Historical Volatility (HV)

Historical volatility is the annualized standard deviation of logarithmic returns over a specified period:

Step 1: Calculate the natural log return for each day: ln(Today's Close / Yesterday's Close)

Step 2: Calculate the standard deviation of these log returns over your chosen period (20 days is standard for short-term, 60 days for intermediate, 252 days for annual)

Step 3: Annualize by multiplying by sqrt(252): HV = Daily Std Dev x sqrt(252)

Example: If a stock's daily returns have a standard deviation of 0.015 (1.5%), then HV = 0.015 x 15.87 = 0.238, or 23.8% annualized.

Common lookback periods:

• 10-day HV: Very responsive to recent moves. Spikes during earnings and news events. Useful for short-term options pricing.
• 20-day HV: The standard short-term measure. Balances responsiveness with stability. Most commonly compared against implied volatility.
• 60-day HV: Intermediate measure. Smooths out short-term spikes. Better for strategy-level position sizing decisions.
• 252-day HV: Full-year measure. Most stable but slowest to react. Used for long-term portfolio risk assessment.

Why log returns? Logarithmic returns are preferred over simple percentage returns because they are additive over time and symmetric (a +10% move and -10% move have equal magnitude in log terms). This makes the standard deviation calculation more mathematically correct.

The relationship between HV and IV is one of the most powerful signals in options trading:

Historical volatility (HV) measures what actually happened — how much the stock moved in the past. It is a backward-looking, observable fact.

Implied volatility (IV) measures what the market expects to happen — how much the stock might move in the future. It is forward-looking and derived from options prices.

When IV > HV (the volatility risk premium): Options are priced as if the stock will move more than it historically does. This is the normal state — IV typically exceeds HV by 2-5 points because options buyers pay a premium for protection. Premium sellers (covered calls, iron condors, credit spreads) profit from this premium.

When IV >> HV (IV much higher than HV): Options are expensive relative to historical norms. This often occurs before earnings, FDA decisions, or other anticipated events. Premium-selling strategies (iron condors, strangles) have a statistical edge. The IV/HV ratio above 1.3 is a strong sell-premium signal.

When IV < HV (rare): Options are cheap relative to actual movement. This is unusual and signals potential opportunity for options buyers — long straddles and strangles may be attractively priced. It also sometimes occurs after a volatility spike when HV remains elevated but IV has already collapsed.

Trading the spread: Volatility traders systematically sell options when IV/HV > 1.3 and buy when IV/HV < 0.8. Over time, this captures the volatility risk premium — one of the most persistent edges in options markets.

Volatility-normalized position sizing: The most important application of HV for non-options traders. Allocate equal dollar risk per position by adjusting size based on each stock's HV. If Stock A has 20% HV and Stock B has 40% HV, buy twice as many shares of Stock A to equalize the dollar risk. This prevents volatile stocks from dominating your P&L.

ATR vs HV for sizing: ATR (Average True Range) measures daily dollar range; HV measures return volatility. Both work for position sizing. ATR is simpler and more intuitive for setting dollar-based stops. HV is better for normalizing across different-priced stocks and for comparing with options IV.

Volatility regime identification: Track the 20-day HV of the S&P 500 (SPY) as a market regime indicator:

• HV below 10%: Low volatility regime. Trend-following strategies work well. Use wider stops and larger positions.
• HV 10-20%: Normal volatility. Standard risk parameters apply.
• HV 20-35%: High volatility. Reduce position sizes, tighten stops, favor mean-reversion.
• HV above 35%: Crisis volatility. Maximum risk reduction, cash preservation mode.

Volatility mean reversion: HV tends to mean-revert over time. After a period of extremely low volatility, an explosion higher is likely (and vice versa). Bollinger Band width (which uses standard deviation, the basis of HV) captures this squeeze-and-expansion cycle visually.