we may encounter and the ramifications they hold in the process of design-
ing trading signals.
The driving principle in the design of trading rules is the maximization
of profits. The right choices could end up altering the profit picture dramat-
ically. It is therefore important to have a robust approach to the design of
trading rules. Also, as noted earlier, the dynamics of the spread have a wide
and varied repertoire. Under the circumstances, it would seem most appro-
priate if we had different design methods for different classes of spreads,
each method tailored to its class, would it not? However, that need not be
the case. We propose here an approach to the design of trading rules whose
main feature is its one-size-fits-all quality. The methodology may be applied
to all spreads regardless of their dynamics, thus making the approach very
attractive.
The game plan for the following material is to start with a simple
example. We consider a white noise series and design trading rules for it.
This will help to familiarize us with the underlying principles behind the de-
sign process. We follow this by discussing various classes of spread dynam-
ics and the possible ways to model them. We then present our approach for
the determination of trading signals.
Band Design for White Noise
Let us discuss the design of trading signals when the spread in question can
be modeled as a white noise series. As noted earlier, the general principle in-
volved in trading a spread is to put on a trade upon deviation from the equi-
librium value and unwind the trade when equilibrium is restored. However,
the actual implementation of the general principle could be wide and varied.
On the one hand, we can adhere closely to the general principle put on
a spread position on a deviation of ∆from the equilibrium value and liqui-
date the position upon mean reversion. On the other hand, we could say that
the spread swings equally in both directions about the equilibrium value and
unwind the trade when it deviates by ∆in the opposite direction. The argu-
ment for it would be that this reduces the trading frequency by a factor of
two. Given that stocks have a bid-ask spread, we would incur a trading slip-
page every time a trade is executed. Reducing the trading frequency reduces
the effect of this slippage. The argument against it would be that this reduces
the trading frequency by a factor of two and increases the holding period in
the trade. This of course exposes us to mean drift, which was discussed in
earlier chapters and may not be well suited to trade spreads with a lower
quality of signal-to-noise ratio.
Another point to take into consideration in the trading process is the
amount of inventory we are willing to hold on a spread. On one end of the
Trading Design 119