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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.
Copyright© 2003 John Wiley and Sons, Inc.
Term (Maturity) Structure of
Interest Rates
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.
Copyright© 2003 John Wiley and Sons, Inc.
Yield Curves in the 2000s
Exhibit 6.1
Copyright© 2003 John Wiley and Sons, Inc.
The Expectations Theory of the
Term Structure
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 interest
rates.
Copyright© 2003 John Wiley and Sons, Inc.
The Expectations Theory of
Term Structure
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.
Copyright© 2003 John Wiley and Sons, Inc.
Term Structure Equation:
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.
Copyright© 2003 John Wiley and Sons, Inc.
Liquidity Premium Theory
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.
Copyright© 2003 John Wiley and Sons, Inc.
Market Segmentation Theory
Maturity preferences by investors 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.
Copyright© 2003 John Wiley and Sons, Inc.
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.
Copyright© 2003 John Wiley and Sons, Inc.
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.
Copyright© 2003 John Wiley and Sons, Inc.
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.
Copyright© 2003 John Wiley and Sons, Inc.
Interest-Rate and Yield-Curve
Patterns Over the Business
Cycle
Copyright© 2003 John Wiley and Sons, Inc.
Default Risk is the Probability of
the Borrowers 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.
Copyright© 2003 John Wiley and Sons, Inc.
Default Risk, cont.
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.
Copyright© 2003 John Wiley and Sons, Inc.
Risk Premiums (2/02)
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)
6.51
6.95
7.37
7.89
5.61
5.61
5.61
5.61
RISK PREMIUM
(PERCENT)
0.90
1.34
1.76
2.28
aTwenty-year
Treasury bond yield.
Source: Federal Reserve Statistical Release H.15 and Dow Jones Market Data
Copyright© 2003 John Wiley and Sons, Inc.
Default Risk
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.
Copyright© 2003 John Wiley and Sons, Inc.
Default Risk
Credit rating agencies measure and grade
relative default risk security issuers
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.
Copyright© 2003 John Wiley and Sons, Inc.
Corporate Bond-Rating
Systems, Exhibit 6.7
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Tax Effects on Yields
The taxation of capital gains and income affects
the yield differences among securities
The after-tax return, iat, is found by multiplying
the before-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 for individuals.
Copyright© 2003 John Wiley and Sons, Inc.
Should You Buy a Municipal or
a Corporate Bond?
INVESTORS’ MARGINAL TAX RATE
0%
10.0%
10
20
30
40
50
MUNICIPAL YIELD
CORPORATE AFTER-TAX
YIELD
7%
10(1 - 0.00) =
7
7
7
7
7
10(1 - 0.10) =
10(1 - 0.20) =
10(1 - 0.30) =
10(1 - 0.40) =
10(1 - 0.50) =
9.0
8.0
7.0
6.0
5.0
Copyright© 2003 John Wiley and Sons, Inc.
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.
Copyright© 2003 John Wiley and Sons, Inc.
Bond Options and Yields
Varied option provisions may explain yield
differences between bonds
An option is a contract provision which gives the
holder the right, but not the obligation, to buy, sell,
redeem, or convert a bond at some specified price
within a defined future time period.
Copyright© 2003 John Wiley and Sons, Inc.
Bond Options and Yields
A call option permits the issuer (borrower) to call
(refund) the bond before maturity
Borrowers will “call” if interest rates decline.
Investors in callable bonds face the risk of losing
their high-yielding bonds.
With increased call risk, investors demand a call
interest premium (CIP).
CIP = ic – inc > 0
A callable bond, ic, will be priced to yield a higher
return (by the CIP) than a noncallable, inc, bond.
Copyright© 2003 John Wiley and Sons, Inc.
Bond Options and Yields
A put option permits the investor (lender) to
terminate the bond at a designated price before
maturity
Investors are likely to “put” their bond back to the
issuer during periods of increasing interest rates.
The difference in interest rates between putable
and nonputable bonds is called the put interest
discount (PID).
PID = ip – inp < 0
The yield on a putable bond, ip, will be lower than
the yield on the nonputable bond, inp, by the PID.
Copyright© 2003 John Wiley and Sons, Inc.
Bond Options and Yields
A conversion option permits the investor to
convert a bond into another security
Convertible bonds generally have lower yields, icon
than non-convertibles incon.
The conversion yield discount (CYD) is the
difference between the yields on convertibles
relative to nonconvertibles.
CYD = icon - incon < 0. Investors accept the lower
yield on convertible bonds because they have an
opportunity for increased rates of return through
conversion.
Copyright© 2003 John Wiley and Sons, Inc.