Volatility example Let's go through a simple calculation of the expected price difference for a stock. Suppose that in a day the stock price fluctuations up and down by 3%. What's the expected fluctuation in the stock price after 200 days? Let's measure time in units of a day. Then with $t=$, the equation for the random walk eq, 2.16 becomes $\langle (p(1)-p(0))^2 \rangle = \nu^2 \times 1$ But we've said the fluctuation in the price in one day is 3% which equals $\sqrt{\langle (p(1)-p(0))^2 \rangle}$. This means that $\nu = 3\%$. So after 200 days, $t=200$ so that $$\sqrt{\langle (p(200)-p(0))^2 \rangle} = \nu \sqrt{200} = .03 * \sqrt(200) = .42$$ (2.17) This means that after 200 days, the stock price will fluctuate up and down from its initial value by more than 40%. People often attempt to describe volatility using a quantity known as $\beta$, or simply "beta". The calculation of it involves an application of linear regression so it's neat example of applying what we've previously learned.