January 2, 2020

Chapter 9

Interest Rates

Slides

9-1. Chapter 9

9-2. Interest Rates

9-3. Learning Objectives

9-4. Interest Rates

9-5. U.S. Interest Rate History, 1800-2014

9-6. Money Market Interest Rates

9-7. Money Market Rates, I.

9-8. Money Market Rates, II.

9-9. Money Market Prices and Rates

9-10. The Bank Discount Basis

9-11. Example: Calculating a Price Using a Bank Discount Rate

9-12. Treasury Bill Quotes (online at www.wsj.com)

9-13. Treasury Bill Prices: November 2, 2015

9-14. Bond Equivalent Yields

9-15. Example I: Bond Equivalent Yield

9-16. Example II: Calculating T-bill Prices Using Bond Equivalent Yield

9-17. More Ways to Quote Interest Rates

9-18. Example: The BEY on a T-bill is Really Just an APR

9-19. Converting APRs to EARs

9-20. Example I: What is the EAR of this T-bill’s BEY (aka APR)?

9-21. Using Excel to Calculate T-bill Prices and Yields and EAR for a Credit Card

9-22. Rates and Yields on Fixed-Income Securities

9-23. The Treasury Yield Curve

9-24. Example: The Treasury Yield Curve (from www.treasury.gov)

9-25. Rates on Other Fixed-Income Investments—Tracking Benchmarks

9-26. The Term Structure of Interest Rates, I.

9-27. The Term Structure of Interest Rates, II.

9-28. U.S. Treasury STRIPS

9-29. Figure 9.5: U.S. Treasury STRIPS

9-30. Example: Pricing U.S. Treasury STRIPS, I.

9-31. Example: Pricing U.S. Treasury STRIPS, II.

9-32. Nominal versus Real Interest Rates

9-33. Real T-bill Rates, 1950 through 2014

9-34. Nominal versus Real Interest Rates

9-35. Inflation Rates and T-bill Rates, 1950 through 2014

9-36. Inflation-Indexed Treasury Securities, I.

9-37. Inflation-Indexed Treasury Securities, I.

9-38. Inflation-Indexed Treasury Securities, III. (from www.wsj.com)

9-39. Traditional Theories of the Term Structure

9-40. Implied Forward Rates (Expectations Theory)

9-41. Implied Forward Rates, Example 1

9-42. Implied Forward Rates, Example 2

9-43. Implied Forward Rates, Example 3

9-44. Implied Forward Rates, Example 4

9-45. Problems with Traditional Theories

9-46. Problems with Traditional Theories

9-47. Modern Term Structure Theory, I.

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Interest Rates 9-2

9-48. Modern Term Structure Theory, II.

9-49. Modern Term Structure Theory, III.

9-50. Useful Internet Sites

9-51. Chapter Review, I.

9-52. Chapter Review, II.

9-53. Chapter Review, III.

Chapter Organization

9.1 Interest Rate History and Money Market Rates

A. Interest Rate History

B. Money Market Rates

9.2 Money Market Prices and Rates

A. Bank Discount Rate Quotes

B. Treasury Bill Quotes

C. Bank Discount Yields versus Bond Equivalent Yields

D. Bond Equivalent Yields, APRs, and EARs

9.3 Rates and Yields on Fixed-Income Securities

A. The Treasury Yield Curve

B. Rates on Other Fixed-Income Investments

9.4 The Term Structure of Interest Rates

A. Treasury STRIPS

B. Yields for U.S. Treasury STRIPS

9.5 Nominal versus Real Interest Rates

A. Real Interest Rates

B. The Fisher Hypothesis

C. Inflation-Indexed Treasury Securities

9.6 Traditional Theories of the Term Structure

A. Expectations Theory

B. Maturity Preference Theory

C. Market Segmentation Theory

9.7 Determinants of Nominal Interest Rates: A Modern Perspective

A. Problems with Traditional Theories

B. Modern Term Structure Theory

C. Liquidity and Default Risk

9.8 Summary and Conclusions

Selected Web Sites

www.money-rates.com (reference for the latest money market rates)

www.gecapital.com (reference for General Electric Capital)

www.bba.org.uk (reference to learn more about LIBOR)

money.cnn.com (price and yield data for Treasuries)

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Interest Rates 9-3

www.sifma.org (source for information on fixed income securities)

www.bloomberg.com (source for current U.S. Treasury rates)

www.smartmoney.com/bonds (view a “living yield curve”)

www.fanniemae.com (one of three mortgage security websites)

www.ginniemae.gov (one of three mortgage security websites)

www.freddiemac.com (one of three mortgage security websites)

www.treasurydirect.gov (information on STRIPS, and other U.S. debt)

For studying interest rates:

www.newyorkfed.org

www.stlouisfed.org

For the latest on money market rates:

www.banx.com

www.bankrate.com

www.bondsonline.com (finding quotes)

Annotated Chapter Outline

9.1 Interest Rate History and Money Market Rates

A. Interest Rate History

Figure 9.1 indicates that the highest interest rates in U.S. history occurred during

the 1970s and 1980s. There were very low short-term interest rates from the

1930s to the 1960s, as well as in the past few years. In the earlier period, this

was due to deliberate Fed actions, which proved to be unsustainable. In recent

years, it was a function of the Crash of 2008 and a flight to quality, combined with

Fed action.

B. Money Market Rates

Prime rate: The basic interest rate on short-term loans that the largest

commercial banks charge to their most creditworthy corporate customers.

Bellwether rate: Interest rate that serves as a leader, or as a leading

indicator of future trends, e.g., interest rates as a bellwether of inflation.

Federal funds rate: Interest rate that banks charge each other for

overnight loans of $1 million or more.

Discount rate: The interest rate the Fed offers to commercial banks for

overnight reserve loans.

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Interest Rates 9-4

Call money rate: The interest rate brokerage firms pay for call money

loans, which are bank loans to brokerage firms. This rate is used as the

basis for customer rates on margin loans.

Commercial paper: Short-term unsecured debt issued by the largest

corporations.

London Interbank Offered Rate (LIBOR): This is the nterest rate that

international banks charge one another for overnight Eurodollar loans.

Eurodollars: These are Certificates of Deposit denominated in U.S.

dollars at foreign commercial banks.

U.S. Treasury bill (T-bill): These are short-term U.S. government debt

instruments issued by the U.S. Treasury.

Certificate of deposit (CD): Large denomination deposits of $100,000 or

more at commercial banks for a specified term.

Bankers Acceptance: This is a postdated check on which a bank has

guaranteed payment; commonly used to finance international trade

transactions.

Loans to corporations with less than the highest credit rating are often quoted as

prime plus a premium, based on the firm’s credit quality. The Fed funds rate is

normally slightly higher than the Fed's discount rate. The Federal Reserve Bank

is the central bank of the U.S. It is charged with managing interest rates and the

money supply to control inflation and maintain stable economic growth. They do

this through the discount rate. An announced change in the discount rate is often

interpreted as a signal of the Fed's intentions regarding future monetary policy,

although at times the discount rate change is simply the Fed catching up with

financial market conditions.

The call money rate (call rate) is the interest rate brokerage firms pay on call

money loans, and brokers typically charge the call money rate plus a premium.

Commercial paper is short-term, unsecured debt issued by the largest

corporations and is popular with portfolio managers with excess funds to invest

short-term.

Large-denomination CDs are usually negotiable instruments, whereas small-

denomination (bank) CDs are simply bank time deposits and are not negotiable.

A banker's acceptance is essentially a postdated check upon which a commercial

bank has guaranteed payment. They are normally used to finance international

trade transactions. After the goods are shipped, the exporter presents the

documentation and the bank stamps the word "accepted" on the check.

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Interest Rates 9-5

Eurodollars (Eurodollar CDs) are negotiable certificates of deposit denominated

in U.S. dollars at foreign commercial banks. The LIBOR is the interest rate

offered by London commercial deposits from other banks. The LIBOR is similar

to the U.S. prime rate. T-bills are short-term U.S. government debt issued

through the U.S. Treasury, and this market is the largest market for short-term

debt in the world. The T-bill rate leads all other credit markets in determining the

general level of short-term interest rates.

9.2 Money Market Prices and Rates

Pure discount security: An interest-bearing asset that makes a single

payment of face value at maturity, with no payments before maturity.

Basis Point: With regard to interest rates or bond yields, one basis point

is 1 percent of 1 percent.

Most money market securities make a single payment of face value at maturity,

with no other payments before maturity. This type of security is termed a pure

discount security because they sell at a discount to face value. There are several

types of these securities, and the prices and yields are quoted in different ways.

The text will present methods for calculating these yields to allow a comparison

between securities.

Bond yields, as well as many interest rates, are quoted as a percentage with two

decimal points. For example, at the time of this writing, the yield on the 10-year

T-note is about 2.2%, or 0.0220. The smallest possible change to this quote is

plus or minus 0.01%, or 0.0001. This amount is called a basis point, which is

one percent of one percent. If the yield on the 10-year note falls to 2.1%, traders

would say that the 10-year note yield has fallen by 10 basis points.

A. Bank Discount Rate Quotes

Bank discount basis: A method for quoting interest rates on money

market instruments.

T-bills and banker’s acceptances are quoted on a bank discount basis (discount

basis), which is also called discount yield. It is calculated as follows:

This formula assumes a 360-day (banker's) year. This practice dates back many

years to the time when these calculations were done manually.

B. Treasury Bill Quotes

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Price =Face Value x

(

1−Days to maturity

360 x Discount yield

)

Interest Rates 9-6

When reviewing T-bill quotes, the maturity is stated in month-day-year format,

followed by the number of days until maturity. The bid discount is the price

dealers are willing to pay, and the asked discount refers to the price at which

dealers are willing to sell the T-bill. The "Ask Yld" is quoted on a bond equivalent

yield basis, which uses a 365-day year.

C. Bank Discount Yields versus Bond Equivalent Yields

A bank discount yield is converted to a bond equivalent yield using the following:

This conversion formula is correct for 6-months (180 days) or less. A more

complicated formula is needed for longer periods. The days to maturity must take

into account the adjustment for leap years.

D. Bond Equivalent Yields, APRs, and EARs

Money market rates are quoted as simple interest rates, similar to annual

percentage rates (APR). Since APR understates the true rate, the rate must be

converted to an effective annual rate (EAR). To convert an APR to an EAR:

9.3 Rates and Yields on Fixed-Income Securities

Fixed-income securities include long-term debt on a wide variety of instruments.

The largest category is U.S. government debt, followed by mortgage debt,

corporate debt, and municipal government debt.

A. The Treasury Yield Curve

Treasury Yield Curve: A graph of Treasury yields plotted against

maturities.

Lecture Tip: Students have usually discussed yield curves in their economics

class and fundamental corporate finance class before taking investments. Even

though they have discussed yield curves and may have even graphed them, they

are usually not aware that this information is available in The Wall Street Journal

or online at www.wsj.com. The WSJ Treasury Yield Curve and Yield Comparisons

charts are excellent sources of information for students. A discussion can be

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BEY =365 xDiscount yield

360 −Days to maturity xDiscount yield

1+EAR =

(

1+APR

m

)

m

Interest Rates 9-7

generated about the shape of the yield curve and what it may foretell for future

interest rates. In Chapters 10 and 11, when discussing corporate bonds, this

table becomes a useful source of information on bond yields.

B. Rates on Other Fixed-Income Investments

Other sources of debt-related information provided in the Yield Comparisons

table include: Yankee bonds, Federal Home Loan Mortgage Corporation

(FHLMC), Federal National Mortgage Association (FNMA), Government National

Mortgage Association (GNMA), high-yield corporates, new tax-exempts, general

obligation bonds, and revenue bonds.

9.4 The Term Structure of Interest Rates

Term Structure of Interest Rates: This is the relationship between time

to maturity and interest rates for default-free, pure discount instruments.

The difference between the yield curve and the term structure is that the yield

curve is based on coupon bonds, whereas the term structure is based on pure

discount instruments.

A. Treasury STRIPS

U.S. Treasury STRIPS: Pure discount securities created by stripping

away the coupons and principal payments of Treasury notes and bonds.

The acronym stands for Separate Trading of Registered Interest and

Principal of Securities.

STRIPS are pure discount instruments created by "stripping" the coupons and

principal payments of U.S. Treasury notes and bonds into separate parts and

then selling the parts separately. STRIPS are quoted as a price per $100 of face

value, and the number to the right of the colon is in thirty-seconds of a dollar.

B. Yields for U.S. Treasury STRIPS

The asked yield for a U.S. Treasury STRIP is an APR. It is calculated using the

following equation:

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STRIPS Price =Face value

(

1+YTM

2

)

2M

Interest Rates 9-8

9.5 Nominal versus Real Interest Rates

Nominal Interest Rates: This is the term for interest rates as they are

normally observed and quoted, with no adjustment for inflation.

A. Real Interest Rates

Real Interest Rates: This is the term for interest rates adjusted for the

effect of inflation, calculated as the nominal rate less the rate of inflation.

To compute (an approximation of) the real interest rate:

Real interest rate = Nominal interest rate - Inflation rate

B. The Fisher Hypothesis

Fisher Hypothesis: This is an assertion that the general level of nominal

interest rates follows the general level of inflation.

According to the Fisher hypothesis, interest rates are on average higher than the

rate of inflation. Therefore, short-term interest rates should reflect current

inflation, and long-term interest rates should reflect expectations of future

inflation.

C. Inflation-Indexed Treasury Securities

In recent years, the U.S. Treasury has issued securities that guarantee a fixed

rate of return in excess of realized inflation rates. These TIPS (or Treasury

inflation protected securities) adjust their principal semiannually according to the

most recent inflation rate and pay a fixed coupon rate on this accrued principal.

For investors wanting long-term protection against inflation along with the safety

of U.S. Treasury bonds, inflation-indexed Treasury securities are perhaps the

perfect investment.

For example, suppose an inflation-indexed note is issued with a coupon rate of 2

percent and an initial principal of $1,000. Six months later, the note will pay a

coupon of 2 percent. However, before the coupon is determined, the principal is

adjusted for inflation. Assuming 1.5 percent inflation over the six months since

issuance, the note’s principal is then increased to $1,000 x 1.015 = $1,015. Thus,

the coupon is $1,015 x 2%/2 = $10.15. Notice this is $0.15 higher than the

coupon would have been without the inflation adjustment. This process continues

throughout the bond’s life. At maturity, the investor receives the final adjusted (or

accrued) principal amount.

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Interest Rates 9-9

You will have to explain to students that the coupon payment changes, but the

coupon rate does not. Price and yield information for inflation-indexed Treasury

securities are reported in The Wall Street Journal in the same section as other

Treasury securities.

9.6 Traditional Theories of the Term Structure

A. Expectations Theory

Expectations Theory: In this theory, the term structure of interest rates is

a reflection of financial market beliefs regarding future interest rates.

Forward Rate: This is an expected future interest rate implied by current

interest rates.

The expectations theory implies that an upward sloping yield curve predicts an

increase in interest rates, and a downward-sloping yield curve predicts a

decrease in rates.

The implied forward rate, (f 1,1), can be calculated by:

(1 + r2)2 = (1 + r1)(1 + f1,1)

If r2>r1, the expectations theory predicts an increase in interest rates, and if r2<r1,

a decrease in interest rates is predicted. Taken together, the expectations theory

and the Fisher hypothesis assert that an upward-sloping term structure predicts

that nominal interest rates and inflation are likely to be higher in the future.

B. Maturity Preference Theory

Maturity Preference Theory: In this theory, long-term interest rates

contain a maturity premium necessary to induce lenders into making

longer term loans.

This theory is based upon the idea that lenders prefer to lend short-term and

borrowers prefer to borrow long-term. So borrowers have to pay a higher rate to

borrow long term to compensate lenders for the longer maturities. The extra

interest is called a maturity premium. The Fisher hypothesis, maturity preference

theory, and expectations theory can coexist without any problem. To summarize:

long-term, default-free interest rates have three components: a real rate, an

anticipated future inflation rate, and a maturity premium.

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Interest Rates 9-10

C. Market Segmentation Theory

Market Segmentation Theory: In this theory, debt markets are

segmented by maturity, with the result that interest rates for various

maturities are determined separately in each segment.

The market segmentation theory asserts that each maturity of debt represents a

separate, distinct market and that there are specific groups of borrowers and

lenders that have a preference for each maturity or segment. So, interest rates

corresponding to each maturity are determined separately by supply and demand

conditions in each market segment.

9.7 Determinants of Nominal Interest Rates: A Modern Perspective

A. Problems with Traditional Theories

Some of the problems include:

The term structure is almost always upward sloping, but interest rates

have not always risen.

With respect to maturity preference, the U.S. government borrows more

short-term than long-term, and many buyers (such as pension funds) have

a preference for long maturities.

With respect to market segmentation, the U.S. government borrows at all

maturities, and many institutional investors will move maturities to obtain

more favorable rates.

B. Modern Term Structure Theory

The modern view of term structure suggests that nominal interest rates on

default-free securities can be stated as follows:

NI = RI + IP + RP

Where:

NI = nominal rate

RI = real rate

IP = inflation premium

RP = risk premium

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Interest Rates 9-11

C. Liquidity and Default Risk

The nominal rate for individual securities (not default-free) can be described as

follows:

NI= RI + IP + RP + LP + DP

Where:

NI = nominal rate

RI = real rate

IP = inflation premium

RP = risk premium

LP = liquidity premium

DP = default premium

In addition, another important determinant of nominal interest rates is tax status.

Municipal bonds, unlike all other bonds (including U.S. Treasuries) are not

subject to federal taxes. All else equal, then, taxable bonds must pay higher rates

than non-taxable bonds. So, one could observe a lower rate on a high-quality

municipal bond than on a U.S. Treasury bond with the same coupon and time to

maturity. That is, it is possible that the tax status could overwhelm two key

advantages of U.S. Treasuries, namely, no default risk and high liquidity.

9.8 Summary and Conclusions

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