🔎 How is volatility calculated?

**Bottom-line:** Stock volatility is calculated as the standard deviation of returns—annualized to make it comparable across time frames—so a higher number means prices swing wider and faster around their average. 📈⚡️ --- ### 1. Step-by-step, what the math really means 😊🔍 1. **Collect daily (or periodic) prices** for the stock you’re analyzing. 2. **Compute the natural log of each day’s return:** ‑ Log-return = log(Price_today / Price_yesterday). 3. **Find the mean (average) of those log-returns.** 4. **Calculate the variance:** ‑ Square each log-return’s difference from the mean, add them up, and divide by the number of observations. 5. **Take the square root of the variance—this is the standard deviation.** 6. **Annualize it:** multiply the daily standard deviation by the square root of 252 (the typical number of trading days in a year) to express volatility on an annual basis . *Why 252? Because price moves are “expected to cancel out,” so the most likely deviation grows with the square root of time, not linearly* . 7. **Optional:** convert to a percentage by multiplying by 100. --- ### 2. Two flavors you’ll often see in the market 🧐📊 | Type | What it measures | How it’s used | Key difference | |------|------------------|---------------|----------------| | **Historical Volatility (HV)** | How much the stock has moved in the past | Risk assessment, position sizing | Looks back at realized price swings | | **Implied Volatility (IV)** | What the market *expects* future swings to be, derived from option prices | Options pricing, trading strategies | Forward-looking, baked into option premiums | --- ### 3. Practical takeaways for your tech-heavy portfolio 💡🛠️ • A stock like Tesla (TSLA) with wide daily moves will naturally show higher historical volatility than a steady dividend payer such as Chubb (CB). • When you’re comparing two names, ensure both volatilities are annualized; otherwise the numbers aren’t apples-to-apples. • Remember, volatility isn’t the same as risk—big swings can be up *or* down, yet a diversified portfolio can smooth out the ride over time . --- Ready to plug in some ticker symbols and see how Apple, Amazon, and friends stack up against each other? 🤔💬