Multiple Regimes and Volatility Transmission in Securitized Real Estate Markets

In contrast, many stock market studies have examined market interdependencies in term of conditional second moments of the distributions of returns. These studies include Hamao et al. (1990), Koutmos and Booth (1995), Susmel and Engle (1994), Theodossiou and Lee (1993), Koutmos (1996), So et al. (1997) and Liu and Pan (1997) and In et al. (2001).

As suggested by the reviewer, we include both return specifications in the empirical investigation. As reported later (“Empirical Results”), although there are instances of different coefficient estimates in the multiple structural and MRDADC results which could possibly related to currency effects, the overall findings do not differ significantly under both return specifications. We wish to thank the reviewer for this suggestion.

See Kroner and Ng (1998) for the detailed mathematical treatments. Multivariate GARCH models have been among the most widely used time-varying covariance models. These models include the VECH model of Bollerslev et al. (1988), the constant correlation (CC) model of Bollerslev (1990), the factor ARCH (FARCH) model of Engle et al. (1990), the BEKK model of Engle and Kroner (1995) and the Asymmetric Dynamic Covariance model (ADC) of Kroner and Ng (1998) These models have been applied to many financial markets and many asset pricing and investment problems.

We estimate the two MRDADC models via BFGS algorithm using RATs software. Our MRDADC models converge in 826 (US$ return) and 357 (local currency return) respectively. The resulting log-likelihood values are, respectively, −40752.2 (US$ return) and −39793.85 (local currency return).

Out of the 10 regime coefficients, there are nine (US$ return) and eight (local currency return) significant estimates respectively.

Earlier studies on this subject assume that the conditional covariance matrix is constant over time such as Ederington (1979) and Anderson and Danthine (1981). Consequently, the OHR is also constant and can be easily estimated as the slope coefficient of a regression of the change in the return in one market on the change in the return in the other market. However, since the OHR estimation depends on the conditional distribution of market price movements, the estimated OHR will likely to vary over time as this conditional distribution changes. In some later studies, GARCH model is widely used to generate time-varying conditional variances and covariances. For example, Cecchetti et al. (1988) estimate time-varying OHRs by using an ARCH model to represent time variation in the conditional covariance matrix of Treasury bond returns and bond futures. They found substantial time variation in the OHRs. Other works include Kroner and Sultan (1993)’s Multivariate Constant Correlation (CC) model and Baillie and Myers (1991)’s VECH model.