Realized Volatility
Realized volatility is a backward-looking measure of how much a price actually moved over some past stretch of time. Instead of guessing at future price swings, it looks at what already happened — a stock, an index, or a currency pair's actual price changes — and turns that into a single number, usually expressed as an annualized percentage so different instruments and time periods can be compared on the same scale.
It is calculated by taking a series of price returns (the percentage change from one period to the next, such as day to day or minute to minute), measuring how spread out those returns are (typically using standard deviation, a statistic that captures how far values tend to stray from their average), and scaling that spread up to a yearly figure. A stock that has been bouncing around 3% a day, up or down, will show much higher realized volatility than one drifting 0.3% a day.
The nuance that trips people up is the difference between realized volatility and implied volatility. Realized volatility is a fact about the past — it can be recalculated exactly once the price data exists. Implied volatility, by contrast, is a market's forward-looking guess, backed out of options prices, about how volatile a price will be between now and some future date. The two are related — traders compare them constantly — but they are not the same number, and a market can have low realized volatility while implied volatility sits high (or vice versa) if traders expect a shift that hasn't happened yet.
Realized volatility is also sometimes called historical volatility, and the terms are used interchangeably in most contexts, though some practitioners reserve "realized" for volatility measured from very frequent (intraday) price data and "historical" for volatility measured from daily closing prices over a longer stretch.
Day traders use realized volatility to size positions and set stop-loss distances appropriately — a stock with high realized volatility needs wider stops and smaller size to avoid getting shaken out by normal noise, and it also helps traders judge whether options are cheap or expensive relative to how the underlying has actually been moving.
Suppose a stock's daily returns over the past 20 trading days average out to a daily standard deviation of 1.5%. Annualizing that (roughly multiplying by the square root of the number of trading days in a year) gives a realized volatility of around 24%. If that same stock's options are pricing in an implied volatility of 40%, a trader might notice the market is expecting much bigger swings ahead than the stock has recently shown — perhaps because of an upcoming earnings report.
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