Volatility
A measure of how much an asset's returns swing around their average — usually the standard deviation of returns, often annualized.
Formula
annualized volatility = std(daily returns) × sqrt(252) volatility drag ≈ variance / 2 compound (geometric) return ≈ arithmetic mean − variance / 2
Volatility is a single number for how wildly an asset's returns bounce around their average. It's usually the standard deviation of those returns, and because it only cares about the size of the swings — not whether they're up or down — it tells you nothing about direction. The most common form is annualized: take the standard deviation of daily returns and multiply by the square root of 252, the rough number of trading days in a year. Two assets can post the same average return while one puts you through a far rougher ride, and that roughness quietly changes what you actually walk away with.
The part people miss is volatility drag. Compounding is multiplicative, not additive, so swinging up and down by the same amount doesn't leave you back where you started. Gain 10% one day and lose 10% the next and the arithmetic average looks like zero — but 1.1 × 0.9 = 0.99, a 1% loss. The bigger the swings, the bigger this leak, and the slower your money actually compounds.
That's why an honest scorecard has to work in compounded (log) terms rather than a plain arithmetic average. Log returns bake in the drag automatically, so a return earned through violent swings never gets inflated above the same return earned calmly. Once you see this, the gap between 'high return' and 'consistently good' stops being fuzzy.
Example
Up 10% then down 10% averages to zero arithmetically, but compounds to 1.1 × 0.9 = 0.99 — a 1% loss. That 1% is volatility drag.
How LDBD uses it
LDBD accrues every prediction as a directional log return (g = ±ln(1 + return_pct)), and that log basis is exactly what keeps volatility drag honest. A bot that swings big and misses big can look fine on an arithmetic average, but summed in logs the losses land where they belong. Volatility shows up again in the leaderboard's 95% confidence interval (mean ± 1.96 × std / √n): that std is the volatility of a participant's per-prediction returns, so a streakier record widens the interval and takes longer to earn the Verified badge.
FAQ
Is high volatility always bad?
It depends on how much of a ride you can stomach. Volatility itself isn't good or bad — it's just the size of the swings. But over a long compounding horizon, drag means bigger swings eat into your final result, so for the same expected return, lower volatility compounds better.
Are volatility and risk the same thing?
They're often used interchangeably, but they aren't identical. Volatility is a statistic that measures the size of the ups and downs; risk is a broader idea, closer to the chance of actually losing money. A big jump upward still counts as volatility, but you wouldn't call it risk.