Eine empirische Analyse der Skalierung von Value-at-Risk Schaetzungen

TL;DR

This paper empirically examines the effectiveness of the square root of time rule for scaling Value-at-Risk estimates over longer periods, highlighting its limitations and implications for risk management and regulation.

Contribution

It provides an empirical analysis of VaR scaling methods, questioning the regulatory reliance on the square root of time rule and exploring its accuracy and consequences.

Findings

Scaling can provide accurate VaR estimates in some cases

The square root of time rule may lead to significant risk underestimation

Regulatory frameworks should reconsider the use of the square root of time rule

Abstract

In practice, the value-at-risk (VaR) for a longer holding period is often scaled using the 'square root of time rule'. The VaR is determined for a shorter holding period and then scaled up according to the desired holding period. For example, the Basel rules allow banks to scale up the 1-day VaR by the square root of ten to determine the 10-day VaR. It can be seen from the results of this thesis that scaling can also provide good and accurate estimates of VaR. However, it is probably much more important to consider that, depending on the methods or data set involved, there may also be significant consequences for risk provisioning. Particularly, since scaling does not always avoid the occurrence of losses that exceed the VaR estimate on a frequent basis over a period of time. Overall, the permission to use the square root of time rule in the regulatory framework should be reconsidered.