$$\sigma = variance(R_{a}) , std=\sqrt{\sigma}$$ It should follow that the variance is not a linear
function of the number of observations. To determine
possible variance over multiple periods, it wouldn't make
sense to multiply the single-period variance by the total
number of periods: this could quickly lead to an absurd
result where total variance (or risk) was greater than
100 demonstrate a decreasing period-to-period increase as the
number of periods increases. Put another way, the
increase in incremental variance per additional period
needs to decrease with some relationship to the number of
periods. The standard accepted practice for doing this is
to apply the inverse square law. To normalize standard
deviation across multiple periods, we multiply by the
square root of the number of periods we wish to calculate
over. To annualize standard deviation, we multiply by the
square root of the number of periods per year.
$$\sqrt{\sigma}\cdot\sqrt{periods}$$
Note that any multiperiod or annualized number should be
viewed with suspicion if the number of observations is
small.