Evidence of Non-Stationary Bias in Scaling by Square Root of Time: Implications for Value-at-Risk
Journal of International Financial Markets, Institutions and Money, Vol 18, No. 3, pp. 272-289, 2008
Posted: 3 Jan 2011
Date Written: January 2, 2008
In this paper, we show that scaled conditional volatilities obtained by the square root formula applied to i.i.d residuals from a sample of Canadian stock market data for various time horizons and error distributions, typically underestimate the true conditional volatility; consistently have a higher standard deviation and exhibit non-stationary kurtosis. Furthermore, the bias produced by volatility scaling is non-stationary in mean and standard deviation and its magnitude is likely influenced by monetary policy regime shifts. Moreover, while VaR is risk-coherence for elliptical distributions, this bias remains even for this class of distributions.
Keywords: Square root of time formula; Value-at-Risk
JEL Classification: C30; G30
Suggested Citation: Suggested Citation