Overnight futures trading: now even Australia and US have common trading hours

Transcription

1 Journal of International Financial Markets, Institutions and Money 12 (2002) Overnight futures trading: now even Australia and US have common trading hours Kingsley Fong a,1, Martin Martens b, * a School of Banking and Finance, Uni ersity of New South Wales, UNSW, Sydney 2052, NSW, Australia b Econometric Institute, Erasmus Uni ersity Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands Received 21 October 2000; accepted 4 June 2001 Abstract Overnight futures trading is available in USA, France and Australia. The overnight prices can be used to compute 24 h returns for two international markets over exactly the same time interval, even though the countries in which these markets operate are in completely different time zones. These synchronous returns make it possible to compute accurate daily correlation measures, which can for example be used for daily value-at-risk (VaR). Using Australian overnight index futures prices we find the correlation between USA and Australia to be about 55%, in stark contrast to near-zero correlation measures obtained from non-synchronous closing prices Elsevier Science B.V. All rights reserved. JEL classification: G14; G15 Keywords: Overnight futures trading; Synchronous prices; Correlation; Value-at-risk 1. Introduction The nineties have seen an introduction of overnight futures trading in USA, France and Australia. 2 Overnight future prices provide the opportunity to obtain * Corresponding author. Tel.: ; fax: addresses: [email protected] (K. Fong), [email protected] (M. Martens). 1 Tel.: ; fax: See Coppejans and Domowitz (1999), Chow et al. (1996), Frino and Hill (1999) for detailed descriptions of overnight futures trading in USA, France, and Australia, respectively /02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S (01)

2 168 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) daily prices taken at exactly the same time from two international markets that previously had no common trading hours. For example, for the US and Japan it is now possible to get an S&P 500 (overnight) index futures price at any time during Japanese daytime trading. These synchronous daily prices can be used to compute short-term (time-varying) correlation measures which are needed, for example, to determine value-at-risk (VaR). An analysis of the existing literature on correlation between international stock markets illustrates the importance and opportunities of overnight futures trading. Martens and Poon (2001) use the S&P 500 and FTSE 100 indices taken at 16:00 h London time, when both USA and UK stock markets are open. They show that (i) The use of close-to-close (non-synchronous) returns underestimates the correlation because the two markets close at different times; (ii) Existing procedures that use closing prices and adjust for data non-synchroneity produce correlation measures that are substantially different from their synchronous counterparts. 3 Other studies try to by-pass the non-synchroneity problem by using weekly or monthly data. Although monthly data avoid any non-synchroneity problems 4, they result in small samples implying large S.E.s and a need to impose restrictions on multivariate dynamic models 5. Overnight futures prices allow us to avoid all these problems even for countries whose stock markets have no common trading hours. In this study we focus on Australian overnight index futures trading. This market is interesting due to the fact that most of US daytime trading happens during the Australian overnight trading hours, whereas non-us markets in general strongly respond to US stock returns as they occur or as soon as their own market starts trading. This is certainly the case for Australia, as we find that the correlation between the US open-to-close return and the corresponding Australian overnight futures return is 83%. The overnight futures prices are sufficiently efficient for the purpose of computing daily correlation measures between Australia and US. Overnight futures prices only trail US prices up to 10 min, although they do appear to overreact to US returns. In addition, we do not find a US lead using daily synchronous futures prices 6 measured at 15:00 eastern standard time (EST). The correlation measures using synchronous prices are robust in that we find a similar correlation of about 55% for the daily, weekly and bi-weekly frequency. These correlation measures are in stark contrast to near zero daily correlation measures obtained from non-synchronous daily closing prices, as reported daily by Riskmetrics. 3 Adjustment procedures are suggested in Riskmetrics (1996), Kahya (1997), Burns et al. (1998). 4 Ramchand and Susmel (1998) use weekly data, but for Australia and USA this is insufficient to eliminate the non-synchroneity problem: Ramchand and Susmel report a correlation of around 24% whereas we find it is about 55%. 5 See for example Longin and Solnik (1995) who use a restricted multivariate GARCH model for 30 years of monthly data, still only 360 observations. 6 We use the S&P 500 index futures prices from daytime trading in Chicago and the Australian share price index (SPI) futures prices from overnight trading in Sydney.

3 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) The remainder of this study is organized as follows. Section 2 describes our data. Section 3 reports on the efficiency of overnight futures prices and the impact of US prices on Australian overnight futures prices. In Section 4 we look at correlation measures between USA and Australia at various frequencies. Finally, Section 5 will conclude. 2. Data In this study we use prices for the S&P 500 index futures and Australian share price index (SPI) futures contracts from January 1994 December The main reason to use futures and not the underlying index is that we can obtain synchronous daily prices for futures but not for the index itself. In addition, the use of futures avoids the so-called infrequent trading problem. Indices are computed from the last transaction price of all the underlying stocks, and these prices are potentially stale. See, for example, Aggarwal and Park (1994) where previous findings using the index are reversed when using index-futures 7. Stoll and Whaley (1990), among many other studies, show that futures returns have a substantial lead over the index returns. Hence, at the intraday level it is superior to use futures instead of the underlying index. SYCOM is the electronic trading system of the Sydney Futures Exchange for overnight futures trading. During the sample period, trading hours were from 16:40 to 06:00 h Australian eastern standard time (AEST), extending to 07:00 h during daylight saving time 8. During this time period the stocks underlying the index do not trade and no new index value is computed. Daytime trading in the index futures trading pit ran from 09:50 to 16:15 h AEST with a lunch break between 12:30 and 14:00 h 9. The Australian Stock Exchange (ASX) trades continuously from 10:00 to 16:00 h AEST. For the Australian SPI futures contract we have the last trade and the last quote for each 5-min interval, as well as the number of trades and number of quote revisions for each 5-min interval, both during daytime and overnight trading 10.For the US S&P 500 futures contract we have all transaction prices with a time stamp 7 Aggarwal and Park find that, unlike prior studies, US equity prices do not lead Japanese equity prices as both US and Japanese opening equity prices reflect overnight price changes in the other market. 8 Full electronic trading at the SFE was introduced by the end of Sydney daylight saving time starts on the last Sunday in October and continues until the last Sunday in March. Note that Chicago/New York daylight saving time starts from the first Sunday in April and continues until the last Sunday in October. As a result, the time difference between Sydney and New York varies from 14 to 16 h. 9 These are the trading hours during the sample period. Since December 1999, trading at the Sydney Futures Exchange fully computerized and trading hours are 17:10 8:00 and 09:50 16:30 h AEST. 10 See Frino and Hill (1999) for a description of daytime and overnight volume, volatility and spreads.

4 170 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) to the nearest second. The S&P 500 futures are traded on the Chicago Mercantile Exchange (CME) from 08:30 to 15:15 h Chicago time (EST-1 h) whereas the underlying stocks on the New York Stock Exchange (NYSE) trade from 09:30 to 16:00 h EST. See Fig. 1 for a comparison of US and Australian trading hours, where all trading hours are expressed in EST. Fig. 1 clearly illustrates that when using closing prices from the ASX and the NYSE on the same calendar day (as done by Riskmetrics, for example) these prices are 16 h apart 11. Fig. 1 also shows that a large fraction of Australian overnight futures trading hours coincide with CME and NYSE trading hours. This allows us to extract synchronous prices for Australian and US index-futures. To obtain an idea of the trading activity in Australian index futures during the night, we computed the average number of trades and quotes in 5-min intervals over all days. Before doing so, we adjusted the Australian time to the corresponding US (New York) time taking into account daylight saving time. The result is presented in Fig. 2. From the start of overnight trading (before 03:00 h EST) trading activity decreases until the first peak at 08:30 h EST. It should be noted that from 08:20 h onwards, interest rate futures and foreign exchange futures start trading at the CME. This includes the USD/AUD futures contract. Also US macroeconomic news announcements are made at 08:30 h. The second peak at 09:30 h EST is at the opening of the NYSE and the start of floor trading in S&P 500 index-futures. The peak at 15:00 h EST coincides with the close of Australian overnight futures trading during US wintertime, whereas the peak at 16:00 h EST coincides with the close of Fig. 1. Trading hours in eastern standard time (EST) for the New York Stock Exchange (NYSE), the Chicago Mercantile Exchange (CME), the Australian Stock Exchange (ASX), and Australian overnight and daytime futures trading. Australian time has been translated into EST (minus 14, 15 or 16 h depending on daylight saving). This figure illustrates Australian trading hours when the time difference is 16 h (US wintertime). During US summertime the time difference is 14 h, but Australian overnight futures trading stops 1 h earlier. In that case overnight futures trading stops at 16:00 h EST. 11 Note that although in Fig. 1 the Australian stock exchange appears to be closing 8 h after the NYSE close, in calendar days Australia is almost one day ahead.

5 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) Fig. 2. Average number of quotes and trades during each 5-min interval for Australian overnight index futures trading. Australian time has been translated into EST (minus 14, 15 or 16 h depending on daylight saving). The time stamp indicates the starting time of the 5-min interval. The sample period is January 1994 December 1998 (1242 days). Australian futures trading during US summertime. Throughout the year 16:00 h EST is also the close of the NYSE. A similar pattern is found for the volatility of Australian futures returns. Fig. 3 shows the average absolute 5-min futures returns taken over all trading days. The seasonal pattern in volatility shows once again the importance of the US markets for Australian overnight futures trading. Given that, on average, there are more quotes than trades, and using midpoints will avoid the bid ask bounce inherent in transaction prices, we use bid ask quotes in our analysis below. For S&P 500 index-futures, however, only transaction prices are available. 3. The efficiency of Australian overnight futures prices Given the low volume during overnight trading, we need to establish that overnight futures prices are sufficiently efficient to be used for computing the daily correlation between the US and Australia. In addition, we want to test the hypothesis that Australian overnight futures prices are primarily driven by overseas markets, the US in particular. After all, during overnight futures trading the underlying stocks do not trade, and there is no specific news for Australian companies.

6 172 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) The correlation between o ernight and daytime futures returns If overnight futures prices are efficient, the closing price of overnight trading should accurately reflect all available information. The problem for overnight futures traders is that the underlying stocks do not trade, and as such they can merely interpret news for the broad market when they observe the performance of overseas markets. In subsequent daytime trading both the index futures contract and the underlying stocks trade. Stock traders will process the overnight information for individual stocks, and the aggregate response of individual stock prices will adjust the value of the index and with it the futures price. Hence, one possible test for the efficiency of overnight futures prices, the closing prices in particular, is that there is no relationship between overnight futures returns and subsequent morning futures returns. Fig. 4 plots the cumulative 5-min returns during morning trading hours grouped by sign and threshold of overnight returns. Overnight returns are computed using the last midpoint of the bid ask quotes during overnight trading period and the last midpoint of the bid ask quotes during the prior daytime trading period. Daytime cumulative returns are computed using the opening futures midpoint of the bid ask quotes of subsequent Australian daytime trading at 17:50 h EST 12, and the last midpoint of the bid ask quotes in Fig. 3. Average return volatility for quotes and trades during each 5-min interval for Australian overnight index futures trading. Australian time has been translated into EST (minus 14, 15 or 16 h depending on daylight saving). The time stamp indicates the starting time of the 5-min interval. The sample period is January 1994 December 1998 (1242 days). 12 Here and below the times relate to US wintertime (October March). For the other half of the year (US daylight saving time) the times are 2 h later than those presented here.

7 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) Fig. 4. Conditional cumulative Australian morning returns. The four lines differ in that each sample is based on the sign and magnitude of the Australian overnight futures return (from the close prior to the daytime trading period to the close of the overnight trading period) and whether the NYSE closes at the same time ( common close ) or after ( non-common close ) Australian overnight futures trading. The sample period is January 1994 December 1998, see also Table 2 for details on the subsamples. The cumulative returns are computed over mid-quotes at the end of each 5-min interval and the 17:50 h opening mid-quote. 17:50 h EST corresponds to the opening of Australian daytime futures trading during US summertime. Two hours should be added to all times during US wintertime. all subsequent 5-min intervals up to the end of the morning session at 20:30 h EST. Note that during US summertime, Australian overnight futures trading closes at the same time as the close of the NYSE ( common close ), whereas during US wintertime Australian overnight futures trading stops 1 h before the NYSE close ( non-common close ). All four lines show that daytime cumulative returns are negatively related to overnight futures returns. Following a negative overnight return in excess of 1%, the average daytime cumulative return is consistently above zero during the morning trading session. The average cumulative return subsequent to a positive overnight return in excess of 1% is consistently below zero. This pattern suggests that overnight futures traders over-react to international news. In addition, the lines tend to drift in the early trading hours up to 19:00 h EST, particularly before 18:30 h. This drift may be due to lagged adjustments in the futures market and the sequential opening of stocks trading on the ASX from 18:00 to 18:10 h. Ito et al. (1998) provide evidence that opening for trading attracts

8 174 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) informed traders 13. The trading of informed traders in specific stocks on the ASX could help to correct pricing errors of index-futures. To investigate the statistical evidence on this return reversal for the entire sample, we present in Table 1 the correlations between overnight futures returns and subsequent daytime returns. The correlations computed over the 521 (695) days when the Australian overnight futures trading closes at 15:00 h EST (16:00 h EST) are contained in panel A (B). Directly related to the results in Fig. 4 are the correlations between the overnight returns and the cumulative returns from 17:50 h EST (19:50 h EST) onwards. These correlations are always negative and statistically significant at the 1% level, and hence overnight returns are partly reversed during subsequent daytime trading 14. The correlations between the overnight returns and Table 1 Correlations between the overnight return and morning floor returns Time (h EST) 5-min returns Cumulative returns Panel A: Australian o ernight futures trading closes at 15:00 h EST (1 h before the NYSE close) 17:50 17: ** [0.097] 0.296** [0.097] 17:55 18: [0.041] 0.252** [0.089] 18:00 18: [0.039] 0.251** [0.079] 18:05 18: * [0.039] 0.200** [0.070] 18:10 18: ** [0.036] 0.277** [0.066] 18:15 18: [0.031] 0.266** [0.063] 18:20 18: [0.063] 0.286** [0.073] 18:25 18: [0.045] 0.285** [0.080] Panel B: Australian o ernight futures trading closes at 16:00 h EST (same time as the NYSE close) 19:50 19: ** [0.030] 0.122** [0.030] 19:55 20: ** [0.035] 0.079** [0.020] 20:00 20: [0.045] 0.104** [0.026] 20:05 20: [0.055] 0.117** [0.030] 20:10 20: ** [0.039] 0.149** [0.032] 20:15 20: * [0.050] 0.179** [0.038] 20:20 20: [0.045] 0.197** [0.037] 20:25 20: [0.035] 0.199** [0.036] Correlations between the overnight returns (close of Australian daytime futures trading to the close of Australian overnight futures trading) and 5-min returns in morning trading, and correlations between the overnight returns and the cumulative morning returns for January 1994 December There are 521 observations for Panel A and 695 observations for Panel B. Inside brackets are heteroscedastic and autocorrelation consistent S.E. ** and * Denotes significance at the 1 and 5% level, respectively. 13 Ito, Lyons and Melvin find that lunchtime volatility in the FX market (YEN/USD and DEM/USD) in Tokyo increases after the abolition of the lunchtime trading restriction, whereas there is little change in the flow of public information. This, together with the reduction in the proportion of volatility attributable to mispricing, leads Ito et al. to conclude that the increased volatility during lunchtime trading is driven by private information. 14 For space reasons, the table stops at 18:30 (20:30) EST, but the correlation between the overnight return and the return from 17:50 to 20:30 (19:50 22:30 h) EST is also negative and significant at the 1% level.

9 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) individual daytime 5-min returns reveal which intervals contribute most to the negative correlation. Note that the returns over the first 5-min interval have a statistically significantly negative correlation with overnight returns 15. Interestingly, during the 5 min after all Australian stocks started trading 16 the correlations are also significantly negative at the 1% level. During this interval all stocks underlying the SPI will have started trading, allowing the index to be computed using information from new stock prices, as opposed to stale prices from the previous trading day. It appears that in the first 5-min interval of daytime futures trading, futures traders agree on a different price than the overnight futures trading closing price, and subsequently the stock market provides the correct response to any news that occurred during non-trading hours. In both cases it seems the overnight futures prices overreact. Given our finding of statistically significant overnight prices overreaction, we also look at a simple trading strategy to see whether the return reversal is economically significant. If the overnight return exceeds 1%, we short the SPI futures contract at the first available bid at the start of futures daytime trading, and eliminate our futures position at the first available ask 40 min later (20 min after the completed opening of stock trading at the ASX). Similarly, when the overnight return is lower than 1%, we go long at the first available ask and eliminate the futures position at the first available bid 40 min later. This way we take into account transaction costs due to the difference between buying and selling prices 17. Table 2 presents statistics of the profits for a round-trip trade of 1 futures contract in multiples of the minimum tick of one index point (one index point corresponds to AUD 25). Profits are possible, with all mean returns being positive. For example, combining long and short trades together ( 1 and 1%) Panel A shows a statistically significant mean return of index points (AUD 180) per contract. On the 13 occasions that overnight returns are less than 1%, the strategy also generates a statistically significant profit, with a mean profit of index points. Interestingly, the profits are much lower and not significantly different from zero for panel B 18. Seemingly 15 We also computed correlations between the overnight return and cumulative returns where the first 5-min interval is excluded from the cumulative return. The correlations are still significant at the 1% level, but only from 18:15 (20:15 h) EST onwards :00 18:15 h EST for Panel A and 20:00 20:15 h EST for Panel B. 17 In addition to the bid-ask spread, the Sydney Futures Exchange also levies a fee of AUD 1 for every executed trade. However, scratch trades (round-trip trades with zero profit) executed by local members are exempted. Transaction costs for off-floor traders are considerably higher. E.g. discount brokers for retail customers charge approximately AUD 30 per trade. 18 Combining all cases of Panel A and B together (102 cases) gives a mean profit of 3.40 index points, which is significant at the 1% level.

10 176 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) Table 2 Profitability of a simple trading strategy Overnight return PANEL A: Australian overnight futures trading closes PANEL B: Australian overnight futures trading closes at 15:00 h EST (1 h before the NYSE close) at 16:00 h EST (same time as the NYSE close) N Mean return S.D. N Mean return S.D. Profit in index points (1 index point=aud25) 1% or 1% * % % * Number of profitable days Overnight return N Wins Losses N Wins Losses 1% or 1% * 24 1% 14 10* * 10 1% If the overnight return is larger than 1% (smaller than 1%), the trading profit is the difference between the first bid (ask) quote observed on the floor and the first ask (bid) quote observed after 10:30. The mean profit and S.D.s are expressed in index points, where 1 index point corresponds to AUD 25. The S.E. of the mean returns (not reported) is computed as the S.D. over the square root of the number of observations (N), and is used to determine the statistical significance of the mean profit. The significance of the number of wins is based on the binomial distribution (one-sided test). ** and * denotes significance at the 1 and 5% level, respectively.

11 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) Table 3 Correlations between US and Australian 5-min returns Total overnight period 9:30 11:00 h EST 11:30 14:00 h EST Corr [r t [0.009] [0.022] [0.010] Corr [r t [0.008] 0.042* [0.019] 0.030** [0.010] Corr [r t [0.007] [0.013] [0.011] Corr [r t 2, r AU t ] 0.033** [0.012] 0.068** [0.027] [0.014] Corr [r t ** [0.014] 0.263** [0.038] 0.219** [0.012] Corr [r US t, r AU t ] 0.317** [0.014] 0.362** [0.037] 0.267** [0.014] Corr [r US t, r t 1 ] [0.011] [0.028] [0.009] US Corr [r t, r t [0.009] [0.024] [0.011] Corr [r US t, r t 3 ] [0.008] [0.017] [0.010] US AU Corr [r t, r t 4 ] [0.007] [0.015] [0.011] Corr [r US t, r t 5 ] [0.012] [0.034] [0.011] Correlations between US and Australian 5-min returns for 10 January December 1998 (1194 common trading days, common 5-min intervals). Heteroscedasticity and autocorrelation consistent (HAC) errors inside brackets. ** And * denotes significance at the 1 and 5% level, respectively. the overnight futures prices are more efficient when Australian overnight futures trading closes at the same time the NYSE closes 19. Table 2 also provides the number of times the strategy wins and loses to provide another look at the riskiness of the trading strategy. The number of times the strategy wins clearly outnumbers the number of times the strategy loses, and in half of the cases the number of wins is statistically significant based on the one-sided binomial test. Hence, it appears that conditional on large overnight returns, the return reversal pattern is exploitable and economically significant This may be related to the large and statistically significant positive correlation between the overnight return (daytime close to overnight close) and the return from the overnight close to the daytime open during the 521 days Australian overnight futures trading closes 1 h before the NYSE close. The absence of price discovery in the Australian market while the US markets are still open increases the futures pricing error at the opening of trading. 20 We also investigated the profits over time. There is no evidence that price efficiency is improving over time. In fact, the strategy is slightly more frequently triggered in 1997 and 1998 and the profit in 1998 is slightly higher than in the earlier years. Finally, we test robustness to potential difficulties in trading at the proposed times, even though that sometimes means we do overestimate the transaction costs. The trading profits are re-estimated using the first trade at the start of floor trading, and the first trade after 10:30 h (instead of the quotes). Occasionally the trade occurs when the bid price equals the ask price, and hence the nature of the trade (buy or sell) cannot be identified. In that case we assume the worst and deduct one tick for the transaction costs. Even in this case profits are positive, for example the mean return for all 27 cases when Australian overnight futures trading closes 1 h before the NYSE close is ticks.

12 178 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) US and Australian intraday futures returns Whereas in the previous subsection we look at Australian futures prices only, we now compare the Australian overnight prices directly with the prices of US futures that trade at the same time. Using 5-min returns for both markets, we can look at the Australian overnight futures market during the common trading hours, i.e. 09:30 through 16:00 h EST (or 15:00 h EST, depending on daylight saving). First of all, to underline the importance of the US market for Australian overnight trading, we computed the correlation between the Chicago trading returns (09:30 16:00 or 09:30 15:00 h EST, depending on daylight saving time) and corresponding Australian futures returns. The correlation is 83%. Second, we computed the cross-correlations between US and Australian 5-min returns 21. The results are presented in Table 3. In general the US lead is small, up to 10 min for the total overnight period, and 09:30 11:00 h EST. There is a stronger response to the US in the 09:30 11:00 h interval than in the 11:30 14:00 h interval. This is presumably due to US news announcements, a greater interest in US opening trading, and observing the direction of the market. In addition, the higher liquidity in the overnight futures market during the 09:30 11:00 h period results in less intervals without observations and reduces spurious cross-correlations. The results indicate that the Australian futures prices are reasonably efficient in this respect, taking into account the low activity. Furthermore, the overnight bid ask spreads are in the order of four index-points (compared with one indexpoint during daytime trading) indicating that economic profits are unlikely. 4. Measuring the correlation between the US and Australia Correlation measures are of vital importance to portfolio managers and risk managers alike. Whereas portfolio managers would be more interested in correlations over longer horizons, VaR requires daily correlation measures. However, with international stock markets having different trading hours, it is difficult to get synchronous measures. For example, Riskmetrics produces daily correlation forecasts, which include a forecast for the US and Australia stock markets. Using closing prices from the same calendar day, the forecasted correlation is usually around zero. The true correlation, we believe, is approximately 55%. Overnight futures trading provides new opportunities. It allows us to synchronize the 24-h returns even for the US and Australian markets. Overnight futures trading features in the USA, France, and Australia. Hence, for many other markets we can synchronize returns and obtain accurate daily correlation measures. We match the 21 In Kofman and Martens (1997) intraday correlations between S&P and FTSE 1-min futures returns are computed, showing a small lead of up to 2 min of the US over the UK during daytime trading when both markets are open at the same time. Here also a description is provided on the exact calculation of the Heteroscedasticity and Autocorrelation Consistent (HAC) errors.

13 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) US and Australian returns during US daytime trading and Australian overnight futures trading. We then measure the correlation at various frequencies (daily, weekly, monthly) and various times (10:00 15:00 h EST). The results are provided in Table 4. The results indicate that the correlation is somewhere between 50 and 56%. The starting time for the 24-h day does not seem to matter, and there is no clear pattern across the various frequencies. We also computed the correlation between lagged daily US returns and current daily Australian returns (not reported here). None of these correlations are significantly different from zero, indicating that there is no US lead in daily returns. Hence the common finding that markets around the world respond to US price movements is all due to a contemporaneous response. This is another indication that the overnight futures market is efficient, particularly for the calculation of daily correlations. In terms of S.E.s, it is obvious that sampling at the monthly frequency leads to small samples and hence larger S.E.s. So even for longer horizons, it will be more accurate to use higher frequencies than monthly data. This becomes even more evident when considering different starting dates from the 17 January 1994, employed here. The monthly correlation varies between and depending on how the 20-day window is laid over the data. Also the large number of observations at the daily level means that multivariate GARCH models can be estimated. Unrestricted models usually require in excess of 700 observations, something that is obviously difficult at the monthly frequency. Subsequently these daily models can be used to make multiple period forecasts of covariance and correlation, and hence will not only be useful for short-term risk management but also for longer horizons relevant to portfolio managers 22. The most direct application, however, is daily value-at-risk (VaR). To compute daily VaR, daily volatility and correlation forecasts are required. The synchronous Table 4 Sample correlations at various times and frequencies Days (obs.) 10:00 h 11:00 h 12:00 h 13:00 h 14:00 h 15:00 h 1 (1180) [0.045] [0.034] [0.033] [0.032] [0.031] [0.032] 2 (590) [0.040] [0.042] [0.044] [0.044] [0.044] [0.045] 4 (295) [0.053] [0.059] [0.061] [0.062] [0.061] [0.063] 5 (236) [0.067] [0.071] [0.066] [0.065] [0.062] [0.067] 10 (118) [0.090] [0.095] [0.090] [0.089] [0.087] [0.083] 20 (59) [0.120] [0.124] [0.120] [0.121] [0.119] [0.115] Correlation between US and Australia for 17 January December 1998 (1180 daily observations). The synchronous times used are 10:00 15:00 EST. The correlation is computed for various frequencies (1-day up to 20-day periods). Inside brackets are heteroscedasticity and autocorrelation consistent (HAC) errors. 22 Burns et al. (1998), for example, show how a multivariate daily GARCH model can be used to construct a term structure of correlations.

14 180 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) prices allow us to correctly compute the correlation. To demonstrate the difference between (non-synchronous) close-to-close returns (16:00 h EST for the US and for Australia 00:00 h EST during US wintertime and 02:00 h EST during US daylight saving) and synchronous returns, the Riskmetrics approach is applied to both. Riskmetrics calculates conditional variance and covariance based on the exponentially weighted moving average (EWMA) method: and t2 = K k=0 k (r t k r ) 2 (1) K k k=0 cov(r t (i ), r t ( j ) )= K k=0 k (i ) (r t k r (i ) ( j ) )(r t k r ( j ) ) (2) K k k=1 (i ) where r t is the daily return for market i (i=us, Australia). For daily data, Riskmetrics sets the decay parameter equal to 0.94, the number of lagged observations K equal to 74, and the mean return for each asset equal to zero. The variance and covariance measures on day t are the forecasts for day t+1. For a portfolio that invests weight w in Australia and (1 w) in US, the S.D. is: Pt = w 2 2 it +(1 w) 2 2 jt +2w(1 w)cov ijt (3) The 1 and 5% VaR are then obtained by multiplying the portfolio S.D. by and 1.645, respectively, following the Riskmetrics assumption of returns following a normal distribution. The 1 and 5% daily VaR is computed for 3 May December 1998 (1122 trading days). The first 74 days of the original sample are needed to compute the first variances and covariance. Each day the actual portfolio return is compared to the VaR. If there is a loss in excess of the VaR, the case is labeled a violation. A side issue is which returns to use for the actual portfolio return. For completeness we use both (non-synchronous) close-to-close returns and synchronous returns, although we obviously think the latter should be used. The results for w=50% are provided in Table 5. The results show that, in all cases, the VaR measures based on synchronous returns have far less violations than their non-synchronous counterparts. Consider, for example, the 5% VaR with portfolio returns computed from synchronous returns. Computing VaR based on synchronous returns leads to 65 violations (5.8% of all observations) as opposed to 86 violations (7.7% of all observations) for VaR based on close-to-close returns. This is obviously caused by underestimating the covariance in the case of non-synchronous close-to-close returns, and subsequently underestimating the VaR.

15 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) Table 5 Number of times the portfolio return is below the value-at-risk Portfolio return based on VaR based on close-to-close returns VaR based on synchronous returns 5% VaR 1% VaR 5% VaR 1% VaR Synchronous returns 86 (0.077) 41 (0.037) 65 (0.058) 28 (0.025) Close-to-close returns 57 (0.051) 27 (0.024) 46 (0.041) 16 (0.014) Number of times the value-at-risk provides insufficient capital to cover the loss on the portfolio that invests 50% in Australia and 50% in the US. The VaR is computed for 3 May December 1998 (1122 trading days) using either closing prices (16:00 h EST for the US and for Australia 00:00 h EST during US wintertime and 02:00 h EST during US daylight saving) or synchronous prices (15:00 h EST for both US and Australia). Inside parentheses is the percentage of times the portfolio return is lower than the VaR. 5. Conclusion In this study we investigate the efficiency of Australian overnight futures prices and we discuss the new opportunities that overnight trading provides us for short-term risk management. We find that Australian overnight futures returns strongly respond to US daytime trading. However, there appears to be overreactions in that subsequent futures returns at the start of Australian daytime futures trading tend to partly reverse the overnight returns. In particular, the returns in the first 5 min of daytime trading as well as the returns during the 5 min after all the stocks underlying the index start trading show a significant negative correlation with the overnight returns, and a simple trading strategy conditioned on large overnight returns yields positive profits. For the computation of Australian 24-h returns that are synchronous with 24-h US returns, the overnight futures prices are sufficiently efficient. There is no US lead in daily returns, and for frequencies of 1 10 days the sample correlation is relatively stable at around 50 56%. Hence, these correlations are useful for short-term risk management. Using daily or weekly closing prices for the US and Australian stock markets on the same calendar day severely underestimates the correlation and hence will underestimate the capital requirements needed for VaR. The use of overnight futures prices makes it possible to compute synchronous returns between stock markets that share no common trading hours. The idea is applied to the Australian and the US markets here, but it could be equally applied to other international stock markets. For instance, it is now possible to compute synchronous daily correlations between the world s two largest stock markets, the US and Japan.

16 182 K. Fong, M. Martens / Int. Fin. Markets, Inst. and Money 12 (2002) Acknowledgements The authors would like to thank Amelia Hill, Petko Kalev, an anonymous referee and seminar participants at the 12th Australasian Banking and Finance conference for helpful comments. We are also grateful to the Futures Industry Institute for providing the S&P 500 index futures data, and the Futures Research Center of SIRCA for providing the Australian futures data. All remaining errors are our own responsibility. References Aggarwal, R., Park, Y.S., The relationship between daily US and Japanese equity prices: evidence from spot versus futures markets. Journal of Banking and Finance 18, Burns, P., Engle, R., Mezrich, J., Correlations and volatilities of asynchronous data. Journal of Derivatives 5, Chow, E., Lee, J., Shyy, J., Trading mechanisms and trading preferences on a 24-hour futures market: a case study of the Floor/GLOBEX switch on MATIF. Journal of Banking and Finance 20, Coppejans, M., Domowitz, I., Pricing behaviour in an off-hours computerized market. Journal of Empirical Finance 6, Frino, A., Hill A., Intranight trading behaviour. Working paper, Sydney University. Ito, T., Lyons, R.K., Melvin, M.T., Is there private information in the FX markets? The Tokyo experiment. Journal of Finance 53, Kahya, E., Correlation of returns in non-contemporaneous markets. Multinational Finance Journal 2 (1), Kofman, P., Martens, M., Interaction between stock markets: an analysis of the common trading hours at the London and New York stock exchange. Journal of International Money and Finance 16, Longin, F., Solnik, B., Is there correlation in international equity returns? Journal of International Money and Finance 14, Martens, M., Poon S.-H., Returns synchronization and daily correlation dynamics between international stock markets. Journal of Banking and Finance 25, Ramchand, L., Susmel, R., Volatility and cross correlation across major stock markets. Journal of Empirical Finance 4, Riskmetrics, In: Morgan, J.P. (Ed.), Technical Document, fourth ed. Stoll, H.R., Whaley, R.E., The dynamics of stock index and stock index futures returns. Journal of Financial and Quantitative Analysis 25,