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

See all articles by Abdul H. Rahman

Abdul H. Rahman

University of Ottawa - Telfer School of Management

Samir Saadi

Smith School of Business

Date Written: January 2, 2008

Abstract

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

Rahman, Abdul H. and Saadi, Samir, Evidence of Non-Stationary Bias in Scaling by Square Root of Time: Implications for Value-at-Risk (January 2, 2008). Journal of International Financial Markets, Institutions and Money, Vol 18, No. 3, pp. 272-289, 2008 . Available at SSRN: https://ssrn.com/abstract=1734007

Abdul H. Rahman

University of Ottawa - Telfer School of Management ( email )

136 Jean-Jacques Lussier Street
Ottawa, Ontario K1N 6N5
Canada

Samir Saadi (Contact Author)

Smith School of Business ( email )

Smith School of Business - Queen's University
143 Union Street
Kingston, Ontario K7L 3N6
Canada

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