Estimating Volatility from Historical Data

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, ui = ln(Si / Si-1)
s = √[(Σni=1 u2i) / (n-1) – (Σni=1 ui)2 / n(n – 1)]

Link to Example: Volatility Calculation

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