Forex Maths & Physics

Entropy — The Hard Limit on Predicting Any Market

There is a deep reason markets are hard to forecast, and it comes not from finance but from information theory. The concept is entropy — a precise measure of surprise and uncertainty — and it places a hard ceiling on how predictable any market can ever be.

Shannon's surprise

Claude Shannon defined the entropy of a source of outcomes as:

\[H = -\sum_i p_i \log_2 p_i\]

The more uniform and unpredictable the outcomes, the higher the entropy. A coin that always lands heads has zero entropy — no surprise, perfectly predictable. A fair coin has maximum entropy for two outcomes — maximum surprise per flip. Entropy is, literally, the average amount of *new information* each observation carries.

What entropy says about markets

A market with high entropy is one where the next move carries little predictable information — close to a random walk. A market with lower entropy has exploitable structure. The practical question for any strategy is: *is there enough predictable information here to overcome costs?*

The self-erasing edge

Here is the beautiful, frustrating part. Suppose you discover a genuine low-entropy pattern — a predictable structure. As you and others trade it, your orders push prices toward fair value and destroy the very pattern you found. Exploiting information consumes it. This is why edges decay, why crowded trades stop working, and why no strategy works forever. Entropy tends to rise as inefficiencies are arbitraged away.

Practical consequences

Edges are perishable. Budget for decay; monitor whether a live strategy still has the structure your backtest relied on.
Costs are the real enemy. If the predictable information is small, spreads and slippage can swallow it entirely. Entropy helps you ask "is the signal even bigger than the friction?"
Diversify your sources of surprise. Different markets and horizons carry different residual predictability; relying on one shrinking edge is fragile.

The honest takeaway

Information theory reframes trading: you are not "beating the market" so much as harvesting the small amount of predictable information it contains before everyone else does — and accepting that your success slowly erases the opportunity. The humility this imposes is not pessimism; it is an accurate map of the terrain.

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