股票收盘价格的确定和股票指数期货套期保值性能.doc

Determination of stock closing prices and hedging performance with stock indices futuresKeywords: Stock closing prices; Futures closing prices; Market efficiency; Hedging effectiveness G14; G15; G18AbstractThis paper examines the impact of the determination of stock closing prices on futures price efficiency and hedging effectiveness with stock indices futures. The empirical results indicate that the increase in the length of the batching period of the stock closing call improves price efficiency in the futures closing prices and then enhances hedging performance in terms of the hedging risks. Additionally, from a utility-maximization point of view, hedging performance does not improve after the introduction of the 5 min stock closing call, which can be explained by an improvement in price efficiency at the futures market close.1. IntroductionThis paper examines the impact of the determination of stock closing prices on futures price efficiency and hedging effectiveness with stock indices futures. Hedging effectiveness has been markedly informed by futures literature (see Yang and Allen, 2004; Fernandez, 2008; Hsu et al., 2008). In contrast, a number of recent studies have examined the effects of the determination of stock closing prices on market efficiency (see Pagano and Schwartz, 2003; Aitken et al., 2005; Huang and Tsai, 2008). Pagano and Schwartz (2003) indicate that a change in the determination of stock closing prices might affect the derivatives markets. In practice, the relationship between stock and futures closing prices is unlikely to change over time because of arbitrage forces (Tong, 1996). Hence, if the determination of stock closing prices affects market efficiency in stock closing prices, it might then have an impact on futures price efficiency and hedging performance. However, no studies have been performed to investigate this impact.On 1 July 2002, the Taiwan Stock Exchange (TSE) expanded the length of the batching period of the stock closing call from 30 sec to 5 min in an attempt to enhance the fairness of stock closing prices. Additionally, the Taiwan Futures Exchange (TAIFEX) closes 15 min later than the TSE. Hence, this institutional change provides an opportunity to study the effect on futures closing price efficiency and hedging effectiveness.A recent study by Lee et al. (2007) reports that an increase in the length of the batching period of the stock closing call affects the behaviour of futures prices, specifically indicating that return volatility and trading volume increased after stock market close when the TSE expanded the length of the batching period of the stock closing call. Furthermore, the study also shows that pre-close stock returns have a great impact on extended futures returns when the batching period is long. However, the impact of increasing the length of the batching period of the stock closing call on futures closing price efficiency and hedging effectiveness is not examined, and the present study extends upon this previous study and investigates this impact with stock indices futures.The empirical results of this study indicate that the determination of stock closing prices affects futures price efficiency and hedging performance. Specifically, the increase in the length of the batching period of the stock closing call improves price efficiency in futures closing prices and then enhances hedging performance in terms of the hedging risks perspective. However, hedging performance with respect to utility-maximization does not improve with a longer batching period of the stock closing call, which can be explained by an improvement in price efficiency at the futures market close (see Figlewski, 1984). These empirical results provide policy-makers with valuable information on the importance of the impact of the determination of stock closing prices on futures markets.The remainder of this research is organized as follows: a literature review and hypotheses are presented next. Sections 4 and 5 describe the data and methodology used in this paper. Section 6 presents the empirical results and the conclusions are presented in Section 7.2. Literature reviewThe determination of the optimal hedge strategy has attracted considerable attention from financial econometricians. In the published hedge ratio estimation literature, the optimal hedge ratio in a static sense is fully addressed. A static hedge ratio proposed by Ederington (1979) is an ordinary least-squares regression-based method.1 Using this method, Figlewski (1984) examines the impact of the different sources of basis risk on hedging performance, finding that hedging duration and time to expiration affects hedging performance. The study also suggests that as the futures market has developed, overreaction of futures prices to changes in the spot index has diminished. Nevertheless, Ederingtons (1979) approach has received increasing criticism, particularly with respect to a constant hedge ratio through time.Previous studies have reported that a time-varying hedge ratio can enhance the degree of hedge effectiveness in comparison with a static hedge ratio. To estimate the time-varying hedge ratio, recent studies use the autoregressive conditional heteroscedastic (ARCH) and generalised autoregressive conditional heteroscedastic (GARCH)-type models to characterize the behaviour of hedge ratios over time.2 Myers (1991) and Baillie and Myers (1991) indicate that GARCH-type time-varying optimal hedge ratios outperform constant hedge ratios, and imply that GARCH models appear ideally suited to estimating time-varying optimal hedge ratios.3 Yang and Allen (2004) also suggest that time-varying GARCH hedge ratios perform better than constant hedge ratios in terms of minimizing risks. Brooks et al. (2002) use the asymmetric GARCH model to estimate time-varying hedge ratios, finding that this model gives a superior in-sample hedging performance. In a recent study, Hsu et al. (2008) introduce a class of copula-based GARCH models, without the assumption of multivariate normality, to estimate time-varying hedge ratios, finding that dynamic conditional correlation (DCC) GARCH models perform more effectively than constant conditional correlation (CCC) GARCH models, and copula-based GARCH models outperform other dynamic models, in terms of hedging effectiveness.4,5On the other hand, the choice of market clearing frequency has received much attention in the field of market microstructure. Previous studies have found that the introduction of a closing call can enhance price efficiency and reduce closing price manipulation. An influential paper by Pagano and Schwartz (2003) suggests that the introduction of a stock closing call is beneficial to market quality, after specifically examining Euronext Paris and finding that the introduction of a closing call reduces execution costs and enhances price discovery. Hillion and Suominen (2004) develop an agency-based model to explain the behaviour of stock closing prices, and indicate that the introduction of a stock closing call can reduce manipulation of closing prices.Utilizing data from the Australian Stock Exchange, Aitken et al. (2005) suggest that the closing call provides a mechanism for consolidating liquidity and reduces transaction costs. Using data from the Singapore Stock Exchange, Comerton-Forde et al. (2007) find that the introduction of opening and closing call auctions can significantly improve price discovery at opening and closing. Similarly, Huang and Tsai (2008) report that a decrease in market volatility and an increase in price efficiency were achieved at the expense of a decrease in market liquidity at the close of trading days when the TSE expanded the length of the batching period of the stock closing call.In summary, previous studies have developed various models to estimate an optimal hedge ratio. Additionally, recent research suggests that the introduction of a stock closing call affects stock price behaviour. However, no research has been performed on the influence of the determination of stock closing prices on futures price efficiency and hedging effectiveness. Accordingly, the present study attempts to fill this gap.3. Theoretical considerationsAn increase in the length of the batching period of the stock closing call can improve price efficiency at the futures market close and enhance hedging performance.6Hillion and Suominen (2004) propose that the introduction of a stock closing call reduces the manipulation of closing prices, and Huang and Tsai (2008) indicate that the increase in the length of the batching period of the stock closing call in the TSE has effectively reduced market volatility at closing and enhanced market efficiency by reducing noise in stock closing prices. On the other hand, Pagano and Schwartz (2003) suggest that the change in the determination of stock closing prices might affect the derivatives markets. As suggested by Lee et al. (2007), stock closing prices have had a great impact on extended futures trading since the TSE expanded the length of the batching period of the stock closing call. Hence, if a long batching period of the stock closing call reduces stock market volatility and manipulation of stock closing prices, futures closing prices will tend towards their intrinsic values when the batching period is long. In this case, the hedging risk will decrease because of a decrease in stock market volatility and a reduction of manipulation of stock and futures closing prices.7According to the above arguments, the hypotheses can be stated as follows:H1: An increase in the length of the batching period of the stock closing call can improve price efficiency at the futures market close.H2: Hedging performance will be enhanced after an increase in the length of the batching period of the stock closing call.4. DataDaily closing prices for three futures indices and the corresponding underlying stock indices are used in this study. The stock indices are the Taiwan Stock Exchange Capitalization Weighted Index (TAIEX), the Taiwan Stock Exchange Electronic Sector Index (TAIEXE), and the Taiwan Stock Exchange Finance Sector Index (TAIEXF). The futures indices of the TAIEX, TAIEXE, and TAIEXF are the TX, TE, and TF traded on the TAIFEX, respectively.8,9The sample period covers almost 3 years, from 4 January 2001 to 4 December 2003 (720 trading days). The first subperiod, with the short stock closing call of 30 sec, consists of the 360 trading days from 4 January 2001 to 28 June 2002. The second subperiod, with the long stock closing call of 5 min, consists of the 360 trading days from 1 July 2002 to 4 December 2003. As discussed by Huang and Tsai (2008), the 30 trading days before and after the event day are discarded in this study. Consequently, the trading periods for the Before and After periods are 360 to 31 and +31 to +360, respectively. To avoid thin markets and expiration effects, the nearby futures contract is rolled over to the next nearest contract when it emerges as the most active contract. All data are obtained from the Taiwan Economic Journal.The contract specifications of the three futures on the TAIFEX are shown in Panel A of Table 1. Panel B of Table 1 presents the trading volume of the three futures for the period between 2001 and 2007, from which it can be seen that the trading volume of TX increased from 2 844 709 in 2001 to 11 813 150 in 2007 and the trading volume of TE increased from 684 862 in 2001 to 1 004 603 in 2007. However, the TF showed a slight decline from 2004 to 2006. Panel C of Table 1 shows the constituents of the investors on the TAIFEX; in contrast to other futures markets around the world, individual investors constitute over 99 per cent on the TAIFEX.Table 1. The basic profile of the Taiwan Futures Exchange (TAIFEX) Panel A: The contract specifications of the main three futures on the TAIFEXFuturesTXTETFUnderlying indexTSE Capitalization Weighted Stock Index (TAIEX)TSE Electronic Sector Index (TAIEXE)TSE Finance Sector Index (TAIEXF)Delivery monthsSpot month, the next calendar month, and the next three quarterly monthsLast trading dayThe third Wednesday of the delivery month of each contractDenominated currencyNew Taiwan Dollar (NT$)Contract sizeIndex NT$200Index NT$4000Index NT$1000Minimum price variation1 TX point = NT$2000.05 TE point = NT$2000.2 TF point = NT$200Panel B: The trading volume of the main futures contracts on the TAIFEXYearTXTETF(TX + TE + TF)/ (TX + TE + TF + MTX)20012 844 709684 862389 53890.17%20024 132 040834 920366 79083.63%20036 514 691990 7521 126 89586.77%20048 861 2781 568 3912 255 47886.72%20056 917 3751 179 643909 62189.22%20069 914 9991 459 821786 47787.35%200711 813 1501 004 603909 38382.24%Panel C: The constituents of the investors on the TAIFEXYearIndividual investorsInstitutional investorsNumber%Number%Note: These data come from the TAIFEX. Furthermore, up to 1 July 2002, the TAIFEX had only launched four futures products, including TX, TE, TF, and MTX.2001368 79399.4221340.582002566 31199.5326910.472003816 08399.4842960.5220041 016 34899.4853510.5220051 126 37899.4759680.5320061 148 24399.4563280.5520071 143 03199.4563550.555. Methodology5.1. Price efficiencyThe relative return dispersion (RRD) suggested by Amihud et al. (1997) is used to compare the price efficiency of the TAIFEX for the two subperiods. To obtain the RRD, the RRD for each index, RRDI, is computed first, by regressing futures returns on the corresponding underlying index returns:10 (1)where FRi,t and SRi,t are the futures and stock returns for index i on day t, respectively, and i,t is the residual for index i on day t. Then, the RRDI for each futures index can be computed as . Equation (1) is estimated separately over the two subperiods. Then, to measure the price efficiency of the TAIFEX, the RRDt can be calculated as follows: (2)A decrease in RRDt is associated with an increase in market efficiency. Therefore, if the increase in the length of the batching period of the stock closing call increases market efficiency for the TAIFEX, a low mean RRD in the second subperiod will be observed. To test the equality of the RRD, the t-test and Wilcoxon rank sum test are used in this research.5.2. Hedging effectivenessTo investigate the hedging effectiveness for the three futures indices, the bivariate error correction model of FRi,t and SRi,t with the CCC GARCH (1,1) structure suggested by Kroner and Sultan (1993) are used: (3) (4) (5) (6) (7) (8)where FRi,t and SRi,t are the futures and stock returns for index i on day t, respectively, Fi,t and Si,t are the logarithms of the futures and spot prices for index i on day t, respectively, and (Si,t1 c Fi,t1) is the error correction term for index i on t 1, which measures how the dependent variable adjusts to the previous periods deviation from the long-run equilibrium. The coefficients i,s and i,f are the speeds of the adjustment parameters. The larger i,f is, the greater the response of Fi,t to the previous periods deviation from the long-run equilibrium, implying that the spot plays a more important role in price discovery. The CCC GARCH model is estimated separately over the two subperiods. Additionally, the optimal time-varying hedge ratio for each index is estimated as: (9)where HRIi,t is the hedge ratio for index i on day t. Therefore, the risk of the hedged portfolio for each index is calculated as follows: (10)where HEIi,t is the hedging effectiveness for index i on day t. Hence, the hedging performance for the TAIFEX is computed as follows: (11)A low mean HE is associated with a high hedging performance. Hence, a low mean HE is expected after the introduction of the long batching period of the stock closing call. Similarly, the t-test and Wilcoxon test are used to test the equality of the HEI and HE in this research.In addition, as indicated by Yang and Allen (2004) and Hsu et al. (2008), hedging performance can be measured by the percentage reduction in variance of the hedged portfolio relative to the unhedged portfolio. The variance reduction for each index i can be calculated as follows: (12)where VRIi,t is the variance reduction of the hedged portfolio for index i on day t. Then, the variance reduction for the TAIFEX is computed as: (13)The larger the mean VR, the greater the improvement in hedging performance. The t-test and Wilcoxon rank sum test are used to test the equality of the VRI and VR in this research.6. Empirical results6.1. Price efficiencyTable 2 shows the RRDIs of the TX, TE, and TF and the RRD of the TAIFEX for the two subperiods. The results show that the increase in the length of the batching period of the stock closing call improves market efficiency at the futures market close. Panel A of Table 2 shows the RRDI of the TX for the two subperiods, from which it can be seen that the mean RRDI of the TX is 0.6067 under the short batching period, dropping to 0.2909 when the batching period is long. The t-test for the TX indicates that the decrease in RRDI is significantly negative, at 3.6467, after the introduction of the 5 min stock closing call. Similarly, the t-tests shown in Panels B and C of Table 2 indicate that the TE and TF exhibit the significant decrease in mean RRDIs after the increase in the length of the batching period of the stock closing call. In addition, Panel D of Table 2 shows the RRD of the TAIFEX for the two subperiods. The results indicate that the mean RRD of the TAIFEX is 0.7328 when the batching period is short, decreasing to 0.3768 after the introduction of the 5 min stock closing call. The value of