Common volatility across Latin American foreign exchange markets

Abstract

This article uses high-frequency exchange rate data for a group of 13 Latin American countries in order to analyse volatility co-movements. Particular interest is posed on understanding the existence of a common volatility process during the 1995–2008 period. The analysis relies on bivariate common factor models. We test for second-order common features using the common autoregressive conditional heteroskedasticity-feature methodology developed by Engle and Kozicki (1993). Overall, the results of this article indicate that while most currencies display evidence of time-varying variance, the volatility movements in the Latin American foreign exchange markets seems to be mainly country specific. Common volatility processes seem to be present only for a few South American markets.

Acknowledgements

This article has benefited from comments by seminar participants at Western Michigan University, St. Cloud State University and the 33rd Academy of Economics and Finance (AEF) annual meeting in Houston, Texas. The author wishes to thank the editor and two anonymous referees for helpful comments and suggestions. I am also thankful for insightful comments from Ana Maria Herrera, David G. McMillan, Juri Marcucci, Susan Pozo, Carlos Vargas-Silva and Mark Wheeler. The author acknowledges the support provided by a Faculty Grant of the Office of Research and Special Programs at Sam Houston State University. The usual disclaimer applies.

Notes

¹ Many of these reforms were included in the Washington consensus of 1990 as a response for the financial crises that the region underwent in the 1980s (Edwards, 1998, 2003).

² This literature on exchange rate volatility has, for the most part, focused on examining spillover effects within volatility across exchange rates. See, for example, Engle et al. (1990), Baillie and Bollerslev (1991), Byers and Peel (1995), Cheung and Ng (1996), Ng (2000) and Speight and McMillan (2001). However, fewer studies have addressed the nature of foreign exchange rate correlations and common movements. Some examples are: Harvey et al. (1994), Alexander (1995a, b), Klaassen (1999), Black and McMillan (2004) and Babetskaia-Kukharchuk et al. (2008).

³ The largest derivative exchanges in the region are located in Argentina (Mercado a Término of Buenos Aires [MATBA], Mercado a Término of Rosario [ROFEX]); Brazil (Bolsa de Mercadorias y Futuros [BM&F], Bolsa de Valores do Estado de São Paulo [BOVESPA] index); and Mexico (Mexican market for derivatives [MexDer]). In addition, OTC exchange derivative markets exist in Chile and Peru.

⁴ Different features have been studied and examples are: seasonal components, nonlinearities, serial correlation, structural breaks, kurtosis, skewness and seasonality. For a complete literature review on different applications of the testing procedure, see the special edition of the Journal of Business and Economics Statistics, 11 (1993) and Journal of Econometrics, 132, 1 (2006), which cover theoretical and empirical advances on common features.

⁵ The idea is that if two individual currency returns have a one-factor model representation with a time-varying variance, we can form a portfolio that does not display time-varying variance; that is, the common factor is eliminated (Engel and Susmel, 1993). However, as pointed out by an anonymous referee, it is important to remember that it is not only conditional (time-varying) volatility, but also unconditional (constant) volatility that a typical investor should be concerned of. Along these lines, forming time-invariant portfolios is an intermediate rather than the final objective of an investor, as long as the remaining constant risk may be still high.

⁶ These three steps are in consonance with the different studies that use the common feature methodology. For an application to the foreign exchange markets, see Alexander (1995a) and Farrell (2001). For an application to international bonds and equity markets, see Engle and Susmel (1993), Arshanapalli and Doukas (1994), Alexander (1995b), Booth et al. (1996), Tse and Booth (1996), Arshanapalli et al. (1997), So et al. (1997), Beliu (2005) and Engle and Marcucci (2006). For an application to interest rates and the futures market, see Booth and Tse (1996).

⁷ We focus on the volatility process of the exchange rates and therefore do not model the mean of the process. Rather, we use the squared returns as a proxy of volatility. The financial literature has focused recently on high-frequency returns between period t − 1 and t to obtain a consistent estimator of volatility for time t (by squaring the returns). This measure of volatility is what is known as ‘realized volatility’ (Anderson and Vahid, 2005).

⁸ For more expositional details, also refer to Enders (2004) or Hamilton (1994).

⁹ From Engle and Kozicki (1993), three axioms follow the common feature methodology: (i) If x _{1 t} has (does not have) the feature, then ax _{1 t} with a ≠ 0 will have (not have) the feature; (ii) If neither x _{1 t} nor x _{2 t} have the feature, then a linear combination of them will not have the feature and finally, (iii) if x _{1 t} does not have the feature and x _{2 t} does have the feature, then y = x _{1 t} + x _{2 t} will have the feature.

¹⁰ The criterion to determine the optimal number of lags is not formally specified in the literature. However, in this study we follow the convention by using four lags of currency 1, four lags of currency 2 and four lags of cross products.

¹¹ The grid search was conducted with inclusive bounds for λ of–100 and 100 and in a 0.01 sequence. We expanded the interval for the grid-search whenever the minimization resulted in λ equalling one of the bounds. These last two methods (BGFS and the grid search) were used as a check for robustness. The results–not presented here–all led to conclusions similar to the ones presented in this article.

¹² While it would be interesting to ascertain the degree to which several currencies respond to common factors, the common volatility test is confined to portfolios of two currencies and therefore the implications of our results only extend to the case of two series.

¹³ While most data comes from Bloomberg, the exceptions are the currencies for Bolivia and the Dominican Republic, for which data comes from their own central banks. Daily data corresponds to five days a week (weekends excluded). The use of daily and weekly data is typical in this literature. Weekly data are often included to avoid the noisiness typically encountered in daily data and to avoid the ‘weekend effect.’ It also eliminates nonsynchronous trading and problems of short-term correlation. It is rather common to find weekly estimates based on Wednesday reports or using an average from ‘Thursday to Thursday’ in which weekend data is excluded. We use both measures in our estimation. Because of space considerations and because the results do not change considerably, we only present the results based on Wednesday reports.

¹⁴ Using the Canadian dollar is of interest because from a financial perspective, incorporating the Canadian dollar would provide an investor with relevant information regarding different options for portfolio diversification.

¹⁵ Initially we included 16 currencies but we excluded the Costa Rican and Nicaraguan currencies. The reason is that their returns were I(1) processes, and therefore not confirming the stationarity property.

¹⁶ The sample for Argentina starts in 2002. In March 1991, the Argentinean Congress passed the ‘Convertibility Law’ fixing the peso's exchange rate at par with the US dollar. The Convertibility Law required the Argentinean's peso to be fully backed with dollar reserves. Moreover, under convertibility, the owner of a peso had the right of freely converting pesos into dollars at the fixed rate of one for one. The Argentinean authorities allowed their currency to freely float in late 2001. For this reason, we chose to start our sample in 2002.

¹⁷ In performing the test, we included 1, 2 and 4 lags. While the results were consistent for different lags, only the results for four lags are presented.

¹⁸ We are grateful to an anonymous referee for suggesting us to conduct the common volatility test in a rolling basis.