Correlations, integration and Hansen-Jagannathan bounds

Abstract

Recent studies have documented the growing economic and financial integration between countries. Among other things, this has led to the argument that greater integration results in higher bilateral correlations between returns on national stock markets. This study endeavours to link the two issues by utilizing the assumption that if countries are integrated, they would have to display a minimum level of correlation. This is achieved by constructing a bound on the level of the bilateral correlation, as originally developed by Kasa (1995). In contrast to Kasa, the present studies demonstrate that the correlation bound may not be downward sloping in all cases and careful interpretation of the results is required.

Acknowledgments

Sections of this paper were written while the first author was a PhD student in the School of Economics and Finance, RMIT. The authors would like to thank Alan Alford for his helpful comments and guidance.

Notes

For evidence on the relationship between integration and liberalization, see, for example, Mittoo (1992) for Canada; and Campbell and Hamao (1992) for Japan.

For a detailed derivation of Hansen-Jagannathan volatility bounds and issues pertaining to the bounds, see Hansen and Jagannathan (1991), Cochrane (2001) and Campbell et al., (1997).

Kasa derives the bound on the correlation using a Taylor series approximation and this may introduce some error which he argues is relatively small. Hence, in some cases, it is found that the intersection of the correlation bound with the unconditional correlation does not occur precisely at the bound for the coefficient of variation of m specified in Table 2.

A further point of interest is to consider the volatility bound for the special case when the slope is equal to zero. Recall that this occurs when (b – a) = 0, that is, when b = a. Substituting this back into Equation 7 gives:

Hence, in the special situation when the slope of Kasa's bound is equal to zero we have the result that the correlation bound is equal to negative unity, for all values of x _m .

Further details are available from the authors upon request.

This issue is addressed in Campbell et al. (1997). Using the results obtained by Mehra and Prescott (1985) on the equity-premium puzzle, they show that standard deviation of the discount factor should be at least 33% to explain their result. They show that models do not produce a result of that variability.