Final_1.pdf

do such premiums exist in real life? As a matter of fact, stocks do trade at a
premium for a variety of reasons. Greater relative liquidity (liquidity pre-
mium), the possibility of the firm being a takeover target (takeover pre-
mium), and pure charisma on the part of some stocks are some reasons that
come to mind. Therefore, in the evaluation of the equilibrium relationship
care must be taken to estimate both the values gthe cointegration coefficient
andmthe premium.
We will discuss two approaches to estimating the equilibrium relation-
ship. The first approach is based on the multifactor framework. The second
approach is the regression approach. Let us begin with the multifactor
approach.

ESTIMATING THE LINEAR RELATIONSHIP:
THE MULTIFACTOR APPROACH

In Chapter 6 we mentioned that the cointegration coefficient could be esti-
mated by performing a regression of the common factor returns of one stock
against the other. The estimated value from the regression is the cointegra-
tion coefficient. Also, the formula for the regression coefficient can be ex-
pressed in terms of the covariance and variance of the stocks involved. Now,
exploiting the multifactor framework the variance and covariance may be
expressed in terms of the factor exposures and the factor covariance matrix.
Thus, the regression formula may be expressed completely in terms of the
constructs of the multifactor framework and may be used to evaluate the
cointegration coefficient.
It is important to note here that we have two values for the cointegra-
tion coefficient depending on the choice of the independent variable. If the
linear relationship is expressed assuming stock Bto be the independent vari-
able, we have

(7.2)

(7.3)

Alternately, if the equilibrium relationship is represented assuming stock A
to be the independent variable, we have

restt=log()pB −γ′log()ptA, (7.4)

γβ==

()

()

AB =

AB

B

A

T

B

B

T

B

rr

r

eFe

eFe

cov ,

var

restt=log()pA −γlog()pBt

Testing for Tradability 107