Returns synchronization and daily correlation dynamics between international stock markets

Transcription

1 Journal of Banking & Finance ) 1805± Returns synchronization and daily correlation dynamics between international stock markets Martin Martens a, *, Ser-Huang Poon b,1 a School of Banking and Finance, University of New South Wales, Sydney, NSW 2052, Australia b Department of Accounting and Finance, University of Strathclyde, Glasgow G4 OLN, UK Received 22 October 1999; accepted 24 July 2000 Abstract The use of close-to-close returns underestimates returns correlation because international stock markets have di erent trading hours. With the availability of 16:00 London time) stock market series, we nd dynamics of daily correlation and covariance, estimated using two non-synchroneity adjustment procedures, to be substantially di erent from their synchronous counterparts. Conditional correlation may have different signs depending on the model and data type used. Other ndings include volatility spillover from the US to the UK and France), and a reverse spillover which is not documented before. Also, unlike previous ndings, we found the increase in daily correlation is prominent only under extremely adverse conditions when a large negative return has been registered. Ó 2001 Elsevier Science B.V. All rights reserved. JEL classi cation: C32; C53; G15 Keywords: Synchronous data; Dynamic correlation; GARCH; Value-at-risk; Asymmetry e ect * Corresponding author. Tel.: ; fax: addresses: m.martens@unsw.edu.au M. Martens), s.poon@strath.ac.uk S.-H. Poon). 1 Tel.: ; fax: /01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S )00159-X

2 1806 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± Introduction The dynamics of daily correlation has a pivotal role in many important applications in nance. Riskmetricse uses it to produce value-at-risk VaR) measures at short horizons. Erb et al. 1994) provide examples on how time varying correlation forecasts can a ect optimal portfolio weights. Kroner and Ng 1998) show how time varying covariance matrices a ect hedge ratios. Burns et al. 1998) show how a term structure of correlation can be built from a daily multivariate GARCH model. Such a correlation term structure can then be used to value derivative products whose payo depends on the values of two or more assets. Under turbulent market conditions, real-time valuation of international portfolios can be critical. To produce accurate portfolio value, we need, among other things, accurate correlation estimates. Given the crucial role of correlation measures, it is not surprising that correlation dynamics and intertemporal relations between international stock markets are areas frequently explored by researchers. Volatility spillovers from the US to the rest of the world are reported in Eun and Shim 1989), Becker et al. 1990), Fischer and Palasvirta 1990), and Hamao et al. 1990). Other studies such as Koch and Koch 1991) and Von Furstenberg and Jeon 1989) nd correlations have increased over time. King and Wadhwani 1990) and Bertero and Mayer 1990) nd a substantial increase in correlation during stock market crises. More recent papers such as Theodossiou and Lee 1993), Longin and Solnik 1995) and Theodossiou et al. 1997) exploit a multivariate GARCH framework where all the conjectured relationships are tested jointly. It has been argued that a multivariate approach is the only right platform for studying the transmission mechanism and correlation dynamics. However, international stock markets have di erent trading hours. Hence the use of daily closing prices leads to an underestimation of the true correlations between stock markets. Some of the studies mentioned above by-pass the non-synchroneity problem by using weekly or monthly data. 2 The use of low frequency data leads to small samples, which is ine cient for multivariate modelling especially when parameters are time varying. Moreover, monthly and weekly data cannot capture daily correlation dynamics. On the other hand, we have studies that use daily non-synchronous open-to-close and close-toopen returns. These studies cannot distinguish a spillover from a contempo- 2 These include Longin and Solnik 1995), Theodossiou et al. 1997) and Ramchand and Susmel 1998). Koch and Koch 1991) uses daily data but for three separate years 1972, 1980 and 1987). King and Wadhwani 1990) and Bertero and Mayer 1990) use high frequency data, but for a short period surrounding the 1987 stock market crash.

3 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± raneous correlation. 3 As a result, Riskmetricse 1996), and Burns et al. 1998) 4 suggest various procedures for computing `synchronized' 5 correlation from non-synchronous returns. To date, these non-synchroneity adjustment procedures have not yet been tested. The validation of these procedures is of paramount importance as they are potentially useful in cases where stock exchanges that do not share common trading hours. The objective of this study is twofold. First, we evaluate two returns synchronization procedures proposed in the literature; the Riskmetricse method and a GARCH-based method proposed by Burns et al. 1998). Second, we investigate the daily dynamics and spillover e ects of the conditional variance, correlation, and covariance, for stock index returns in the US, the UK and France. The study of daily dynamics of second moments of stock returns is still incomplete because of the problem of non-synchronous data. The availability of Datastream 16:00 London time 6 ) synchronous stock market series makes such a study possible now and allows us to make a clear distinction, as never before, between a spillover and a contemporaneous correlation. Another innovation in this paper is the use of the asymmetric dynamic covariance ADC) Kroner and Ng, 1998) model, which, because of its all-encompassing nature, will indicate if multivariate GARCH models tted previously are adequate for modelling correlation dynamics. 7 Results obtained here suggest that there is no spillover e ect at the returns level. Previous studies have reported nding a volatility spillover e ect from the US to the other countries. Here, we nd also a reverse volatility spillover from Europe to the US. The asymmetric e ect in conditional variance is already well documented, and there have been claims that correlation increases when markets are more volatile. Here, we nd evidence that asymmetry permeates both conditional covariance and conditional correlation. But, unlike ndings in previous studies, we nd correlation responds to volatility only if a large negative return occurred on the previous day. Using both synchronous and non-synchronous daily returns, we nd synchronized conditional measures to be substantially di erent from their 3 See, for example, Hamao et al. 1990) and Koutmos and Booth 1995). 4 Kahya 1997) computes synchronized correlations from non-synchronous returns. However, since Kahya assumes constant correlation, it will not be pursued any further in this study. 5 From now onwards we will use `synchronized' to indicate that adjustment for non-synchroneity has been performed on close-to-close returns before the measure of interest is calculated. 6 16:00 London time is equal to 16:00 GMT in winter and 15:00 GMT in summer. Most of the time apart for a short period around the change to daylight saving time) it corresponds to 11:00 New York time. 7 Booth et al. 1997) also studied dynamics in conditional measures. But, they assume constant correlation and they study returns of Scandinavian markets, which include Copenhagen in Denmark, Oslo in Norway, Stockholm in Sweden and Helsinki in Finland. Since these exchanges are in the same time zone, the issue of non-synchroneity is not discussed in Booth et al. 1997).

4 1808 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 synchronous counterparts. The conditional measures are also found to be sensitive to the model used to calculate them. The correlation among the conditional covariances, across models and data types, ranges from to But, the correlation of the corresponding conditional correlations can be as low as ) This is alarming because di erent models are producing di erent hedge ratios and even con icting hedging strategies. Our results show that the Riskmetricse model leads to more volatile hedge ratios and more conservative VaR estimates than the ADC model. The remainder of this study is organized as follows. Section 2 describes the data and computes sample correlations from synchronous and non-synchronous returns. Section 3 describes the Riskmetricse and the ADC models. The Riskmetricse model has built-in procedures for adjusting non-synchroneity. For the ADC model, we adopt the non-synchroneity adjustment procedures proposed in Burns et al. 1998). Section 4 reports and discusses the correlation dynamics and results from estimating the ADC model. In Section 5, we examine the in-sample sensitivity of the conditional measures with respect to model and data type. In Section 6, we compare the one-step-ahead forecasts for conditional correlation and covariance produced by the two models, and evaluate the economic signi cance of the di erences using a VaR example. Finally, Section 7 concludes the paper. 2. Data and unconditional correlation The data consists of daily stock market closing prices and prices recorded at 16:00 London time for the US S&P500 index), the UK FTSE100 index) and France CAC40 index). 8 Trading at the London Stock Exchange starts at 9:00 and nishes at 16:30 London time. Paris trades from 10:00 to 17:00 Paris time and the New York Stock Exchange trades from 9:30 to 16:00 eastern standard time. Apart from a few weeks when these countries change to the summer daylight saving time and again later to the winter time, the trading hours in Paris New York) correspond to London time 9:00 to 16:00 13:30±20:00). The data is extracted from Datastream for the period 3 August 1990±11 November After removing holidays in each country, there are 1994 common trading days among the three series. Panel A of Table 1 shows the unconditional sample correlations for daily and weekly returns, which are de ned as the 8 To date, Datastream provides synchronous stock market prices for a small number of leading stock markets only. Our validation analysis requires at least some overlapping trading periods, hence we are restricted to European and American stock market indices. It is not possible to investigate correlation with Japanese stock returns because the Japanese stock market has no common trading time with other major stock markets.

5 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± Table 1 Correlations and lagged correlations computed from closing prices and prices recorded at 16:00 London time 3 August 1990±11 November 1998) a DCAC DFTSE WCAC WFTSE Panel A: Contemporaneous correlations a) Non-synchronous closing) prices DFTSE WFTSE [0.026] [0.047] DS&P WS&P [0.034] [0.036] [0.046] [0.049] b) Synchronous 16:00 London time) prices DFTSE WFTSE [0.028] [0.048] DS&P WS&P [0.029] [0.032] [0.042] [0.047] c) Synchronized closing) prices DFTSE WFTSE [0.043] [0.082] DS&P WS&P [0.051] [0.063] [0.078] [0.086] Panel B: Lagged correlations DCAC DFTSE DS&P WCAC WFTSE WS&P a) Non-synchronous closing) prices LDCAC LWCAC ) [0.028] [0.027] [0.030] [0.054] [0.055] [0.059] LDFTSE LWFTSE )0.082 )0.057 )0.017 [0.023] [0.026] [0.030] [0.048] [0.046] [0.050] LDS&P LWS&P )0.106 )0.014 )0.083 [0.032] [0.027] [0.039] [0.056] [0.052] [0.053] b) Synchronous 16:00 London time) prices LDCAC LWCAC ) [0.028] [0.029] [0.032] [0.053] [0.053] [0.056] LDFTSE ) )0.023 LWFTSE )0.093 )0.055 )0.032 [0.026] [0.031] [0.033] [0.050] [0.045] [0.051] LDS&P )0.024 )0.009 )0.057 LWS&P )0.118 )0.023 )0.067 [0.029] [0.033] [0.032] [0.053] [0.050] [0.050] a a) `DCAC', `DFTSE' and `DS&P' are the daily returns on Paris CAC 40, UK FTSE100 and US S&P500 index, respectively. `WCAC', `WFTSE' and `WS&P' are the weekly counterparts. The pre x `L' indicates the lag, e.g., LDS&P is the S&P daily return from the previous trading day. b) The weekly returns are calculated from Wednesday to Wednesday index values. If a particular Wednesday happens to be a holiday, the previous trading day's value is used. c) There are 1994 observations in the daily series after excluding all holidays. The weekly series consists of 434 observations. d) Heteroskedasticity and autocorrelation consistent HAC) standard errors are in brackets.

6 1810 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 di erence of log index values. 9 The weekly returns are computed from Wednesday to Wednesday log index values. If a particular Wednesday happened to be a holiday, we use the index values recorded on the previous day. In this paper, we will use the term `synchronous correlation' to refer to correlation calculated using the synchronous 16:00 prices, `non-synchronous correlation' to refer to correlation calculated from non-synchronous closing prices without adjustment, and `synchronized correlation' for correlation calculated from closing prices and adjusted for non-synchroneity. As expected, there are large di erences between synchronous and non-synchronous correlation estimates for the daily correlations between the European and the US markets, where the closing times are the furthest apart. Using 16:00-to-16:00 returns in part b), instead of close-to-close returns in part a), raises the daily correlation between US and UK French) stock returns from to ±0.607). The di erences between weekly non-synchronous correlations between the US and the two European countries in part a) and their synchronous counterparts in part b) are not statistically signi cant. Many previous studies have used weekly data instead of daily data to alleviate the non-synchroneity problem. The idea is that the 5 hour time di erence between UK close and US close has a greater impact on returns measured across 24 hours than return measured across 168 hours i.e., 24 times 7 days). If cross-market correlation is positive, the use of non-synchronous returns will always lead to an underestimation of the true correlation. Panel B of Table 1 presents the lag-1 returns cross-correlations. Without controlling for non-synchroneity, US returns appear to lead returns in the two European markets in part a) of Panel B, which is reported in previous studies see, for example, Hilliard, 1979; Ja e and Wester eld, 1985). These spurious lead±lag correlations 10 disappear once the non-synchroneity is controlled for in synchronous correlation in part b) of Panel B. Both synchroneity adjustment models mentioned in Section 1 make the assumption of zero serial correlation and zero serial cross-correlation in e cient markets. With such an assumption, synchronous covariance can then be estimated from non-synchronous returns by summing up the contemporaneous, the rst lead and the rst lag cross products as follows: 9 The stock market returns have not been adjusted for dividends because the dividend information in Datastream is not consistent for all countries. Since we are only comparing correlation estimates derived from synchronous and non-synchronous returns, the omission of dividend adjustment should have little impact on our conclusions. 10 Trading stops 5 hours later in the US than in the UK. Hence, some price movements in the US in response to global news will not be re ected in the UK prices till the following day because of the earlier closing time in the UK.

7 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± c~ov R i R 0 ˆ1 X T j r it r jt r it r jt 1 r it 1 r jt ; T t 1 1 where R t and r t are synchronous and close-to-close returns, respectively. The tilde on top of the `cov' operator indicates that the covariance is a synchronized one in contrast to a synchronous covariance calculated from synchronous data. Dividing this expression by the S.D. of the individual returns, we get the synchronized correlation as the sum of the contemporaneous, lead-1 and lag-1 cross-correlations of close-to-close returns. The results are provided in Panel A, part c) of Table 1. All the daily synchronized correlations in part c) are higher than the synchronous correlations in part b) of the same panel. 11 On the other hand, the weekly synchronize correlations between the US and the two European markets are lower than the synchronous counterparts. 3. Methodology In this section, we describe the procedures proposed in Riskmetricse 1996) and Burns et al. 1998) for dealing with data non-synchroneity Riskmetrics model The Riskmetricse model has been widely used due to its simplicity, widespread publicity and the availability free of charge!) of Riskmetricse data sets. The Riskmetricse data sets contain huge matrices of variance±covariance estimates of hundreds of assets. These variance±covariance estimates are updated and released daily through the world-wide-web. In the Riskmetricse model, Eq. 1) is similarly applied except that the covariance is now changing through time: c~ov R it ; R jt ˆcov r it ; r jt cov r it ; r jt 1 cov r it 1 ; r jt : 2 The second and the third terms on the right-hand side of Eq. 2) are needed only when non-synchronous close-to-close returns are used. Riskmetricse calculates conditional variance and covariance based on the exponentially weighted moving average EWMA) method, 11 For example, the point estimate for the synchronized daily correlation between the UK and the US 0.690) is outside the 90% con dence region for the synchronous estimate 0.632). However, none of the di erences are statistically signi cant due to the noise in the data and the noise added by the synchronization procedure.

8 1812 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 r 2 t ˆ XK kˆ0 cov r it ; r jt ˆ XK k k r t k r 2, X K kˆ0 cov r it ; r jt 1 ˆ XK kˆ0 kˆ0 k k ; k k r it k r i r jt k r j, X K k k r it k r i r jt k 1 r j kˆ0 k k ;, X K For daily data, Riskmetricse sets the decay parameter k equal to 0.94, the number of lagged observations K equal to 74, and the mean return for each asset equal to zero. 12 The synchronized correlations can then be derived from Eqs. 2) and 3) as follows: ~q R it ; R ˆc~ov R it; R jt jt : 6 r it r jt The main disadvantage of the Riskmetricse model is that the correlation, as derived from Eqs. 2)± 6), may not be bounded between 1 and that the covariance matrix is not guaranteed to be positive de nite Asymmetric dynamic covariance ADC) model Burns et al. 1998), which we shall refer to as BEM from now on, assume that the close-to-close returns vector, r t, follows a rst-order moving average MA 1)) process due to non-synchroneity: r t ˆ e t Me t 1 ; 7a e t ju t 1 N 0; H t ; 7b where M is the matrix containing the moving average terms, and H t is the covariance matrix of e t conditional on the information set at time t. Notations in bold print indicate vectors or matrices. Similar to the Riskmetricse model, BEM assume stock returns are not serially cross) correlated in an e cient market setting. However, unlike the Riskmetricse model, BEM permit return adjustments in one direction only. For example, the UK closes earlier than the US. Events that take place later in the day, after the London market closes, will be re ected in US returns on the same day, but will a ect UK returns on the next day when the London market re-opens. Hence, in the BEM model, the covariance between UK returns and previous day US returns is added to the contemporaneous covariance but not the other way around. Therefore, the diagonal and the above-diagonal elements of matrix M must be zero our kˆ0 k k : In our study, we use a non-zero mean, but this leads to only marginal di erences in results.

9 return vector puts the US rst, followed by the UK). Like BEM we impose this structure on M when estimating our models. In BEM's model, the synchronized return, ~R t, is equal to ~R t ˆ e t Me t ; 8a and the synchronized conditional covariance matrix is E R ~ t R ~ 0 t ˆ I M H t I M 0 : 8b In BEM, H t is of the component form as in Engle and Lee 1999). Here we choose to model H t with a more general ADC model Kroner and Ng, 1998), which nests a number of well-known multivariate conditional heteroskedastic models and guarantees a positive de nite covariance matrix. Estimating the ADC model for both synchronous and non-synchronous returns, we obtain, for synchronous 16:00-to-16:00 returns in two countries, R t ˆ l e t ; 9a and for non-synchronous close-to-close returns, r t ˆ ~l e t Me t 1 : 9a 0 In both cases, where M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± e t ju t 1 N 0; H t ; 9b h iit ˆ h iit for i ˆ 1; 2; 9c p p h 12t ˆ q 12 h 11t h 22t /12 h 12t ; 9d h ijt ˆ x ij B ij h ijt 1 a 0 i e t 1e 0 t 1 a j g 0 i g t 1g 0 t 1 g j for all i; j; 9e R t ˆ R 1t ; R 2t Š 0 ; l ˆ l 1 ; l 2 Š 0 ; e t ˆ e 1t ; e 2t Š 0 ; a i ˆ a 1i ; a 2i Š 0 ; g i ˆ g 1i ; g 2i Š 0 ; g t ˆ min 0; e 1t ; min 0; e 2t Š 0 : To study daily correlation dynamics, we use synchronous returns only and t Eqs. 9a), 9b)± 9e) omitting Eq. 9a 0 ). The results are reported and discussed in Section 4. The synchronous conditional covariance, h 12t, is given by Eq. p 9d). The synchronous conditional correlation is computed as h 12t = h 11t h 22t with h 11t and h 22t derived from 9c) and 9e). The process for deriving the synchronized version of correlation measures is less direct. First, we t 9a 0 ) to close-to-close returns together with Eqs. 9b)± 9e). Next, the synchronized returns, Rt ~, are derived from Eq. 8a) and the synchronized covariance, h ~ 12t, from 8b). Finally, the synchronized correlation is computed as h ~ p 12t = ~h 11t h22t ~, where h ~ 11t and h ~ 22t are the diagonal elements on the right-hand side of 8b). Comparisons of synchronous and synchronized estimates are made in Section 5.

10 1814 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 We adopt the ADC model instead of other multivariate models because of two of its appealing features. First, it permits asymmetry in both the conditional variance and the conditional covariance. The asymmetry is captured by the third term, g 0 i g t 1g 0 t 1 g i, on the right-hand side of 9e). Second, and as noted before, it nests several well-known time varying covariance models. The ADC model reduces to: i) the constant correlation model in Bollerslev 1990) if Table 2 ADC model estimation with synchronous data estimation period: 3 August 1990±2 October 1996) a;b Parameter US i ˆ 1) and UK i ˆ 2) Estimate Standard error l l x x 12 ) x a 11 US on US) ) a 21 UK on US) a 12 US on UK) a 22 UK on UK) ) g 11 US on US) g 21 UK on US) ) g 12 US on UK) ) g 22 UK on UK) q / B B B a There are 1484 observations used in the estimation. Heteroskedasticity-consistent standard errors are reported. b For synchronous 16:00-to-16:00 returns in the US and the UK, R t ˆ l e t ; e t ju t 1 N 0; H t ; h iit ˆ h iit for i ˆ 1; 2; p p h 12t ˆ q 12 h 11t h 22t /12 h 12t ; h ijt ˆ x ij B ij h ijt 1 a 0 i e t 1e 0 t 1 a j g 0 i g t 1g 0 t 1 g j for all i; j; where R t ˆ R 1t ;R 2t Š 0 ; l ˆ l 1 ;l 2 Š 0 ; e t ˆ e 1t ;e 2t Š 0 ; a i ˆ a 1i ;a 2i Š 0 ; g i ˆ g 1i ;g 2i Š 0 ; g t ˆ min 0;e 1t ;min 0;e 2t Š 0 : * Statistically signi cant at the 10% level. ** Statistically signi cant at the 5% level. *** Statistically signi cant at the 1% level.

11 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± / 12 ˆ 0, ii) the BEKK model in Engle and Kroner 1995) if q 12 ˆ 0 and / 12 ˆ 1, iii) the VECH model of Bollerslev et al. 1988) if q 12 ˆ 0 with some imposed constraints on the vector a and the values of B ij, and iv) the Factor ARCH FARCH) model of Engle et al. 1990) if q 12 ˆ 0, / 12 ˆ 1 and with some imposed constraints on the vector a and the values of B ij. For further details we refer to Kroner and Ng 1998). 4. Modelling correlation and covariance dynamics In this section, we report the results of tting the ADC model to synchronous returns for the subperiod from 3 August 1990 to 2 October observations). The start date is constrained by the availability of the data. The end date is the same as that in Burns et al. 1998). We use the remaining data, from 3 October 1996 to 11 November observations), in a forecasting exercise in Section 6 that has a VaR application. Table 2 reports the parameter estimates for conditional correlation and covariance between US and UK returns Volatility spillovers The results reported in Table 2 show that conditional variance is highly persistent and there are volatility spillovers from the UK to the US in addition to that from the US to the UK. All, except one, of the g ij parameters are particularly strong indicating a more magni ed asymmetric e ect for shocks generated locally or from abroad. 14 The asymmetry is also evident from the news impact surfaces 15 plotted in Fig. 1. Fig. 1 a) shows the impact of previous day US and UK returns on US conditional variance, while Fig. 1 b) shows their impacts on UK conditional variance. It is interesting to note that asymmetry exists in both countries, in the sense that the impact on volatility is greater from a negative shock than that from a positive shock. But the greatest volatility shock is one that is caused by 13 All of the analysis below was also conducted on US and French returns, and the conclusions were identical. 14 Note that a positive or a negative) value for a ij alone cannot be interpreted as a positive or a negative) impact due to the complicated product terms. Take the US case, for example, a 0 i e t 1e 0 t 1 a j with i ˆ j ˆ 1) expands into a 2 11 e2 1t 1 a2 21 e2 2t 1 2a 11a 21 e 1t 1 e 2t 1. The rst and second terms are always positive or zero). The third term represents a joint e ect, whose sign and size are jointly determined by a 11 ; a 12 ; e 2t 1 and e 2t 1. The same applies to the estimates for g ij. 15 Kroner and Ng 1998) introduced this multivariate generalization of the graphical `news impact curve' from Engle and Ng 1993). The conditional variance covariance, or correlation) is plotted against US and UK shocks from the last period, holding the past conditional variances covariances, or correlations) constant at their unconditional sample mean levels.

12 1816 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 Fig. 1. News impact surfaces for conditional measures. a large negative local return that coincided with a large positive foreign return. 16 There are volatility spillovers from the US to the UK and vice versa. Although the results are not reported here, we found the same pattern between US and France. The strong volatility spillover from the US to the UK has also been reported in Theodossiou et al. 1997), Theodossiou and Lee 1993), and Hamao et al. 1990). The rst two papers study weekly returns for the period 1984±1994. Hamao et al., using open-to-close and close-to-open daily returns for the period 1 April 1985±31 March 1988, report the same nding. But Hamao et al. 16 This phenomenon seems at odds with common sense initially. However, further investigations show that this is indeed the feature of the data. First, when plotting UK versus US synchronous returns, there are no cases where the UK US) return is large and negative and the US UK) return is large and positive. Hence, Figs. 1 a) and b) include extrapolations in areas for which there are no observations. Secondly, the pattern observed here corresponds to the parameters estimated and reported in Table 1. These parameter estimates are based on returns closer to zero, which apparently have this pattern. All the estimates for a 11 ; a 21 ; a 12 ; a 22 ; g 11 ; g 21 ; g 12 ; g 22 have opposite signs within each pair. This means that the impact on conditional volatility is the greatest when the e 1 ; e or g 1 ; g 2 ) also have opposite signs.

13 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± could not con rm, at that time, if it was a true spillover e ect or a contemporaneous correlation because the stock returns they use are not synchronous. To our knowledge, this is the rst time signi cant spillovers from Europe to the US are documented Covariance and correlation The dynamics for the conditional covariance and conditional correlation are much less straightforward to analyse based on the estimates reported in Table 2, due to the numerous product terms involved. To appreciate the asymmetry e ects, we use the news impact surface for the covariance plotted in Fig. 1 c). Fig. 1 c) indicates that the covariance between the US and the UK returns increases more when the absolute value of the lagged residual return is higher. Covariance increases substantially when shocks in both countries are negative and large in absolute term. p Fig. 1 d) shows the conditional correlation h 12t = h 11t h 22t against lagged US and UK residual returns. Note that conditional correlation did not increase dramatically when the lagged residual returns are positive and large. Correlation increases sharply when the lagged residual return is negative and large in absolute term. 17 Correlation has little relationship with lagged residual returns within the midrange from )2 to + 2% Comparison with previous studies Finally, given that q 12 6ˆ 0, / 12 6ˆ 0, and / 12 6ˆ 1, all special cases of multivariate GARCH models nested within the ADC model, and used in previous studies of correlation dynamics, can be rejected. 19 The fact that / 12 6ˆ 0 also implies that the asymmetry in the conditional covariance is not purely driven by the asymmetry in the conditional variance. The fact that our ndings here on correlation dynamics are di erent from all previous studies is potentially due to the more exible structure for correlation 17 This corresponds to the observation made in Longin and Solnik 1998) who nd a similar relationship for monthly returns using extreme value theory. 18 We also plotted not included here) estimated correlations versus lagged US residual return which shows this lack of pattern in the midrange. This plot also shows an outlier where a lagged US residual return of almost 6% was followed by an extremely low correlation. Removing this outlier does not change our conclusion, namely that correlations do not respond as much to positive shocks as they do to negative shocks. 19 Using a likelihood ratio test, the BEKK q 12 ˆ 0 and / 12 ˆ 1) and constant correlation / 12 ˆ 0) models are rejected at the 1% signi cance level.

14 1818 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 in 9d) of the ADC model. 20 Previous studies make the assumption that correlation is either constant or varying according to a speci c dynamic. Eq. 9d) allows correlation to p have both a constant component, q 12, and a variable component, / 12 h 12t = h 11t h 22t. Studies that assume a constant correlation have only the rst term on the right-hand side of 9d) and lose all correlation dynamics. Studies that do not cater for this constant component have allowed all the spillovers, asymmetric e ects and relationships between conditional volatility and conditional covariance to be carried over to conditional correlation. There are yet another type of studies that impose ad hoc structures to the correlation dynamics. Longin and Solnik 1995), for example, x / 12 ˆ 0 and make q 12 a function of four predetermined dummy variables designed to capture the asymmetric e ect and the impact of large volatility on correlation. When we include the Longin and Solnik dummies into our ADC model, the dummy variable parameters are all statistically insigni cant. The more exible ADC model has allowed us to disentangle the subtle di erences between the correlation dynamics and the covariance dynamics here. 5. Sensitivity analysis In this section, we examine the sensitivity of conditional estimates with respect to model Riskmetricse versus ADC) and data type synchronous versus synchronized). We tted the Riskmetricse and the ADC models to both 16:00- to-16:00 returns London time) and the close-to-close returns using a subset of the sample from 3 August 1990 to 2 October Both models have procedures for adjusting data non-synchroneity when close-to-close returns are used see Section 3). Some summary statistics and correlation among the conditional measures are reported in Table Synchronous versus synchronized data We rst look at the e ect of using synchronized, instead of synchronous, data. There are no dramatic di erences among the summary statistics that are data type driven. The only consistent pattern is the large S.D. when the conditional measure is estimated using the synchronized data. This is a re ection that returns synchronization has added much noise to the already noisy estimation process. 20 Note that another possible explanation for these di erences is that we use synchronous daily prices here, whereas previous studies use non-synchronous daily closing prices, or closing prices at lower frequencies such as weekly or monthly.

15 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± Table 3 Summary statistics and correlation of conditional measures in-sample estimation period: 3 August 1990±2 October 1996) a Conditional Data type ADC Riskmetricse measure Mn S.D. Min Max Mn S.D. Min Max Panel A: Summary statistics US variance Synchronous Synchronized UK variance Synchronous Synchronized Covariance Synchronous ) Synchronized ) Correlation Synchronous ) Synchronized ) ADC synchronous ADC synchronized Riskmetricse synchronous Panel B: Correlation of conditional measures US variance ADC synchronized Riskmetrics synchronous Riskmetrics synchronized UK variance ADC synchronized Riskmetrics synchronous Riskmetrics synchronized Covariance ADC synchronized Riskmetrics synchronous Riskmetrics synchronized Correlation ADC synchronized Riskmetrics synchronous )0.012 Riskmetrics synchronized a Mean Mn), Standard deviation S.D.), Minimum Min) and Maximum Max) for the conditional variance, covariance and correlation. Returns are in percent i.e., multiplied by 100). Synchronous indicates returns are calculated from 16:00 London time) prices. Synchronized indicates that returns are calculated from closing prices with adjustment for non-synchroneity. The rst 73 observations are lost because of the lag structure in the Riskmetrics TM model. ADC refers to the asymmetric dynamic covariance model. The correlation estimates reported in Table 3, Panel B are more alarming, especially those of conditional correlations. The correlations among the relevant conditional variances are in the range of to The correlation between synchronous and synchronized covariances is for Riskmetricse and for the ADC model. The correlation between synchronous correlation and synchronized correlation, however, is only for the ADC model and for Riskmetricse. Hence, the use of

16 1820 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 close-to-close returns or synchronous returns produces substantially di erent conditional measures. The impact on conditional correlation estimates is particularly dramatic. We have noted that the conditional measures estimated from synchronous data are much less volatile through time than their synchronized counterparts Riskmetrics versus ADC models Next we compare the conditional measures produced by tting di erent models to the same data. From Table 3, the mean values of the conditional measures produced from the two models are about the same. However, the conditional measures produced by the Riskmetricse model are more volatile than those produced by the ADC model. Riskmetricse conditional variances are 20±50% more volatile than ADC conditional variances. Riskmetricse conditional covariances are about twice as volatile as the ADC counterparts, while Riskmetricse conditional correlations are 4±6 times as volatile as the ADCs. The other more worrying features are the Riskmetricse Min and Max statistics. Not only that its maximum correlation estimates have exceeded 1.0, 21 it also has negative values for Min correlation and Min covariance while those produced by the ADC model are never negative. 22 If one has to follow these correlation estimates strictly, one would have adopted completely opposite hedging strategies! To follow, we look at the corresponding correlation of the conditional measures produced by tting di erent models to the same data, and reported in Table 3, Panel B. The correlations among the relevant conditional variances range from to The correlation between the conditional covariances of the ADC model and Riskmetricse is for the synchronous prices and for the synchronized prices. The correlation between the conditional correlations is again lower at for synchronous prices and for synchronized prices. It is also worth noting that synchronous data, as compared with synchronized data, generally gives higher correlation between conditional measures produced from di erent models. 21 Here and in Section 6 forecasting) we used the Riskmetricse correlation measures as they are, even if they are above 1. Arguably, one could restrict the correlations to be between )1 and 1. Here, we have chosen to use the Riskmetricse correlation in its raw form. 22 Di erences in results for synchronous data are model Riskmetricse or ADC) driven. Di erence in results when the same model is used is due to data synchronization. In cases where model and data type both di er, due care has to be exercised in interpreting the results because the di erence may be model driven, or due to data synchronization, or both.

17 5.3. Summary M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± The key ndings in Section 5 can be summarised as follows. Returns synchronization has added much noise to the estimation process. Correlation dynamics are highly sensitive to model tted and data type used. If one has to produce conditional measure at all, it is perhaps less wrong to produce conditional covariances. Without knowing the `true' dynamics, it is not possible to conclude which model i.e., Riskmetricse or ADC) is better. But we want to highlight the fact that di erent models will produce di erent conditional estimates even with di erent signs in the case of conditional correlation and conditional covariance). A similar conclusion is reached in Kroner and Ng 1998), who compare four di erent multivariate GARCH models tted to returns on a large- rm and a small- rm portfolios. Finally, we have documented here several undesired properties in the conditional measures produced by the Riskmetricse model. 6. Illustration of economic signi cance and a VaR example The observations and comments made in the previous section are reiterated in our out-of-sample analysis. In this section, we compare the forecasting performance of the Riskmetricse and ADC models and examine the economic signi cance of their di erence using a VaR example. Recall from Section 3 that the ADC model was estimated using data from 3 August 1990 to 2 October The ADC model is not re-estimated, but the one-day-ahead conditional measures are updated each day with the latest observed returns. Forecasts are made one-step ahead for the period 3 October 1996±11 November The same process is repeated for the Riskmetricse model. Fig. 2 shows the one-step-ahead forecasts for the conditional correlation between US and UK returns. Fig. 2 shows, vividly, the lack of similarity among the conditional correlations of all models and all data types. The conditional correlation is particularly unstable in Fig. 2 d) when the Riskmetricse model and close-to-close returns are used. Clearly, this will result in di erent hedge ratios, and even di erent hedging strategies! To examine the size of forecasting errors of the two models, we implement a VaR example. First, we create a two-asset portfolio with equal proportion invested in the US and the UK. Assume for simplicity that the UK returns are measured in US$ and fully hedged for exchange rate risk, and the portfolio is re-balance each day to keep the portfolio weights constant. Next, we perform the `forward' test as prescribed by the Bank for International Settlement 1996), which involves counting the number of times the negative portfolio returns exceeded the forecast VaR gures.

18 1822 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 Fig. 2. Daily conditional correlation estimates US versus UK) out-of-sample forecast: 3 October 1996 to 11 November 1998). Fig. 3 plots the 1% VaR provision i.e., )2.33 times one-day-ahead forecast portfolio S.D. plus the mean) and the incidents of violation represented by larger dots) when portfolio losses are greater than the VaR provision. With 509 days in our forecasting period, the synchronous

19 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± Portfolio returns Fig. 3. VaR forward test for a two-asset portfolio US and UK) out-of- sample forecast: 3 October 1996±11 November 1998). synchronized) Riskmetricse VaR provisions were violated 15 13) times, while the synchronous synchronized) ADC VaR provisions were violated 17 15) times. Using back testing where each VaR measure is compared to the

20 1824 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 portfolio returns of the preceding 250 trading days leads to a similar conclusion. The large number of VaR-violations is not too surprising given the implicit assumption of a normal distribution for the stock index returns, and the absence of other leading indicators in the models. Nevertheless, the VaR example indicates that it is not critical to use synchronous data for predicting portfolio VaR. Although conditional correlation is unstable, conditional covariance, the more important measure for measuring portfolio risk, does not appear to be too sensitive to data type in our out-of-sample forecasting period. The use of the Riskmetricse model has led to fewer prediction errors. The smaller number of VaR violations produced by the Riskmetricse model should not be interpreted as a superior performance over the ADC model. First, it is clear from Fig. 3 that some of the ADC violations fall only just outside the VaR critical value. Second, the volatility in the out-of-sample period is higher than the in-sample period. The covariance structure in Riskmetricse has a higher level of persistence. As a result, the Riskmetricse covariance is higher than the ADC covariance in the out-of-sample period. The high covariance estimates translated into more generous VaR provisions leading to fewer VaR violations than the ADC model i.e., 2 each for both synchronous and synchronized returns). In practice, a more generous VaR provision represents a real opportunity loss due to additional capital being set aside. 23 Finally, and closely related to the previous point, the relatively poor out-of-sample performance of the ADC model can partly be explained by the fact that the parameters are not re-estimated in the out-of-sample period. Re-estimating the ADC model for the last 1000 observations i.e., including the out-of-sample period), and then using the estimated conditional variances and covariances to produce new VaR numbers for the out-ofsample period results in only 10 violations instead of 17. Hence, there is room for improvement As one of the referees has pointed out, in practice the actual VaR provision depends not only on the VaR estimate as presented here, but also on the multiplication factor applied to the VaR estimate in order to derive the capital requirement. The multiplicative factor depends on the number of violations. So the bigger number of violations produced by ADC model could be one potential weakness of this model. 24 Re-estimating the ADC model frequently requires huge amounts of computation time due to the di culty in achieving model convergence. It is beyond the scope of this study to determine the optimal number of observations and estimation frequency to estimate the ADC model for out-ofsample forecasting.

21 7. Conclusion M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805± The need to model daily correlation dynamics has intensi ed due to the recent shift in emphasis on short-term risk management. Yet, correlations are not directly observable and they vary day-by-day. Unfortunately, international nancial markets have di erent trading hours and the use of non-synchronous closing prices has led to a downward bias in correlation estimates. Modelling correlation using low frequency data mitigates the non-synchroneity problem, but misses out on the short-term dynamics and, at the same time, reduces model e ciency. E orts have been made recently in correcting daily correlation for bias due to data non-synchroneity. In this study we make use of Datastream 16:00 London time) stock market series to test the e ectiveness of these non-synchroneity adjustment models, and to study the daily correlation dynamics between the US and two European countries, viz. France and the UK. The parameter estimates produced from tting the ADC model con rm that there are asymmetry e ects in the conditional covariances of international stock markets similar to those found in conditional variances. A large) negative return leads to a larger increase in covariance than a large) positive returns. Kroner and Ng 1998) reported a similar asymmetry e ect among covariances of portfolio returns of small and large stocks. In addition to this, we also nd volatility spillovers from the US to the UK France), and vice versa. Our ndings clarify the results of Hamao et al. 1990). With the problem of data non-synchroneity, they could not distinguish if the US `lead' they found was a contemporaneous relation or a true lead. We nd correlations increase sharply when there is a large negative shock on the previous day, but they are much less sensitive to large positive returns, and returns that are smaller than 2% in absolute value. Our ndings here regarding correlation dynamics may have a potential impact in practice. We nd the conditional correlation estimates to be highly sensitive to model and data type. The synchronized and synchronous conditional measures are substantially di erent. The correlation of the conditional correlations, across models and data types, ranges from )0.012 to The correlation among the conditional covariance, across models and data types, is slightly higher and ranges from to A greater caution is called for since the huge di erence may result in completely di erent hedging strategies, for example. From a risk-management point of view, the use of the Riskmetricse model will lead to more volatile hedge ratios and more conservative VaR estimates than the ADC model. Although both dynamic covariance models were not able to cap the forecasting errors in the left tail to within the 1% criteria in our outof-sample forecast period, they just fell into the so called `yellow zone' according to the regulation laid out by the Bank for International Settlements.

22 1826 M. Martens, S.-H. Poon / Journal of Banking & Finance ) 1805±1827 Between the two combinations of returns synchronization methods and dynamic covariance models, we prefer the Burns et al. 1998) BEM) nonsynchroneity adjustment procedures with the Kroner and Ng 1998) ADC model for the GARCH speci cation. Such a combination provides correlation estimates that do not uctuate wildly and are guaranteed to be bounded between 1 and +1. However, much work is still needed to improve the procedures for adjusting non-synchroneity. The synchronized conditional measures produced by models of our preferred choice are still di erent from their synchronous counterparts. One possible way to improve the BEM GARCH method is to allow the moving average matrix, M, in the returns equation to also vary through time with the use of a Kalman lter. This is an important issue since adjustment for non-synchroneity is crucial for many stock markets that have no common trading hours. Acknowledgements This paper was written at the time when Ser-Huang Poon was visiting the Economics Department at University of California, San Diego, and the Department of Finance at Erasmus University, Rotterdam. She would like to thank these two institutions for their hospitality and Erasmus Center for Financial Research for nancial support. We are grateful for the helpful comments from Jan Annaert, Bernard Dumas, Graham Elliott, Giampiero Gallo, Clive Granger, Ken Peasnell, Stephen Taylor, Ruey Tsay, Ton Vorst, two anonymous referees, and participants of research seminars at Chicago Business School, Erasmus Center for Financial Research, and University of Technology, Sydney. This paper has also bene ted from comments from participants and the discussants at the French Finance Association conference in Aix- Provence discussant, Francois Longin), and the European Finance Association conference in Helsinki discussant, Jenke ter Horst). All remaining errors are our own. References Bank for International Settlement, Supervisory framework for the use of `backtesting' in conjunction with the internal models approach to market risk capital requirements. Becker, K.G., Finnerty, J.E., Gupta, M., The intertemporal relation between the US and Japanese stock markets. Journal of Finance 45, 1297±1306. Bertero, E., Mayer, C., Structure and performance: Global interdependence of stock markets around the crash of October European Economic Review 34, 1155±1180. Bollerslev, T., Modelling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH approach. Review of Economics and Statistics 72, 498±505.