I was reading a little bit today about the signal to noise ratio as it applies to sound, which uses a general equation:
, where
P = average power
A = amplitude measured as a quadratic mean

Signal To Noise is often referred to in finance, specifically when it comes to Black’s paper “Noise.” (in the Papers section)

While glancing through that and JSTOR, I came across Truman’s Theory of Noise in Trading paper (also in the Papers section), which used a comparable line of thought to that found in O’Hara’s book Market Microstructure Theory.

I can refer to the equations when I get near the book, but it has a number of them built upon two period models, much like Truman, that determine how a market maker may adjust the bid/ask spread based upon their interpretation of informed trading. Magnitude would play a role, meaning when a market maker felt trading was informed to a scale that would impact their inventory, the bid/ask spread would adjust by a larger amount to handle that. That reasoning is very intuitive, assuming the market maker is risk neutral.

On a tick frequency, could we get a signal to noise ratio based upon larger-than-normal moves, using this logic? I’ll look to find out. If we have:
,
then we could derive:
,
which results in:

The question then becomes if a ratio of 1 is the correct breakpoint, and whether or not the signal and noise measures should be aggregated over a set time bin. There are still a number of questions that relate to this, but it is a framework for starting.