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Introduction
In the discussions so far, we have established that a key requirement for
pairs trading is the existence of an equilibrium relationship between the log
price series of two stocks. We also discussed that the equilibrium relationship
is characterized by two quantities: the cointegration coefficient and the equi-
librium value. Once they are known, they can be used to construct the lin-
ear combination of the log prices of the two stocks, which is referred to as
the spread. Pairs trading is a bet on the mean reversion property of the
spread. When we make the determination that the spread has diverged suf-
ficientlyfrom the equilibrium value, we enter into an appropriate position in
the two stocks, betting that the divergence will correct itself, and the spread
would revert back to equilibrium. It is therefore important for us to explic-
itly define what would qualify as a sufficient divergence of the spread value
from equilibrium for us to consider entering into a trade. The explicit spec-
ification of the divergence level enables us to boil down the actual trading of
the spread to an unambiguous set of simple rules, which we will also refer
to as trading signals. Obviously, the proper design of trading signals has a
strong bearing on the profit loss picture and is therefore an important topic
for discussion.
Let us look at what we would need in order to design the trading rules.
Well, if the dynamics of the spread are known, then we can design our trad-
ing signals in an appropriate fashion. So, what do we know about the dy-
namics of spreads? For one, we can expect all of them to be highly mean
reverting, since that is the criterion we used to choose the pairs in the first
place. Let us assume for the sake of argument that all spreads are stationary
ARMA processes. ARMA processes are mean reverting in nature and there-
fore do not violate the basic requirement we set forth for a pair to be trad-
able. So, now it is clear that the spread can at a minimum be drawn from a
rich repertoire of ARMA processes and can therefore have dynamics that are
wide and varied. We will discuss the different kinds of spread dynamics that
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