Chapter 4 of 9
Moving averages and trend filters
Calculate simple and exponential averages and understand lag, whipsaws and parameter sensitivity.
In this chapter
Smoothing reduces detail #
A simple moving average is the arithmetic mean of the most recent n observations. It removes some short-term variation but also delays its response to new information. A longer window generally smooths more and reacts more slowly.
An exponential moving average weights recent observations more heavily. A common convention uses alpha = 2 ÷ (n + 1), with EMA today = alpha × price today + (1 − alpha) × prior EMA. Initialization conventions can differ, especially early in a series.
A crossover is a rule-defined event #
Price crossing an average, or one average crossing another, can be used to define a hypothesis. It does not prove a new trend will persist. Sideways observations can repeatedly reverse around an average, creating whipsaws and cumulative execution costs.
Signals based on a closing price cannot generally assume execution earlier at that same bar’s best price. Write down whether the simulation acts at the next available quote and how gaps affect the result.
Parameter selection creates research risk #
Trying many windows and reporting only the best one is a selection process that can fit historical noise. Look for stability across reasonable parameter variations and out-of-sample observations. Do not state that a familiar window is optimal for every market and timeframe.
Moving averages transform the same price information; adding several versions does not create several independent sources of evidence. Their role is to organize observations under explicit assumptions.
Decision lab: A filter changes the exposure profile #
A moving-average rule can reduce some participation during declines and also exit before recoveries or whipsaw in ranges. Its effect depends on when decisions are observable, how orders execute and which costs accumulate. Smoothing does not create new information.
Compare identical sizing under two frozen filters and an exposure baseline. Report time invested, turnover, drawdown and net return. If the winning lookback was chosen from dozens of trials, disclose that selection and require fresh evaluation instead of calling the best curve an edge.
Hypothetical worked example
A three-observation average can rise while price falls
For fictional closes 100, 102 and 104, the three-point SMA is 102. If the next close is 103, the new SMA is (102 + 104 + 103) ÷ 3 = 103.
Price has fallen from 104 to 103, while the moving average rises because the older 100 has left the window. This is a mechanical property, not a contradictory market message.
With n = 3, the conventional EMA alpha is 0.5. If the previous EMA was 102 and the new close 104, the updated EMA is 103. Different initial values can change the earliest results.
Common mistakes
- Treating a lagging average as advance knowledge of a turning point.
- Selecting the best historical window and promising the same performance.
Why can an SMA rise even if the latest price falls?
Make this chapter useful
Can you defend the reasoning?
Before moving on, answer the self-check in your own words and write why each alternative fails. Use the worked example to test that explanation. Then apply it in the module research task; keep the assumptions and the evidence that could change your answer.
Sources and further reading
- SEBI investor education ↗
- NISM: Research Analyst learning topics (scope reference; independent lessons) ↗
- CME Group: technical analysis of commodity prices ↗
- Bailey et al.: The Probability of Backtest Overfitting ↗
Further-reading references from the curriculum source list. Contract sizes, expiry calendars, settlement references, margin parameters and tax treatment can change; verify the current operative documents for the actual product. Worked figures are illustrative, not current quotes.
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