15.4 VOLATILITY

The volatility, σ, of a stock is a measure of our uncertainty about the returns provided by the stock. Stocks typically have a volatility between 15% and 60%.

From equation (15.7), the volatility of a stock price can be defined as the standard deviation of the return provided by the stock in 1 year when the return is expressed using continuous compounding.

When Δt is small, equation (15.1) shows that σ2 Δ t is approximately equal to the variance of the percentage change in the stock price in time Δt. This means that σ Δ t is approximately equal to the standard deviation of the percentage change in the stock price in time Δt. Suppose that σ = 0.3, or 30%, per annum and the current stock price is $50. The standard deviation of ...

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