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Testing for Asymmetry in the Price-Volume Relationship of Listed Australian Banks 1 Testing for Asymmetry in the Price-Volume Relationship of Listed Australian Banks Darren Henry* La Trobe University, Australia Param Silvapulle Monash University, Australia Abstract In this paper, we test for the presence of temporal asymmetry in the price-volume relationship for a unique industry sub-group, comprising the four major listed Australian trading banks, using daily share price and trading volume series. We have used a current popular methodology to capture the asymmetric relation between the two series. The major findings are (i) there is evidence of causality from prices to volumes, but not vice versa; (ii) there is causality from both positive and negative price changes to volume changes for all four banks, but only very weak evidence of causality from negative volume to price for the National Australia Bank and Westpac Banking Group; and (iii) negative price and volume changes have stronger effects than positive price and volume changes. These findings suggest the existence of significant feedback trading associated with these banking stocks, which can potentially be generalised to the wider Australian sharemarket. The findings can be explained in terms of short selling action of traders in response to price falls and the mentality and trading actions of bull and bear traders in response to price or volume movements. Keywords Temporal Asymmetry; Causality Testing; Australian Banks. Introduction This paper tests for the existence of temporal asymmetry in the relationship between price and volume movements for major listed Australian banks trading on the Australian Stock Exchange (ASX). Temporal asymmetry exists if the banks’ share price changes depend on the direction of lagged volume changes or, alternatively, if changes in the banks’ share volume traded depend on the direction of lagged share price changes. Most prior studies have tested the contemporaneous relationship between price and volume changes, applying the volume to price change ratio for testing purposes. Temporal asymmetry is different in that it tests for asymmetry in terms of the direction of lagged volume (price) changes and their effect on price (volume) changes. Temporal asymmetry is present if the effect of positive lagged volume changes on price changes is significantly * Corresponding author for communication. Address: Department of Economics and Finance, School of Business, La Trobe University, Bundoora, Victoria 3086, Australia. Phone: +61 3 94791730. Fax: +61 3 94791654. E-mail: [email protected] + The authors acknowledge helpful comments from two anonymous reviewers, Buly Cardak and participants at the 2000 Australasian Finance and Banking Conference, Sydney. 2 Henry and Silvapulle / Journal of Accounting and Finance 2 (2003) 1~13 different from the effect of negative lagged volume changes on price changes. Similarly, temporal asymmetry is evident if trading volume responds significantly differently to positive lagged price changes than to negative lagged price changes. Testing for temporal asymmetry is important due to the implications of its existence on the trading actions and investment strategies of market participants. This is particularly prevalent in relation to the sequential information arrival, market efficiency and feedback trading hypotheses. In terms of the sequential information arrival hypothesis, temporal asymmetry may cause differential price adjustment and volume trading between optimists and pessimists or informed and uninformed traders. Also, temporal asymmetry from volume to price changes is consistent with market inefficiency, and could suggest the potential for an effective trading strategy using volume movements as a predictor of future price changes. The finding of temporal causality from lagged price changes to trading volume levels has similar implications for the feedback trading strategy, with past price movements having predictive content for future volume trading and its price implications. The price and volume series of major Australian banks are tested for their symmetrical properties in this paper as they are heavily traded shares on the ASX, and represent some of the largest companies, in terms of market capitalisation, on the ASX. The four listed banks analysed in this paper, the ANZ Banking Group (ANZ), the Commonwealth Bank of Australia (CBA), the National Australia Bank (NAB) and the Westpac Banking Corporation (WBC), have consistently been ranked among the ten largest listed companies on the ASX and all have significant weightings in market benchmark indices such as the All Ordinaries Index and the S&P/ASX 200. As at June 1998, the weightings of ANZ, CBA, NAB and WBC in the formation of the ASX All Ordinaries Index were 4.03%, 5.41%, 7.18% and 4.21% respectively. At this point in time the total All Ordinaries Index contribution of these four banking stocks was 20.83%, with no other industry grouping in the Australian market having such a degree of concentration and influence on market index movement as the banking sector. As such, significant ownership and trading in these banking shares is maintained by the various classes of institutional investors, as well as by smaller individual investors holding less-diversified portfolios of blue-chip stocks. Also, of interest are the significant regulatory and competition (including industry deregulation) changes which have taken place in the banking sector over the past two decades, and the influence on fundamental bank price and volume activity of industry-specific as well as economy-wide and global factors such as interest rate and exchange rate movements. The remainder of the paper is structured in the following manner. The next section presents the theoretical background for asymmetry testing of the price-volume relationship. Following this we present the model development and hypotheses to test for the existence of asymmetric properties in the price-volume relationship. The description of the trading bank data used and the discussion and interpretation of the empirical results from the causality and asymmetry testing form the content of the next section. Lastly, we provide some concluding remarks and potential implications of the results. Theoretical Background for Price-Volume Asymmetry Testing Contemporaneous symmetry can be defined in notational form as: Testing for Asymmetry in the Price-Volume Relationship of Listed Australian Banks v pt vt pt t 3 (1) where p is the asset price and v is the associated volume of trading and the positive and negative signs represent the direction of price change. Symmetry, as defined in equation (1), exists when the average trading volume associated with positive price changes is equal to the average trading volume in response to price falls. Asymmetry would therefore be present if average trading volume is significantly different for price increases and decreases, such as (vt pt+) > (vt pt-) or (vt pt+) < (vt pt-). A similar representation of symmetry can be made using the volume to price change ratio, as follows: S t pt S t pt (2) where St = vt / pt. Thus, symmetry would prevail if the value of the volume-price change ratio associated with a positive price change is not significantly different than the absolute ratio value in the case of a negative price change. Contemporaneous asymmetry in the volume to price change ratio can be defined in a similar manner to that outlined above. Temporal symmetry in the influence of volume changes on price would exist if: p t vt1 , vt2 , ... , vtn pt vt1 , vt2 , ..., vtn (3) Here, the effect of positive lagged volume changes on price is equal to the effect of negative lagged volume changes on price. Similarly, temporal symmetry in the effect of lagged price changes on volume would exist if: v t pt1 , pt2 , ... , ptn vt pt1 , pt2 , ..., ptn (4) Ying (1966) was the first to evaluate the existence of asymmetry in the relationship between prices and volumes and, in particular, differentiated between the signed price change and the absolute price change in the volume to price change ratio. Ying (1966) suggested that asymmetry in the volume to price change ratio may not be bi-directional, and that asymmetry may differ depending on the direction of price movements (in terms of positive or negative price changes). Ying (1966) concluded that there was a positive correlation between volume and both price change (p) and absolute price change (p), with small (large) volume being associated with a fall (rise) in price. The first relationship is analogous to the idea of temporal asymmetry, where volume changes are greater in the presence of positive price changes (upticks) than in the situation of price declines (downticks). The existence of a positive correlation between volume and absolute price change (p) has been a consistent finding in the literature. This conclusion has been reported by Crouch (1970), Westerfield (1977), Harris (1986) and Richardson, Sefcik and Thompson (1987) using daily or weekly data, Epps and Epps (1976) and Jain and Joh (1988) using transactions data and for futures contracts trading by Cornell (1981), Tauchen and Pitts (1983) and Grammatikos and Saunders (1986). A positive correlation has also been identified between volume and price change (p) by Epps (1977), Hanna (1978), Smirlock and Starks (1985), Harris (1986) and Jain and Joh (1988) for various security forms including stocks, aggregate 4 Henry and Silvapulle / Journal of Accounting and Finance 2 (2003) 1~13 portfolios and bonds and for a range of data intervals. No empirical support, however, has been identified for a similar positive correlation between volume and price change in futures markets. Various arguments have been put forward to explain the presence of asymmetry in the price-volume relationship. The most prominent explanation provided for the existence of temporal asymmetry lies with the heterogeneity of traders. Differences in investors’ expectations, preferences, information assimilation and other diverse investment characteristics have been suggested as reasons for differential price (volume) movements in response to positive or negative lagged volume (price) changes. Time delays between the arrival of new information and when actions are taken by traders in response to that new information, in the form of buying and selling activity, have been suggested as one source of temporal asymmetry. Copeland (1976) proposed a model based on sequential information arrival and the existence of informed and uninformed traders, with uninformed traders failing to learn from informed trading actions. This results in different demand functions for informed (or optimists) and unimformed (pessimists) traders, causing an asymmetrical volume reaction to price movements. Jennings, Starks and Fellingham (1981) arrived at a similar conclusion to Copeland (1976) based on the existence of optimistic and pessimistic traders and costly short sale positions and margin requirements. With short positions being more costly than long positions, pessimists are less responsive to price movements than optimists, resulting in higher volumes with price increases (optimists buying) than price decreases (pessimists selling). Further support is provided by Wang (1994) on the basis of the diversity associated with the availability of information to different investors. Similar to the winner’s curse idea with IPO pricing, uninformed traders require a higher price discount when buying assets from informed traders due to the risk premium associated with trading against private information. In a similar vein, Moosa and Korczak (1999) suggest that expectation differences of traders cause asymmetry in the price-volume relationship, particularly where expectations differ between bull and bear markets. Such expectation asymmetry is thought to flow through to the trading actions of these investors. Other arguments of a similar nature have also been put forward. Morgan (1976) linked volume with systematic risk, suggesting from this a positive correlation between volume and return movements. Epps (1975) distinguished between investors on the basis of their risk profiles. Epps (1975) characterised two groups of investors: those that are ‘bullish’ about a security (bulls) and those that are bearish about a security (bears). As such, they will respond differently to the arrival of new information about the security. Epps (1975) suggested that bulls are relatively more optimistic about asset values and only react to positive information or price movements, whereas bears only respond to negative information. Any information increasing the security’s price will be reacted to immediately by bulls, but will be disregarded by bears due to their negative perception of the security. This relative optimism of bulls compared to bears is suggested to result in a greater trading volume being associated with a positive price change than with a price decrease. Various concerns have been raised regarding the applicability of these models, primarily based on their assumptions regarding the behaviour and classification of investor classes (such as optimistic versus pessimistic) and their interpretation of investor heterogeneity (see Karpoff, 1987, for a discussion of this issue). The differential cost of short sales positions is suggested as the most plausible explanation for the positive correlation between volume and price change, particularly in light of the general finding in futures markets of no such correlation, where the costs of long and short positions are symmetrical. Testing for Asymmetry in the Price-Volume Relationship of Listed Australian Banks 5 Recent empirical findings have also increasingly documented the application of noninformational or feedback trading strategies by different categories of investors. These studies support the existence of a dominating influence of past price changes driving volume trading in various markets, reflecting the prevailing influence of momentum traders and the trading patterns of institutional investors and the price impact of institutional trading actions. Grinblatt, Titman and Wermers (1995), Wermers (1999), Nofsinger and Sias (1999) and Sias and Starks (1999) all report findings consistent with positive feedback trading by institutional investors in equity markets, and Odean (1998) and Bange (2000) find significant negative and positive feedback trading, respectively, by small individual investors. Further, Chan, Hameed and Tong (2000) and Griffin, Ji and Martin (2002) provide evidence of the profitability of feedback and momentum trading strategies using the All Ordinaries Index and winner-loser portfolios respectively. In addition, Kodres (1999) and Koutmos (2002) present results consistent with the existence of positive feedback trading in index futures securities. Methodology for Testing for Causality in the Presence of Asymmetry Testing for temporal causality between prices and volumes traded is centred on a bivariate VAR model comprising two stationary series, x and y. The model can be written as: p q i 1 j 1 p q i 1 j 1 x t i x t i j y t j u x ,t y t i y t i j x t j u y ,t (5) (6) where x and y are stationary variables and p and q are the lag lengths for x and y respectively. Equations (5) and (6) are valid for testing the causality of lagged volume changes on price changes (where x is the stationary price series) and lagged price changes on volume changes (where y is the stationary volume series). They are not suitable, however, for testing for temporal asymmetry in the price-volume relationship, as they do not distinguish between rising and falling prices and volumes. In order to capture these temporal asymmetric effects, we decompose y and x as follows: y y t = t 0 y yt = t 0 if yt 0 (7) otherwise if yt 0 (8) otherwise and xt xt = 0 if x t 0 otherwise (9) xt xt = 0 if x t 0 otherwise (10) 6 Henry and Silvapulle / Journal of Accounting and Finance 2 (2003) 1~13 Applying the decompositions in equations (7) through (10), equations (5) and (6) can be rewritten as: p q q i 1 j 1 j 1 xt i xt i a j yt j b j yt j u x ,t p q i 1 j 1 yt i yt i c j x t j (11) q d j xt j u y ,t (12) j 1 For equation (5), the null hypothesis of the Granger causality test, suggesting that y has no effect on x, can be represented as: H0 : 1 2 q 0 (13) and the alternative hypothesis of causality is given by: H1 : j 0 for at least one j (14) Similar null and alternative hypotheses can be stated for equation (6) to test for causality of lagged price changes on volume. The associated test statistic has a standard F distribution with (q, T-p-q-1) degrees of freedom, where T is the sample size of the series. In this paper results are reported for p = q = 5, 7 and 14 (daily) lags. To test for temporal causality in equation (11), the null and alternative hypotheses in the Granger causality test to determine whether y+ has any effects on x are: H 0 : a j 0 for j 1, 2, ..., q (15) and H1 : a j 0 for at least one j (16) where the test statistic has a standard F distribution with (q, T-p-2q-1) degrees of freedom. Similarly, to test if y- has any effect on x, the null and alternative hypotheses can be written as: H 0 : b j 0 for j 1, 2, ..., q (17) H1 : b j 0 for at least one j (18) and Similar hypotheses are created to test for causality of x+ and x- on y in equation (12). To determine whether x has a stronger effect on y than x the following null and alternative hypotheses are used in conjunction with equation (12). H a0 : d j c j for j 1, 2, ..., q (19) Testing for Asymmetry in the Price-Volume Relationship of Listed Australian Banks 7 and H a1 : d j c j for j 1, 2, ..., q (20) Now, equation (12), with d j c j j , becomes p p q j 1 j 1 i 1 yt c j ( xt j xt j ) j xt j i yt i u y ,t (21) For equation (21) the hypotheses represented by (19) and (20) are equivalent to H 00 : j 0 and H11 : j 0 respectively. The statistic for testing H 00 against H 11 and its p- value are described in Silvapulle (1992a) and (1992b). Furthermore, since daily data are used to test these hypotheses, it is likely that the normality assumption will not hold. For this reason, we use the robust tests developed by Silvapulle (1992a) and (1992b), which are based on the M-estimators. Data and Empirical Results The data used in this study comprises daily last-sale share prices and corresponding daily trading volume for the four largest listed trading banks on the ASX, these being the Australian and New Zealand Banking Group (ANZ), the Commonwealth Bank of Australia (CBA), the National Australia Bank (NAB) and the Westpac Banking Corporation (WBC). The sample consists of 4,270 daily observations covering the period from September 1, 1981 to August 31, 1998 for the ANZ, NAB and WBC companies. The sample for the Commonwealth Bank of Australia consists of only 1,713 daily observations from September 12, 1991 to August 31, 1998. Prior to September 1991 the Commonwealth Bank of Australia was owned and operated by the Australian Government and became listed on the ASX initially in September 1991 as part of a segmented privatisation program. This bank is included in the analysis due to the ‘four pillars’ or ‘four big banks’ market structure in Australia. These data was obtained from the Core Research Database maintained by the Securities Industry Research Centre of Asia-Pacific (SIRCA). The dilution and adjustment factors computed and provided by SIRCA were used to adjust the bank share price series for equity capitalisation changes such as rights or bonus issues and derivative and note security conversions. Dividend payments by the banks were also incorporated into the price series to reflect the total return provided by these stocks. This is particularly important in respect to these listed banking companies, as they are historically very profitable companies and pay substantial dollar-value dividends and relatively high dividend yields to investors. The sample period evaluated, particularly for ANZ, NAB and WBC, includes the deregulation of the financial system in Australia which occurred during the early- to mid1980s and the sharemarket crash in October 1987. Stationarity testing of these data series (results are not provided in the paper, but are available from the authors on request) suggest that the series are stationary in returns (or first differences). Graphical examination of the data did not reveal evidence of structural breaks in the price or volume return series for the banks. Table 1 provides descriptive information regarding the daily trading activity and size and share price information for the four banking stocks over the sample analysis period. 8 Henry and Silvapulle / Journal of Accounting and Finance 2 (2003) 1~13 Table 1. Descriptive Statistics for the Four Australian Banks over the Sample Period from September 1981 to August 1998 Variable National Australia Bank (NAB) Daily share return Daily traded volume Share price Market cap* ($Mill) National Australia Bank (NAB) Daily share return Daily traded volume Share price Market cap* ($Mill) Westpac Banking Corporation (WBC) Daily share return Daily traded volume Share price Market cap* ($Mill) Commonwealth Bank (CBA)** Daily share return Daily traded volume Share price Market cap* ($Mill) Mean Median Standard Deviation Minimum Maximum 0.012% 1,387,781 $5.223 7,034.76 0.000% 1,068,742 $4.850 5,081.74 1.779% 1,830,368 $1.790 4,508.21 -24.440% 200 $2.520 3,336.96 9.200% 68,849,417 $11.880 17,016.00 0.048% 1,139,483 $8.007 14,387.05 0.000% 924,165 $6.460 14,126.00 1.438% 1,315,254 $4.949 9,131.72 -20.910% 1,200 $2.300 4,461.47 9.200% 29,387,250 $23.350 29,971.00 0.027% 1,477,009 $4.887 8,691.78 0.000% 1,110,183 $4.670 7,046.00 1.580% 1,794,764 $1.725 4,488.89 -27.190% 7,584 $2.430 4,658.67 7.910% 60,336,827 $11.380 17,634.00 0.060% 737,624 $10.556 11,020.00 0.000% 618,500 $9.350 9,608.00 1.124% 547,524 $3.770 4,197.37 -6.140% 45,100 $5.820 7,031.00 7.430% 10,432,900 $20.550 17,383.00 Notes * Market capitalisation figures are expressed in A$Million and are calculated as the Number of ordinary shares on issue Daily closing share price. ** The figures for the Commonwealth Bank are for the period from September 1991 to August 1998. The mean daily returns for the four banks are all positive, ranging from 0.01% for ANZ to 0.06% for CBA. The large minimum returns observed for ANZ, NAB and WBC in excess of 20.00% all occurred at the time of the 1987 sharemarket crash, with no individual positive daily return exceeding 10% for any of the four banks. Average daily trading volume exceeded one million shares for ANZ, NAB and WBC, with lower mean daily trading observed for the Commonwealth Bank (CBA). Yearly examination of the volume data for the four banks shows an increase in trading volume levels over time, in line with expansions in the equity capital bases of the banks and the general increase in sharemarket investment and trading activity. Consistent with the respective All Ordinaries Index weightings for the four banks outlined above, NAB is the largest of the listed banks based on mean market capitalisation, followed in descending order by CBA, WBC and ANZ. The maximum market capitalisation figures were recorded in either the 1997 or 1998 financial years for the four banks1. As these banks are among the largest listed companies on the ASX market, they enjoy significant institutional investor patronage, with institutional shareholdings representing up to 50% of the total ownership of these companies. Ownership restrictions are also in place within the 1 These individual bank capitalisation figures can be compared to the average market capitalisation of the Australian Stock Exchange in the 1998 financial year of approximately $480,000 million. Testing for Asymmetry in the Price-Volume Relationship of Listed Australian Banks 9 banking sector in Australia, with legislative prohibition preventing any individual investor from obtaining ownership of more than 10% of the issued and voting capital of any of these four listed banks. Table 2. Results of Causality Testing Between Prices and Volumes using the F-Test l =5 Lag Length l=7 l = 14 ANZ Banking Group vt pt pt vt vt+ pt vt- pt pt+ vt pt- vt 1.804 0.882 1.320 0.633 3.451 8.308 1.516 0.788 0.982 0.626 3.616 6.029 1.072 1.138 1.734 1.043 3.201 3.139 National Australia Bank vt pt pt vt vt+ pt vt- pt pt+ vt pt- vt 1.891 2.622 0.835 2.584 5.460 9.666 1.367 2.599 0.526 1.849 4.026 7.200 1.073 3.500 0.820 1.244 3.212 3.927 Westpac Banking Corporation vt pt pt vt vt+ pt vt- pt pt+ vt pt- vt 0.736 0.777 0.215 1.038 8.544 11.808 0.621 0.611 0.229 0.647 5.888 8.579 1.140 1.299 1.199 2.087 2.669 5.751 Commonwealth Bank vt pt pt vt vt+ pt vt- pt pt+ vt pt- vt 0.642 2.415 0.409 0.306 4.824 7.659 0.433 1.666 0.482 0.364 4.916 6.739 0.406 1.548 0.426 0.418 2.768 3.741 Hypothesis Note: Five percent critical values of F5,, F7, and F14, are 2.21, 2.01 and 1.67 respectively. For the purpose of causality testing on the basis of equations (5) and (6) and equations (11) and (12), x represents pt and y is representative of vt. The results of the causality testing are provided in Table 2. The results suggest that causality runs primarily from price changes to volume changes. The results based on equations (5) and (6) indicate no causality from lagged volume changes to price changes, whereas there is evidence of causality in the effect of lagged price changes on volume changes for the National Australia Bank and the Commonwealth Bank. The results based on equations (11) and (12) indicate that causality 10 Henry and Silvapulle / Journal of Accounting and Finance 2 (2003) 1~13 runs from both positive and negative price changes to volume changes. This is a consistent finding for all four banks, with the evidence in Table 3 suggesting that negative price changes have stronger effects on volume changes than positive price changes2. This finding of both positive and negative price causality to volume is intriguing, particularly in the absence of similarly strong contemporaneous causality from price changes to volume changes, except for the National Australia Bank. There is also weak evidence of causality from negative volume changes to price for the National Australia Bank and Westpac Banking Corporation. Table 3. Results of Testing for Asymmetrical Causality Test Statistic pt vt ( H 00 d i ci ) ANZ Banking Group F RM RW 1.02 (0.35) 0.91 (0.39) 0.99 (0.36) National Australia Bank F RM RW 0.98 (0.38) 0.72 (0.48) 0.79 (0.43) Westpac Banking Corporation F RM RW 0.78 (0.52) 0.70 (0.67) 0.71 (0.66) Commonwealth Bank F RM RW 1.20 (0.28) 1.13 (0.39) 0.11 (0.43) Note: The model with 7 lags was used to calculate the test statistics. The p-values, in parentheses, are computed using the methodology described in Silvapulle (1992a) and (1992b). RM and RW are the robust statistics when the error distribution is non-normal, which is true in daily financial market data series. See Silvapulle (1992a) and (1992b) for details. These results offer some very interesting interpretations. The absence of bi-directional causality, and particularly no causality from volume changes to price changes, is consistent with market efficiency, where volume changes cannot be used to determine future share price movements. The finding of a causal relationship from lagged prices to volume is consistent with the noise trading model of De Long, Shleifer, Summers and Waldman (1990) where noise traders employ a positive-feedback strategy, basing trading decisions on past price movements. This also supports the recent evidence, outlined above, regarding the existence of 2 The results in Table 3 are based on equation 21 employing the model based on seven lags. This lag length was chosen based on examination of the models’ respective Akaike information criterion (AIC). Only tests for the difference in the effects of positive and negative price changes on volume changes were undertaken in Table 3, as there was no strong evidence, from the results in Table 2, of causality from lagged volume changes to price changes. Testing for Asymmetry in the Price-Volume Relationship of Listed Australian Banks 11 significant non-informational or feedback trading in equity and futures markets and the profitability of such strategies in the Australian sharemarket. The findings in this paper of temporal asymmetry are inconsistent, however, with much of the prior literature and, in particular, the conclusions of Epps (1975) and Jennings, Starks and Fellingham (1981). This is particularly the case with the conclusion that negative price (volume) changes have a greater effect on volume (price) changes than positive changes. This firstly suggests that bears have a steeper demand function than bulls, which contrasts directly with the conclusion of Epps (1975). This finding, however, is consistent with the proposition that bears are likely to react quickly to negative price changes by selling securities to minimise their losses, whereas bulls are unlikely to react to price falls, rather waiting for the price to increase before they sell. Similar arguments can be applied to the actions of pessimists or uninformed traders, and it is not unreasonable to conclude that due to the general risk-averse nature of most investors that such actions are likely to dominate ‘bull’ characteristics. In terms of traders’ expectations, the findings in this paper suggest that traders’ expectations are stabilising in a bull (rising) market and destabilising in a bear (falling) market. As such, when prices rise in a bull market, traders may not expect further price increases and sell (so-called profit-taking), putting downward pressure on prices and subsequent trading volumes. Alternatively, when prices fall in a bear market, traders may have expectations of further price falls so they sell, thus increasing the downward pressure on prices and increasing trading volumes as other traders begin selling. Another potential explanation for the stronger volume reaction to negative price changes compared to positive price movements may relate to the regulations governing the shortselling of equity securities (including the four banking stocks analysed in this paper, which are all approved securities for short-selling purposes) on the ASX. As opposed to United States sharemarkets, share trading rules on the ASX permit the short sale of approved securities on a down tick, as long as the short-sale order price is not lower than the last sale price for the security and the short seller was not involved in the last trade for that particular security. As such, the predominance of feedback trading and the existence of temporal asymmetry between negative and positive price changes and volume movements may be reflective of such short-selling activity in response to negative price changes. The results also suggest that testing only for contemporaneous causality, without regard for the sign of volume or price movements, may not fully characterise the symmetrical properties of equity securities and trading behaviour. Concluding Remarks This paper has tested for the presence of temporal causality in the price-volume relationship for the four major listed Australian banks, namely the ANZ Banking Group, the Commonwealth Bank of Australia, the National Australia Bank and the Westpac Banking Corporation. Using daily share price and trading volume data covering the period from September 1981 to August 1998 (September 1991 to August 1998 for the Commonwealth Bank of Australia), the major findings are as follows: 1. There is evidence of causality from price changes to volume changes, but not from volume changes to price changes. 12 Henry and Silvapulle / Journal of Accounting and Finance 2 (2003) 1~13 2. There is causality from both positive and negative price changes to volume changes for all four banks, but only very weak evidence of causality from negative volume changes to price changes for the National Australia Bank and Westpac Banking Corporation. 3. Negative price and volume changes have stronger effects than positive price and volume changes. These findings have various implications for traders’ investment actions and expectations, but they are inconsistent with the Epps (1975) hypothesis regarding the relative demand functions of bull and bear traders. They do support the existence of significant feedback trading by market participants in major banking stocks on the Australian Stock Exchange, and the findings can be explained in terms of short-selling activity in response to share price falls and the mentality and trading actions of bull and bear traders in response to price or volume movements. The ability to generalise the findings in this paper to overall trading activity on the Australian Stock Exchange cannot be confirmed without evaluation across an extended company sample although, given the characteristics of the banking stocks evaluated in this paper, similar trading outcomes and the existence of temporal asymmetry and feedback trading is likely to exist in actively traded companies on the Australian Stock Exchange, and those stocks having a predominant influence on overall market performance and index movement. References Bange, M., 2000, Do the Portfolios of Small Investors Reflect Positive Feedback Trading, Journal of Financial and Quantitative Analysis, 35, 239-255. Chan, K., Hameed, A. and W. Tong, 2000, Profitability of Momentum Strategies in the International Equity Markets, Journal of Financial and Quantitative Analysis, 35, 153-172. Copeland, T.E., 1976, A Model of Asset Trading under the Assumption of Sequential Information Arrival, Journal of Finance, 31, 1149-1168. Cornell, B., 1981, The Relationship Between Volume and Price Variability in Futures Markets, Journal of Futures Markets, 1, 303-316. Crouch, R.L., 1970, The Volume of Transactions and Price Changes on the New York Stock Exchange, Financial Analysts Journal, 26, 104-109. De Long, J., Shleifer, A., Summers, L. and B. Waldman, 1990, Positive Feedback, Investment Strategies and Destabilising Rational Speculation, Journal of Finance, 45, 379-395. Epps, T.W., 1975, Security Price Changes and Transaction Volumes: Theory and Evidence, American Economic Review, 65, 586-597. Epps, T.W., 1977, Security Price Changes and Transaction Volumes: Some Additional Evidence, Journal of Financial and Quantitative Analysis, 12, 141-146. Epps, T.W. and M.L. Epps, 1976, The Stochastic Dependency of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis, Econometrica, 44, 305-321. Griffin, J.M., Ji, S. and J.S. Martin, 2002, Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole, Working Paper, Arizona State University. Grammatikos, T. and A. Saunders, 1986, Futures Price Variability: A Test of Maturity and Volume Effects, Journal of Business, 59, 319-330. Testing for Asymmetry in the Price-Volume Relationship of Listed Australian Banks 13 Grinblatt, M., Titman, S. and R. Wermers, 1995, Momentum Investment Strategies, Portfolio Performance, and Herding: A Study of Mutual Fund Behavior, American Economic Review, 85, 1088-1105. Hanna, M., 1978, Security Price Changes and Transaction Volumes: Additional Evidence, American Economic Review, 68, 692-695. Harris, L., 1986, Cross-Security Tests of the Mixture of Distributions Hypothesis, Journal of Financial and Quantitative Analysis, 21, 39-46. Huber, P.J., 1981, Robust Statistics, John Wiley and Sons, New York. Jennings, R.H., Starks, L.T. and J.C. Fellingham, 1981, An Equilibrium Model of Asset Trading with Sequential Information Arrival, Journal of Finance, 36, 143-161. Karpoff, J.M., 1987, The Relation Between Price Changes and Trading Volume: A Survey, Journal of Financial and Quantitative Analysis, 22, 109-126. Kodres, L., 1999, The Existence and Impact of Destabilizing Positive Feedback Traders: Evidence from the S&P 500 Index Futures Market, Working Paper, International Monetary Fund. Koutmos, G., 2002, Testing for Feedback Trading in Index Futures: A Dynamic CAPM Approach, Working Paper, Fairfield University. Moosa, I.A. and M. Korczak, 1999, Is the Price-Volume Relationship Symmetric in the Futures Markets?, Journal of Financial Studies, 6, 29-42. Morgan, I.G., 1976, Stock Prices and Heteroskedasticity, Journal of Business, 49, 496-508. Nofsinger, J. and R. Sias, 1999, Herding and Feedback Trading by Institutional and Individual Investors, Journal of Finance, 54, 2263-2295. Odean, T., 1998, Are Investors Reluctant to Realize Their Losses?, Journal of Finance, 53, 1775-1798. Richardson, G., Sefcik, S.E. and R. Thompson, 1986, A Test of Dividend Irrelevance Using Volume Reaction to a Change in Dividend Policy, Journal of Financial Economics, 17, 313-333. Sias, R. and L.T. Starks, 1999, Institutions, Individuals and Return Autocorrelations, Working Paper, Washington State University. Silvapulle, M.J., 1992a, Robust Wald-Type Tests of One-Sided Hypotheses in the Linear Models, Journal of the American Statistical Association, 417, 156-161. Silvapulle, M.J., 1992b, Robust Tests of Inequality Constraints and One-Sided Hypotheses in the Linear Model, Biometrika, 79, 621-630. Smirlock, M. and L.T. Starks, 1985, A Further Examination of Stock Price Changes and Transactions Volume, Journal of Financial Research, 8, 217-225. Tauchen, G. and M. Pitts, 1983, The Price Variability-Volume Relationship on Speculative Markets, Econometrica, 51, 485-505. Wang, J., 1994, A Model of Competitive Stock Trading Volume, Journal of Political Economy, 102, 127-168. Wermers, R., 1999, Mutual Fund Trading and the Impact on Stock Prices, Journal of Finance, 54, 581622. Westerfield, R., 1977, The Distribution of Common Stock Price Changes: An Application of Transactions Time and Subordinated Stochastic Models, Journal of Financial and Quantitative Analysis, 12, 743-765. Wolak, F.A., 1987, An Extract Test for Multiple Inequality and Equality Constraints in the Linear Regression Models, Journal of the American Statistical Association, 399, 782-793. Ying, C.C., 1966, Stock Market Prices and Volumes of Sales, Econometrica, 34, 676-685.