Volatility – Meaning & Measurement
Volatility is the most important variable in financial derivatives and risk management. It represents the "speed" and "magnitude" of price changes.
What is Volatility?
Volatility measures the dispersion of returns for a given security or market index.
- High Volatility: Prices swing wildly (e.g., Bitcoin, Tesla).
- Low Volatility: Prices are stable (e.g., Government Bonds, Utility stocks).
Analogy: If Return is the "Speed" of a car, Volatility is the "Bumpiness" of the road. You can have high speed on a smooth road (High Return, Low Volatility) or low speed on a bumpy road (Low Return, High Volatility).
Measuring Volatility: Standard Deviation (Sigma)
The most common measure of volatility is the Standard Deviation of returns.
Steps to Calculate:
- Calculate returns (Rt) for the period.
- Calculate the Mean (Average) Return (R_avg).
- Find the deviation of each return from the mean (Rt - R_avg).
- Square the deviations (to remove negative signs).
- Average the squared deviations (this is Variance).
- Take the square root of Variance to get Standard Deviation.
Variance = Sigma(Rt - Mean)^2 / (N - 1)
Volatility (Sigma) = Sqrt(Variance)
Annualizing Volatility
Volatility is usually quoted in annual terms. If you calculate daily volatility (Sigma_daily), you must scale it up.
- Rule: Annual Volatility = Daily Volatility * SquareRoot(252)
- (We use 252 because there are roughly 252 trading days in a year).
Example: If Daily Volatility of Nifty 50 is 1%, then: Annual Volatility = 1% * 15.87 = 15.87%.
Historical vs Implied Volatility
Historical Volatility (HV)
- Source: Past prices.
- Meaning: How risky the asset WAS.
- Usage: Risk reporting, Backtesting.
- Nature: Backward-looking.
Implied Volatility (IV)
- Source: Option prices (Black-Scholes).
- Meaning: How risky the market EXPECTS it to be.
- Usage: Option trading, Sentiment analysis.
- Nature: Forward-looking.
Test Your Knowledge
Question 1 of 5
1. Volatility primarily measures: