Do Stock Prices Really Follow a Random Walk? (TLDR- No)
Efficient Market Hypothesis, Gaussian Assumptions, Fractals, Complexity and Fat Tails
Imagine you're watching the stock price of a company — say, it’s ₹100 today. Tomorrow, it’s ₹102. The day after, it drops to ₹99. Is there a pattern here? Can we predict what comes next?
Welcome to one of the oldest debates in finance and economics: Can we predict markets, or are they fundamentally random?
This post takes you through some core ideas — the Efficient Market Hypothesis (EMH), random walks, Gaussian (normal) distributions, and finally, why thinkers like Benoit Mandelbrot and Edgar Peters challenge those views with the concept of fat tails.
The Efficient Market Hypothesis (EMH) – A Quick Primer
The Efficient Market Hypothesis, or EMH for short, suggests that:
All available information is already reflected in asset prices.
In simple terms, you can’t consistently “beat the market” by studying past prices or public news — because the price already “knows” it.
There are three levels of EMH:
Weak form: Past prices are already priced in.
Semi-strong form: All public info is priced in.
Strong form: Even insider info is priced in.
For this post, let’s stick to the weak form, which is where random walk and normal distributions come in.
Random Walk: Prices on a Drunken Journey
Imagine a drunk person taking steps on a sidewalk — they move forward, backward, maybe sideways, but you can't predict where they’ll go next.
That’s the idea of a random walk.
According to EMH, stock prices follow a random walk. That is, the change in price from one day to the next is completely unpredictable.
If today’s price is ₹100, tomorrow it might be ₹101 or ₹99 — the change is random, because any new information that could change the price is itself unpredictable.
What About Returns?
When we talk about how much a price changes, we usually talk about returns — how much you gain or lose over a time period.
There are two kinds of returns:
Simple Return:
Easy to understand. If a stock goes from ₹100 to ₹105, your return is 5%.
Log Return:
Slightly more technical, but preferred in financial models because:
Log returns are time-additive (you can add them across days).
They fit better with models that assume normal distributions.
In most academic models, especially those based on EMH and random walks, log returns are assumed to be normally distributed.
The Gaussian World: Calm and Predictable
A normal (Gaussian) distribution is that familiar bell-shaped curve:
Most values cluster near the average.
Extreme values (very high or low) are very rare.
It’s symmetrical.
Under this view, the daily returns of stocks are assumed to look something like this:
Most days: -1% to +1%
Some days: -3% or +3%
Very rare: -10% or +10%
It’s neat. It's mathematically elegant. But — is it real?
Enter Mandelbrot and the Problem of Fat Tails
In the 1960s, mathematician Benoit Mandelbrot took a closer look at financial markets and said:
“This is not how markets behave.”
And he was right.
In real markets:
Crashes happen more often than the normal distribution predicts.
Wild price jumps (up and down) occur more frequently.
Calm periods are often followed by storms — and vice versa.
These “fat tails” mean the distribution of returns has more extreme values than the normal bell curve suggests. So instead of this:
A normal distribution graph
we get this:
[a fat tailed distribution graph]
The tails are "fatter" — more extreme events. So the odds of a -20% drop or a +25% surge are not negligible. They’re real, and they happen.
Edgar Peters: Chaos and Complexity
Building on Mandelbrot’s work, Edgar Peters argued that markets behave more like chaotic systems — dynamic, nonlinear, and sensitive to small changes.
He used fractal geometry and chaos theory to describe market behavior. According to Peters:
Markets aren’t perfectly efficient.
They are complex systems, like weather patterns or ecosystems.
Traditional models underestimate risk and volatility.
Why This Matters
If you're building financial models using the normal distribution, you're likely underestimating how bad things can get — or how wild they can swing. That’s not just an academic issue — it’s a real-world problem that has contributed to financial crises, hedge fund failures, and risk mismanagement.
So, where does that leave us?
EMH and normal distributions give us a clean, simple framework to think about prices and risk.
But thinkers like Mandelbrot and Peters remind us that real markets are messy, complex, and far from normally distributed.
Understanding both views helps you become a more thoughtful, better-prepared investor or analyst.
The takeaway?
Don't blindly trust the bell curve. Sometimes, markets go off-script — and when they do, you want to be ready.
If you are curious and want to dig deeper, try plotting real stock returns and compare them with a normal distribution. You might just see those fat tails for yourself.