Volatility

Volatility is the finance word for “how much this thing tends to wiggle.” More precisely: it’s the standard deviation of returns.

People argue about whether volatility is “risk.” It’s not the whole story — a slow grind down can be less volatile than a choppy uptrend — but as a first-order proxy, it’s useful. If two assets have similar expected returns, the one with lower volatility is usually easier to hold and easier to size.

The key thing to remember is that volatility is not stable. Markets have calm regimes and storm regimes. So treat any single volatility number as an average over a window, not a law of nature.

The formula

We start with daily simple returns:

$$r_t = \frac{P_t}{P_{t-1}} - 1$$

Daily volatility is the standard deviation of $r_t$. Annualized volatility scales by the square root of the annualization factor:

$$\sigma_{annual} = \sigma(r_t) \times \sqrt{N}$$

How we calculate volatility at Gale Finance

1. Returns: daily simple returns from close‑to‑close.

2. No forward-filling: we use the observed closes. If an asset doesn’t trade on weekends/holidays, those dates simply aren’t in the series.

3. Annualization uses the asset’s calendar:

• Crypto/stablecoins: $N = 365$ (weekends are real trading days and are often volatile).
• Equities/ETFs/metals: $N \approx 252$ trading days (or we infer the effective frequency from the data).

This choice matters. If you force a 24×7 market onto a 252-day calendar, you’re smoothing away weekend moves and understating realized risk.

4. Percent units: we report annualized volatility in percent terms.

“Typical day” moves

On compare pages we sometimes translate annualized volatility into a “typical daily swing” by dividing by $\sqrt{N}$. It’s a helpful intuition pump, but it’s not a forecast — fat tails and volatility clustering mean “typical” days aren’t the whole distribution.

If you want a better feel for tail behavior, look at Value at Risk (VaR), Expected Shortfall, and fat tails.