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We examine the presence or absence of asymmetric volatility in the exchange rates of Australian dollar (AUD), Euro (EUR), British pound (GBP) and Japanese yen (JPY), all against US dollar. Our investigation is based on a variant of the heterogeneous autoregressive realized volatility model, using daily realized variance and return series from 1996 to 2004. We find that a depreciation against USD leads to significantly greater volatility than an appreciation for AUD and GBP, whereas the opposite is true for JPY. Relative to volatility on days following a positive one-standard-deviation return, volatility on days following a negative one-standard-deviation return is higher by 6.6% for AUD, 6.1% for GBP, and 21.2% for JPY. The realized volatility of EUR appears to be symmetric. These results are robust to the removal of jump component from realized volatility and the sub-samplings defined by structural-changes. The asymmetry in AUD, GBP and JPY appears to be embedded in the continuous component of realized volatility rather than the jump component.

It is well known that volatility in equity markets is asymmetric, i.e. negative returns are associated with higher volatility than positive returns. Robert Engle in his 2003 Nobel Lecture emphasizes the importance of asymmetric volatility. For a portfolio of S&P500 stocks, Engle (2004) shows that ignoring the asymmetry in volatility leads to a significant underestimation of the value at risk (VaR). In the foreign exchange markets, however, the consensus seems to be that there is no asymmetric volatility. Bollerslev et al. (1992) suggest that “[W]hereas stock returns have been found to exhibit some degree of asymmetry in their conditional variances, the two-sided nature of the foreign exchange market makes such asymmetries less likely.” All of the studies in their survey adopt symmetric models for exchange rate volatility. Since then the theoretical advances in volatility models, together with the availability of intraday exchange rate data, led to a proliferation of studies of exchange rate volatility. Almost all of them do not consider asymmetric volatility models. Recently Andersen et al., 2001 and Andersen et al., 2003a (ABDL hereafter) provide an extensive examination of the statistical properties, modelling and forecasting of realized volatility of foreign exchange rates. Again, the possibility of asymmetric volatility is not investigated in their articles. The “two-sided nature of the foreign exchange market” is probably the primary reason for the overwhelming choice of symmetric models for exchange rate volatility. For bilateral exchange rates, because positive returns for one currency are necessarily negative returns for the other, “good news” and “bad news” appear indistinguishable. This implies that exchange rate volatility should have symmetric responses to positive and negative shocks in exchange rate return. Furthermore, it is unclear how the standard explanations for asymmetric volatility in equity markets, i.e. the leverage effect and the volatility feedback effect, apply to the currency markets. The debt-to-equity ratios in equity markets vary from zero to several hundred percents. With the exception of some small open economies, the debt-to-GDP ratios for most countries are below 5%, and the debt-to-national asset ratios are much lower.1 If an investor anticipates higher volatility, say for USD/AUD rate, it is unclear whether she should sell USD or AUD if she holds both currencies. Empirically, the standard asymmetric GARCH models regularly detect asymmetric volatility in daily equity returns. However, these models typically fail to detect asymmetry in daily exchange rate volatility. This is probably another reason for favouring symmetric volatility models for bilateral exchange rates. Despite the bilateral nature of exchange rates, there are at least two reasons for the presence of asymmetry in bilateral exchange rates. First, some currencies have greater economic importance than others. For example, many companies and financial institutions use the US dollar (USD) as the base currency for profit and loss calculations but few uses the Australian dollar (AUD). For these institutions, higher expected USD/AUD volatility implies greater risk in AUD-denominated assets but not necessarily in USD-denominated assets. This may lead to the sale of AUD-denominated assets, which lowers USD/AUD exchange rate. This base-currency effect is likely to be stronger in some currencies than in others, depending on the size and development level of the local economy. For example, the Euro (EUR) area and the United States are of similar sizes and levels of economic development. The base-currency effect should be weaker for the USD/EUR rate than for USD/AUD, because higher expected USD/EUR volatility may lead Europeans to sell USD-denominated assets and Americans to sell EUR-denominated assets. Second, a unique feature of the foreign exchange markets is central bank intervention. Most studies report that interventions lead to higher volatility.2 Since central banks intervene on one side of the market but not the other, interventions may lead to an asymmetric relationship between exchange rate return and volatility. For example, if a central bank were concerned with the depreciation of its currency, it would buy its domestic currency and sell USD. As a result, the higher volatility from market intervention would be associated with past depreciation of the domestic currency. This could be the case when the Reserve Bank of Australia intervened to support AUD in mid-2001 when USD/AUD dropped to a historical low of 0.49 (Fig. 1). Conversely, if the central bank were to sell its domestic currency to slow down its appreciation, the resulting higher volatility would be associated with past appreciation. This could be the case for the Japanese yen (JPY) since the Bank of Japan is known to be a heavy seller of JPY over our sample period. Clearly this explanation does not apply to currencies that did not have any central bank intervention during the sample period, e.g. GBP. Full-size image (100 K) Fig. 1. Exchange rates and realized volatility. Figure options Given the common perception against asymmetric volatility and the above arguments for its presence, this paper sets out to empirically test for asymmetric volatility in major currencies. The issue is important for several reasons. First, the foreign exchange markets are several times larger than the equity markets and present a substantial risk to investors. As argued by Engle (2004), the presence of asymmetric volatility, if unaccounted for, will lead to the underestimation of VaR. Second, an empirical examination of asymmetric volatility will enhance our understanding of exchange rate dynamics, particularly in the second moment. This in turn may improve volatility forecasting and derivative pricing. Last but not least, the presence of asymmetric volatility in bilateral exchange rates will provide support for alternative explanations for asymmetric volatility, as listed in the previous paragraph. An early study of the volatilities of bilateral exchange rates by Hsieh (1989) shows that EGARCH models, which accommodate asymmetric effect, produce slightly better fits than GARCH models. However, the asymmetry parameter estimates of the EGARCH models are not reported in his article. McKenzie (2002) finds some support for the hypothesis that central bank intervention cause asymmetric volatility in exchange rates, using USD/AUD daily return series from 1983 to 1997. Several authors have documented some evidence for asymmetric volatility in exchange rates while studying other issues. For instance, Byers and Peel (1995) document asymmetric volatility in European exchange rates during 1922–1925. Andersen et al. (2003b) show asymmetric responses of major exchange rates to economic announcements in the United States. Asymmetric volatility has also been documented for Malaysian ringgit (Tse and Tsui, 1997), Australian dollar (McKenzie, 2002), and Mexian peso (Adler and Qi, 2003), all against US dollar. To our knowledge, the presence or absence of asymmetric volatility in major exchange rates has not been systematically examined, using realized volatility series, in the literature. The goal of this paper is to formally test for the presence of asymmetric volatility in the four major bilateral exchange rates (AUD, EUR, GBP and JPY against USD), using intraday quotes from January 1996 to March 2004. Specifically, we examine the relationship between current daily realized volatility and lagged daily return. Realized volatility based on intraday quotes is a consistent and highly efficient estimator of the underlying true volatility. Our long series of realized volatility contain rich information about the underlying true volatilities of the four currencies. Hence, models directly built on realized volatility offer an efficient framework to describe the dynamics of the underlying volatility and to test relevant hypotheses. As a contrast, the dynamics of the underlying volatility cannot be efficiently captured by the conventional GARCH type models because they are based solely on daily return series and do not explore intraday observations. Therefore, our realized-volatility-based approach is able to uncover volatility features (asymmetric volatility in particular) that the conventional GARCH type models fail to reveal. The model used in this paper is a variant of the heterogeneous autoregressive realized volatility (HAR-RV) model of Corsi (2004) and Andersen et al. (2005), Andersen et al. (2005) hereafter. In addition to its simplicity, the model adequately accounts for the long-memory autocorrelations observed in realized volatility series. We report the following findings. First, our testing reveals that equal-sized positive and negative returns have significantly different effects on the next-day realized volatility for AUD, GBP and JPY. A depreciation against USD leads to more volatility than an appreciation for AUD and GBP, whereas the opposite is true for JPY. These results are robust to alternative specifications and sub-samplings defined by structural changes. They are in sharp contrast to those of the GARCH type models estimated from daily return series, which uniformly imply the absence of asymmetry for all currencies considered. This contrast is consistent with the argument that daily realized volatility is much more informative about underlying true volatility than daily return. It may serve as an explanation for general lack of support for asymmetric volatility in exchange rates in the GARCH literature. Second, the realized volatility of EUR appears symmetric to equal-sized negative and positive returns. Other statistical properties of EUR are also different: its return distribution is closer to normal and its realized volatility is less persistent than those of other currencies. Third, using the procedure proposed by Andersen et al. (2005) and Barndorff-Nielsen and Shephard, 2006a and Barndorff-Nielsen and Shephard, 2006b, we estimate the jump components of realized volatility. We show that the asymmetry in AUD, GBP and JPY is embedded in the continuous component of realized volatility, rather than the jump component. In the analyses above, we find that the long-term (i.e. weekly, monthly or quarterly) price trends, measured by absolute returns, have significant explanatory power for realized volatility. Section II provides details on the data, the calculation of daily realized volatility, and summary statistics of daily returns and realized volatility. Section III presents GARCH type models with return series and explores why GARCH type models fail to capture asymmetry effects. Tests for asymmetric volatility are carried out in section IV. Section V is sensitivity analysis. Concluding remarks are given in section VI.

We present in this paper some new evidence for asymmetric volatility in the exchange rates AUD, GBP and JPY (against USD). The results are robust to a number of variations in model specification and data series. However, the economic reasons for asymmetric volatility in exchange rates are not clear at this point. Plausible explanations include base-currency effect and central bank intervention effect. The results for AUD and GBP appear to be consistent with the base-currency effect, whereas the results for JPY seem to be related to the effect of central bank intervention. Future research should explore these and other economic factors affecting the asymmetric relationship between volatility and price movements of exchange rates.