different values of ∆, assuming that we trade exactly in the manner de-
scribed. The plot of the profit against different values of ∆is shown is Fig-
ure 8.1b. Note that it is identical to the curve in Figure 8.1a. We can
therefore safely conclude that the inventory constraints do not matter in the
process of deciding the value of ∆.
Now that we understand the principles underlying the design process,
it would be a good time to discuss its limitations as well. Note that there is
an implicit assumption that the stocks would be uniformly liquid at all lev-
els of divergence of the spread from equilibrium. This, of course, is far
from reality. It may be that due to liquidity issues the value of delta at
which the spread may be put on in size could be lesser than the one sug-
gested by this approach. That would then be the true delta at which the
profits are maximized.
This leads us to our next peeve about this approach. It says nothing at
all about position size. It seems as though we could keep adding on to a pairs
position and make unlimited profit when the spread converges. Needless to
say, it would be naive to believe that would be the case. To see why, consider
the following. By engaging in pairs trading, we are contributing to the mar-
ket forces that cause the convergence of the spread. We need to make sure
122 STATISTICAL ARBITRAGE PAIRS