Journal of Risk

Risk.net

Scaling by the square-root-of-time rule: an empirical investigation using five market indexes

James Cameron, Chandra Gulati and Yan-Xia Lin

  • Five composite stock indexes are analyzed to determine the different behaviors of scaling across markets
  • Empirical methods of calculating scaling coefficient are used
  • Both developed and emerging markets are considered

ABSTRACT

The value of the theoretical constant used to scale daily volatility to both a five-day volatility estimate and a ten-day volatility estimate is compared with empirical estimates using a volatility modeling framework. Five composite stock indexes are analyzed to determine the different behaviors of scaling across markets. Both developed and emerging markets are considered, to provide additional detail to the comparisons. The results provided are considered in a value-at-risk application. While using the square-root-of-time rule on a weekly or ten-day basis is appropriate in certain cases, for time series with a linear dependence component the rule can drastically err from observed volatility levels. It is demonstrated that there are potential hazards when using the square-root-of-time rule for risk or compliance purposes.

To continue reading...

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here: