Volatility & Max Drawdown: The Two Numbers Behind Every Ratio

We've covered three ratios so far — Sharpe, Sortino, Calmar — and if you've noticed the same two ingredients keep showing up in slightly different forms, you're not imagining it. Every one of them is really just "return, divided by some version of risk." The differences between them all come down to which risk number sits on the bottom of the fraction.

So before we go further into the series, it's worth stopping and explaining those two risk numbers properly on their own: volatility and max drawdown. Once these actually make sense, every ratio we've covered — and the ones still to come — gets a lot easier to read.

Volatility: how much does it bounce around?

Volatility measures how far your portfolio's returns swing away from their own average, over some period of time. A portfolio that returns roughly 1% every single month has very low volatility. A portfolio that returns +8% one month and -6% the next, even if it averages out to the same overall number, has much higher volatility.

Technically, volatility is the standard deviation of returns — a standard statistical measure of spread. You don't need to know how to calculate a standard deviation by hand to use it; you just need to know what it's telling you: the bigger the number, the bumpier the ride.

For the technically curious

$$\sigma_p = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(R_i - \bar{R})^2}$$

Where:

• Rᵢ — the portfolio's return in period i (e.g. one specific month)
• R̄ — the average return across all the periods
• n — the number of periods measured

In words: take every period's return, work out how far it sits from the average, square that distance (so negative and positive swings both count, and bigger swings count disproportionately more), average those squared distances, then take the square root to bring the units back to something readable.

This is the σₚ (sigma-p) you've seen sitting on the bottom of Sharpe's formula — it's exactly this calculation.

Max drawdown: how bad did it get, at the worst point?

Volatility measures the typical bounciness of a portfolio. Max drawdown measures something different and much blunter: the single largest fall from a peak to the lowest point that followed it, before a new peak was reached.

This isn't an average of bad periods — it's the worst single continuous decline in the portfolio's whole history. If your portfolio peaked at $500,000, then fell all the way to $430,000 before eventually recovering and climbing past $500,000 again, your max drawdown for that stretch is -14% ($70,000 down from the peak) — regardless of how choppy or smooth the fall actually was along the way.

For the technically curious

$$Max\ Drawdown = \min_{t}\left(\frac{V_t - V_{peak}}{V_{peak}}\right)$$

Where:

• Vₜ — the portfolio's value at any given point in time t
• V_peak — the highest value the portfolio had reached up to that point

You calculate this by tracking the running peak value as time moves forward, and at every point measuring how far the current value has fallen below that running peak. The single worst of those measurements, across the whole history, is your max drawdown.

Why both numbers matter, and why they're not the same thing

Here's the distinction that trips people up: a portfolio can have low volatility and still have a large max drawdown. Imagine a portfolio that sits almost perfectly flat for two years, then has one sharp 25% fall over a single bad month, then recovers and stays flat again. Averaged across the whole history, that portfolio might have quite modest overall volatility — most months looked completely calm. But its max drawdown is a brutal -25%, because that one month happened.

The reverse is also possible: a portfolio that constantly wobbles up and down by 3-4% every single month, never once has a fall bigger than -8% from any peak, could show high volatility but a comparatively mild max drawdown.

This is exactly why Sharpe (which uses volatility) and Calmar (which uses max drawdown) can tell noticeably different stories about the same portfolio. Neither one is "more correct" — they're answering different questions. Volatility asks "how bumpy is the typical ride." Max drawdown asks "how bad was the single worst moment."

What to actually do with these two numbers

You don't need to memorise the maths. What's worth carrying forward is this:

• High volatility, low max drawdown — a choppy portfolio, but one that's never fallen too far from a peak. Uncomfortable day to day, less dangerous in a real downturn.
• Low volatility, high max drawdown — a calm-looking portfolio hiding one genuinely painful stretch somewhere in its history. Comfortable most of the time, but capable of a nasty surprise.
• Both high — exactly what it sounds like. Buckle up.
• Both low — the calmest possible ride, usually at the cost of lower long-run returns.

Neither number tells you whether a portfolio is "good" — that always depends on the return you got for carrying that risk, which is exactly what Sharpe, Sortino, and Calmar are each built to answer, just using a different one of these two ingredients.

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This is part 4 of a series on the risk numbers behind your portfolio. Next up: Jensen's Alpha — the number that tries to answer whether you actually beat the market, or just took on more risk to keep up with it.