A Drunk Walk Through Paris - the random walk and the efficient market

The valley’s water market, where the price at the stall is set by the queues of bids and asks. This lesson asks the question the board leaves open: can anyone tell which way that price moves tomorrow?

Education, not financial advice.

Before you start. From Under a Buttonwood Tree - the exchange, the order book and the spread you need the stall: buyers queue with bids, sellers with asks, and the price sits in the gap between them, moving as the queues change. From The Maths Floor, Part 2: Probability, Softmax and Temperature you need only that a probability is a share of the possible outcomes, so a fair coin lands heads a half of the time.

The idea in 30 seconds

In 1900 Louis Bachelier assumed a speculator’s expected gain on the next move is zero, and from that alone worked out how prices wander.
A random walk is a path of steps each decided by chance, with no memory of the last; a walk can look like a trend and not be one.
A random walk’s spread grows with the square root of time: four times as long, only twice as far.
An efficient market is one where prices already reflect what is known, so only surprises move them, and surprises are as likely good as bad.
Fama’s three strengths ask what is already in the price: past prices (weak), all public news (semi-strong), even secrets (strong).
Efficiency does not say prices are right or that nobody wins. It says nobody wins predictably on what everyone already knows.

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