Volatility

### What it actually measures Volatility is dispersion, not direction. Formally it is the degree of variation in a price series over time, usually measured as the standard deviation of returns. It tells you how far price is likely to travel, never which way. A pair can be violently volatile and finish the week exactly where it started. Traders who read "moving a lot" as "going somewhere" pay for that confusion. There are two kinds, and they answer different questions. **Realised (historical) volatility** looks backwards at what price actually did, which is what ATR and standard deviation give you. **Implied volatility** looks forwards, extracted from what people are currently paying for options. The best known implied gauge is Cboe's VIX, which Cboe itself describes as a leading measure of market expectations of near-term volatility conveyed by S&P 500 index option prices. One is a record. The other is a forecast with real money behind it. ### Why it clusters The clustering in the definition above is not folklore, it is one of the oldest documented facts in finance. Benoit Mandelbrot wrote in 1963 (*The Variation of Certain Speculative Prices*) that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes." It was formalised later by Robert Engle's ARCH model (1982) and Tim Bollerslev's GARCH (1986), which drop the assumption that volatility is constant and let it depend on its own recent history. The practical translation is blunt. **The regime you are in right now is the best available guess for the regime you will be in shortly.** Quiet begets quiet, until it doesn't, and the handover is abrupt rather than gradual. So size for the market actually in front of you, not for the average of the last year and not for the one that burned you in March. ### The maths beginners get wrong Volatility scales with the square root of time, not linearly. Daily volatility is annualised by multiplying by the square root of roughly 252 trading days. Read that backwards: holding a position four times longer does not expose you to four times the expected range, it exposes you to about double. Beginners extrapolate in a straight line and end up wrong in both directions, over-fearing the short hold and under-respecting the long one. ### Why it decides your size Risk in money is stop distance multiplied by position size. If one instrument's typical range is four times another's, an equivalent stop has to sit four times wider, so to keep the same money at risk your position must be roughly a quarter the size. Same 1% on paper, same 1% in reality. Skip that adjustment and the identical-looking trade quietly becomes four times the damage. One last link worth carrying: volatility and liquidity are usually the same event seen from opposite sides. On 3 January 2019 the yen appreciated about 3% against the US dollar in roughly 30 seconds with no material news, and the Reserve Bank of Australia records bid-ask spreads blowing out from around 2 pips to 100 to 300 pips in the process. The volatility spike *was* the liquidity hole.