# SECTION VII - CHAPTER 41 - Objective Rules & Evaluation

Dean at Corporate PGDM à Professional Training Academy
23 Mar 2023
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### SECTION VII - CHAPTER 41 - Objective Rules & Evaluation

• 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 different conclusions. • 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 neutral). • Objective TA methods are also referred to as mechanical trading rules or trading systems • 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 filter. • 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 moving average.
• 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 components. • 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.
• 13. Rule with Restrictive Short Condition and Long Position Bias.
• 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 price change. •The mathematical equivalence between the two methods discussed, (1) detrending the market data and (2) subtracting a benchmark with a equivalent position bias
• 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 performances. •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.