Final_1.pdf

The process works as follows:

1. First, we get the sample small size population of time between crossings
   by counting the time between subsequent crossings in the residual series.


2. A probability distribution is then constructed by resampling repeatedly
   from the existing sample. The large sample obtained as a result of the re-
   sampling exercise is then used to construct the probability distribution.


3. Percentile levels may then be constructed for the population. We can
   then check to see if the rates at the desired percentile levels on either side
   of the median satisfy our trading requirements. If they do, then we de-
   clare the pair tradable and vice versa.

Example

We now illustrate with an example the application of the process just de-
scribed. For illustrative purposes, we carefully picked two stocks from the
semiconductor sector and sampled their prices as of the day’s close for 90
days. Although we advocate the use of VWAP prices to do the regression, for
sake of expediency we ran an ordinary least squares method on it two times,
changing the independent variable. Results from the regression for the larger
of the two gvalues are as follows:

Equilibrium value m= –0.6971

Cointegration coefficient g= 1.0617

R-squared from the regression is 0.7965

Figure 7.2a is a scatter plot of the log-price series of the two stocks against
each other. Figure 7.2b is the residual time series. A cursory look at the

Testing for Tradability 115

FIGURE 7.2A Scatter Plot.

Log (Stock A)

1.4 1.5 1.6 1.7 1.8

2.1

2.4

Log ( Stock B)