The Mathematics of Financial Modelingand Investment Management

2-Financial Markets Page 32 Wednesday, February 4, 2004 1:15 PM

32 The Mathematics of Financial Modeling and Investment Management

Fama, as well as others, defines “fully reflects” in terms of the

expected return from holding a security. The expected return over some

holding period is equal to expected cash distributions plus the expected

price change, all divided by the initial price. The price formation process

defined by Fama and others is that the expected return one period from

now is a stochastic (i.e., random) variable that already takes into

account the “relevant” information set.

In defining the “relevant” information set that prices should reflect,

Fama classified the pricing efficiency of a market into three forms: weak,

semistrong, and strong. The distinction between these forms lies in the

relevant information that is hypothesized to be impounded in the price

of the security. Weak efficiency means that the price of the security

reflects the past price and trading history of the security. Semistrong effi-

ciency means that the price of the security fully reflects all public infor-

mation (which, of course, includes but is not limited to historical price

and trading patterns). Strong-form efficiency exists in a market where

the price of a security reflects all information, whether or not it is pub-

licly available.

A price-efficient market has implications for the investment strategy

that investors may wish to pursue. Throughout this book, we shall refer

to various active strategies employed by investors. In an active strategy,

investors seek to capitalize on what they perceive to be the mispricing of

a security or securities. In a market that is price efficient, active strate-

gies will not consistently generate a return after taking into consider-

ation transaction costs and the risks associated with a strategy that is

greater than simply buying and holding securities. This has lead inves-

tors in certain markets that empirical evidence suggests are price effi-

cient to pursue a strategy of indexing, which simply seeks to match the

performance of some financial index.

Operational Efficiency

In an operationally efficient market, investors can obtain transaction

services as cheaply as possible, given the costs associated with furnish-

ing those services. Commissions are only part of the cost of transacting

as we noted above. The other part is the dealer spread. Bid-ask spreads

for bonds vary by type of bond. Other components of transaction costs

are discussed below.

In an investment era where one-half of one percentage point can

make a difference when an asset manager is compared against a perfor-

mance benchmark, an important aspect of the investment process is the

cost of implementing an investment strategy. Transaction costs are more