The only statistics you actually need

You don't need a stats degree to trade systematically — you need four ideas. Returns, the average, the spread, and how two things move together. We'll build each one with a picture you can actually see.

Returns, not prices

A stock goes from $100 to $105. We almost never feed that price into a strategy — we use the return: the percent change, here +5%. Why? Because a $5 move means something completely different on a $100 stock than on a $1,000 stock, but +5% means the same thing everywhere. Returns put every asset on one common scale.

There are two flavours you'll see:

• Simple return — (new − old) / old. The everyday "it went up 5%." Intuitive, and what most people mean.
• Log return — ln(new / old). A mathematical convenience: log returns add up across time, which makes a lot of formulas cleaner. For small moves the two are nearly identical.

As a beginner, think in simple returns. Just know that when you see log returns in a library or a paper, it's the same idea wearing a more convenient coat.

The average and the spread

Collect a strategy's daily returns and two numbers describe almost everything that matters.

The mean is the plain average — your typical daily gain or loss. The standard deviation, which traders call volatility, measures how far returns scatter around that average. A calm strategy clusters tightly near its mean; a wild one flings returns far in both directions. Same average, very different ride — and, as Module 2 will show, very different quality.

The normal distribution — and its lie

That bell shape is the normal distribution. It's a wonderfully simple model: about 68% of returns fall within one σ of the mean, about 95% within two. If you know the mean and σ, you know roughly how often to expect a given move.

It's also where the bell curve quietly lies. Real market returns have fat tails: crashes and melt-ups — the extreme moves way out at the edges — happen far more often than a perfect bell predicts. A "once in a thousand years" day shows up every few years.

Why this matters now. Every risk number that assumes a tidy bell curve understates the danger. Keep this in your back pocket: the worst day is usually worse than the model says. We'll put it to work in Module 2 and especially in the risk module.

Correlation: do two things move together?

Correlation is one number, from +1 to −1, for how two assets move together:

• +1 — lockstep. When one rises, the other rises.
• 0 — unrelated. One tells you nothing about the other.
• −1 — opposite. When one rises, the other falls.

Correlation is the engine behind diversification (holding things that don't all sink together) and behind pairs trading (betting two related assets snap back into line). But it carries two traps worth learning early:

• Correlation isn't causation. Two things can move together by coincidence, especially over short windows.
• Correlation isn't cointegration. Two assets can be highly correlated and still drift apart forever — which is exactly why most "they move together, so I'll trade the gap" strategies quietly fail. We took that idea apart in a real teardown.

Where to go next

You can now read a strategy's returns. Module 2 turns these raw ingredients into the scoreboard — the handful of numbers that say whether a strategy is actually good: CAGR, the Sharpe ratio, drawdown, and expectancy.

See volatility and correlation at work