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Abstract
Real estate risk management tools are traditionally based on mean‐variance analysis. The non‐normal behaviour of financial asset returns including real estate securities is a violation of one of the fundamental assumptions of mean‐variance analysis. In this paper, the pitfalls of using the correlation coefficient as a measure of dependency are discussed first. The use of copulas as an alternative to modelling the dependence structure and more generally as a risk‐management tool is then proposed. Copula‐based value‐at‐risk computations are also carried out. The results confirm that the linear correlation measure is unable to capture the dependence between the US and the UK publicly listed real estate securities. The limitations of the joint multivariate normal distribution are also shown.
Acknowledgements
I am grateful to Juri Pill, David Barker, Jim Clayton, Joseph Pagliari and the participants of the ERES 2007 conference for valuable comments and help provided.
Notes
1. Mills (Citation1927) was perhaps the first to report that economic variables are non‐normal.
2. Bennett and Kennedy, Citation2004; Cherubini et al. Citation2004; Hull and White (Citation2006); Li, Citation2000.
3. For instance, Hull (Citation2006)
4. See Embrechts et al. (Citation2002) and the references therein.
5. Bartram et al. (Citation2004).
6. Coleman and Mansour (Citation2005) suggest the use of a non‐central T distribution in order to model the NCREIF returns.
7. For a more detailed discussion of copulas, the reader can consult Embrechts et al.'s (Citation2005) excellent textbook. The term copula is of Latin origin meaning ‘link’.
8. Although the term correlation and dependence are often used interchangeably, the correlation measure is only one of the various ways the dependence structure can be characterized.
9. The normal distribution is part of the elliptical family. For a discussion on the properties of the elliptical distribution, see Section 3.3 of Embrechts et al. (Citation2005).
10. If Φ(X) and denote the standard normal distribution function and an arbitrary transformation respectively, then Kendall and Stuart (Citation1979) show that
.
11. It also illustrates the well known statistical result that a low correlation does not necessarily imply statistical independence.
12. A detailed description of the construction methodology of the EPRA series can be found at http://www.epra.com
13. The full set of GARCH specifications and density functions representation are available from the author upon request.
14. The functional form of the copulas can be found in the appendix.
15. Dias and Embrechts (Citation2003) show how to formally test for the non‐constancy of the parameters across the sample.
16. This implies that VaR does not take into account the gains from diversification.
17. It is obvious that ES α⩾VaRα.