Historical Volatility: Calculation, Annualization, and Risk Interpretation
Summary
The document explains historical volatility as the dispersion of asset returns and distinguishes it from implied volatility, which is inferred from option prices. It describes calculating the standard deviation of daily returns and annualizing it by multiplying by the square root of the assumed number of trading days in a year. A short sample of daily stock returns illustrates the calculation and reports both daily and annualized volatility.
It also gives low, medium, and high volatility examples and discusses how an investor’s horizon, market conditions, and financial position can affect tolerance for price swings. The note frames volatility as an input to risk management, portfolio allocation, and derivatives pricing. Its examples are illustrative rather than empirical evidence, and the return ranges are simplified comparisons rather than forecasts. The annualization assumes a fixed trading calendar, while historical volatility summarizes past variation and does not by itself describe future risk or capture all forms of market risk.
Key ideas
- Historical volatility is commonly measured as the standard deviation of asset returns.
- Daily volatility can be annualized by multiplying it by the square root of the assumed annual trading-day count.
- Historical volatility uses past price changes, while implied volatility is derived from option pricing.
- Volatility can inform risk management, portfolio allocation, and derivatives pricing.
- Risk tolerance depends in part on investment horizon, market conditions, and personal finances.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.