CHAPTER

33Structure of Interest Rates

© 2003 South-Western/Thomson Learning

Chapter ObjectivesChapter Objectives

Learn why individual interest rates differ or why security prices vary or change

Analyze theories explaining why rates vary by term or maturity, called the term structure of interest rates

Factors Affecting Security YieldsFactors Affecting Security Yields

Risk-averse investors demand higher yields For added riskiness

Risk is associated with variability Of returns Increased riskiness generates lower security

prices or higher investor required rates of return

Factors Affecting Security YieldsFactors Affecting Security Yields

Security yields and prices are affected by levels and changes in: Default risk (also called Credit Risk) Liquidity Tax status Term to maturity Special contract provisions such as embedded

options

Factors Affecting Security YieldsFactors Affecting Security Yields

Benchmark—risk-free treasury securities for given maturity

Default risk premium = risky security yield – treasury security yield of same maturity

Default risk premium = market expected default loss rate

Rating agencies set default risk ratings Anticipated or actual ratings changes impact

security prices and yields

Factors Affecting Security YieldsFactors Affecting Security Yields

The Liquidity of a security affects the yield/price of the security

A liquid investment is easily converted to cash At minimum transactions cost

Investors pay more (lower yield) for liquid investment

Liquidity is associated with short-term, low default risk, marketable securities

Factors Affecting Security YieldsFactors Affecting Security Yields

Tax status of income or gain on security impacts the security yield

Investor concerned with after-tax return or yield

Investors require higher yields For higher taxed securities

Factors Affecting Security YieldsFactors Affecting Security Yields

Yat = Ybt(1 – T)

Where:Yat = after-tax yield

Ybt = before-tax yield

T = investor’s marginal tax rate

Factors Affecting Security YieldsFactors Affecting Security Yields

Example: a taxable security that offers a before-tax yield of 14 percent. The investor’s tax rate is 20 percent. Calculate the after-tax yield.

Yat = 14%(1 – 0.2) = 11.2% The fully taxable pre-tax equivalent corporate

bond for a 11.2% municipal bond is:

Ybt = 11.2%/(1 – .2) = 14%

Factors Affecting Security YieldsFactors Affecting Security Yields

Term to maturity Interest rates typically vary by maturity. The term structure of interest rates defines the

relationship between maturity and yield. The Yield Curve is the plot of current interest yields

versus time to maturity.

Yield CurveYield Curve

An upward-sloping yield curve indicates that TreasurySecurities with longer maturities offer higher annual yields

Yield

%

Time to Maturity

Yield Curve ShapesYield Curve Shapes

Normal Level or Flat Inverted

Factors Affecting Security YieldsFactors Affecting Security Yields

Special Provisions Call Feature: enables borrower to buy back the

bonds before maturity at a specified price Call features are exercised when interest rates have

declined Investors demand higher yield on callable bonds,

especially when rates are expected to fall in the future

Factors Affecting Security YieldsFactors Affecting Security Yields

Special provisions Convertible bonds

Convertibility feature allows investors to convert the bond into a specified number of common stock shares

Investors will accept a lower yield for convertible bonds because investor returns include expected return on equity participation

Estimating the Appropriate YieldEstimating the Appropriate Yield

The appropriate yield to be offered on a debt security is based on the risk-free rate for the corresponding maturity plus adjustments to capture various security characteristics

Yn = Rf,n + DP + LP + TA + CALLP + COND

Estimating the Appropriate YieldEstimating the Appropriate Yield

Yn = Rf,n + DP + LP + TA + CALLP + CONDWhere:

Yn = yield of an n-day security

Rf,n = yield on an n-day Treasury (risk-free) security

DP = default premium (credit risk)LP = liquidity premiumTA = adjustment for tax statusCALLP = call feature premiumCOND = convertibility discount

The Term Structure of Interest RatesThe Term Structure of Interest Rates

Pure Expectations Theory Liquidity Premium Theory Segmented Markets Theory

Theories Explaining Shape of Yield Curve

The Term Structure of Interest RatesThe Term Structure of Interest Rates

Pure Expectations Theory Long-term rates are average of current short-term

and expected future short-term rates Yield curve slope reflects market expectations of

future interest rates Investors select maturity based on expectations

The Term Structure of Interest RatesThe Term Structure of Interest Rates

Pure Expectations Theory Assumes investor has no maturity preferences and

transaction costs are low Long-term rates are averages of current short rates

and expected short rates Forward rate: market’s forecast of the future interest

rate

The Term Structure of Interest RatesThe Term Structure of Interest Rates

Expected higher interest rate levels

Expansive monetary policy

Expanding economy

Expected lower interest rate levels

Tight monetary policy Recession soon?

Upward-Sloping

Yield Curve

Downward-Sloping

Yield Curve

The Term Structure of Interest RatesThe Term Structure of Interest Rates

Liquidity Premium Theory Investors prefer short-term, more liquid, securities Long-term securities and associated risks are

desirable only with increased yields Explains upward-sloping yield curve When combined with the expectations theory,

yield curves could still be used to interpret interest rate expectations

The Term Structure of Interest RatesThe Term Structure of Interest Rates

Segmented Markets Theory Theory explaining segmented, broken yield curves Assumes investors have maturity preference

boundaries, e.g., short-term vs. long-term maturities

Explains why rates and prices vary significantly between certain maturities

The Term Structure of Interest RatesThe Term Structure of Interest Rates

Uses of the term structure Forecast interest rates

The market provides a consensus forecast of expected future interest rates

Expectations theory dominates the shape of the yield curve

Forecast recessions Flat or inverted yield curves have been a good predictor of

recessions. See Exhibit 3.14.

Investment and financing decisions Lenders/borrowers attempt to time investment/financing based on

expectations shown by the yield curve Riding the yield curve Timing of bond issuance

Exhibit 3.14 Yield Curve as a Signal for Exhibit 3.14 Yield Curve as a Signal for RecessionsRecessions

7654321

0–1–2–3–4

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

*The general shape of the yield curve is measured as the differential between annualized 10-year and three-month interest rates.Recessionary periods are shaded.

Year

2001Inte

rest

Rat

e D

iffer

entia

l (10

-Yea

r R

ate

Min

us T

hree

-Mon

th R

ate)

Treasury Debt Management and the Treasury Debt Management and the Yield CurveYield Curve

U.S. Treasury attempts to finance federal debt at the lowest overall cost

Treasury uses a mixture of Bills, Notes, and Bonds to finance periodic deficits and refinance outstanding securities

Treasury focuses on short-term issuance, phasing out 30-year bonds

Treasury 10-year bond now the standard issue Leave the long-term issuance to private issuers

Historic Review of the Term StructureHistoric Review of the Term Structure

Yield curves levels and shapes at various times indicate: Inflation expectations Level of economic activity or phase of business cycle Monetary policy at the time

Usually high positive slope in short-term Represents demand for liquidity Short-term securities desired; higher prices; lower rates Short-term securities provide liquidity with maturity

Exhibit 3.17 Yield Curves at Various Exhibit 3.17 Yield Curves at Various Points in TimePoints in Time

0 5 10 15 20 25 30

17

16

15

14

13

12

11

10

9

8

7

6

5

2

3

4

February 17, 1982

January 2, 1985

October 22, 1996

September 18, 2001

August 2, 1989

October 15, 2000

An

nu

ali

zed

Tre

as

ury

Se

cu

rity

Yie

lds

Number of Years to Maturity

Exhibit 3.18 Change in Term Premium Exhibit 3.18 Change in Term Premium Over TimeOver Time

0

5

10

15

20

Per

cen

tag

es

Year

199619951994 19991998 20012000199719931992199119901989198819871986198519841983198219811980

30-yearT-BondYield

Three-monthT-BillRate

International Structure of Interest RatesInternational Structure of Interest Rates

Capital flows to the highest expected after-tax, real (inflation and other risk-adjusted), foreign exchange adjusted rates of return

International Structure of Interest RatesInternational Structure of Interest Rates

Yield differences between countries are related to: Expected changes in forex rates Varied expected real rates of return Varied expected inflation rates Varied country and business risk Varied central bank monetary policy