🔎 How is volatility calculated?

**Bottom-line:** Volatility is simply the statistical “spread” of an asset’s price movements—most often measured as the standard deviation of returns and then annualized. 📈✨ --- ### 1. Historical Volatility (HV) – “What actually happened” 🕰️🔍 • Collect daily (or periodic) prices for the asset. • Compute the natural logarithm of each day’s return: `ln(Price_today / Price_yesterday)`. • Find the standard deviation of those log-returns. • Multiply that standard deviation by the square root of the number of trading days in a year (typically 252) to annualize the figure . • Result: an annualized percentage that tells you how “far” prices typically move from their average each year. 📊 ### 2. Implied Volatility (IV) – “What the market expects next” 📅🔮 • Start with the current price of an option on the asset. • Plug every variable of the Black-Scholes formula—except volatility—into the model. • Back-solve for the volatility number that makes the model’s output match the real-world option price . • The result is a forward-looking estimate of how much the underlying asset is expected to swing over the option’s life. 🎯 ### 3. Portfolio Volatility – “Your whole basket” 🛒🧮 • For a portfolio with multiple assets, you need: 1. The weight of each asset in the portfolio. 2. The historical volatility of each individual asset. 3. The correlation between every pair of assets. • Use matrix algebra or the expanded variance formula to combine these inputs; the result is the portfolio’s overall volatility . --- #### Quick reference cheat-sheet 📝 | Step | Input Data | Formula / Method | Output | |------|------------|------------------|--------| | 1 | Historical prices | Standard deviation of log-returns × √252 | Annualized Historical Volatility | | 2 | Option price | Black-Scholes inverse for volatility | Implied Volatility | | 3 | Portfolio weights & asset volatilities | Variance-covariance matrix | Portfolio Volatility | *(Table included to show the distinct calculation paths that a visualization alone can’t capture.)* --- Ready to plug in your favorite tech names—say, NVDA or AAPL—and see how their volatilities stack up? 😄💡