function value. Note that the maximum occurs at 0.75s. This would be the
value that maximizes the profit.
Let us now consider the case where we restrict the inventory held at any
time to one spread unit. The spread unit for our purposes is a fixed quantity
of shares for the two stocks in the appropriate ratio as defined by the coin-
tegration coefficient. Naturally, this quantity is dictated by the average trade
volume of the two stocks comprising the pair.
When the spread value is more than delta and we are long one unit of
spread, we sell two spread units: one to unwind the long spread position and
another to have short position on the spread. The results of the analysis as
already described still hold in this case. To check that this is true, we ran a
simulation using 5,000 white noise realizations and calculated the profits for
Trading Design 121
FIGURE 8.1A White Noise Threshold Design.Amount of Sigma Away from Mean0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0Profit Value0.1FIGURE 8.1B Threshold Simulation with Unit Inventory Constraint.Amount of Sigma Away from Mean0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00Profit Value^300600900