CJed3.Chapter9

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Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

9Interest Rates



9-3

Interest Rates

� Our goal in this chapter is to discuss the many differentinterest rates that are commonly reported in thefinancial press.

� We will also:± Find out how different interest rates are calculated and quoted,

and± Discuss theories of what determines interest rates.



9-4

U.S. Interest Rate History



9-5

Money Market Interest Rates



9-6

Money Market Rates, I.

Prime rate - The basic interest rate on short-term loansthat the largest commercial banks charge to their mostcreditworthy corporate customers.

Bellwether rate - Interest rate that serves as a leader or as a leading indicator of future trends, e.g. inflation.

Federal funds rate - Interest rate that banks chargeeach other for overnight loans of $1 million or more.

Discount rate - The interest rate that the Fed offers tocommercial banks for overnight reserve loans.



9-7

Money Market Rates, II.

C all money rate - The interest rate brokerage firms payfor call money loans from banks. This rate is used asthe basis for customer rates on margin loans.

C ommercial paper - Short-term, unsecured debt

issued by the largest corporations.

C ertificate of deposit ( C D) - Large-denominationdeposits of $100,000 or more at commercial banks for aspecified term.

Banker¶s acceptance - A postdated check on which abank has guaranteed payment. Commonly used tofinance international trade transactions.



9-8

Money Market Rates, III.

L ondon Eurodollars - Certificates of depositdenominated in U.S. dollars at commercial banks inLondon.

L ondon Interbank Offered Rate ( L IBOR) - Interestrate that international banks charge one another for overnight Eurodollar loans.

U.S. Treasury bill (T-bill) - A short-term U.S.government debt instrument issued by the U.S.Treasury.



9-9

Money Market Prices and Rates

� A Pure Discount Security is an interest-bearing asset:± It makes a single payment of face value at maturity .± It makes no payments before maturity .

There are several different ways market participantsquote interest rates.± Banker¶s Discount Basis± Bond Equivalent Yields (BEY)± Annual Percentage Rates (APR)± Effective Annual Rates (EAR)



9-10

The Bank Discount Basis

� The Bank Discount Basis is a method of quotinginterest rates on money market instruments.± It is commonly used for T-bills and banker¶s acceptances.

� The formula is:

± Note that we use 360 days in a year in this (and many other)money market formula.

± The term ³discount yield´ here simply refers to the quotedinterest rate.

¹º¸

©ª¨! YieldDiscountx

360MaturitytoDays

1xValueFacePrice Current



9-11

Example: Calculating a PriceUsing a Bank Discount Rate

� Suppose a banker¶s acceptance that will be paid is 60days has a face value of $1,000,000.� If the discount yield is 3%, what is the current price of

the banker¶s acceptance?

$99 ,000.

0.00- 1 $1,000,000

36060

1 $1,000,000

yieldDiscount 360

maturitytoDays1 alueacePrice Current

!

v!

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ª¨ vv!

¹º¸

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03.0

R emember tomultiply beforeyou subtract.



9-13

Treasury Bill Prices,March 20, 2003

� Look at Figure 9.3 for the T-bill that expires on October 9, 2003.± It has 142 days to maturity.± The ask discount is 1.03 (you use this to calculate the ask

price, i.e., the price you will pay for the T-bill)

± Prices are quoted for $1,000,000 face values.

0.$99 ,93 .2

0.0040 3- 1 $1,000,000

3 0142

1 $1,000,000

yieldiscount 3 0

maturitytoays1 alueFacePrice bill-T urrent

!

v!

¹º¸

©ª¨

vv!

¹º¸

©ª¨ vv!

0103.0

Verify that the bid priceis $995,897.80



9-14

Bond Equivalent Yields

� Bond Equivalent Yields (BEY) are another way to quotean interest rate.� You can convert a bank discount yield to a bond

equivalent yield using this formula:

N ote that this formula is correct only for maturities of six months or less.Moreover, if February 29 occurs within the next 12 months, use 366 days.

yieldiscountmaturitytoaysyieldiscount

BEY !



9-15

Example I: Bond Equivalent Yield

� Look at Figure 9.3 for the T-bill that expires on October 9, 2003.± It has 142 days to maturity.± The ask discount is 1.03.± What is the Bond Equivalent Yield?

1.05%. about or 0.010486,

0.01031423600.0103365

BEY

yieldDiscountxmaturitytoDays360yieldDiscountx365BEY

!

vv

!

!

R emember tomultiply beforeyou subtract.



9-16

Example II: Calculating T-bill PricesUsing Bond Equivalent Yield

� We can calculate a Treasury bill asked price using the asked yield,which is a bond equivalent yield.� Look at Figure 9.3 for the T-bill that expires on October 9, 2003.

± It has 142 days to maturity.± The ask yield is 1.05.

2.995,931.6

1.0040 51,000,000

142/365 0.0105 11,000,000

365 aturity / to ays YieldEquivalend Bond 1alueFace Price Bill

!

!

v!

v!

N ote: The price differs from a previousslide by about $6 due to rounding.



9-17

More Ways to Quote Interest Rates

³ Simple´ interest basis - Another method to quoteinterest rates.± Calculated just like annual p e rc e ntag e rat e s (APRs).± Used for CDs.± The bond equivalent yield on a T-bill with less than six months

to maturity is also an APR.

� An APR understates the true interest rate, which isusually called the effective annual rate (EAR) .



9-18

Example: The BEY on a T-billis Really Just an APR

� Earlier, using the ask discount rate, we calculated anasking price for a 142-day T-bill to be $995,937.20.± At maturity, this T-bill will be worth $1,000,000.± Therefore, you earn $4,062.80 of interest on an investment of

$995,937.20 over 142 days, a percentage return of 0.4079%.± In a 365-day year, there are 365/142 = 2.5704 periods of 142

days in length.± 0.4079 times 2.5704 is 1.0484%.

� This is the bond equivalent yield that we calculatedbefore (actually, it was 1.0486%)

B ut, The Wall Street Journal rounds to 2 decimal places.



9-19

Converting APRs to EARs

� In general, if we let m be the number of periods in ayear, an APR can be converted to an EAR as follows:

� EARs are sometimes called effective annual yields,effective yields, or annualized yields.

m

mAPR1EAR1 ¹

º¸©

ª¨!



9-20

Example I: What is the EAR of this T-bill¶s BEY (aka APR)?

0.4084%. EAR the so,

1.004084

1.001587

2.57040.0040791 EAR 1

mAPR1EAR1

2.5704

m

!

!

!

¹º¸©

ª¨!

¹º¸©

ª¨!

57 04.2

N ote that when interest rates are low, the AP R will be close to the EA R .



9-21

Example II: Converting CreditCard APRs to EARs

� Some Credit Cards quote an APR of 18%.± 18% is used because 18 = 12 times 1.50± That is, the monthly rate is really 1.50%.± What is the EAR?

19.5 %. EAR the so,

1.195

1.015

120.181 EAR 1

m

APR1EAR1

12

m

!

!

!

¹º¸

©ª¨!

¹

º

¸©

ª

¨!

12

O uch.



9-22

Rates and Yields on Fixed-Income Securities

� Fixed-income securities include long-term debtcontracts from a wide variety of issuers:± The U.S. government,± Real estate purchases (mortgage debt),± Corporations, and± Municipal governments

� When issued, fixed-income securities have a maturity of

greater than one year.

� When issued, money market securities have a maturityof less than one year.



9-23

The Treasury Yield Curve

� The T r e asury yi e ld curv e is a plot of Treasury yieldsagainst maturities.

� It is fundamental to bond market analysis, because itrepresents the interest rates for default-free lendingacross the maturity spectrum.



9-24

Example: The Treasury Yield Curve



9-25

Yield Comparisons



9-26

The Term Structure of Interest Rates, I.

� The term structure of interest rates is the relationshipbetween time to maturity and the interest rates for default-free, pure discount instruments.

� The term structure is sometimes called the ³z e

rocoupon yi e ld curv e ´ to distinguish it from the Treasuryyield curve, which is based on coupon bonds.



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The Term Structure of Interest Rates, II.

� The term structure can be seen by examining yields onU.S. Treasury STRIPS.

� STRIPS are pure discount instruments created by³stripping´ the coupons and principal payments of U.S.Treasury notes and bonds into separate parts,which arethen sold separately.

� The term STRIPS stands for Separate Trading of Registered Interest and Principal of Securities.



9-28

U.S. Treasury STRIPS

� An asked yield for a U.S. Treasury STRIP is an APR,calculated as two times the true semiannual rate.

� Recall:

� Therefore, for STRIPS:

r alueuturealue Present !

2M

2YTM

ValueacePriceSTRIPS !

M is the number of years to maturity.



9-29

U.S. Treasury STRIPS



9-30

Example: Pricing U.S. Treasury STRIPS, I.

� Let¶s verify the price of the May 2013 Strip.± The ask quote is 68:24, or $68.75.± The ask YTM is 3.79%.± Matures in about 10 years from the time of the quote

± Close.

$68.70. 1.4556100

2

0.03791

100

20.03791

100

2YTM1

ValueFacePriceSTRIPS

102

1022M

!!!

!!

v

v



9-31

Example: Pricing U.S. Treasury STRIPS, II.

� Let¶s calculate the YTM from the quoted price.

� Close again.

? A 3. . or . 3 3, 11.

1.

1 1Price STRIPS

alueaceYTM

.

11

M1

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¼¼

½

»

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¹º

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¨v!¼¼

¼

½

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v



9-32

Nominal versus Real Interest Rates

N ominal interest rates are interest rates as they areobserved and quoted, with no adjustment for inflation.

R eal interest rates are adjusted for inflation effects.

R eal interest rate = nominal interest rate ± inflation rate



9-35

Inflation Rates and T-bill Rates



9-36

Traditional Theories of the Term Structure

Expectations Theory : The term structure of interestrates reflects financial market beliefs about futureinterest rates.

M arket Segmentation Theory : Debt markets aresegmented by maturity, so interest rates for variousmaturities are determined separately in each segment.

M aturity Preference Theory : Long-term interest rates

contain a maturity premium necessary to inducelenders into making longer term loans.



9-37

Problems with Traditional Theories

Expectations Theory ± The term structure is almost always upward sloping, but

interest rates have not always risen.

± It is often the case that the term structure turns down at verylong maturities.

Maturity Preference Theory

± The U.S. government borrows much more heavily short-termthan long-term.

± Many of the biggest buyers of fixed-income securities, such aspension funds, have a strong preference for long maturities.



9-38

Problems with Traditional Theories

Market Segmentation Theory

± The U.S. government borrows at all maturities.

± Many institutional investors, such as mutual funds, are morethan willing to move maturities to obtain more favorable rates.

± There are bond trading operations that exist just to exploitperceived premiums, even very small ones.



9-39

Modern Term Structure Theory, I.

� Long-term bond prices are much more sensitive tointerest rate changes than short-term bonds. This iscalled interest rate risk .

� So, the modern view of the term structure suggeststhat:

NI = RI + IP + RP

� In this equation:

NI = Nominal interest rateRI = Real interest rateIP = Inflation premiumRP = Interest rate risk premium



9-40

Modern Term Structure Theory, II.

� The previous equation showed the component of interest rates on default-free bonds that trade in a liquidmarket.

� Not all bonds do.

� Therefore, a liquidity premium ( L P) and a default premium (DP) must be added to the previous equation:

NI = RI + IP + RP + LP + DP



9-41

Useful Internet Sites

www.money-rates.com (latest money market rates)www.bba.org.uk (learn more about LIBOR)www.govpx.com (price and yield data for U.S.

Treasuries)www.bondmarkets.com (fixed income securities)www.bloomberg.com (current U.S. Treasury rates)www.smartmoney.com/bonds (view a ³living yield

curve´ *exceptional*)www.publicdebt.treas.gov (information on STRIPS, andother U.S. debt)



9-42

Chapter Review, I.

� Interest Rate History and Money Market Rates± Interest Rate History± Money Market Rates

� Money Market Prices and Rates± Bank Discount Rate Quotes± Treasury Bill Quotes± Bank Discount Yields versus Bond Equivalent Yields

± Bond Equivalent Yields, APRs, and EARs



9-43

Chapter Review, II.

� Rates and Yields on Fixed-Income Securities± The Treasury Yield Curve± Rates on Other Fixed-Income Investments

� The Term Structure of Interest Rates± Treasury STRIPS± Yields for U.S. Treasury STRIPS

� Nominal versus Real Interest Rates± Real Interest Rates± The Fisher Hypothesis



9-44

Chapter Review, III.

� Traditional Theories of the Term Structure± Expectations Theory± Maturity Preference Theory± Market Segmentation Theory

� Determinants of Nominal Interest Rates: A ModernPerspective± Problems with Traditional Theories

± Modern Term Structure Theory± Liquidity and Default Risk

CJed3.Chapter9

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