CHAPTER 6
THE STRUCTURE OF
INTEREST RATES
Copyright  2000 by Harcourt, Inc.
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Interest Rate Changes &
Differences Between Interest
Rates Can Be Explained by
Several Variables

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Term to Maturity.
Default Risk.
Tax Treatment.
Marketability.
Call or Put Features.
Convertibility.
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Selected Rates of Interest,
January 1998
Notice that the U.S. Treasury rate is the lowest interest rate in the economy for comparable
maturities.
FINANCIAL SECURITY
Commercial Paper, 3 months
Finance company paper, 3 months
Banker’s Acceptance, 3 months
U.S. Government Securities:
3-month Treasury bills
12-month Treasury bills
5-year Treasury notes
10-year Treasury bonds
Aaa municipals (state and local obligations)
Aaa corporate bonds
Aa corporate bonds
A corporate bonds
Baa corporate bonds
INTEREST RATE (%)
4.77
4.81
4.80
4.45
4.51
4.60
4.72
5.02
6.24
6.68
6.84
7.29
Source: Federal Reserve statistical release G.13 and Moody’s Investor Services.
Copyright  2000 by Harcourt, Inc.
6-3
Term (Maturity) Structure May Be
Studied Visually by Plotting a
Yield Curve at a Point in Time


The yield curve may be ascending, flat, or
descending.
Several theories explain the shape of the yield
curve.
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6-4
Yield Curves on Treasury
Securities in the 1980’s and 1990’s
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6-5
The Expectations Theory of the
Term Structure -- Interest Rate
Expectations Shape the Yield Curve

The slope of the yield curve reflects investors’
expectations about future interest rates.
– Ascending: future interest rates are expected to
increase.
– Descending: future interest rates are expected to
decrease.

Long-term interest rates represent the geometric
average of current and expected future (implied,
forward) interest rates.
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6-6
The Expectations Theory of Term
Structure (concluded)

Investors are assumed to trade in a very efficient
market with excellent information and minimal
trading costs. Other theories discussed later
presume less efficient markets.
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6-7
Term Structure Formula from
Expectation Theory
1 t Rn   1 t R1 1 t 1f1 1 t 2 f1  1 t n1f1  n
1
where :
R  the observed market rate,
f  the forward rate,
t  time period for which the rate is applicable ,
n  maturity of the bond.
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6-8
An Implied One Year Forward
Rate from the Term Structure
Formula
 1 t Rn  
f


1


t n 1 1
n 1
 1 t Rn1  
n
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6-9
Finding a One-Year Implied
Forward Rate

Using term structure of interest rates from January 29,
1999, find the one-year implied forward rate for year three.
– 1-year Treasury bill
– 2-year Treasury note
– 3-year Treasury note
4.51%
4.58%
4.57%
 1  .0457 3 

1

0
.
0455
or
4.55%

3 f1  
2
 1  .0458  
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6-
Liquidity Premium Theory of
Term Structure of Interest Rates

Long-term securities have greater risk and
investors require greater premiums to give up
liquidity.
– Long-term securities have greater price variability.
– Long-term securities have less marketability.

The liquidity premium explains an upward sloping
yield curve.
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6-11
Market Segmentation Theory of
Term Structure -- Maturity preferences
may affect security prices (yields),
explaining variations in yields by time


Market participants have strong preferences for
securities of particular maturity and buy and sell
securities consistent with their maturity
preferences.
If market participants do not trade outside their
maturity preferences, then discontinuities are
possible in the yield curve.
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Preferred Habitat Theory



The Preferred Habitat Theory is an extension of
the Market Segmentation Theory.
The Preferred Habitat Theory allows market
participants to trade outside of their preferred
maturity if adequately compensated for the
additional risk.
The Preferred Habitat Theory allows for humps
or twists in the yield curve, but limits the
discontinuities possible under Segmentation
Theory.
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6-
Which Theory is Right?


Day-to-day changes in the term structure are
most consistent with the Preferred Habitat
Theory.
However, in the long-run, expectations of future
interest rates and liquidity premiums are
important components of the position and shape
of the yield curve.
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6-
Yield Curves and the Business
Cycle

Interest rates are directly related to the level of
economic activity.
– An ascending yield curve notes the market
expectations of economic expansion and/or
inflation.
– A descending yield curve forecasts lower rates
possibly related to slower economic growth or
lower inflation rates.

Security markets respond to updated new
information and expectations and reflect their
reactions in security prices and yields.
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6-
Interest-Rate and Yield-Curve
Patterns Over the Business Cycle
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6-
Default Risk Is the Probability of
the DSU Not Honoring the Security
Contract


Losses may range from “interest a few days late”
to a complete loss of principal.
Risk averse investors want adequate
compensation for expected default losses.
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Investors Charge a Default Risk
Premium (Above Riskless or Less
Risky Securities) for Added Risk
Assumed

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
DRP = i - irf
The default risk premium (DRP) is the difference
between the promised or nominal rate and the
yield on a comparable (same term) riskless
security (Treasury security).
Investors are satisfied if the default risk premium
is equal to the expected default loss.
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6-
Risk Premiums for Selected
Securities (January 1999)
Notice that as bond rating quality declines, the default risk premium increases.
SECURITY
Corporate bonds: Aaa
Corporate bonds: Aa
Corporate bonds: A
Corporate bonds: Baa
SECURITY YIELD
(PERCENT)
EQUIVALENT RISK-FREE RATEa
(PERCENT)
6.24
6.68
6.84
7.29
5.16
5.16
5.16
5.16
RISK PREMIUM
(PERCENT)
1.08
1.52
1.68
2.13
aThirty-year
Treasury bond yield.
Source: Moody’s Investor Services, January, 1999.
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6-
Default Risk Premiums Increase
(Widen) in Periods of Recession
and Decrease in Economic
Expansion


In good times, risky security prices are bid up;
yields move nearer that of riskless securities.
With increased economic pessimism, investors
sell risky securities and buy “quality” widening the
DRP.
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Credit Rating Agencies Measure
and Grade Relative Default Risk
Among DSUs and Their
Securities


Cash flow, level of debt, profitability, and
variability of earnings are indicators of default
riskiness.
As conditions change, rating agencies alter rating
of businesses and governmental debtors.
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6-
Corporate Bond-Rating Systems
Investment grade quality bonds are those rated Baa or above by Moody’s (or BBB by Standard and Poor’s). Financial institutions are typically
allowed to purchase only investment grade securities.
EXPLANATION
Best quality, smallest degree of risk
High quality, slightly more long-term risk than top rating
Upper-medium grade, possible impairment in the future
Medium grade, lack outstanding investment characteristics
Speculative issues, protection may be very moderate
Very speculative, may have small assurance of interest and
principal payments
Issues in poor standing, may be in default
Speculative in a high degree, with marked shortcomings
Lowest quality, poor prospects of attaining real investment standing
MOODY’S
Aaa
Aa1
Aa2
Aa3
A1
A2
A3
Baa1
Baa2
Baa3
Ba1
Ba2
Ba3
B1
B2
B3
Caa
Ca
C
STANDARD
& POOR’S
AAA
AA+
AA
AAA+
A
ABBB+
BBB
BBBBB+
BB
BBB+
B
BCCC
CC
C
D
DEFAULT RISK
PREMIUM
Lowest
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Highest
Note: The top four rating categories are investment grade binds. Bonds below Baa are speculative grade.
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6-
The Taxation of Security Gains
and Income Affects the Yield
Differences Among Securities



The after-tax return, iat, is found by multiplying
the pre-tax return by one minus the marginal tax
rate.
iat = ibt(1-t)
Municipal bond interest income is tax exempt.
Coupon income and capital gains have been
taxed differently in the past, but are now both
taxed at the same rate as ordinary income.
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6-
Should You Buy a Municipal or a
Corporate Bond?
INVESTORS’ MARGINAL TAX RATE
0%
10
20
30
40
50
MUNICIPAL YIELD
7%
7
7
7
7
7
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CORPORATE AFTER-TAX
YIELD
10(1 - 0.00) = 10.0%
10(1 - 0.10) = 9.0
10(1 - 0.20) = 8.0
10(1 - 0.30) = 7.0
10(1 - 0.40) = 6.0
10(1 - 0.50) = 5.0
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Differences in Marketability Affect
Interest Yields

Marketability -- The costs and rapidity with which
investors can resell a security.
–
–
–
–

Cost of trade.
Physical transfer cost.
Search costs.
Information costs.
Securities with good marketability have higher
prices (in demand) and lower yields.
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Varied Option Provisions May
Explain Yield Differences Between
Securities

An option is a contract provision which gives the
holder the right, but not the obligation, to buy,sell,
redeem, or convert an asset at some specified
price within a defined future time period.
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A Call Option Permits the Issuer
(Borrower) to Call (Refund) the
Obligation Before Maturity



Borrowers will “call” if interest rates decline.
Investors in callable securities bear the risk of
losing their high-yielding security.
With increased call risk, investors demand a call
interest premium (CIP).
– CIP = ic - inc
– A callable bond, ic, will be priced to yield a higher
return (by the CIP) than a noncallable, inc, bond.
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A Put Option Permits the Investor
(Lender) to Terminate the Contract
at a Designated Price Before
Maturity



Investors are likely to “put” their security or loan
back to the borrower during periods of increasing
interest rates. The difference in interest rates
between putable and nonputable contracts is
called the put interest discount (PID).
PID = ip - inp
The yield on a putable bond, ip, will be lower than
the yield on the nonputable bond, inp, by the PIP.
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A Conversion Option Permits the
Investor to Convert a Security
Contract Into Another Security



Convertible bonds generally have lower yields,
icon, than nonconvertibles, incon.
The conversion yield discount (CYD) is the
difference between the yields on convertibles
relative to nonconvertibles.
CYD = icon - incon. Investors accept the lower yield
on convertible bonds because they have an
opportunity for increased rates of return through
conversion.
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