On time-scaling of risk and the square-root-of-time rule

Many financial applications, such as risk analysis and derivatives pricing, depend on time scaling of risk. A common method for this purpose, though only correct when returns are iid normal, is the square root of time rule where an estimated quantile of a return distribution is scaled to a lower frequency by the square-root of the time horizon. The aim of this paper is to examine time scaling of risk when returns follow a jump diffusion process. It is argued that a jump diffusion is well-suited for the modeling of systemic risk, which is the raison d'etre of the Basel capital adequacy proposals. We demonstrate that the square root of time rule leads to a systematic underestimation of risk, whereby the degree of underestimation worsens with the time horizon,the jump intensity and the confidence level. As a result,even if the square root of time rule has widespread applications in the Basel Accords, it fails to address the objective of the Accords.(This abstract was borrowed from another version of this item.)