64 CHAPTER ◆ 5 Types of Trading Systems
To create a more stable value for the ratio, our system uses a 30-day moving average of
the end of the day stock price of each company. Observed spread prices around this 30-day
moving average are essentially noise and not a true reflection of the value of the company.
The goal of a statistical arbitrage trading system is to exploit this noise. Our system compares
the observed market price of the spread to the more stable value, the 30-day moving average.
To normalize the difference between the observed price and the 30-day moving average, our
system uses a simple z -transform method:^1norm MA
30
30()
()
● Where is the observed price of the spread and the normalized prices, (^) norm ,
expresses the normally distributed price in terms of standard deviation from the mean.
● The mean prices, MA 30 ( ), is defined as the 30-day spread-price moving average.
Assumptions of the strategy:
● A long position in the spread is defined as short Stock A and long Stock B.
● A short position then is defined as long Stock A and short Stock B.
● Same holding horizons of 20 trading days to measure the strength of the signal. (An
alternative method is to have a signal to close the position, as well.)
● We assume that all opening trades are executed at the closing price on the day the
signal is received and closing trades executed at the closing price n days hence.
● Dollar amounts assume that long positions are paid for in full and a margin of 50%
is assessed on short trades.
The strategy is to monitor the spread price and calculate the normalized price. When (^) norm
exceeds 2, we consider this a bearish signal as we expect a reversion of the spread price
down to the mean, 0, and take a hypothetical short position in the spread. Alternatively,
when (^) norm is less than 2, we consider this a bullish signal as we expect to see a rever-
sion of the spread price up the mean. In this case the system simulates a long position in the
spread. The system holds positions for five trading days, at which time positions are closed.
5.5. Example Filter System: Buy Write
Filtering an investable universe to select securities that should outperform a benchmark is
a standard methodology. The key research in the validation of filters was done by Fama
and French in 1992, who showed the effects of fundamental classifications on predic-
tions of stock returns. A second application of filtering can add covered call positions
to increase the return. This strategy was developed by Whaley for the Chicago Board
Options Exchange and is even a tradable index (BXM). Each strategy in and of itself is
designed to outperform a benchmark index. By combining the two, we hope to create a
portfolio that will outperform the index with lower volatility.
The filter trading strategy incorporates these two filters combined into a single sys-
tem. The first filter selects the basket of stocks; the second selects the moneyness of the
call options to be sold. Stock selection starts with the S & P 500 as the investable universe.