APPENDIX I: A Multivariate Regime-switching Model for Equity and Bond Returns
Avouyi-Dovi, S. and D. Neto (2004) “Equity Market Interdependence: The relationship between European and US stock markets” Banque de France, Financial Stability Review, No. 4, June 2004.
Bordo, M., B. Eichengreen, and D. Irwin (1999) “Is Globalization Today Really Different from Globalization One Hundred Years Ago?,” NBER Working Paper No. 7195.
Forbes, K. and R. Rigobon (2002) “No Contagion, Only Interdependence: Measuring Stock Market Movements” Journal of Finance, Vol. 57(5), pp. 2223–61.
Gravelle T., M. Kichian and J. Morley (2003) “Shift Contagion in Asset Markets,” Bank of Canada Working Paper 2003-5, February 2003.
International Monetary Fund (2003), Global Financial Stability Report, World Economic and Financial Surveys (Washington, September).
Kim, C.-J., J. Morley, and C. Nelson (2004) “Is There A Positive Relationship between Stock Market Volatility and the Equity Premium?,” Journal of Money, Credit, and Banking, Vol. 36(3), pp. 339–360.
Prepared by Daniel Hardy.
The international linkages are of long standing. The precursors of many of today’s major French financial institutions were important actors in the globalized economy of the nineteenth century.
Prepared by Daniel Hardy.
Banks from countries such as Japan, Spain, and the UK have traditionally had strong presences in certain geographical areas such as East Asia and Latin America that have fewer connections to France.
One mutualist bank already has limited links with mutual banks in other countries, notably Germany, including ownership links through their apex organizations.
Prepared by Daniel Hardy.
This information is taken from Axa’s published reports and presentations.
They may, however, have more significant exposure to risks to French companies’ assets abroad, for example, in shipping and aviation.
The June 2004 issue of the Banque de France’s Financial Stability Review contains a survey of the market for credit derivatives and similar instruments. The survey is summarized in the FSSA. The evidence presented there suggests that French insurance companies’ involvement in this market, in which the counterparts are largely American financial institutions, is not yet large relative to their balance sheet size.
Prepared by Toni Gravelle.
Recent work at the Bank de France looks into similar issues examined in this study (see Avouyi-Dovi and Neto (2004))
See Bordo, Eichengreen, and Irwin (1999), who show that since the mid-1970s, globalization has led economies and financial markets to be more integrated. See also Chapter 3 of the September 2003 issue of the Global Financial Stability Report (IMF 2003) for more on the dependence of the financial market volatility and recessions.
Both correlation coefficient and volatility measures in this study are based on an exponentially weighted moving average of past returns, where weights decay by a factor of 0.90. These exponentially weighted measures put greater weight on more recent observations rather than, as is the case with the traditional measure, an equal weighting across all observations in the sample.
Equity and bond correlation coefficient estimates for other country pairs are available upon request.
See for example Forbes and Rigobon (2002) for a discussion how volatility may bias unconditional correlation measures.
The data sources are Data Stream and Bloomberg.
Using a similar methodology, other studies find significant shifts in the degree of interdependence, after controlling for volatility, in emerging market bonds and advanced countries’ exchange markets (Gravelle et al. 2003).
Returns are measured as the percentage log difference in price.
Another reason behind this limitation is due to computational constraints. The optimization routine for calculating the parameter estimates becomes increasingly time consuming and unstable, as the number of equations and in turn parameters in the common factor system (equation (2) or (3)) increases.
That is, investor who become more risk averse or more uncertain about future asset fundamentals, would seek higher expected returns. This would translate into contemporaneous declines in current asset prices (i.e., negative contemporaneous returns). See Kim, Morley and Nelson (2004) for more details on this.
Hamilton’s (1996) textbook offers a detailed exposition of the Markov-switching econometric approach.
Lagged parameter coefficient estimates from equation (1) were all insignificant. As a result, actual equity returns were used in equations (3) and (4) in the place of any residuals derived from equation (1). Idiosyncratic means were also added to equations (3) to allow for the individual equity returns to have different average means rather than a common, regime dependent mean. However these were found to be insignificant and the original specification (equation (3)) is used in the analysis.
Note this need not be the case. The estimation procedure allows for the possibility that some loading factors to be smaller in state one δi(1)<δi(0)) while for others it is the reverse.
More specifically, regime one French equity volatility is,
Researchers typically define a regime switch as having occurred if the probability of being in the new state is greater than 0.5.
A further question, which goes beyond the scope of this note, is what causes periods of heightened volatility, and whether such episodes are themselves linked to globalization.
Again, lagged parameter coefficient estimates estimated from equation (1) were all insignificant. As was the case for equity returns, actual bond returns were used in equations (3) and (4) in the place of the residuals derived from equation (1). Idiosyncratic means were also added to equations (3) to allow for the individual returns to have different average returns. But these were found to be insignificant and the original specification is used in the analysis.
Technically, hypothesis testing should be carried out to ascertain the correct number of regimes (one versus two) and/or the correct type of switching process (Markov-switching versus independent-switching). However, this would require the calculation of bootstrapping or Monte Carlo methods and lies outside of the scope of this study.