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a subset of it. For example, high tech stocks generally have high P/E ratios given the
perception of high growth rates, whereas basic materials stocks, where demand is rela-
tively flat, are perceived as having low growth, and therefore have low P/Es. Ranking
all stocks together by P/E, would effectively create a first decile consisting of all high
tech stocks. To ensure a diversity in selection, algorithms should rank instruments within
their sectors first. A blended P/E rank, weighted between the sector rank and the universe
rank, produces a more robust signal. For price momentum signals, we normally recom-
mend sticking with the universe rank, since the goal of a price momentum signal is to
find instruments that are increasing in value the fastest.
Ranked signals should be tested individually, independent of each other, using sta-
tistics to determine their predictive ability. Individual signals are often grouped to form
a single overall signal for position selection. Grouped signals should also be tested. The
goal is to find a linear relationship between both the individual indicators and the group
indicator, and returns using the Spearman correlation. (The correlation value is normally
referred to as the information coefficient.) Sophisticated money managers mine data in
this fashion to find anomalies and inefficiencies.
A multifactor system is effectively an ANOVA/regression test. The normal outputs of
a signal strength trade to be analyzed and controlled using statistical process control are● Ranks and returns by quantile, including cumulative active returns chart (fan chart).
● Standard deviations by quantile.
● Scorecard performance cart (i.e., growth of $10,000 versus benchmark).
● Sortino and Sharpe ratios by quantile.
● Statistical tests to determine if the means are different and the variances are homo-
geneous between quantiles.
● Drawdowns.
● Information coefficient.
● Number of weeks the top ranks have outperformed the bottom ranks.
● Correlation of the algorithms return to the benchmark. (Preferably zero.)5.4. Example Trigger System: Statistical Arbitrage
In the trading industry, statistical arbitrage of stocks within a particular industry sector
is popular because of their convergence characteristics. Statistical arbitrage is based on
fundamental analysis. On a fundamental basis, the companies in the pair are very similar.
This is the foundation of all pairs trades. Statistical arbitrage is a bet that the relationship
between the prices of two stocks will diverge and then revert back to some predetermined
mean ratio, since the market tends to price the two similarly. Therefore, short-term devia-
tions from the mean will eventually correct itself for two fundamentally similar compa-
nies. Instead of correlation analysis, which does not work that well, this book will focus
on looking for absolute return performance as opposed to performance relative to an
index or peer group.
So, our trading system seeks out pairs of stocks that are in the same sector and have
similar fundamentals. This similarity produces a relatively stable ratio between the prices
of the two stocks. Our trading system monitors this ratio and uses it to generate trading
signals as the ratio diverges or converges.5.4. EXAMPLE TRIGGER SYSTEM