Treating cross-dependence in event studies: the Canadian income trust leak

Abstract

An alleged Canadian income trust announcement leak of 23 November 2005 provides a remarkable example of the sensitivity of event study analysis to the treatment of cross-sectional dependence in returns. Whereas a leak should chiefly have affected the returns on other securities, not income trusts, we find that a mechanical application of standard event study methodology yields the seemingly strong but spurious finding that income trust returns were affected. The treatment of cross-sectional dependence reverses this finding.

Acknowledgements

A preliminary version of this article was presented at the 2007 meetings of the Canadian Economics Association in Halifax, Nova Scotia. We thank session participants for their comments, especially our discussant Eric Santor. Comments by an anonymous referee are also gratefully acknowledged.

Notes

¹ For a more detailed review of income trusts than is possible here, see King (2003).

² At least in the most common situation where, as in our study, the event has its effect over a short horizon. The same may not be true for long horizons; see Mitchell and Stafford (2000).

³ This is the special case of expression (4.4.9) of Campbell et al. (1997). Their more general expression is for the case of a multiperiod event window, and is the standard expression for a multiperiod OLS forecast error covariance matrix as presented in, for example, Equation 4.11 of Theil (1971).

⁴ There is an alternative event study methodology to the one considered here, in which nonzero expected abnormal returns on the event date are parameterized as coefficients on dummy variables in an MR system. In this technique cross-sectional dependence is treated automatically through the covariance matrix of the system. For comments on the treatment of cross-dependence in this context see Bernard (1987). Although, when applicable, this method has much to recommend it, it often sees little discussion in surveys of event study methodology. This may be because, in typical applications where many asset returns are under study and so the MR system has many equations, the method can encounter two difficulties: numerical problems often afflict the computation of the relevant test statistics and asymptotic test criteria exhibit large size distortions in these circumstances. However the numerical problems can be overcome with programming that exploits the particular structure of the model (Seaks, 1990) and improved inference is available through the use of appropriate exact distributional results (Stewart, 1997). The more serious limitation of the method is that it does not apply in the often-encountered situation in which the number of assets exceeds the sample size, because in these circumstances the relevant covariance matrix is singular. Our own application is just such a case: our N = 114 income trusts well exceeds the T = 54 observations in our estimation window. For a survey that compares the two methodologies, see Binder (1998).