ponent increases linearly with the trading horizon, then, all things being
equal, having a shorter trading horizon is definitely closer to the ideal con-
dition of cointegration. This is of course determined by the dynamics of the
spread and the rate at which the spread oscillates about the mean.
Based on Equation 6.25, the overall spread may also be interpreted as
the specific return spread with a varying mean that is dictated by the com-
mon factor spread. If the common factor spread is a nonstationary time se-
ries, then the overall spread is equal to the specific spread with a stochastic
drift to its mean value. Thus, deviation from ideal cointegration conditions
results in what we shall call mean drift. The fallout from mean drift is that
trading with symmetric bands may not be optimal because the movement of
the spread series may be skewed. The worse part is that it could skew either
way depending on the movement of the common factor spread, and it is not
possible to know in advance. Also, if the common factor spread is nonsta-
tionary, then the variance of the skew scales linearly with time. An impor-
tant insight to be gleaned in the process is that the mere passage of time
represents an increase in risk in pairs trading and must be taken into account
to design time-based stop orders.
Model Error
Model error occurs when our model specification is way off the mark. Let
us say that there is dramatic news that could potentially result in a drastic
change in fundamentals of a firm. The market immediately begins the
process of adjustment to the news, predicting in some sense where the fac-
tor exposures of the firm would be under the new circumstances.
In such cases where the expectation is for a dramatic change in the fac-
tor exposure, the common factor correlation evaluated before becomes
dated, and the correlation structure between the two stocks breaks down. It
is important to be aware of this and be constantly on the lookout for such
events when trading pairs.
Numerical Example
Consider three stocks A,B, and Cwith factor exposures in a two factor
model as follows:
xA= [1 1]
xB= [0.75 1]
xC= [1 0.75]Let the factor covariance matrix F=
..
..
0625 0225
0225 1024
Pairs Selection in Equity Markets 99