CHAPTER
3
Structure of
Interest Rates
© 2003 South-Western/Thomson Learning
Chapter Objectives
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Learn why individual interest rates differ or
why security prices vary or change
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Analyze theories explaining why rates vary by
term or maturity, called the term structure of
interest rates
Factors Affecting Security Yields
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n
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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 Yields
n
Security yields and prices are affected by
levels and changes in:
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Default risk (also called Credit Risk)
Liquidity
Tax status
Term to maturity
Special contract provisions such as embedded
options
Factors Affecting Security Yields
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n
n
n
n
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 Yields
n
n
n
n
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 Yields
n
n
n
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 Yields
Yat = Ybt(1 – T)
Where:
Yat = after-tax yield
Ybt = before-tax yield
T = investor’s marginal tax rate
Factors Affecting Security Yields
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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 Yields
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Term to maturity
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Interest rates typically vary by maturity.
The term structure of interest rates defines the
relationship between maturity and yield.
u
The Yield Curve is the plot of current interest yields
versus time to maturity.
Yield Curve
Yield
%
Time to Maturity
An upward-sloping yield curve indicates that Treasury
Securities with longer maturities offer higher annual yields
Yield Curve Shapes
Normal
Level or Flat
Inverted
Factors Affecting Security Yields
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Special Provisions
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Call Feature: enables borrower to buy back the
bonds before maturity at a specified price
u
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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 Yields
n
Special provisions
l
Convertible bonds
u
u
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 Yield
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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 Yield
Yn = Rf,n + DP + LP + TA + CALLP + COND
Where:
Yn
Rf,n
= yield of an n-day security
= yield on an n-day Treasury
(risk-free) security
DP
= default premium (credit risk)
LP
= liquidity premium
TA
= adjustment for tax status
CALLP = call feature premium
COND = convertibility discount
The Term Structure of Interest Rates
Theories Explaining Shape of Yield Curve
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Pure Expectations Theory
Liquidity Premium Theory
Segmented Markets Theory
The Term Structure of Interest Rates
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Pure Expectations Theory
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l
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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 Rates
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Pure Expectations Theory
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l
Assumes investor has no maturity preferences and
transaction costs are low
Long-term rates are averages of current short rates
and expected short rates
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Forward rate: market’s forecast of the future interest rate
The Term Structure of Interest Rates
DownwardSloping
Yield Curve
UpwardSloping
Yield Curve
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Expected higher interest
rate levels
Expansive monetary
policy
Expanding economy
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n
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Expected lower interest
rate levels
Tight monetary policy
Recession soon?
The Term Structure of Interest Rates
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Liquidity Premium Theory
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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 Rates
n
Segmented Markets Theory
l
l
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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 Rates
n
Uses of the term structure
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Forecast interest rates
u
u
l
Forecast recessions
u
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The market provides a consensus forecast of expected future
interest rates
Expectations theory dominates the shape of the yield curve
Flat or inverted yield curves have been a good predictor of
recessions. See Exhibit 3.14.
Investment and financing decisions
u
u
u
Lenders/borrowers attempt to time investment/financing based on
expectations shown by the yield curve
Riding the yield curve
Timing of bond issuance
Interest Rate Differential (10-Year Rate
Minus Three-Month Rate)
Exhibit 3.14 Yield Curve as a Signal for
Recessions
7
6
5
4
3
2
1
0
–1
–2
–3
–4
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2001
Year
*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.
Treasury Debt Management and the Yield
Curve
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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 Structure
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Yield curves levels and shapes at various times
indicate:
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Inflation expectations
Level of economic activity or phase of business cycle
Monetary policy at the time
Usually high positive slope in short-term
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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
Points in Time
17
16
Annualized Treasury Security Yields
15
February 17, 1982
14
13
January 2, 1985
12
11
10
9
August 2, 1989
8
October 22, 1996
7
October 15, 2000
6
5
September 18, 2001
4
3
2
0
5
10
15
20
Number of Years to Maturity
25
30
Exhibit 3.18 Change in Term Premium
Over Time
20
Percentages
15
10
5
30-year
T-Bond
Yield
Three-month
T-Bill
Rate
0
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Year
International Structure of Interest Rates
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Capital flows to the highest expected after-tax,
real (inflation and other risk-adjusted),
foreign exchange adjusted rates of return
International Structure of Interest Rates
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Yield differences between countries are related
to:
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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