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Signal and Noise as Expected Return Relative to Volatility

Article Quant Q&A · Author: low_snr
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Summary

The document interprets the common claim that financial markets have a low signal-to-noise ratio as informal shorthand for modest expected returns relative to substantial volatility. Under this usage, the signal is the asset's expected return, while noise describes the uncertainty around realized outcomes. The distinction is statistical rather than a claim that an observer can cleanly decompose each price into a known signal and noise component.

The answer illustrates the idea with an asset whose annual expected return is 8% and annualized standard deviation is 20%. It notes that a positive average return does not prevent a long position from losing money over a given period, with the example indicating a loss probability above 40%. This explanation is a broad intuition, not a precise universal definition of signal-to-noise ratio or a trading method. The meaning depends on the chosen horizon, return model, and what an analyst is trying to predict.

Key ideas

  • In this usage, signal refers to expected return and noise to volatility around realized outcomes.
  • A positive expected return can coexist with a substantial probability of loss.
  • The example contrasts an 8% expected annual return with 20% annualized standard deviation.
  • Signal-to-noise is presented as informal financial language rather than a precise universal decomposition.

Tags

StatisticsVolatilityRisk management
Full text
# What is the precise meaning of signal and noise in finance


# What is the precise meaning of signal and noise in finance












A lot of people working in the finance industry are saying that what makes finance hard is that the signal to noise ratio (SNR) is extremely low.

I don't get what is precisely meant by that. How are the signal & noise precisely defined?

If I have a stock with price $P(t)$, then we can rewrite it as: $P(t) = s(t) + \epsilon(t)$ with $s$ the signal and $\epsilon$ the noise. But what's the definition of $s$ here?

Because let's say I have an algo that tells me at every time $t$ what $s$ is what $\epsilon$ is. From knowing $s(t)$ and $\epsilon(t)$, I still don't know what $s(T)$ will be for $T > t$, so I can't make money from knowing what $s(t)$ is?

Hence I would like to know how people are defining the signal and the noise in finance, and how seperating both of them is what can make you money.

## Answer by dm63 (score 4)

https://quant.stackexchange.com/a/81561

I believe this is just financial slang that expresses the idea that volatility is quite high versus expected returns. For example, an asset might have an expected annual return of 8% but an annualized standard deviation of 20%. Just getting long the asset will on average make money (‘signal’), but there is a >40% chance of losing money. Thus, a lot of ‘noise’.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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