TRADING SYSTEMS
Across Time And Tradables
Trading Trends With The Bollinger Bands Z-Test
by Jacinta Chan
Standard deviation bands are helpful in determining trends.
Here, the author develops a trading system based on this idea that yields
high returns with low, controlled risk.
The set of trading techniques that I will
present here uses standard deviation bands to determine trends and help
develop a trading system that yields high returns at low, controlled risk.
The name for this trading system, BBZ, is an acronym derived from "Bollinger
Bands" and the "z-score," based on a Working Money article published
in October 2002 by Veronique Valcu. In "Z-Score Indicator," Valcu
related z-scores to Bollinger Bands. Intrigued by the article and to continue
that discussion, I wanted to take a closer look at that relationship and
introduce the Bollinger Bands z-test (BBZ).
RECAP
The z-score (Z) measures the difference (direction) between the closing
price (C) from the mean (n-period moving average) given the n-period standard
deviation(s). Thus, the formula becomes:
Positive or negative values show that the closing price (C) is above
(C>µ) or below (C<µ) the mean, respectively.
The properties that interest traders are return and risk. In finance,
average depicts expected return and standard deviation depicts expected
risk. In statistics, we can define range trading as prices that are observed
within the expected one (1) standard deviation band. We define trend trading
as prices that are observed above +1 standard deviation band (for uptrends)
and below -1 standard deviation band (for downtrends).
This article will show how to design and develop this trading system.
It outlines the research, why the z-score indicator is used, the tests,
and the results.
DESIGNING THE SYSTEM
Step 1: Data Analysis
Perform a data analysis on the price series. The most basic statistical
tool is the mean and standard deviation of returns. This will give you
an idea of the prevailing trend; a positive mean for most days shows an
uptrend, and a negative mean for most days shows a downtrend. You can also
determine the volatility of returns.
