2. Subjective Technical Analysis
• Subjective TA is comprised of analysis methods and patterns that
are not precisely defined.
• A conclusion derived from a subjective method reflects the private
interpretations of the analyst applying the method.
• This creates the possibility that two analysts applying the same
method to the same set of market data may arrive at entirely
• Subjective methods are untestable, and claims that they are
effective are exempt from empirical challenge.
• This is fertile ground for myths to flourish.
3. Objective Technical Analysis
• Objective methods are clearly defined.
• When an objective analysis method is applied to market data, its signals or
predictions are unambiguous.
• This makes it possible to simulate the method on historical data and
determine its precise level of performance.
• This is called back testing.
• A method is objective if and only if it can be implemented as a computer
program that produces unambiguous market positions (long, short, or
• Objective TA methods are also referred to as mechanical trading rules or
• Objective TA methods are referred to simply as rules.
4. Objective Technical Analysis
• A rule is a function that
transforms one or more items of
information, referred to as the
rule's input, into the rule's
output, which is a
recommended market position
(e.g., long, short, neutral).
• Input(s) consists of one or more
financial market time series.
• The output is typically
represented by a signed number
(e.g., +1 or −1).
• Positive values to indicate long
positions and negative values to
indicate shorts position.
5. Binary Rules and Thresholds
• An investment strategy based on a
binary long/short rule is always in
either a long or short position in the
market being traded. Rules of this type
are referred to as reversal rules
because signals call for a reversal from
long to short or short to long.
• The specific mathematical and logical
operators that are used to define rules
can vary considerably.
6. Binary Rules and Thresholds
• One theme is the notion of a threshold,
a critical level that distinguishes the
informative changes in the input time
series from its irrelevant fluctuations.
• The premise is that the input time
series is a mixture of information and
noise. Thus the threshold acts as a
• These critical events can be detected
with logical operators called
inequalities such as greater-than (>)
and less-than (<). For example, if the
time series is greater than the
threshold, then rule output = +1,
otherwise rule output = −1.
7. Traditional Rules and Inverse Rules
• Many of the rules generate market
positions that are consistent with
traditional principles of technical analysis.
• For example, under traditional TA principles,
a moving-average-cross rule is interpreted
to be bullish (output value +1) when the
analyzed time series is above its moving
average, and bearish (output value of −1)
when it is below the moving average.
• I refer to these as traditional TA rules.
• The inverse of the moving-average-cross
rule would output a value of −1 when the
input time series is above its moving
average, and +1 when the series is below its
8. The Use of Benchmarks in Rule Evaluation
• Performance relative to a benchmark that is informative rather
than an absolute level of performance.
• Performance figures are only informative when they are
compared to a relevant benchmark.
• The isolated fact that a rule earned a 10 percent rate of return in
a back test is meaningless.
• If many other rules earned over 30 percent on the same data, 10
percent would indicate inferiority, whereas if all other rules were
barely profitable, 10 percent might indicate superiority.
9. Conjoint Effect of Position Bias and Market Trend on Back-Test Performance
• In reality, a rule's back-tested performance is comprised of two independent
• One component is attributable to the rule's predictive power, if it has any. This
is the component of interest.
• The second, and unwanted, component of performance is the result of two
factors that have nothing to do with the rule's predictive power:
(1) the rule's long/short position bias, and
(2) the market's net trend during the back-test period.
10. The rule's long/short position bias
• This refers to the amount of time the rule spent in a +1
output state relative to the amount of time spent in a −1
output state during the back test.
•If either output state dominated during the back test, the
rule is said to have a position bias.
• For example, if more time was spent in long positions, the
rule has a long position bias.
11. The market's net trend during the back-test period.
•The market's net trend or the average daily price change
of the market during the period of the back test.
•If the market's net trend is other than zero, and the rule
has a long or short position bias, the rule's performance
will be impacted.
•If, however, the market's net trend is zero or if the rule
has no position bias, then the rule's past profitability will
be strictly due to the rule's predictive power
12. Rule with Restrictive Short Condition and Long Position Bias.
•If the rule's long condition is more easily satisfied than its
short condition, all other things being equal, the rule will
tend to hold long positions a greater proportion of the
time than short positions.
•Such a rule would receive a performance boost when back
tested over historical data with a rising market trend.
•Conversely, a rule whose short condition is more easily
satisfied than its long condition would be biased toward
short positions and it would get a performance boost if
simulated during a downward trending market.
14. Detrending the Market Data
•Detrending is a simple transformation, which results in a
new market data series whose average daily price change is
equal to zero.
•If the market being traded has a net zero trend during the
back-test period, a rule's position bias will have no
distorting effect on performance.
•Thus, the expected return of a rule with no predictive
power, the benchmark, will be zero if its returns are
computed from detrended market data.
•Consequently, the expected return of a rule that does have
predictive power will be greater than zero when its returns
are computed from detrended data.
15. Detrending the Market Data
•To perform the detrending transformation, one first
determines the average daily price change of the
market being traded over the historical test period.
• This average value is then subtracted from each day's
•The mathematical equivalence between the two
methods discussed, (1) detrending the market data
and (2) subtracting a benchmark with a equivalent
16. Look-Ahead Bias and Assumed Execution Prices
• Look-ahead bias,14 also known as “leakage of future
information,” occurs in the context of historical testing
•The information that would be required to generate a
signal was not truly available at the time the signal was
assumed to occur.
•Look-ahead bias can also infect back-test results when
a rule uses an input data series that is reported with a
lag or that is subject to revision.
17. Trading Costs
• Trading costs be taken into account in rule back-tests?
•If the intent is to use the rule on a stand-alone basis for
trading, the answer is clearly yes.
•For example, rules that signal reversals frequently will incur
higher trading costs than rules that signal less frequently
and this must be taken into account when comparing their
•Trading costs include broker commissions and slippage.
•Slippage is due to the bid-asked spread and the amount
that the investor's order pushes the market's price—up
when buying or down when selling.