1. Structure of Interest Rates
Chapter 3
Structure of Interest Rates
Financial Markets and Institutions, 7e, Jeff Madura
Copyright ©2006 by South-Western, a division of Thomson Learning. All rights reserved.

2. Chapter Outline
Characteristics of debt securities that cause their yields to vary
Explaining actual yield differentials
Estimating the appropriate yield
A closer look at the term structure
International structure of interest rates

3. Characteristics of Debt Securities
Credit (default) risk
Securities with a higher degree of risk have to offer higher yields to be chosen
Credit risk is especially relevant for longer-term securities
Investors must consider the creditworthiness of the security issuer
Can use bond ratings of rating agencies
The higher the rating, the lower the perceived credit risk
Ratings can change over time as economic conditions change
Ratings for different bond issues by the same issuer can vary

4. Characteristics of Debt Securities (cont’d)
Credit (default) risk (cont’d)
Rating agencies
Moody’s Investor Service and Standard and Poor’s Corporation are the most popular
Agencies use different methods to assess the creditworthiness of firms and state governments
A particular bond issue could have different ratings from each agency, but differences are usually small
Financial institutions may be required to invest only in investment-grade bonds rated Baa or better by Moody’s and BBB or better by Standard and Poor’s

5. Characteristics of Debt Securities (cont’d)
Ratings Assigned by:
Description of Security
Moody’s
Standard and Poor’s
Highest quality
Aaa
AAA
High quality Aa AA
High-medium quality A
Medium quality
Baa
BBB
Medium-low quality Ba BB
Low quality (speculative) B
Poor quality
Caa
CCC
Very poor quality Ca CC
Lowest quality (in default) C
DDD, D

6. Characteristics of Debt Securities (cont’d)
Credit (default) risk (cont’d)
Shifts in credit risk premiums
The risk premium corresponding to a particular bond rating can chance over time
Accuracy of credit ratings
In general, credit ratings have served as reasonable indicators of the likelihood of default
Credit rating agencies do not always detect financial problems of firms

7. Characteristics of Debt Securities (cont’d)
Liquidity
Liquid securities can be easily converted to cash without a loss in value
Short-maturity securities with an active secondary market are liquid
Securities with lower liquidity have to offer a higher yield to be preferred

8. Characteristics of Debt Securities (cont’d)
Tax status
Investors are more concerned with after-tax income than before-tax income
Taxable securities have to offer a higher before-tax yield to be preferred
The after-tax yield is equal to:

9. Characteristics of Debt Securities (cont’d)
Tax status
Computing the equivalent before-tax yield
The before-tax yield necessary to match the after-tax yield on a tax-exempt security is:
State taxes should be considered along with federal taxes

10. Computing the Equivalent Before-Tax Yield
Assume a firm in the 30 percent tax bracket is aware of a tax-exempt security that pays a yield of 9 percent. To match this after-tax yield, taxable securities (with similar maturity and risk) must offer a before-tax yield of:

11. Characteristics of Debt Securities (cont’d)
Term to maturity
The term structure of interest rates defines the relationship between maturity and annualized yield
Special provisions
A call feature allows the issuer of bonds to buy the bonds back before maturity
The yield on callable bonds should be higher than on noncallable bonds
A convertibility clause allows investors to convert the bond into a specified number of common stock shares
The yield on convertible bonds is lower than on nonconvertible bonds

12. Explaining Actual Yield Differentials
Yield differentials are often measured in basis points
100 basis points equal 1 percent
Yield differentials of money market securities
Commercial paper rates are higher than T-bill rates
Eurodollar deposit rates are higher than yields on other money market securities
Market forces cause the yields of all securities to move in the same direction

13. Explaining Actual Yield Differentials (cont’d)
Yield differentials of capital market securities
Municipal bonds have the lowest before-tax yield
After-tax yield is higher than that of Treasury bonds
Treasury bonds have the lowest yield
No default risk
Very liquid
Investors prefer municipal or corporate bonds over Treasury bonds only if the after-tax yield compensates for default risk and lower liquidity

14. Estimating the Appropriate Yield
The yield on a debt security is based on the risk-free rate with adjustments to capture various characteristics:
Maturity is controlled for by matching the maturity of the risk-free security to that of the security of concern

15. Computing the Appropriate Yield
A company wants to issue 180-day commercial paper. Six-month T-bills currently have a yield of 7 percent. Assume that a default risk premium of 0.8 percent, a liquidity premium of 0.1 percent, and a 0.2 percent tax adjustment are necessary to sell the commercial paper to investors. What is the appropriate yield the company should offer on its commercial paper?

16. A Closer Look at the Term Structure
Pure expectations theory
Pure expectations theory suggests that the shape of the yield curve is determined solely by expectations of future interest rates
Assuming an initially flat yield curve:
The yield curve will become upward sloping if interest rates are expected to rise
The yield curve will become downward sloping if interest rates are expected to decline

17. Sudden Expectation of Higher Interest Rates
Market for short-term risk-free debt
Market for long-term risk-free debt S1 S2 S2 S1 i1 i2 D1 D2 i2 i1 D2 D1

18. Sudden Expectation of Higher Interest Rates (cont’d)
Yield Curve
YC2
YC1

19. Sudden Expectation of Lower Interest Rates
Market for long-term risk-free debt
Market for short-term risk-free debt S1 S2 S2 S1 i1 i2 D1 D2 i2 i1 D2 D1

20. Sudden Expectation of Lower Interest Rates (cont’d)
Yield Curve
YC1
YC2

21. A Closer Look at the Term Structure (cont’d)
Pure expectations theory (cont’d)
Algebraic presentation
The relationship between interest rates on two-year and one-year securities is:
The one-year interest rate in one year (the forward rate) can then be estimated:

22. Computing the Forward Rate
Assume that the annualized two-year interest rate today is 8 percent. Furthermore, one-year securities currently offer an interest rate of 5 percent. What is an estimate of the forward rate?

23. A Closer Look at the Term Structure (cont’d)
Pure expectations theory (cont’d)
Algebraic presentation (cont’d)
The one-year interest rate in two years (the forward rate) can also be estimated:

24. Computing the One-Year Interest Rate Two Years from Now
Continuing with the previous example, assume that three-year securities currently offer an interest rate of 10 percent. What is an estimate of the one-year interest rate that will prevail two years from now?

25. A Closer Look at the Term Structure (cont’d)
Pure expectations theory (cont’d)
Algebraic presentation (cont’d)
Future annualized interest rates for periods other than one year can also be computed using the yield curve
A one-year investment followed by a two-year investment should offer the same yield as a three-year security:

26. Computing the Two-Year Interest Rate One Year from Now
Continuing with the previous example, what is an estimate of the two-year interest rate that will prevail in one year?

27. A Closer Look at the Term Structure (cont’d)
Pure expectations theory (cont’d)
The theory assumes that forward rates are unbiased estimators of future interest rates
If forward rates are biased, investors should attempt to capitalize on the discrepancy

28. A Closer Look at the Term Structure (cont’d)
Liquidity premium theory
According to the liquidity premium theory, the yield curve changes as the liquidity premium changes over time due to investor preferences
Investors who prefer short-term securities will hold long-term securities only if compensated with a premium
Short-term securities are typically more liquid than long-term securities
The preference for short-term securities places upward pressure on the slope of the yield curve

29. A Closer Look at the Term Structure (cont’d)
Liquidity premium theory (cont’d)
Estimation of the forward rate based on a liquidity premium
The yield on a security will not necessarily be equal to the yield from consecutive investments in shorter-term securities:
The relationship between the liquidity premium and the term to maturity is:

30. A Closer Look at the Term Structure (cont’d)
Liquidity premium theory (cont’d)
Estimation of the forward rate based on a liquidity premium (cont’d)
The one-year forward rate can be derived as:
A positive liquidity premium means that the forward rate overestimates the market’s expectations of the future interest rate
A flat yield curve means the market is expecting a slight decrease in interest rates
A slight upward slope means no expected change in interest rates

31. Computing the Forward Rate With A Liquidity Premium
Assume that one-year interest rates are currently 10 percent. Further assume that two year interest rates are equal to 8 percent. The liquidity premium on a two-year security is 0.7 percent. What is an estimate of the one-year forward rate?

32. A Closer Look at the Term Structure (cont’d)
Segmented market theory
According to segmented markets theory, investors and borrowers choose securities with maturities that satisfy their forecasted cash needs
Pension funds and life insurance companies prefer long-term investments
Commercial banks prefer short-term investments
Shifting by investors or borrowers between maturity markets only occurs if the timing of their cash needs change

33. Impact of Different Scenarios – Segmented Markets Theory
Investors Have Mostly Short-Term Funds Available; Borrowers Want Long-Term Funds
Investors Have Mostly Long-Term Funds Available; Borrowers Want Short-Term Funds
Supply of short-term funds provided by investors
Upward pressure
Downward pressure
Demand for short-term funds by borrowers
Yield on new short-term securities
Supply of long-term funds provided by investors
Demand for long-term funds issued by borrowers
Yield on long-term securities
Shape of yield curve
Upward slope
Downward slope

34. A Closer Look at the Term Structure (cont’d)
Segmented market theory (cont’d)
Limitations of the theory
Some borrowers and savers have the flexibility to choose among various maturity markets
e.g., Corporations may initially obtain short term funds if they expect long-term interest rates to decline
If markets were segmented, an adjustment in the interest rate in one market would have no impact on other markets, but evidence shows this is not true

35. A Closer Look at the Term Structure (cont’d)
Segmented market theory (cont’d)
Implications
The preference for particular maturities can affect the prices and yields of securities with different maturities and therefore the shape of the yield curve
The preferred habitat theory is a more flexible perspective
Investors and borrowers may wander from their markets given certain events

36. A Closer Look at the Term Structure (cont’d)
Research on term structure theories
Interest rate expectations have a strong influence on the term structure
The forward rate from the yield curve does not accurately predict future interest rates
Variation in the yield-maturity relationship cannot be explained by interest rate expectations or liquidity
General research implications
Some evidence for pure expectations, liquidity premium, and segmented markets theory

37. A Closer Look at the Term Structure (cont’d)
Uses of the term structure
Forecast interest rates
Pure expectations and liquidity premium theories can be used
Forecast recessions
A flat or inverted yield curve may indicate a recession in the near future since lower interest rates are expected

38. A Closer Look at the Term Structure (cont’d)
Uses of the term structure (cont’d)
Investment decisions
Riding the yield curve involves investment in higher-yielding long-term securities with short-term funds
Financial institutions whose liability maturities are different from their asset maturities monitor the yield curve
Financing decisions
Assessing prevailing rates on securities for various maturities allows firms to estimate the rates to be paid on bonds with different maturities

39. A Closer Look at the Term Structure (cont’d)
Impact of debt management on term structure
If the Treasury uses a relatively large proportion of long-term debt, this places upward pressure on long-term yields
If the Treasury uses short-term debt, long-term interest rates may be relatively low
Historical review of the term structure
Early 1980s: downward sloping yield curve
1982 to 2001: an upward sloping yield curve generally persisted
September 11, 2001: investors shifted funds into short-term securities and the Fed provided funds to the banking system, causing the yield curve to become steeper

40. International Structure of Interest Rates
Yield curves vary among countries
Interest rate movements across countries tend to be positively correlated
Interest rates may vary across countries at any particular point in time
Supply and demand conditions across countries cause differences