10A.1Term Structure Varieties

There are a variety of term structures. The paryield curvefor the United States represents the

yields and interpolated yields of on-the-run coupon-paying Treasury securities of various matu-

rities (see Chapter 2). The annuity term structurerepresents the yields to maturity of riskless

bonds with level payments. There also is the spot term structure, which represents the yields

to maturity of zero-coupon bonds of various maturities.

In contrast to the Treasury term structures, par, annuity, and spot LIBOR term structures

are derived from the Treasury term structures and swap spreads in the interest rate swap mar-

ket. Adding the swap spreads to the par yield curve of Treasury securities gives the par LIBOR

term structure. This represents a set of almost riskless yields because LIBOR rates are based on

corporate credits that are comparable to AAand AAA-rated bonds. LIBOR rates may be pre-

ferred to Treasury rates in some instances because many Treasury yields are articially low due

to exceptionally favorable nancing.¹

Uses of Spot Yields and Where They Come From.The DCFapproach, as exhibitedin equa-

tion (10.1), makes use of the spot (or zero-coupon) yield curve. Generally, one obtains a more

accurate picture of spot yields by looking at the implied zero-coupon yields of par (straight

coupon) bonds than by looking at the yields of zero-coupon bonds.

Forces Driving the Term Structure of Interest Rates.Historically, the yield curve has had

many shapes. Moreover, yield curves for different countries can have different shapes at the

same time. Sometimes it is upward sloping, sometimes downward sloping, sometimes nearly at,

and sometimes it has bumps in it, particularly at the short end. Exhibit 10A.1 shows graphs of

par yield curves at four different points in time.

The activities of central banks (for example, the Federal Reserve System in the United States

or the European Central Bank) generally determine the rates at the short end of the yield curve.

Attempts to slow down the economy generally drive up short-term rates while expansionary

monetary policy tends to lower short-term rates. Often these policies have an opposite effect at

the long end of the yield curve because inationary expectations tend to drive the long end of

the yield curve. Acontractionary monetary policy is often intended to reduce ination, which

reduces long-term yields while simultaneously driving short-term yields upward.

Rates at the short end of the yield curve are generally 30 to 40 percent more volatile than

rates at the long end, probably because monetary policy acts primarily at the short end of the

curve and is countercyclical. Hence, if long-term prospects are in some sense an average of

short-term prospects, and if subsequent short-term prospects tend to reverse mistakes in previ-

ous policies or eliminate shocks, then long-term rates will be more stable.

¹See Dufe (1996) or Grinblatt with Han (2000) for a discussion of this issue.

Grinblatt742Titman: Financial	III. Valuing Real Assets	10. Investing in Risk742Free	© The McGraw742Hill
Markets and Corporate		Projects	Companies, 2002
Strategy, Second Edition

364Part IIIValuing Real Assets

EXHIBIT10A.1U.S. ParYield Curves at FourDifferent Points in History

10

9

8

7

Yield%

6

5
4	Feb. 14. 1992 Mar. 23, 1989
3	Dec. 9, 1988
2	Dec. 18, 1996
1

0

5	10 15	20	25	30
	Maturity (Years)