Asset returns conforming to a Gaussian random walk are characterised by the temporal independence of the moments of the distribution. Employing currency returns, this note demonstrates the conditions that are necessary for risk to be estimated in this manner.

When asset returns are normally distributed the risk of an asset over a long return interval may be estimated by scaling the risk from shorter return intervals. While it is well known that asset returns are not normally distributed a key empirical question concerns the effect that scaling the...