Momentum in Australia: Sensitivity and Implementation

Transcription

1 Momentum in Australia: Sensitivity and Implementation Gary Smith* JEL classification: G12 Keywords: Momentum, Australia Gary Smith is a PhD candidate from the University of Western Australia, School of Economics and Commerce, M250, 35 Stirling Highway, Crawley, Western Australia, We have benefited from discussions with Terry Walter, Stephen Gray and participants at the 2007 AFAANZ conference. * Corresponding author: Phone Fax Gary.Smith@uwa.edu.au 1

2 MOMENTUM IN AUSTRALIA: Sensitivity and Implementation ABSTRACT Australian studies of momentum where portfolios formed from past winners outperform portfolios of past losers have presented contradictory results. In this study we reconcile some of the previous research and then extend these results. After applying an array of robustness tests to the findings we document evidence that momentum is time-specific. The sensitivity of these results to both methodological choices and transaction costs causes us to remain sceptical of the existence of implementable momentum strategies in the Australian market. 2

3 1. INTRODUCTION One of the most striking results in recent empirical finance was the identification of short to medium term momentum where portfolios formed from past winners outperform portfolios of past losers in the United States (Jegadeesh and Titman, 1993, 2001) and subsequently in other countries (Rouwenhorst, 1998). Such studies have challenged notions of market efficiency, although later studies argue that momentum is not robust to transaction costs (Lesmond et.al 2004) or risk-based explanations (Chordia and Shivakumar, 2002). Studies of momentum in Australia have not produced consistent results. Replicating the methodology in the seminal studies of Jegadeesh and Titman (1993, 2001), Durand, Limkriangkrai and Smith (2006a; subsequently, DLS) find little supporting evidence in Australia for a momentum effect over the period. However, they did report strong evidence of a July contrarian effect which appears similar to the US January effect observed by Jegadeesh and Titman (1993). Gaunt and Gray (2003) found that large stocks were positively autocorrelated and that small stocks were negatively autocorrelated. They were sceptical that exploiting momentum could generate abnormal returns. Hurn and Pavlov (2003) examined momentum in Australian monthly data and found the presence of a significant medium term momentum effect when limiting their examination to the top 200 market capitalisation firms. Demir, Muthuswamy and Walter (2004) (DMW) have also found strong evidence of momentum. Unlike the three previously mentioned Australian studies on momentum, DMW used daily data and found 3

4 that the size of the momentum effect in Australia was greater than that of comparable effects in other countries. Ensuring that their strategy was implementable, DMW argue that their results are robust both to the time period examined and to risk, and that a trading strategy, particularly over the intermediate horizon, is potentially profitable. O Brien and Brailsford (2007) find that the returns of momentum portfolios in Australia are driven by the loser portfolio, which continues to under-perform after the formation period. They document a relative size effect, where momentum results are most economically significant amongst mid-cap securities. Section 2 discusses the data and methodology used in this paper. In Section 3 we document a penny stock effect that appears independent of size. We find evidence supporting the important role of a penny stock effect in the calculation of Australian portfolio returns and how its inclusion may influence findings on the presence of momentum. Using our dataset to consider the time periods of key Australian findings we reconcile the apparently contradictory results. We reconcile DMW s results to those of Durand, Limkriangkrai and Smith (2006a), who replicated Jegadeesh and Titman s (1993, 2001) methodology with Australian monthly-return data. In Section 4 we consider how momentum interacts with seasonality in the Australian market. Section 5 looks at out-of-sample performance of the investment strategies, and Section 6 considers the impact of transaction costs on possible implementation. Evidence of momentum as a financial market phenomenon, found in some of the largest and most liquid securities markets in the world, challenges the notion of market efficiency so profoundly that it is worthy of further scrutiny. We document evidence of 4

5 momentum in specific periods, for segments of the Australian market, however, we are sceptical of the existence of implementable momentum strategies. 2. DATA AND METHODOLOGY The formation of momentum portfolios requires sorting stocks by their performance over a J-day period. We form portfolios from fully paid ordinary shares listed on the Australian Stock Exchange which have been traded on at least one occasion during the formation period (that is, in the J-day estimation period). All stocks that meet this criterion are ranked by total return in the J-day period and formed into ten portfolios with P1 containing the 10% of the highest prior performing stocks, P2 containing the next best performing stocks et cetera until we form P10 which contains the 10% of the lowest prior performing stocks. As is common with the literature on momentum, in order to assist comparability with other studies, we form the portfolios into deciles and focus only on P1 and P10. We then examine the performance of these portfolios over the following K- days testing to see if P1 is significantly different from P10 1. Share price data is obtained from the Securities Industry Research Centre of Asia- Pacific s (SIRCA) Core Research Database (CRD) and we test four different sample periods: The full sample 1980 to 2004, September 1990 to July 2001 that used by DMW as well as two out-of-sample tests January 1980 to September 1990, and July 2001 to December In tests of the robustness of the momentum results to risk 5

6 adjustment the daily All Ordinaries Accumulation Index from Datastream is used as the Australian market index and the risk free rate used is the yield on Australian 10 year Government bonds. Australian daily Fama French (1993) small minus big (SMB) and high book-to-market minus low book-to-market (HML) factors are obtained from Durack, Durand and Maller (2004). 3. MOMENTUM IN AUSTRALIA An early, unpublished, momentum study referred to by DMW (2004) was that of Darling (2000) at the University of Technology in Sydney. Darling, looking at the entire Australian market, found strong evidence of momentum. Table 1 shows the results from forming momentum portfolios over the full sample of our data ( ) including all fully paid ordinary shares in the Australian market. In stark contrast to Darling s results, instead of momentum, short-term reversals are clearly evident with no sign of intermediate momentum 2. This result is consistent with DLS s finding over a similar period ( ) using a different data set consisting of Australian monthly returns. [INSERT TABLE 1 ABOUT HERE] The major difference between the methodologies employed by DLS and Darling was that Darling used, as is commonly done in the US, a penny stock filter. Stocks with share 1 We form formation and holding portfolios over both calendar days and trading days. Reported results use calendar days only. The results of choosing trading days are available from the corresponding author on request although our conclusions are not altered by this choice. 6

7 prices of less than 50c were filtered out of the sample prior to formation of the portfolios. Table 2 repeats the analysis of Table 1, this time employing the condition that to be included in the sample of securities from which both P1 and P10 are formed the shares must have traded at some point in the formation period at a price above 50c. After employing this methodological change, as opposed to the reversals evident in Table 1, Table 2 reports significant positive momentum for the Australian market across virtually all combinations of holding and formation periods. [INSERT TABLE 2 ABOUT HERE] Gaunt et al. (2000) examine price effects on returns in Australia over After ranking stocks into size quintiles at the end of the month they sorted each of these quintiles into five different price groups and measured the returns to these 25 portfolios over the following month. Through this they show that there is a negative relationship in July between share prices and returns and that this result is independent of any small firm market capitalisation effect. As, by definition, past loser stocks will have relatively lower share prices it is likely that by employing a penny stock filter during the formation period we would be reducing any July P10 loser portfolio contrarian effect which would work against finding momentum 3. Another possible explanation for the observed contrast in results is that the filtering out of penny stocks acts as a proxy for a size based filter (removing the small sized end of the 2 Note that at this point in the paper we are using a standard t-statistic in testing for difference between 7

8 market) and that a relationship exists between market capitalisation and that of either positive or negative auto-correlation in returns. Consistent with this hypothesis Gaunt and Gray (2003) find that the profitability of the auto-correlation strategies which they employ relied heavily upon stocks with small market capitalisations. In contrast however, when directly looking at momentum, DMW found that when sorting their sample into size based portfolios generally the smallest quartile of market capitalisation stocks had the highest levels of momentum. Table 3 shows the results of restricting the market sample to only stocks which form part of the top 500 or the top 200 market capitalisation stocks over the period of the study. With no significant momentum results it appears that the 50c filter is not simply a substitute for a size based one 4. So while we can reconcile the lack of momentum findings for the entire market of DLS to those of Darling (2000) to that of the employment of a price filter questions remain as to the robustness of the overall momentum result. Requiring what seems to be an arbitrary filter on our full sample results in order to generate significance does not, to us, make for a persuasive endorsement of momentum as a market phenomenon. [INSERT TABLE 3 ABOUT HERE] portfolios P1 and P10. 3 In Section 4 we examine the performance of momentum portfolios in July. 4 An alternative explanation is that the 50c price filter is acting as a proxy for microstructure effects such as the bid-ask spread or a non-trading bias which serve to confound the results in Table 1. 8

9 DMW s (2004) momentum results over the period of September 1990 to July 2001 demonstrate remarkably strong evidence of the existence of momentum in the Australian market. DMW, unlike DLS and Darling (2000), did not examine the entire market and instead restricted their sample to one of two possibilities. Either the stocks formed a part of the All Ordinaries Index, or the security was listed as an Approved Security by the ASX. Shares listed by the ASX as an approved security are exempt from the Corporations Law prohibition on the short selling of securities which would in practice prevent the creation of the short P10 portfolio. While the data sample is not identical Table 4 reports return results broadly consistent with DMW over the 1990 to 2001 period in terms of both size and distribution across the J/K portfolios, although less clearly significant under the 30 day holding portfolios. Panel A examines the full market applying the 50c filter, whereas Panel B restricts the sample by market capitalisation to a sample size similar to that used by DMW. 5 Our examination also includes J/K strategies calculated over longer time periods than those discussed in DMW; these strategies are shaded in grey to distinguish them from those reported by DMW. Applying these longer formation and holding periods in both panel A and panel B there is also evidence of momentum, with more than 60% of the additional 40 strategies combined displaying statistically significant momentum. [INSERT TABLE 4 ABOUT HERE] 5 Future work will include a sample restricted to the approved securities list only. 9

10 Tables 1 to 4 in DMW test the null hypothesis that winners outperform losers using a standard t-statistic 6. Our tests have so far replicated the methodology used in Table 1 of DMW using the data described in section 2 of this paper. Our Table 4 shows that when applying the price filter we see return results broadly consistent with DMW over the 1990 to 2001 period in terms of both size and distribution across the J/K portfolios. When filtered by market capitalisation (Panel B) the short holding period results are generally smaller and less significant whereas intermediate and longer term momentum still holds relatively strongly. In Table 4 we find similar levels of statistical significance in the momentum strategies to DMW. However, we believe that the statistical methodology they have used is problematic. In addition to the distributional assumptions underpinning the use of the t- test (that is, that the data conforms to the distribution), the standard t-test requires that the observations are independent. This is not the case with DMW s data as they have used overlapping holding periods to form the portfolios they study. For example, in the creation of portfolios based on returns in the preceding 30 days and then examining the returns in the subsequent 180 days (that is, where J=30 and K=180), they would use the first 30 days to create the momentum portfolios and then determine the returns from 6 DMW use the following t statistic: n10n1 ' ' ( R10 R1 ) ( n10 + n1 ) t = ' 2 ' ( R10i R10 ) + ( R1 i R1 ) n + n DLS argue that a paired test is appropriate to control for the contemporaneous performance of the portfolios. DMW test that, over a period, the average returns of the winner portfolio is different to the average returns of the portfolio of losers. DLS test that the monthly difference between winners and losers (P1-P10) t is not zero. 10

11 holding over days in their dataset 7. The next formation period would be created using the returns from day and then held over days This overlap in the holding periods creates a problem in the assumption underpinning their tests: the data is clearly not independent. The use of overlapping (and thus dependent) data has attracted some attention in the finance literature (Nelson and Kim, 1993; Goetzmann and Jorion (1993); and Kirby, 1997). It is possible that using the standard t-statistic may have led DMW to make incorrect inferences about their analyses. One way to overcome this problem is to use non-overlapping data in the formation of the holding periods although this will also have the effect of significantly reducing the sample size and the power of the tests. In Table 5 we again use our data set to test the time period examined by DMW, but this time we do not allow any of our holding periods to overlap. Looking at the full sample with the 50c filter employed, where in Table 4 we witnessed generally a stronger momentum result, the returns are of similar magnitude to those observed in Table 4 but, as the number of observations fall, the t-test s 8 power to reject the null falls and, accordingly, we cannot reject the null that the returns of P1 equal P10 in about half as many cases: there are simply too few observations. [INSERT TABLE 5 ABOUT HERE] 7 To avoid introducing a bid-ask bias against finding momentum caused by the observed closing price in the formation period also being included at the start of the prediction period, DMW use value average weighted prices (VWAP) to determine their portfolio returns. For all data post 1990 we test using both VWAP and closing prices and find the change does not affect our results. Prior to 1990 VWAP data is unavailable to us and only closing prices are used. 11

12 Another way of dealing with overlapping data is to utilise a more appropriate teststatistic. Therefore, we require a valid technique that allows valid inferences to be made when the data is not independent. Goetzmann and Jorion (1993) and Kirby (1997) suggest the use of a bootstrap methodology as an alternative to an analytic solution (see, for example, Shao and Tu, 1995, especially Chapter 3). In Table 6 we recreate our Table 4 with one change; we use the bootstrapped skewnessadjusted t-statistic (Johnson, 1978; Sutton, 1993) 9,10 which allows for the data to diverge from the t-distribution. The critical values were derived by drawing 10,000 samples. DMW s results appear to be robust to the improvement in statistical analysis, if anything the bootstrapped results provide marginally more convincing evidence supporting the existence of momentum in the Australian market. [INSERT TABLE 6 ABOUT HERE] Remembering, in contrast to the examination in the following paragraph, that we are using the same standard t-test used by DMW (discussed in footnote 1). b b b b b The statistic is t = + + sa nb S 1 1 ˆ γ S 2 ˆ γ where: 3 6nb S b b ( R iτ R τ ) R τ + R τ b i = 1 =, and ˆ γ = b b 3 σ ( R τ ) n b σ ( R τ ) nb b b 3 Like DLS, this is a paired test which examines if (P1-P10) t = 0. It is the t-statistics and their significance that changes, not the average return to the momentum strategy. 12

13 4. SEASONALITY One of the major findings of DLS in their replication of Jegadeesh and Titman (1993) was that the prior loser portfolio provided in July significantly positive returns leading to a significant contrarian effect at the beginning of the Australian financial year. Gaunt and Gray (2003), in their examination of short-run autocorrelation, observed this July reversal across all size portfolios. Durand, Juricev and Smith (2007) also find strong evidence of a July reversal in small firm returns. The existence of a strong P10 performance in July is a seasonality that would work in the opposite direction to that of momentum; a reversal in the underperformance of the losers would reduce the difference between P1 and P10. It is possible this could cloud our results seen over the full sample in Table 3. In Table 7 we see that a July reversal is evident, with P10 significantly greater than P1 for more than half the strategies examined (Panel A). However in Table 7 Panel B we can see that this July reversal has not altered our overall findings. Only looking at the returns of the non-july months over the period of 1980 to 2004 we continue to see little evidence of momentum when sorting by market capitalisation 11. [INSERT TABLE 7 ABOUT HERE] Table 8 reports the findings on the effect of seasonality for J/K strategies during the 1990 to 2001 period analysed by DMW applying our bootstrap methodology. In Panel A we 13

14 see that loser returns in July outperform winners in virtually all (32 of the 36) strategies we examine. In non-july months (Panel B) return results are slightly higher than those we found in Tables 1 and 3 and we see a small increase in the number of significant strategies when compared to Table 3. The 1990 s momentum findings are robust to consideration of the July effect. [INSERT TABLE 8 ABOUT HERE] 5. CONSISTENCY OVER TIME If momentum is present, and if it can be exploited, the strategy should generate returns outside the period in which the prima facie anomaly has been discovered. This is an important issue to consider if we are looking for an implementable trading strategy. Recently Hwang and Rubesam (2007) looking at NYSE, AMEX and Nasdaq stocks reported a major break in the momentum effect after the year In fact between January 2000 and June 2005 a US momentum investor would have found that the momentum effect had disappeared with an average negative alpha. We consider whether the momentum result is serendipitous by applying in Table 9 the methodology to the subsequent period of July 2001 to January 2004 for the top 330 market capitalisation securities. Again bootstrapping our result we find that none of the sixteen momentum strategies are significant over this period of time. If the original momentum results had held consistently, a period of this length should be sufficient to 11 Similar results are obtained when restricting the sample to the top 200 and top 500 market capitalisation 14

15 exploit the anomaly. This suggests that an investor following this strategy after the 1990 s momentum result would have been disappointed. [INSERT TABLE 9 ABOUT HERE] One possible explanation for this is that after the anomaly was widely reported investors may have begun to exploit it and through their trading drove away the profitability of the strategy. As a further robustness check, given that we have found momentum in the period 1990 to 2001, we apply the momentum strategy to the decade prior to this sample in Table 10. [INSERT TABLE 10 ABOUT HERE] Over the 1980 to 1990 period none of the momentum strategies were significantly positive. In fact many of them were significantly negative, indicating that a contrarian strategy may have proved beneficial. While the original momentum result in the 1990 s is robust to both the choice of statistical test we have applied and to an examination of seasonality, overall the out-ofsample tests provide little support for the robust existence of profitable momentum strategies. firms. Remember that when filtering by share price we do obtain a significant momentum result over this 15

16 6. TRANSACTION COSTS In order to be of economic value, any investment strategy must overcome the transaction costs involved in its implementation. So far we have found that the momentum result of the 1990 s was robust to using an appropriate test statistic (the bootstrapped skewnessadjusted t-statistic) and in Section 4 of this paper, we found the results were robust to considerations of seasonality in Australian stock returns. However, in section 5 we found that the returns could not have been exploited out-of-sample (even before transaction costs). In this section, we consider whether or not the 1990 s in-sample findings of momentum are robust to the consideration of trading costs. If momentum represented a profitable trading strategy the incorporation of transaction costs should not alter the findings of momentum presented in Table 6. In the U.S. Lesmond et al (2004) argues that in undertaking a momentum strategy the investor is required to disproportionately hold stocks with relatively high trading costs. Consequently, they find that profits to momentum strategies in the United States disappear when trading costs are included in the calculations. Not only the direct costs of the transactions themselves need to be considered but also indirect costs such as the bid-ask spread, impact on the order book price and the costs involved in setting up a margin account for the necessary short positions. DMW, who period (Table 2), this significant result is also unchanged by the exclusion of July. 16

17 found significant momentum, did not directly examine transaction costs. Instead they focused on liquid stocks, looking only at stocks on the Approved Securities list as well as those that make up the market index. Comparing their results of value-weighted to equalweighted momentum portfolios they note that smaller stocks do yield higher momentum returns and that this impact on implementable strategies needs to be further examined. In the United States, examination of trading rules have used a round-trip cost ranging from 0.727% for large stocks to 4.12% for smaller stocks for a sample that is roughly contemporaneous to the 1990 momentum period (Barber, Lehavy, McNicholls and Trueman, 2001). We do not have similarly well-considered data on transaction costs for Australia but it is not unreasonable to assume that the trading costs in Australia (a less liquid market that the United States) were of a similar, or greater, magnitude. Consequently, in Table 11, we consider the sensitivity of the findings in Table 6 to transaction costs. [INSERT TABLE 11 ABOUT HERE] When examining the top 330 market capitalisation securities in the Australian market over the period of September 1990 to July 2001, originally in 24 out of the 36 strategies P1 was significantly greater than P10 (Table 6). After the imposition of a 1% transaction cost the number of significant strategies falls to only 5 (Table 11, Panel A). It appears that the 1990 s momentum findings may be sensitive to consideration of transaction costs. 17

18 O Brien and Brailsford (2007), who looked at just the 6 month formation and 6 month holding period, found that momentum is strongest amongst the market capitalisation firms ranked stronger than the momentum effect witnessed in the top 200 firms. For the stocks ranked below 500, they found no significant momentum effect at all. DMW also found that their smallest quartile of stocks in their sample offered the highest available momentum returns. Their sample was limited to higher market capitalisation firms, excluding those argued by O Brien and Brailsford (2007) that do not show momentum. Panel B shows results consistent with O Brien and Brailsford (2007). Extending our sample to the top 500 market capitalisation firms (Table 11, Panel B) the momentum results are stronger and are significant now for 10 of the 36 strategies, including the strategy used by O Brien and Brailsford. This result is not consistent across all momentum strategies. In almost 60% of cases the momentum result is higher when limiting the sample to the top 330 firms rather than in the top 500 firms. This may indicate that the conclusions are again sample-specific and further work is required here. Should these results prove robust to the time period chosen the fact that we need to move from larger to relatively smaller mid-cap stocks to find a significant momentum result is at odds with an implementable strategy. Transaction costs are likely higher amongst the exact stocks that we need to include in our portfolio to generate a profitable return. 7. CONCLUSION In seeking to reconcile the results of prior momentum studies we have seen evidence of a momentum effect between 1990 and While simultaneously using long (six-month 18

19 or greater) formation and holding periods, and also limiting our sample to one based on large market capitalisation, the results are generally significant. When sorted by share price we still see momentum in the 1990 s, although now more highly concentrated amongst the shorter formation period strategies. After considering the impact of seasonality upon this momentum effect, seeing evidence supporting the penny stock effect of Gaunt et. al (2000) which appears independent of size and also considering the appropriateness of statistical techniques applied, we cannot dismiss the existence of momentum. If momentum profits are in some way abnormal a prima facie violation of market efficiency then that abnormality must not be expected given a generally accepted model of returns. Jegadeesh and Titman (1993) assess momentum profits against the static- CAPM and find that the alphas are positive and statistically significant; therefore, there were returns that could not be explained by the generally accepted model at that time. Jegadeesh and Titman (2001) assess momentum against the three-factor model (Fama and French, 1993) and also find that momentum strategies generate significant alphas. Using a case re-sampling methodology to bootstrap out the critical values in the regressions, we find that the momentum alphas are robust to an Australian daily three factor model 12. That is, even after risk adjustment these momentum alphas remain significant. 12 Using daily Fama-French (1993) factors. Omitted for space considerations - the inclusion of risk adjustment did not alter our conclusions. Results available from the corresponding author on request. 19

20 Has this significant momentum result challenged the notion of market efficiency? Our concerns about the economic profitability of momentum lie in several areas. Firstly, it appears that the in-sample results are highly sensitive to the introduction of transaction costs, plus the types of stocks required for a successful momentum strategy appear to be those which would involve higher trading costs to begin with. Secondly, the profitable formation and holding periods chosen appear to vary with the data sample. Thirdly, and of an even greater concern, when we test previously significant strategies out of sample we fail to see evidence of potential profitability. We remain sceptical of the existence of truly profitable momentum strategies in the Australian market. 20

21 References Barber, Brad, Reuven Lehavy, Maureen McNichols, and Brett Trueman "Can Investors Profit from the Prophets? Security Analyst Recommendations and Stock Returns." The Journal of Finance, vol. 56, no. 2 (April), Chan, H.W. & Faff, R.W An investigation into the role of liquidity in asset pricing: Australian evidence, Pacific-Basin Finance Journal, vol. 11, no. 5, pp Chan, H.W. and R.W. Faff, 2005, Asset pricing and illiquidity premium, Financial Review 40, Chordia, T., and L. Shivakumar, 2002, "Momentum, Business Cycle, and Time-Varying Expected Returns," Journal of Finance, 57, Demir, I., Muthuswamy, J., & Walter, T. 2004, Momentum Returns in Australian Equities: The influences of Size, Risk, Liquidity and Return Computation, Pacific-Basin Finance Journal, vol. 12, no. 2, pp Durack, N., Durand, R.B., & Maller, R.A. 2004, A best choice among asset pricing models? The Conditional Capital Asset Pricing Model in Australia, Accounting and Finance, vol. 44, no. 2, pp

22 Durand, R.B., A. Juricev and Gary Smith, 2007, SMB Arousal, Disproportionate Reactions and the Size-Premium, Pacific-Basin Finance Journal, forthcoming. Durand, Robert B., Manapon Limkriangkrai, Gary Smith 2006a Momentum in Australia A Note, Australian Journal of Management, Vol. 31, No. 2, pp Durand, Robert B., Manapon Limkriangkrai, Gary Smith 2006b In America's thrall: the effects of the US market and US security characteristics on Australian stock returns, Accounting & Finance 46 (4), Faff, R., 2001, An examination of the Fama and French three-factor models using commercially available factors, Australian Journal of Management, vol. 26, no. 1, pp Faff, R. 2004, A simple test of the Fama and French model using daily data: Australian evidence, Applied Financial Economics 14, pp Fama, E.F., & French, K.R. 1993, Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics, vol. 33, no. 1, pp Gaunt, C., 2004, Size and book to market effects and the Fama French three factor asset pricing model; evidence form the Australian stock market, Accounting and Finance 44, pp

23 Gaunt, C., & Gray, P., 2003, Short-Term Autocorrelation in Australian Equities, Australian Journal of Management 28, pp Gaunt, C., Gray, P., McIvor, J., 2000, The impact of share price on seasonality and size anomalies in Australian equity returns, Accounting and Finance 40, Goetzmann, William M. and Philippe Jorion 1993, Testing the Predictive Power of Dividend Yields, The Journal of Finance, Vol. XLVII, no. 2, June, pp Halliwell, J., Heaney, R. & Sawicki, J. 1999, Size and Book to Market Effects in Australian Share Markets: A Time Series Analysis, Accounting Research Journal, vol. 12, no. 2, pp Hurn, S., & Pavlov, V., 2003, Momentum in Australian Stock Returns, Australian Journal of Management 28, pp Hwang, S., and Rubesam, A., "The Disappearance of Momentum" (March 2007). Available at SSRN: Jegadeesh, N., & Titman, S. 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance, vol. 48, no.1, pp Jegadeesh, N., & Titman, S. 2001, Profitability of Momentum Strategies: An Evaluation of Alternative Explanations, Journal of Finance, vol. 56, no. 2, pp

24 Johnson, N.J., 1978, Modified t tests and confidence intervals for asymmetrical populations, Journal of the American Statistical Association 73, Kirby, Chris 1998, The Restrictions on Predictability Implied by Rational Asset Pricing Models, The Review of Financial Studies, Vol. 11, no. 2, Summer, pp Lesmond, David A., Michael J. Schill, and Chunsheng Zhou, 2002, The illusory nature of momentum profits, Journal of Financial Economics 71, Nelson, Charles R. and Myung J. Kim 1993, Predictable Stock Returns: The Role of Small Sample Bias, The Journal of Finance, Vol. XLVII, no. 2, June, pp O Brien, M., and Brailsford T., 2007, Disentangling Size from Momentum in Australian Stock Returns, Working Paper, UQ Business School. Rouwenhorst, G.K. 1998, International Momentum Strategies, Journal of Finance, vol. 53, no. 1, pp Shao, J., and D. Tu, 1995, The Jackknife and Bootstrap (Springer Verlag, New York). Sutton, C.D., 1993, Computer-intensive methods for tests about the mean of an asymmetrical distribution, Journal of the American Statistical Association 88,

25 Table 1 - Momentum Returns, Full Sample, All Stocks Using the set of all Fully Paid Ordinary securities in the Australian market over the period of 1 January 1980 to 31 December 2004 zerocost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formationperiod perfomers minus the bottom decile formation-period performers excluding all securities which did not trade during the formation period. The t-statistic used is that used by DMW in their Table 1. ** represents significance at the 1% level and * significance at the 5% level. K-Day J-Day % ( ) -7.1% ( ) -6.9% ( ) -8.6% ( ) -8.8% ( ) -9.8% ( ) % ( ) -5.9% ( ) -6.1% ( ) -8.3% ( ) -9.0% ( ) -12.2% ( ) % ( ) -5.0% ( ) -5.0% ( ) -7.3% ( ) -5.1% ( ) -7.1% ( ) % ( ) -3.3% ( ) -4.1% ( ) -4.1% ( ) -2.8% ( ) -2.2% ( ) % ( ) -4.0% ( ) -4.7% ( ) -6.9% ( ) -3.3% ( ) -2.7% ( ) % ( ) -3.9% ( ) -4.9% ( ) -5.0% ( ) -0.9% ( ) -2.7% ( ) 25

26 Table 2 - Momentum Returns, Full Sample, All Stocks, Penny Stock Filter Employed Using the set of all Fully Paid Ordinary securities in the Australian market over the period of 1 January 1980 to 31 December 2004 zerocost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formation-period perfomers minus the bottom decile formation-period performers excluding all securities which did not trade at any point during the formation period at a price greater than 50c. The t-statistic used is that used by DMW in their Table 1. ** represents significance at the 1% level and * significance at the 5% level. K-Day J-Day % ( 0.95 ) 2.1% ( 2.40 ) * 3.7% ( 3.15 ) ** 6.9% ( 3.81 ) ** 7.8% ( 3.27 ) ** 7.8% ( 2.77 ) ** % ( 2.17 ) * 3.5% ( 3.75 ) ** 5.8% ( 4.69 ) ** 9.8% ( 5.39 ) ** 10.9% ( 4.43 ) ** 11.1% ( 3.86 ) ** % ( 2.81 ) ** 4.1% ( 4.43 ) ** 6.8% ( 5.64 ) ** 10.8% ( 5.81 ) ** 12.3% ( 4.84 ) ** 13.5% ( 4.05 ) ** % ( 3.91 ) ** 5.0% ( 5.36 ) ** 7.1% ( 5.72 ) ** 9.8% ( 4.81 ) ** 12.2% ( 4.00 ) ** 17.8% ( 3.89 ) ** % ( 2.09 ) * 3.1% ( 2.67 ) ** 4.8% ( 3.20 ) ** 7.6% ( 2.84 ) ** 13.5% ( 3.02 ) ** 18.7% ( 3.34 ) ** % ( 1.53 ) 2.8% ( 2.75 ) ** 4.9% ( 3.65 ) ** 10.0% ( 3.22 ) ** 16.1% ( 3.37 ) ** 19.2% ( 3.28 ) ** 26

27 Table 3 - Momentum Returns, Full Sample, Large Stocks Only Using the top 500 (panel A) and top 200 (panel B) market capitalisation Fully Paid Ordinary securities in the Australian market over the period of 1 January 1980 to 31 December 2004 zero-cost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K- day buy and hold returns of the top decile formation-period perfomers minus the bottom decile formation-period performers excluding all securities which did not trade during the formation period. The t-statistic used is that used by DMW in their Table 1. ** represents significance at the 1% level and * significance at the 5% level. Panel A: Top 500 Market Capitalisation Securities K-Day J-Day % ( ) -5.3% ( ) -5.2% ( ) -7.1% ( ) -7.3% ( ) -7.4% ( ) % ( ) -4.0% ( ) -3.8% ( ) -6.6% ( ) -7.5% ( ) -9.2% ( ) % ( ) -3.2% ( ) -2.6% ( ) -4.8% ( ) -2.1% ( ) -2.9% ( ) % ( ) -1.0% ( ) -1.3% ( ) -0.8% ( ) 1.9% ( 0.29 ) 4.0% ( 0.51 ) % ( ) -2.9% ( ) -3.0% ( ) -4.1% ( ) 1.1% ( 0.16 ) 1.6% ( 0.19 ) % ( ) -2.2% ( ) -2.2% ( ) -0.6% ( ) 3.7% ( 0.50 ) 2.1% ( 0.25 ) Panel B: Top 200 Market Capitalisation Securities K-Day J-Day % ( ) -2.9% ( ) -3.2% ( ) -6.7% ( ) -5.1% ( ) -1.6% ( ) % ( ) -1.9% ( ) -1.8% ( ) -6.7% ( ) -4.3% ( ) -3.6% ( ) % ( ) -1.2% ( ) -0.6% ( ) -6.9% ( ) -0.1% ( ) -0.2% ( ) % ( 0.02 ) 0.0% ( 0.00 ) -0.8% ( ) -1.7% ( ) 5.9% ( 0.73 ) 13.5% ( 1.38 ) % ( ) -1.1% ( ) -0.5% ( ) -2.5% ( ) 8.4% ( 0.85 ) 10.4% ( 0.91 ) % ( 0.63 ) 1.1% ( 0.40 ) 0.8% ( 0.20 ) 0.7% ( 0.07 ) 9.7% ( 0.94 ) 11.3% ( 0.94 ) 27

28 Table 4 - Momentum Returns, 1990 to 2001 Using all securities with a 50c price filter (panel A) and the top 330 market capitalisation with no price filter (panel B) in the Australian market over the period of 1 September 1990 to 1 July 2001 zero-cost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formation-period perfomers minus the bottom decile formation-period performers excluding all securities which did not trade during the formation period. The t-statistic used is that used by DMW in their Table 1. ** represents significance at the 1% level and * significance at the 5% level. Additional periods not reported by DMW are shaded. Panel A: All Securities, 50c Formation Period Price Filter K-Day J-Day % ( 0.90 ) 3.5% ( 2.61 ) ** 6.8% ( 3.64 ) ** 10.2% ( 3.65 ) ** 11.7% ( 3.37 ) ** 11.0% ( 2.50 ) * % ( 2.29 ) * 5.9% ( 3.99 ) ** 9.6% ( 4.95 ) ** 13.8% ( 4.95 ) ** 15.6% ( 4.18 ) ** 15.1% ( 3.33 ) ** % ( 2.82 ) ** 6.4% ( 4.44 ) ** 10.1% ( 5.43 ) ** 13.8% ( 4.65 ) ** 14.7% ( 3.77 ) ** 14.4% ( 3.06 ) ** % ( 3.36 ) ** 6.8% ( 4.50 ) ** 9.6% ( 4.67 ) ** 10.5% ( 3.00 ) ** 9.8% ( 2.19 ) * 8.9% ( 1.75 ) % ( 1.97 ) * 4.0% ( 1.93 ) 5.5% ( 2.07 ) * 5.2% ( 1.30 ) 2.9% ( 0.60 ) 2.5% ( 0.47 ) % ( 1.62 ) 4.2% ( 2.71 ) ** 6.7% ( 3.45 ) ** 6.5% ( 2.04 ) * 6.0% ( 1.48 ) 5.4% ( 1.18 ) Panel B: Top 330 Market Capitalisation Securities K-Day J-Day % ( ) 0.7% ( 0.44 ) 2.1% ( 0.98 ) 4.4% ( 1.33 ) 6.0% ( 1.28 ) 7.1% ( 1.20 ) % ( 0.60 ) 3.3% ( 1.99 ) * 5.3% ( 2.72 ) ** 9.4% ( 2.91 ) ** 11.6% ( 2.60 ) ** 15.1% ( 2.65 ) ** % ( 0.56 ) 3.3% ( 2.17 ) * 5.9% ( 2.72 ) ** 9.0% ( 2.55 ) * 12.4% ( 2.78 ) ** 14.7% ( 2.52 ) * % ( 1.54 ) 4.3% ( 2.59 ) ** 5.4% ( 2.49 ) * 9.4% ( 2.71 ) ** 12.2% ( 2.75 ) ** 15.4% ( 2.70 ) ** % ( 0.55 ) 2.4% ( 1.42 ) 4.7% ( 2.24 ) * 7.6% ( 2.28 ) * 9.6% ( 2.27 ) * 11.2% ( 2.03 ) * % ( 1.30 ) 3.3% ( 2.13 ) * 4.5% ( 2.31 ) * 6.8% ( 2.11 ) * 8.3% ( 1.98 ) * 10.0% ( 1.91 ) 28

29 Table 5 - Non-Overlapping Portfolios Using the set of all Fully Paid Ordinary securities in the Australian market over the period of 1 September 1990 to 1 July 2001 zerocost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formation-period perfomers minus the bottom decile formation-period performers excluding all securities with a share price of less than 50c for the entirety of the formation period. The t-statistic used is that used by DMW in their Table 1. ** represents significance at the 1% level and * significance at the 5% level. Additional periods not reported by DMW are shaded. No holding periods used in this table are overlapping. K-Day J-Day % ( 0.90 ) 3.9% ( 2.30 ) * 6.1% ( 2.04 ) * 10.4% ( 1.95 ) 15.5% ( 1.24 ) 17.8% ( 1.27 ) % ( 2.29 ) * 5.3% ( 2.49 ) * 9.8% ( 2.85 ) ** 10.7% ( 2.24 ) * 15.8% ( 1.33 ) 12.3% ( 0.94 ) % ( 2.82 ) ** 6.8% ( 3.41 ) ** 10.6% ( 3.18 ) ** 20.8% ( 2.69 ) ** 12.1% ( 1.24 ) 9.4% ( 0.54 ) % ( 3.36 ) ** 6.2% ( 2.75 ) ** 8.9% ( 2.39 ) * 8.5% ( 1.09 ) 15.6% ( 1.70 ) -3.4% ( ) % ( 1.97 ) * 5.2% ( 2.40 ) * 8.5% ( 2.19 ) * 14.7% ( 1.91 ) 13.1% ( 0.72 ) -0.6% ( ) % ( 1.62 ) 3.6% ( 1.57 ) 7.0% ( 2.00 ) * 2.1% ( 0.25 ) 3.9% ( 0.40 ) 4.7% ( 0.35 ) 29

30 Table 6 - Momentum Returns, 1990 to 2001, Bootstrapped t-statistics Using all securities with a 50c price filter (panel A) and the top 330 market capitalisation with no price filter (panel B) in the Australian market over the period of 1 September 1990 to 1 July 2001 zero-cost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formation-period perfomers minus the bottom decile formation-period performers excluding all securities which did not trade during the formation period. A bootstrap has been used to determine the critical values. ** represents significance at the 1% level and * significance at the 5% level. Additional periods not reported by DMW are shaded. Panel A: All Securities, 50c Formation Period Price Filter K-Day J-Day % ( 1.23 ) 3.5% ( 4.91 ) ** 6.8% ( 7.01 ) ** 10.2% ( 7.04 ) ** 11.7% ( 6.83 ) ** 11.0% ( 3.13 ) ** % ( 3.45 ) ** 5.9% ( 6.63 ) ** 9.6% ( 8.65 ) ** 13.8% ( 9.59 ) ** 15.6% ( 4.58 ) ** 15.1% ( 3.27 ) * % ( 4.53 ) ** 6.4% ( 7.75 ) ** 10.1% ( 9.46 ) ** 13.8% ( 7.51 ) ** 14.7% ( 4.02 ) ** 14.4% ( 3.38 ) * % ( 5.00 ) ** 6.8% ( 6.32 ) ** 9.6% ( 6.72 ) ** 10.5% ( 5.19 ) ** 9.8% ( 2.92 ) * 8.9% ( 2.57 ) * % ( 2.52 ) * 4.0% ( 1.65 ) 5.5% ( 1.99 ) 5.2% ( 1.71 ) 2.9% ( 0.91 ) 2.5% ( 0.76 ) % ( 2.13 ) 4.2% ( 3.51 ) ** 6.7% ( 4.79 ) ** 6.5% ( 3.06 ) * 6.0% ( 2.13 ) 5.4% ( 1.87 ) Panel B: Top 330 Market Capitalisation Securities K-Day J-Day % ( ) 0.7% ( 0.59 ) 2.1% ( 1.43 ) 4.4% ( 1.87 ) 6.0% ( 1.96 ) 7.1% ( 1.85 ) % ( 0.73 ) 3.3% ( 2.81 ) ** 5.3% ( 3.89 ) ** 9.4% ( 4.47 ) ** 11.6% ( 3.23 ) ** 15.1% ( 4.13 ) ** % ( 0.67 ) 3.3% ( 2.84 ) ** 5.9% ( 4.03 ) ** 9.0% ( 3.13 ) * 12.4% ( 3.63 ) ** 14.7% ( 3.81 ) ** % ( 1.79 ) 4.3% ( 3.54 ) ** 5.4% ( 3.14 ) ** 9.4% ( 3.46 ) ** 12.2% ( 3.74 ) ** 15.4% ( 4.30 ) ** % ( 0.67 ) 2.4% ( 1.70 ) 4.7% ( 2.90 ) * 7.6% ( 3.28 ) ** 9.6% ( 3.09 ) * 11.2% ( 3.34 ) ** % ( 1.76 ) 3.3% ( 2.45 ) * 4.5% ( 3.02 ) * 6.8% ( 2.98 ) * 8.3% ( 3.00 ) * 10.0% ( 3.32 ) ** 30

31 Table 7 - Momentum and Seasonality, Full Sample Using the top 330 market capitalisation securities in the Australian market over the period of 1 January 1980 to 31 December 2004 zerocost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formationperiod perfomers minus the bottom decile formation-period performers excluding all securities which did not trade during the formation period. Panel A shows the portfolio returns in July only while Panel B shows the returns of non-july months. Critical values are determined using a bootstrap. ** represents significance at the 1% level and * significance at the 5% level. Panel A: July Returns K-Day J-Day % ( ) -0.5% ( ) -0.7% ( ) * -0.6% ( ) -1.6% ( ) ** -1.5% ( ) * % ( ) * -0.8% ( ) ** -0.8% ( ) * -1.2% ( ) ** -2.1% ( ) ** -2.1% ( ) ** % ( ) -0.7% ( ) * -0.6% ( ) -1.1% ( ) * -2.1% ( ) ** -2.2% ( ) ** % ( ) -0.3% ( ) -0.5% ( ) -1.4% ( ) ** -2.4% ( ) ** -3.0% ( ) ** % ( ) -0.7% ( ) ** -0.8% ( ) ** -1.6% ( ) ** -2.6% ( ) ** -3.5% ( ) ** % ( ) -0.4% ( ) -0.6% ( ) * -1.6% ( ) ** -2.7% ( ) ** -3.6% ( ) ** Panel B: Non-July Months K-Day J-Day % ( ) -2.4% ( ) -2.4% ( ) -5.9% ( ) -3.0% ( ) 0.3% ( 0.00 ) % ( ) -1.0% ( ) -0.9% ( ) -5.1% ( ) -1.7% ( ) -0.8% ( ) % ( ) -0.5% ( ) 0.0% ( ) -5.5% ( ) 2.3% ( 0.14 ) 2.5% ( 0.19 ) % ( 0.17 ) 0.3% ( 0.01 ) -0.3% ( ) -0.2% ( ) 8.5% ( 0.74 ) 16.5% ( 1.55 ) % ( ) -0.3% ( ) 0.4% ( ) -0.6% ( ) 11.2% ( 1.03 ) 14.5% ( 1.39 ) % ( 0.86 ) 1.5% ( 0.39 ) 1.5% ( 0.20 ) 2.5% ( 0.16 ) 12.7% ( 1.18 ) 15.4% ( 1.44 ) 31

32 Table 8 - Momentum and Seasonality Using the set of all Fully Paid Ordinary securities in the Australian market over the period of 1 September 1990 to 1 July 2001 zero-cost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formation-period perfomers minus the bottom decile formation-period performers excluding all securities with a share price of less than 50c for the entirety of the formation period. Panel A shows the portfolio returns in July only while Panel B shows the returns of non-july months. Critical values are determined using a bootstrap. ** represents significance at the 1% level and * significance at the 5% level. Panel A: July Returns K-Day J-Day % ( ) -0.4% ( ) -0.3% ( ) 0.2% ( 0.59 ) -0.4% ( ) 0.0% ( ) % ( ) * -0.4% ( ) -0.1% ( ) 0.0% ( 0.13 ) -0.2% ( ) -0.2% ( ) % ( ) -0.2% ( ) 0.0% ( 0.06 ) -0.2% ( ) -0.8% ( ) -0.5% ( ) % ( ) -0.2% ( ) 0.0% ( 0.13 ) -0.4% ( ) -0.6% ( ) -0.9% ( ) % ( ) -0.2% ( ) -0.3% ( ) -0.5% ( ) -1.0% ( ) * -1.3% ( ) * % ( ) -0.1% ( ) 0.0% ( ) -0.5% ( ) -1.2% ( ) * -1.5% ( ) * Panel B: Non-July Months K-Day J-Day % ( 1.65 ) 3.9% ( 5.64 ) ** 7.0% ( 7.46 ) ** 9.9% ( 7.14 ) ** 11.8% ( 7.65 ) ** 10.8% ( 3.24 ) ** % ( 4.35 ) ** 6.3% ( 7.64 ) ** 9.6% ( 9.22 ) ** 13.5% ( 9.90 ) ** 15.4% ( 4.79 ) ** 14.9% ( 3.25 ) * % ( 4.96 ) ** 6.5% ( 7.86 ) ** 10.0% ( 9.23 ) ** 13.8% ( 7.71 ) ** 15.2% ( 4.33 ) ** 14.5% ( 3.41 ) * % ( 5.01 ) ** 6.9% ( 6.27 ) ** 9.4% ( 6.56 ) ** 10.7% ( 5.39 ) ** 10.2% ( 2.99 ) * 9.5% ( 2.85 ) * % ( 2.62 ) * 4.2% ( 1.70 ) 5.7% ( 2.02 ) 5.6% ( 1.81 ) 3.9% ( 1.30 ) 3.8% ( 1.27 ) % ( 2.22 ) * 4.2% ( 3.46 ) ** 6.7% ( 4.71 ) ** 6.9% ( 3.26 ) * 7.0% ( 2.57 ) * 6.7% ( 2.45 ) * 32

33 Table 9 - Momentum Returns, Large Stocks, Recent Sample Using the top 330 market capitalisation securities in the Australian market over the period of 1 July 2001 to 31 December 2004 zero-cost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formation-period perfomers minus the bottom decile formation-period performers excluding all securities which did not trade during the formation period. Critical values are determined using a bootstrap. ** represents significance at the 1% level and * significance at the 5% level. K-Day J-Day % ( 0.87 ) 2.0% ( 0.53 ) 0.2% ( 0.00 ) 1.6% ( 0.31 ) 4.9% ( 0.78 ) 9.3% ( 1.22 ) % ( 0.01 ) -2.1% ( ) -2.6% ( ) -4.4% ( ) -0.1% ( ) 3.6% ( 0.45 ) % ( ) -3.2% ( ) -4.9% ( ) -5.6% ( ) -0.8% ( ) 3.1% ( 0.37 ) % ( ) -1.3% ( ) -3.2% ( ) -2.6% ( ) 1.8% ( 0.31 ) 1.5% ( 0.23 ) % ( ) -0.6% ( ) 0.3% ( 0.02 ) 4.9% ( 0.92 ) 6.8% ( 1.28 ) 4.1% ( 0.75 ) % ( 0.45 ) 4.1% ( 1.10 ) 4.9% ( 1.08 ) 5.4% ( 1.27 ) 4.6% ( 1.15 ) 3.1% ( 0.65 ) 33

34 Table 10 - Momentum Returns, Large Stocks, Early Sample Using the top 330 market capitalisation securities in the Australian market over the period of 1 January 1980 to 1 September 1991 zerocost momentum portfolios are formed as follows. The securities are ranked according to their performance over the J-day formation period and then held for the following K-day period. Reported below are the K-day buy and hold returns of the top decile formation-period perfomers minus the bottom decile formation-period performers excluding all securities which did not trade during the formation period. Critical values are determined using a bootstrap. ** represents significance at the 1% level and * significance at the 5% level. K-Day J-Day % ( ) * -7.8% ( ) * -9.3% ( ) * -19.9% ( ) * -18.6% ( ) -12.8% ( ) % ( ) * -7.0% ( ) * -8.8% ( ) -23.4% ( ) * -21.2% ( ) * -24.1% ( ) % ( ) * -5.4% ( ) -6.3% ( ) -23.3% ( ) * -12.7% ( ) -16.1% ( ) % ( ) -4.0% ( ) -6.5% ( ) -12.8% ( ) 0.5% ( ) 14.3% ( 0.66 ) % ( ) -4.7% ( ) -6.0% ( ) -14.4% ( ) 7.6% ( 0.31 ) 11.1% ( 0.44 ) % ( ) -1.8% ( ) -3.8% ( ) -6.6% ( ) 12.4% ( 0.51 ) 14.4% ( 0.56 ) 34