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Evidence of non-stationary bias in scaling by square root of time: Implications for Value-at-Risk

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  • Saadi, Samir
  • Rahman, Abdul

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.

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  • Saadi, Samir & Rahman, Abdul, 2008. "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, Elsevier, vol. 18(3), pages 272-289, July.
    • Handle: RePEc:eee:intfin:v:18:y:2008:i:3:p:272-289
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