Final_1.pdf

measure to the fundamentals of the firm. Accomplishing this would help
provide a theoretical justification for the use of the score/distance measure
and therefore a sound economic rationale for our expectation of cointe-
grated behavior.
In this chapter, we focus on defining, justifying, and interpreting the
score/distance measure. It is therefore a bit theoretical in nature. To help mo-
tivate the choice of the score/distance measure, the nexus between cointe-
gration and arbitrage pricing theory (APT) is explored. We draw parallels
between the common trends model for cointegration and the ideas of APT.
Conditions to be satisfied for cointegration in the common trends model are
translated into APT constructs. This makes it possible to evaluate the
score/distance measure in the APT framework. Moreover, if the multifactor
implementation of APT is composed of fundamental variables, then the dis-
tance measure calculated relates to the fundamentals of the firm. We will
then have an easy evaluation procedure for the distance measure that is
firmly based on the fundamentals of the firm, thus satisfying the require-
ments of the score/distance measure.
In addition, we bridge the gap between theoretical expectations and
practical observations. Assumptions, caveats, and loopholes that are en-
countered in the process are stated explicitly. Insights gained in the exercise
will help us understand what can go wrong and the things to beware of
while trading. Sources of risk are identified and quantified with a view to en-
hance the understanding of the dynamics involved in pairs trading and the
kinds of pairs to avoid. Let us start with the common trends model.

Common Trends Cointegration Model

Let us recall the common trends model from Chapter 5. We are given two
seriesytandzt, as shown in Equation 6.1.

(6.1)

represent the so-called common trends or random walk compo-
nents of the two time series; are the stationary and specific compo-
nents of the time series. If the two series are cointegrated, then their common
trends must be identical up to a scalar,

(6.2)

wheregis the cointegration coefficient. Let us examine some of the implica-
tions of the common trends model.

nnyztt=γ

εεyztt,

nnyztt and

yn

zn

tyy

tzz

tt

tt

=+

=+

ε

ε

Pairs Selection in Equity Markets 87