## Estimating Volatility from Historical Data

01/16/2011 4:21 pm Leave a comment

Volatility (θ) is the standard deviation of the return provided by the stock in 1 year using continuous compounding. Stocks typically have a volatility between 15% and 60%.

The standard deviation of the % change in stock price in time T is:

θ√T

The standard deviation increases by the square root of time (T) i.e. 4 weeks is about 2* the standard deviation of 1 week. The equation to estimate volatility is the following:

where, u_{i} = ln(S_{i} / S_{i-1})

s = √[(Σ^{n}_{i=1} u^{2}_{i}) / (n-1) – (Σ^{n}_{i=1} u_{i})^{2} / n(n – 1)]

**Link to Example: Volatility Calculation**