(^3) A fine term coined by theoretical physicists in an era where the average physicist was
expected to toil at the laboratory conducting real experiments.
that at no point in time the spread position size gets to a point where we be-
come the dominant force contributing to the convergence. If that happens,
then it becomes difficult to unwind the position without a substantial slip-
page. Any gains we make in the spread will be lost in the slippage. It is there-
fore important to recognize that there is a physical limit to which we could
increase the size of the pairs position, even though the design process says
nothing in that regard.
So, what do we make of the design process when it does not handle
these issues? A good way to look at the results of the design process is that
in the absence of any information whatsoever and having to deal with mak-
ing decisions in a vacuum, the results of design process serve as a strong
guideline to aid in the process of designing trading rules. We now move on
to some reflections on spread dynamics.
Spread Dynamics
The purpose of this section is to demonstrate that the modeling of the spread
in parametric terms could indeed get complex. To get an idea of the plausi-
ble range of models for spread dynamics, we will engage in a series of what
we shall call “Thought Experiments.”^3 We will look at some empirical ob-
servations and the implications they bear for us when attempting to model
spread dynamics. We will start with the simplest case of Gaussian white
noise and reason our way toward more complicated models.
Case 1: Mixture Gaussian Model
We can expect a white noise time series for the spread to occur when trad-
ing security pairs that have a strict parity relationship. An example of this is
index arbitrage, which involves trading the S&P futures against the index.
But is it reasonable to expect the white noise to be strictly Gaussian? Gauss-
ian white noise would mean the value of the spread at any point in time is
drawn from a fixed Gaussian distribution. But the trading of securities is
more brisk around the open and close. This causes increased volatility
around these times. Hence, it would not be too much of a stretch to expect
the spread series to also exhibit higher volatility around these times. We can
therefore extend the white noise model by asserting that the white noise
spread values are drawn from Gaussian distributions with higher standard
deviations around the market open and close and a relatively low standard
deviation around midday.
Trading Design 123