The Efficient Market Hypothesis and Martingale Stock Prices

Summary

The document asks why the efficient market hypothesis is associated with stock prices following a martingale under the true probability distribution, while discounted prices are martingales under a risk-neutral measure. Its answer gives a brief interpretation: a martingale means future price direction cannot be forecast from available information.

The post does not develop the mathematical framework requested, offer a derivation, or cite supporting evidence beyond pointing to another document. It therefore conveys only an intuitive connection between martingale behavior and unpredictable directional moves. It leaves important distinctions unresolved, including the assumptions and information set behind the martingale claim, and how the physical-measure statement differs from risk-neutral pricing. Readers seeking a formal explanation will need material beyond this brief answer.

Key ideas

• The response interprets a stock price martingale as making future price direction unforecastable.
• The question distinguishes physical-measure prices from discounted prices under a risk-neutral measure.
• The answer supplies no derivation or framework for connecting the efficient market hypothesis to the martingale claim.

Tags

# Why do stock prices follow a martingale?


# Why do stock prices follow a martingale?












I have a quick question: why does the Efficient Market Hypothesis (EMH) assume that stock prices follow a martingale process?

I understand that discounted prices under the risk-neutral probability measure are a martingale. This can be shown explicitly. But how is this related to the statement that (pre-discounted, and under the true distribution) prices are martingale under the EMH? Is there any mathematical framework that supports this statement?

## Answer by Phil (score 2)

https://quant.stackexchange.com/a/60883

It only means that the directions of future movements of stock prices are impossible to forecast.

For a more mathematical explanation, consider this document.

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.