🔎 How is volatility calculated?

**Bottom-line:** Volatility is calculated as the annualized standard deviation of price or return movements—historical volatility uses past data, while implied volatility is “backed out” from option prices. 📊✨ --- ### 1. Historical Volatility (HV) – “What actually happened” 📅🔍 • Gather daily prices over a look-back window (e.g., 20, 60, or 252 trading days). • Compute the natural log of each day’s price ratio to get log returns: **ln(Pt / Pt-1)**. • Take the standard deviation of those log returns, then multiply by the square root of the number of trading days in a year (usually 252) to **annualize** it. • Result: a percentage figure that tells you how much the price typically swings in a year. 📈 --- ### 2. Implied Volatility (IV) – “What the market expects” 🕵️‍♂️💡 • Plug all known option variables (spot price, strike, time to maturity, option price) into the Black-Scholes formula. • Solve for the volatility term that makes the model price match the market price; that solution is **implied volatility**. • IV reflects the trader’s consensus on future price swings and is “forward-looking,” unlike historical data. 🚀 --- ### 3. Quick & Dirty Alternative – Realized Volatility 🏃‍♀️⚡ • Instead of daily closes, use intraday high-frequency data (e.g., 5-minute bars). • Sum the squared intraday returns, then take the square root—this is **realized volatility**. • It’s more precise than a simple standard deviation but still annualized by convention. 📊 --- ### 4. Why the “annualize”? 🧮🌍 • A one-day standard deviation is tiny; annualizing lets you compare assets with very different trading frequencies (e.g., a penny stock vs. an index). • The factor **√252** converts daily data to an annual scale, assuming 252 trading days per year. 📅 --- ### 5. Practical Tips for You 🛠️😊 1. Use **HV** when you want to size risk based on past experience. 2. Use **IV** when you trade options or want to gauge market sentiment. 3. For intraday traders, **realized volatility** (optionally volume-weighted) can sharpen your edge. 4. Remember: volatility reverts toward its long-term mean over time, so a spike today doesn’t guarantee another next week. 🔄 --- Ready to try calculating the volatility of your favorite tech stock—or perhaps compare its implied and historical readings before the next earnings season? 😄📈