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.

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

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

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

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

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

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

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:

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

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:

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

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

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

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

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?

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

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

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

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

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

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:

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?

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:

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?

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:

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?

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

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

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:

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

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?

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

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

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

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

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

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

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

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

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