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$1 $1.2250
2. Buy a two-year bond. Reinvest all proceeds in a one-year bond in the third year, which will
provide a return in that year of r3. Total proceeds per dollar invested will be the result of
two years™ growth of invested funds at 6% plus the final year™s growth at rate r3:
r 3) r 3)
$1 (1 $1.1236 (1
The forward rate is the rate in year 3 that makes the total return on these strategies equal:
f3 )
1.2250 1.1236 (1
f3) 1.0902, so that f3 is
We conclude that the forward rate for the third year satisfies (1

The Liquidity Preference Theory
The expectations hypothesis starts from the assertion that bonds are priced so that “buy and
hold” investments in long-term bonds provide the same returns as rolling over a series of
short-term bonds. However, the risks of long- and short-term bonds are not equivalent.
We have seen that longer term bonds are subject to greater interest rate risk than short-term
bonds. As a result, investors in long-term bonds might require a risk premium to compensate
them for this risk. In this case, the yield curve will be upward sloping even in the absence of
any expectations of future increases in rates. The source of the upward slope in the yield curve
is investor demand for higher expected returns on assets that are perceived as riskier.
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

326 Part THREE Debt Securities

This viewpoint is called the liquidity preference theory of the term structure. Its name de-
rives from the fact that shorter term bonds have more “liquidity” than longer term bonds, in
preference theory
the sense that they offer greater price certainty and trade in more active markets with lower
The theory that
bid“ask spreads. The preference of investors for greater liquidity makes them willing to hold
investors demand
these shorter term bonds even if they do not offer expected returns as high as those of longer
a risk premium on
long-term bonds. term bonds.
We can think of a liquidity premium as resulting from the extra compensation investors
liquidity premium demand for holding longer term bonds with lower liquidity. We measure it as the spread be-
tween the forward rate of interest and the expected short rate:
The extra expected
return demanded
fn E(rn) Liquidity premium
by investors as
compensation for In the absence of a liquidity premium, the forward rate would equal the expectation of the fu-
the greater risk of
ture short rate. But generally, we expect the forward rate to exceed that expectation to com-
longer term bonds.
pensate investors for the lower liquidity of longer term bonds.
Advocates of the liquidity preference theory also note that issuers of bonds seem to prefer
to issue long-term bonds. This allows them to lock in an interest rate on their borrowing for
long periods. If issuers do prefer to issue long-term bonds, they will be willing to pay higher
yields on these issues as a way of eliminating interest rate risk. In sum, borrowers demand
higher rates on longer term bonds, and issuers are willing to pay higher rates on longer term
bonds. The conjunction of these two preferences means longer term bonds typically should
offer higher expected rates of return to investors than shorter term bonds. These expectations
will show up in an upward-sloping yield curve.
If the liquidity preference theory is valid, the forward rate of interest is not a good estimate
of market expectations of future interest rates. Even if rates are expected to remain unchanged,
for example, the yield curve will slope upward because of the liquidity premium. That upward
slope would be mistakenly attributed to expectations of rising rates if one were to use the pure
expectations hypothesis to interpret the yield curve.

Suppose that the short-term rate of interest is currently 8% and that investors expect it to re-
main at 8% next year. In the absence of a liquidity premium, with no expectation of a change
9.12 EXAMPLE in yields, the yield to maturity on two-year bonds also would be 8%, the yield curve would be
flat, and the forward rate would be 8%. But what if investors demand a risk premium to in-
vest in two-year rather than one-year bonds? If the liquidity premium is 1%, then the forward
Premia and
rate would be 8% 1% 9%, and the yield to maturity on the two-year bond would be de-
the Yield Curve
termined by
(1 1.08 1.09 1.1772
implying that y2 .085 8.5%. Here, the yield curve is upward sloping due solely to the
liquidity premium embedded in the price of the longer term bond.

9. Suppose that the expected value of the interest rate for year 3 remains at 8% but
that the liquidity premium for that year is also 1%. What would be the yield to ma-
CHECK turity on three-year zeros? What would this imply about the slope of the yield
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

9 Bond Prices and Yields

F I G U R E 9.13
Yield to
maturity Illustrative
yield curves
Yield curve

short-term rate

Maturity date

Yield to

Yield curve
short-term rate
Maturity date

A Synthesis
Of course, we do not need to make an either/or choice between expectations and risk premi-
ums. Both of these factors influence the yield curve, and both should be considered in inter-
preting the curve.
Figure 9.13 shows two possible yield curves. In Figure 9.13A, rates are expected to rise
over time. This fact, together with a liquidity premium, makes the yield curve steeply upward
sloping. In Figure 9.13B, rates are expected to fall, which tends to make the yield curve slope
downward, even though the liquidity premium lends something of an upward slope. The net
effect of these two opposing factors is a “hump-shaped” curve.
These two examples make it clear that the combination of varying expectations and li-
quidity premiums can result in a wide array of yield-curve profiles. For example, an upward-
sloping curve does not in and of itself imply expectations of higher future interest rates,
because the slope can result either from expectations or from risk premiums. A curve that is
more steeply sloped than usual might signal expectations of higher rates, but even this infer-
ence is perilous.
Figure 9.14 presents yield spreads between 90-day T-bills and 10-year T-bonds since 1970.
The figure shows that the yield curve is generally upward sloping in that the longer-term
bonds usually offer higher yields to maturity, despite the fact that rates could not have been
expected to increase throughout the entire period. This tendency is the empirical basis for the
liquidity premium doctrine that at least part of the upward slope in the yield curve must be be-
cause of a risk premium.
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

328 Part THREE Debt Securities

F I G U R E 9.14 20
Term spread. Yields
to maturity on 90-day
T-bills and 10-year
T-bonds 10-year T-bonds


90 day T-bills


1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

SUMMARY • Debt securities are distinguished by their promise to pay a fixed or specified stream of
income to their holders. The coupon bond is a typical debt security.
• Treasury notes and bonds have original maturities greater than one year. They are issued at
or near par value, with their prices quoted net of accrued interest. T-bonds may be callable
during their last five years of life.
• Callable bonds should offer higher promised yields to maturity to compensate investors
for the fact that they will not realize full capital gains should the interest rate fall and the
bonds be called away from them at the stipulated call price. Bonds often are issued with a
period of call protection. In addition, discount bonds selling significantly below their call
price offer implicit call protection.
• Put bonds give the bondholder rather than the issuer the option to terminate or extend the
life of the bond.
• Convertible bonds may be exchanged, at the bondholder™s discretion, for a specified
number of shares of stock. Convertible bondholders “pay” for this option by accepting a
lower coupon rate on the security.
• Floating-rate bonds pay a fixed premium over a referenced short-term interest rate. Risk is
limited because the rate paid is tied to current market conditions.
• The yield to maturity is the single interest rate that equates the present value of a security™s

cash flows to its price. Bond prices and yields are inversely related. For premium bonds,
the coupon rate is greater than the current yield, which is greater than the yield to maturity.
The order of these inequalities is reversed for discount bonds.
• The yield to maturity often is interpreted as an estimate of the average rate of return to an
investor who purchases a bond and holds it until maturity. This interpretation is subject to
error, however. Related measures are yield to call, realized compound yield, and expected
(versus promised) yield to maturity.
• Treasury bills are U.S. government-issued zero-coupon bonds with original maturities of
up to one year. Prices of zero-coupon bonds rise exponentially over time, providing a rate
of appreciation equal to the interest rate. The IRS treats this price appreciation as imputed
taxable interest income to the investor.
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

9 Bond Prices and Yields

• When bonds are subject to potential default, the stated yield to maturity is the maximum
possible yield to maturity that can be realized by the bondholder. In the event of default,
however, that promised yield will not be realized. To compensate bond investors for
default risk, bonds must offer default premiums, that is, promised yields in excess of those
offered by default-free government securities. If the firm remains healthy, its bonds will
provide higher returns than government bonds. Otherwise, the returns may be lower.
• Bond safety often is measured using financial ratio analysis. Bond indentures are another
safeguard to protect the claims of bondholders. Common indentures specify sinking fund
requirements, collateralization of the loan, dividend restrictions, and subordination of
future debt.

bond, 296 face value, 296 put bond, 300
callable bonds, 296 floating-rate bonds, 300 sinking fund, 319
collateral, 320 forward rate, 325 speculative grade or junk
convertible bonds, 299 horizon analysis, 312 bonds, 316
coupon rate, 296 indenture, 318 subordination clauses, 320
current yield, 308 investment grade bonds, 316 term structure of interest
debenture, 320 liquidity preference rates, 322
debt securities, 295 theory, 326 yield curve, 322
default premium, 322 liquidity premium, 326 yield to maturity, 306
discount bonds, 309 par value, 296 zero-coupon bond, 296
expectations hypothesis, 324 premium bonds, 308

1. Which security has a higher effective annual interest rate?


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