Historical Volatility: Volatility Clusters

Annualize how spread out the daily moves are

historical volatility takes the standard deviation of the last N days' returns and multiplies by √252 to get annualized volatility. It's a percentage, so you can compare volatility directly across different prices and instruments.

Volatility clusters

Big swings tend to follow big swings, and calm tends to follow calm: this is volatility clustering. But calm doesn't last forever; use the percentile rank to see where today sits in its own history.

Size, but no direction

Low volatility only means wilder moves are becoming more likely; it doesn't say whether price will rise or fall. It's better for adjusting stop distance and position size than for guessing direction.

Key takeaways

• Historical volatility = the standard deviation of the last N daily returns × √252, expressed as an annualized percentage.
• Volatility scales with the square root of time: 1% daily volatility is about 15.9% annualized, not 252%.
• Volatility clusters: high volatility tends to come in stretches, low volatility lasts a while too, but eventually they switch.
• Volatility at a historical low only means bigger swings have become more likely, not which way price will go. It's better used to adjust stops and position size.

Try it yourself

You can do these exercises in this lesson's interactive simulation:

1. Click "Example: 1% daily volatility": roughly what's the annualized volatility? Why isn't it 1% × 252?
2. Click "Jump to the quietest moment": what are HV and the "Historical percentile" right now? Keep playing: what's the "Max move over the next 20 bars," and in which direction?
3. Move the cursor to the crash around bar 65: what's HV? Is the historical percentile high or low?
4. Pull the calculation window from 20 to 60: does the HV curve get smoother or jumpier? What happens to the amber "low volatility" stretches?

Quiz and explanations

1. A stock's daily volatility is about 2%. Roughly what's its annualized volatility?

Answer: About 32%.2% × √252 ≈ 2% × 15.87 ≈ 31.7%.

2. A stock's historical volatility drops to its lowest level of the past two years. What's the most sensible conclusion?

Answer: Volatility may expand, but the direction is unknown.Low volatility signals that the size of moves may grow, not their direction.

3. Stock A trades at $10 and stock B at $500. To compare which is more volatile, what's better?

Answer: Compare annualized historical volatility (as a percentage).Percentages remove the effect of price level. ATR is in price units, so it can't be compared directly across instruments.

Terms in this lesson

• annualized volatility (Annualized Volatility): Daily swings scaled up to a yearly figure; volatility grows with the square root of time, so daily volatility × √252 ≈ annual volatility (about 252 trading days a year).
• historical volatility (Historical Volatility): How violently price has moved, measured by the standard deviation of past returns and usually shown as an annual percentage; it describes the past and doesn't predict direction.
• percentile rank (Percentile Rank): Where the current reading sits within its own history; the 10th percentile means only about 10% of past readings were at or below it.
• standard deviation (Standard Deviation): A statistic for how far data spreads from its average; the bigger the swings, the bigger the standard deviation.
• volatility clustering (Volatility Clustering): Big moves tend to follow big moves and small moves follow small ones; volatility cycles between high and low but says nothing about direction.