Correlations and spillovers among three euro rates: evidence using realised variance

Abstract

This paper uses three euro exchange rates – the US dollar, sterling and yen – to test for the presence of volatility spillovers and time-varying correlations using the realised variance approach, which has significant advantages over the multivariate-GARCH methodology. Our results suggest that the three currencies do exhibit some degree of volatility spillover and hence commonality in the driving force behind volatility movement. With regard to the nature of time-variation within the correlation coefficients, there is substantial evidence that correlations are time-varying but that the strength of correlation coefficients has not increased over the sample period. Furthermore, there is evidence that correlations themselves are predictable and interrelated. These results support the view that the three rates do exhibit interrelationships, commonality and time-varying correlation, factors that are important to portfolio managers. This latter point is illustrated by using the realised variances and covariances to determine portfolio weights, the portfolio variance of which is lower than constructing portfolios using (rolling) unconditional values.

Keywords:

• exchange rates
• spillovers
• correlation
• realised variance

JEL :

• C22
• F31

Notes

For further examples of work examining stock return correlation, see Taylor and Tonks (1989), Kasa (1992), Corhay, Rad, and Urbain (1993), Aggarwal and Kyaw (2005), Fraser and Oyefeso (2005), Berben and Jansen (2005), Kim, Moshirian and Wu (2005).

Such spillovers can be seen as a by-product of greater financial integration, or alternately can arise from contagion effects. See, for example, Baillie and Bollerslev (1991), Byers and Peel (1995), Kearney and Patton (2000), Speight and McMillan (2001) and Melvin and Peiers (2003) for the case of exchange rates. For the case of stock markets refer to Cheung and Ng (1996), Ng (2000), Chow and Lawler (2003) and Miyakoshi (2003).

All these papers consider US dollar denoted currency for industrialised countries. Ruiz (2009) and Babetskaia-Kukharchuk, Babetskii and Podpiera (2008) are two related papers that examine the nature of foreign exchange rate correlations and common movements for Latin-American and Central European currencies, respectively.

Different specifications include the diagonal model (Bollerslev, Engle, and Wooldridge 1988), the constant conditional correlation model (Bollerslev 1990), the BEKK model (Engle and Kroner 1995) and more recently the dynamic conditional correlation model (Engle 2002).

Also see Andersen et al. (2001a), Andersen et al. (2001b) and Barndorff-Nielsen and Shephard (2004). Furthermore, Andersen et al. (2000) and Andersen et al. (2001b) focus on the particular case of exchange rate realised volatility.

See www.olsendata.com.

The data set consists of the last bid and ask quote in each 5 min interval, with the price taken as the mid-point. As trading in the foreign exchange market is continuous, i.e. the trading day is 24 h long, we follow convention and mark a day beginning and ending at 21:00 GMT.

Previous studies that have used Granger causality to tests for volatility spillovers in stock markets include Chow and Lawler (2003) and Ramasamy and Yeung (2005).

More specifically, we calculate unconditional variances as the square of each series return and the covariance as the multiple of cross series returns. This introduces time-variation into the calculation of the unconditional variances and covariances. Moreover, we could compare the realised approach with a GARCH approach, however, we refrain from doing this, first, we wanted to compare methodologies that are simple in construction and hence of use for practitioners, second, as noted in the introduction the GARCH model can become cumbersome (especially when there are more than two assets) and there is no commonly accepted specification for the covariance matrix. Nonetheless, a study by McMillan, Speight, and Evans (2008) does make comparison between the realised and GARCH approaches to portfolio construction.