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Why MACD Uses Moving Average Differences Instead of Log Ratios

Article Quant Q&A · Author: flxh
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Summary

The document asks why MACD subtracts two moving averages rather than taking the logarithm of their ratio. The question notes that a log ratio could keep readings centered around zero while making them more comparable across assets with different price scales. The response offers a historical explanation: MACD was developed when computing resources were limited, and subtracting averages was easier to calculate by hand than taking logarithms.

That explanation is explicitly framed as the respondent’s most likely guess, not as a documented design rationale. The exchange does not analyze the mathematical or trading consequences of either formulation, test whether log normalization improves cross-asset comparability, or explain MACD’s original design in detail. It therefore supplies context about historical calculation convenience, but leaves the main methodological comparison unanswered.

Key ideas

  • MACD is formed by subtracting two moving averages rather than taking their log ratio.
  • A log ratio could make oscillator values more comparable across instruments with different price scales.
  • The reply speculates that subtraction was easier to compute by hand when MACD was developed.
  • The exchange does not establish a definitive rationale or compare the trading behavior of the two formulations.

Tags

Technical indicatorsStatistics
Full text
# Why does MACD not use log normalization


# Why does MACD not use log normalization












Today I wondered why the MACD oscillator uses the differences of two averages instead of the log of their quotient just like it's done for volatility estimation.

With this kind of log normalization values would be comparable across all asset pairs and the values would still be centred around 0.

Is there any point I am missing out or any particular reasoning behind this?

## Answer by Joshua Ulrich (score 3, accepted)

https://quant.stackexchange.com/a/37831

The most likely reason I can think of is the ease of computation. Gerald Appel developed the MACD in the late 1970's, when computing resources were very limited. When doing calculations by hand, on paper, it's much easier to take the difference of two simple (or exponential) moving averages than the log of their quotients.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.