A book that I'm reading (Paul Wilmott, Derivatives) states the following:

The standard deviation of the stock price over this time horizon is $$ \sigma S = \sqrt(1/52) $$

where, the time horizon is one week.

Why is this the std. dev? Does this mean that the general formula for the standard deviation of a stock price over time horizon $t$ is : $$ \sigma S \sqrt(t)$$

I'm assuming that the $\sqrt(t)$ is for converting annual returns to weekly returns?



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