CHAPTER 6
THE STRUCTURE OF
INTEREST RATES
Interest Rate Changes &
Differences Between Interest
Rates Can Be Explained by
Several Variables
•
•
•
•
•
•
Term to Maturity.
Default Risk.
Tax Treatment.
Marketability.
Call or Put Features.
Convertibility.
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
Source: Federal Reserve statistical release G.13 and Moody’s Investor Services.
4.45
4.51
4.60
4.72
5.02
6.24
6.68
6.84
7.29
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.
Yield Curves on Treasury Securities in
the 1980’s and 1990’s
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.
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.
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.
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
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
4.51%
– 2-year Treasury note
4.58%
– 3-year Treasury note
4.57%
 1  .0457 3 
 1  0.0455 or 4.55%
3 f1  
2
 1  .0458  
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.
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.
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.
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.
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.
Interest-Rate and Yield-Curve
Patterns Over the Business Cycle
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.
Investors Charge a Default Risk
Premium (Above Riskless or Less Risky
Securities) for Added Risk Assumed
• 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.
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
aThirty-year
SECURITY YIELD
(PERCENT)
EQUIVALENT RISK-FREE RATEa
(PERCENT)
6.24
6.68
6.84
7.29
5.16
5.16
5.16
5.16
Treasury bond yield.
Source: Moody’s Investor Services, January, 1999.
RISK PREMIUM
(PERCENT)
1.08
1.52
1.68
2.13
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.
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.
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
Note: The top four rating categories are investment grade binds. Bonds below Baa are speculative grade.
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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





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Highest
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.
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
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
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.
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.
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.
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.
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.