r e s

a

eL q u d t

P efe enceheo

Expectat ons

heo

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The preferred habitat theory is a corollary ofthe market segmentation theory.

Market segmentation theory assumes thatinvestors have specific maturity preferencesthat they will not leave regardless of theadditional compensation. This assumption

is too restrictive.

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The preferred habitat theory assumes thatinvestors have a desired time to maturity forinvestment (a preferred habitat), but ifadequately compensated for the additionalrisk of moving from their desired maturity,they will move to other maturities.

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The preferred habitat theory is the only theorythat allows for ¶humps· or ¶twists· in the yieldcurve. In other words, it allows for a change in

the direction of the slope of the yield curve.

This is important because this frequently occurs inplots of market yields.

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0

1

2

3

4

5

6

7

8

Years

Y i e l d s

May-00

Apr-04

May-00 6.33 6.81 6.77 6.69 6.69 6.44

Apr-04 1.53 2.21 2.74 3.52 4.01 4.43

1 2 3 5 7 10

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Default on a debt contract occurs when theborrower violates any of the conditions of thecontract.

When examining default risk, a lender isconcerned with how a default will impair theexpected cash flows from the debt contract.

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So, the lender is concerned about the expectedlosses from a default and builds those expectedlosses into the debt contract rate through a

default risk premium.

There is a wide range of possible losses fromdefault, so we need a way to measure default

risk.

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� Credit rating agencies provide bond ratings� The two primary rating agencies are

Moody·s and Standard & Poor·s.� A bond rating is the agency·s opinion on a

company·s ability to meet its financialobligations.

� To determine a company·s bond rating, the

rating agency does an in-depth analysis ofthe company, which includes a completeanalysis of the company·s financialstatements.

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� 1. They have done a very poor job of assessingthe default risk of MBS and new asset backedsecurities. Defaults have been much greater

that suggested by the rating.� 2. Many blame this on the fact that the rating

agencies get their funding from the issuingfirm, who has a vested interest in getting highratings, since this lowers the interest expensefor the issuer.� Conflict of interest.

� What should be done?

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Moo ¶s R t ng &P R t ng Ex n t on

Inv stm nt G s

Aaa AAA Extremely strong, best quality

Aa AA Very strong, high quality

A A Strong, upper -medium grade

Baa BBB Adequate, medium-grade

t v G s

Ba BB Judged to have speculative elements

B B Lack the characteristics of a desirable investment

Caa CCC Currently vulnerable, of poor standing

Ca CC Currently highly-vulnerable, marked shortcomings

C C Extremely poor prospects

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Years 1 5 10 15 20

Aaa 0.00% 0.20 1.09 1.89 2.38

Aa 0.08 0.97 3.10 5.61 6.75

A 0.08 1.37 3.61 6.13 7.47

Baa 0.30 3.51 7.92 11.46 13.95

Ba 1.43 10.04 19.05 25.95 30.82

B 4.48 20.89 31.90 39.17 43.70

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Investors look at after-tax returns because taxesare a cash outflow for investors.

Investors pay federal taxes on interest receivedfrom corporate debt, but not on interestreceived from municipal debt.

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Accordingly, municipal bonds can competewith corporate bonds of similar risk while

paying lower interest rates.

The formula used to make the comparison is:

r r municipal corpora e! 1 investor's marginal feder al tax r ate

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r r municipa corporat ! 1 investor 's marginal federal tax rate

3.35%or 335.28.1*465. !!muni i

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Assume a AAA corporate bond has a rate equal to 4.65%

and an investor has a marginal tax rate of 28%. Then

what rate would a AAA muni have to pay to

compete?

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Less marketable securities are harder to sell, soinvestors demand higher interest rates.

Long-term debt securities are often assumed to beless marketable than similar short-term debtsecurities, but we feel it is dangerousassumption to make.

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� Price concession necessary for the sale

� The cost of executing the trade

� Search costs

� Information costs

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Marketability refers to the speed and cost with which

an investor can sell a security.

The costs to consider are:

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1. Embedded call option allows the issuingfirm (borrower) to retire the debt before

maturity.

An embedded call provides a valuable rightto the borrower and creates additional risk

for the investor (lender), so callable debtpays higher interest rates than similar non-callable debt.

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2. Embedded put option allows the investor tosell the bond back to the issuing firm(borrower) before maturity.

An embedded put provides a valuable right tothe investor and creates additional risk for theissuer, so putable debt pays lower interestrates than similar non-putable debt.

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3. Embedded conversion option allows theinvestor to convert the debt contract intoother type of security (typically stock)

from the issuing firm (borrower) beforematurity.

The investor acquires the valuable right by payinga higher price for the convertible debt than

similar non-convertible debt, which results in alower yield on the convertible debt.

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