Risk in often calculated as the variation in returns both above and below the average. This can cause objections as investors are quite happy with higher returns, so why would a higher return somehow add to risk? The statistical assumption is that the return series is part of an (unseen) distribution and every observation contributes to our understanding of this distribution. A high return is just as significant a piece of the distribution as a low return. The standard deviation will then convert the observed return series into a full distribution.