Abstract
The study examines the pervasiveness of eight well-documented anomalies in global equity markets for the Australian stock market. After partitioning stocks into three size categories (micro, small and big), we find that none of the eight anomalies are pervasive across size groups in either sorts or cross-sectional regressions. The existence of size, value, profitability, asset growth and accruals anomalies is primarily attributable to micro-cap stocks. Momentum and asset growth predict the expected returns of big stocks, but momentum does not predict the returns on micro stocks, and asset growth does not matter for small stocks. Contrarian returns are largely explained by stock size and value dimensions. Evidence for the earnings growth anomaly contradicts the growth extrapolation hypothesis. By looking at the hedge portfolio returns of anomalies in different regimes, we also show that many anomalies tend to exist in bear markets rather than bull markets. This evidence contradicts the risk-based explanations for the existence of anomalies.
1. Introduction
Anomalies are empirical patterns in stock returns that violate the efficiency of the market pricing mechanism in the context of the Capital Asset Pricing Model (CAPM). A large amount of US literature is devoted to the discovery of such patterns. For example, Banz (1981) documents the well-known size effect that stocks with low market capitalisation have abnormally high average returns. Rosenberg et al. (1985) and Chan et al. (1991) also find a value effect where stocks with higher book-to-market ratios significantly outperform the market and stocks with lower book-to-market ratios. A momentum anomaly documented by Jegadeesh and Titman (1993) claims that stocks that experienced high (low) past 6–12 months returns tend to generate high (low) future 6–12 months returns. De Bondt and Thaler (1985) find an opposite contrarian effect where stocks that experienced low (high) long-term (3–5 years) returns tend to have high (low) future returns. Stocks returns are also shown to be anomalous in pricing accounting information. Haugen and Baker (1996) and Cohen et al. (2002) find that stocks with higher levels of profitability generate higher returns. Lakonishok et al. (1994) document an earnings growth extrapolation effect where stocks with higher (lower) historical earnings growth rates have lower (higher) future returns. Cooper et al. (2008) find that stocks’ historical asset growth rates negatively predict future returns. The accruals anomaly initially documented by Sloan (1996) states that stocks with high accruals, the non-cash portion of earnings, have lower average returns.
Nevertheless, Fama and French (2008) partition stocks into different size groups (60% of total number of stocks are micro, 20% of stocks are small and 20% of stocks are big) and find that many of anomalies are not pervasive across size groups. In some cases, anomalies only exist in micro (extremely small) stocks (i.e. asset growth and profitability). They argue that, because micro stocks are so plentiful and are more likely to be in the extremes, they are influential in cross-sectional asset pricing tests. But because micro stocks are tiny in nature (they represent only 3% of the total market capitalisation), anomalous returns associated with them are probably not exploitable because of high illiquidity and trading costs. Therefore, ‘It is important to know whether anomalous patterns in returns are market-wide or limited to illiquid stocks that represent a small portion of market wealth’ (Fama and French, 2008: 1655).
Motivated by the findings of Fama and French (2008), this study examines eight well-documented anomalies, namely size, value, momentum, contrarian, profitability, earnings growth, asset growth and accruals, in the Australian stock market, using adapted methodologies proposed by Fama and French (2008). Specifically, we investigate whether these anomalies are pervasive across different size groups. In addition, the study is also the first to examine the mainstream anomalies together in the Australian market, and hence assess which anomaly variables provide additional information in determining Australian stocks’ expected returns. Furthermore, we examine whether the existence of an anomaly is consistent with risk-based explanations. If an anomaly variable captures information about risk, it is argued by Lakonishok et al. (1994) that the anomaly should underperform in the state of the world where the marginal utility of wealth is high (i.e. a bear market). We therefore ask whether any of these anomaly variables are risk factors by testing their performance in different market states.
Dissecting anomalies in the Australian market is interesting in a number of important respects. Firstly, out-of-sample comparisons to the US market provide context to the investment strategies that have been documented in the cross-section by Fama and French (2008) and to the question of whether Australia’s market exhibits unique characteristics. The aggregate Australian stock market capitalisation is dominated by a small number of large stocks, coupled with a very large number of tiny stocks. 1 Past Australian anomaly studies tend to focus on equally weighted (EW) returns of decile or quintile portfolios sorted on anomaly variables. 2 These studies are largely influenced by the characteristics of micro stocks. If historically documented anomalies are primarily associated with micro stocks in Australia, the evidence are not useful to investors due to the costs of exploiting them. Some studies also choose to examine the value-weighted (VW) returns on decile or quintile portfolios (see, e.g., Bettman et al., 2011; Brailsford and O’Brien, 2008; Gaunt, 2004). However, if decile or quintile portfolio sorting approaches are used for partitions of micro, small and big stocks, then VW returns can be dominated by a few big stocks. The results again are not representative of the true picture of the anomaly.
Secondly, evidence of Australian market anomalies is not only limited, but also often controversial. Studies in general confirm the existence of the size effect in Australia, but find that the returns across size portfolios are not monotonic, with the smallest two deciles generating particularly high returns (Beedles et al., 1988; Brailsford and O’Brien, 2008; Brown et al., 1983; Gaunt, 2004; Gaunt et al., 2000). Halliwell et al. (1999) document the existence of a value premium in Australia. However, using VW returns, Gaunt (2004) finds the value premium to be statistically significant only for the largest three quintiles. For evidence on the momentum anomaly, Hurn and Pavlov (2003) find momentum returns to be stronger for larger stocks than smaller stocks. Gaunt and Gray (2003), however, document that smaller stocks exhibit more positive autocorrelation in returns based on one-month prior returns. Demir et al. (2004) confirm the existence of momentum profits and also find them to be strongest for smaller stocks. In contrast, recent studies (Brailsford and O’Brien, 2008; O’Brien et al., 2010) find that the smallest size quintile loser stocks significantly outperform winners. Gray and Johnson’s (2011) work is the first Australian study that adopts the size group partitioning methodology of Fama and French (2008) and finds the existence of the asset growth anomaly. However, they find that the VW average hedge return is not statistically significant for big firms. Bettman et al. (2011) concludes that the asset growth anomaly is attributed to the influence of small stocks. While the evidence of Clinch et al. (2012) confirms the existence of an accruals anomaly in Australia, Anderson et al. (2009) find this anomaly to be more concentrated amongst larger firms. There is a notable gap in the Australian literature examining long-term contrarian, profitability and earnings growth anomalies in Australia.
Using EW and VW hedge returns in sorts and Fama and MacBeth (1973) cross-sectional regressions, we find that none of the eight anomalies are pervasive across the three (big, small and micro) stock size groups. In particular, size, value, contrarian, profitability, earnings growth and accruals anomalies do not predict the cross-sectional returns of big stocks. Momentum and asset growth predict the expected returns of big stocks using regressions; however, EW momentum hedge returns (i.e. long/short portfolio returns) are negative for micro stocks and VW asset growth hedge returns are statistically insignificant for micro and big stocks. Hedge returns on the earnings growth anomaly are negative across the size groups, which contradicts the growth extrapolation hypothesis. High-profitability big stocks tend to underperform low-profitability big stocks, indicating that Australian investors may overly extrapolate past level of earnings, rather than changes in earnings, for big stocks.
By examining the performance of anomalies in different market regimes, we show that many anomalies (size, value, profitability, asset growth and accruals) tend to generate superior returns in bear markets rather than in bull markets. Our evidence suggests that the existence of anomalies in certain size groups cannot be attributed to risk-based explanations.
The reminder of the paper is organised as follows. Section 2 provides the description of the data used for this study. Section 3 discusses the empirical results using sorts and cross-sectional regression. Section 4 provides the evidence on the performance of anomalies in different regimes. Section 5 concludes.
2. Data
Data for the study come from two sources. Monthly stock returns and market capitalisation data are obtained for each firm from the SIRCA Share Price & Price Relative (SPPR) database. The VW market returns are also obtained from the SPPR file, from 1968 to 2010. We obtain data for all stocks listed on the Australian Securities Exchange from January 1974 to December 2010. The accounting data is obtained from Aspect Huntley for the period from 1989 to 2009. This enables us to examine the returns on asset pricing anomalies from January 1992 to December 2010, covering 19-year period.
Table 1 shows the time-series average of the number of stocks and descriptive statistics on market capitalisation of stocks for the SPPR and Aspect Huntley combined file from 1992 to 2010, as well as the two sub-sample periods pre- and post-2000. The table also shows the average market capitalisation composition of different categories of stocks. It is important to note that the average mean market capitalisation is more than 20 times the median market capitalisation and the top 10 stocks represent around 40% of the total market capitalisation, indicating that the distribution of market capitalisation is heavily skewed towards the extremely large stocks. The Australian stock market composition becomes more concentrated in the top 10 stocks in the post-2000 period (42.39%, comparing to 38.04% in the pre-2000 period). The top 100 stocks represent on average 86% of the total market. The penny stocks outside the top 500 stocks (on average 887 number of stocks) only comprise less than 2% of the total market. This evidence illustrates that a crude decile or quintile partitioning approach is likely to result in a mixture of big, small and micro stocks in the same portfolio, and hence a careful size partitioning is required.
Australian Stock Exchange (ASX) stocks and market capitalisation, 1992–2010.
The table shows the time-series average of the number of stocks and descriptive statistics on market capitalisation of stocks for the Share Price & Price Relative (SPPR) and Aspect Huntley combined data from 1992 to 2010, as well as the two sub-sample periods pre- and post-2000. The table also shows the average market capitalisation composition of different categories of stocks.
As shown in Table 2, the final sample contains on average 1060 firms each year after we eliminate stocks with missing accounting information and negative book-to-market ratio from the merged SPPR and Aspect Huntley file. We then carefully partition the final sample into big, small and micro stocks. Fama and French (2008) use market capitalisation sorted percentile breaks, such as 60%, 20% and 20%, to divide all US stocks into micro, small and big stocks, respectively. The micro, small and big stocks therefore on average represent 90.48%, 6.45% and 3.07% of total US market cap in their study. Gray and Johnson (2011), instead of using percentile breaks, use the proportion of total market cap composition to classify micro, small and big stocks. That is, big stocks are those that comprise the top 90% of the total market cap. Small stocks are those that comprise the next 7% and micro stocks represent the remaining 3%. Their procedure results in a 70/16/14 split for micro, small and big stocks, respectively. Both Fama and French (2008) and Gray and Johnson (2011) adhere to the partitioning approach that defines big, small and micro stocks as those approximately represent 90%, 7% and 3% of total market capitalisation, respectively. We choose to use percentile breaks as they are more concise and similar to industry classification than fixing the market cap composition. For example, because our final sample contains 1060 stocks, the top 10% stocks would on average resemble the Australian Stock Exchange (ASX) 100 and the top 30% stocks would resemble the ASX 300.
Value- and equally weighted average monthly returns, and averages and cross-section standard deviations of anomaly variables, 1992–2010.
The table shows averages of monthly value-weighted (VW) and equally weighted (EW) average stock returns, and monthly cross-section standard deviations of returns for all stocks (Market) and for micro, small, and big stocks. It also shows the average number of stocks, average market capitalisation in millions (market cap) and the percent of the total market cap in each size group each month. It also shows the averages of annual EW average values and annual cross-section standard deviations of the anomaly variables used to sort stocks into portfolios and as independent variables in regressions. We assign stocks to size groups by the market cap at the end of December each year. Micro stocks are the bottom 70% stocks, Small stocks are between the 70th and 90th percentiles, and big stocks are the top 10% stocks. The anomaly variables, which are used to predict the monthly returns for January of t + 1 to December of t + 1 in the tables that follow, are: Size, the natural log of market cap in December of t; BM, the ratio of book equity for the last fiscal year-end t divided by market equity in December of t; Mom (momentum), the 12-month buy-and-hold returns preceding December of t; Con (contrarian), the 60-month buy-and-hold returns preceding December of t; ROA (Return on Assets), the earnings before interest and taxes (EBIT) in t divided by the average of total assets for t and t − 1; EG (earnings growth) the trailing three-year average of changes in EBIT from t − 1 to t scaled by the average book equity for t and t − 1; AG (asset growth), natural log of total assets in t divided by total assets in t − 1; Acc (accruals), the difference between EBIT and cash flow from operations in t, scaled by average total assets in t and t − 1. Except for Size and BM, the variables are multiplied by 100.
The approach in partitioning sample stocks into size groups is similar to that used by Fama and French (2008). At the end of each December from 1991 to 2009, each stock is allocated to one of the three size groups – micro, small and big stocks. Micro stocks are the bottom 70% stocks, small stocks are between the 70th and 90th percentiles and big stocks are the top 10% stocks of December-end market cap. 3 The time-series average numbers of stocks are 733, 218 and 108 for micro, small and big stock portfolios, respectively. As a result of the partitioning, micro stocks have $22 million average market cap and only represent 2.50% of the total market cap, whereas small and big stocks represent 8.59% and 88.91% of the total market cap with average market cap of $257 million and $5376 million, respectively. Although stocks that fall outside the ASX 300 are generally considered not investable by Australian institutional investors, for better comparison, we examine the bottom 70% micro stocks because they are included in most of the previous Australian anomaly studies in computing EW returns and performing market-wide regression tests (see, e.g., Bettman et al., 2011; Brailsford and O’Brien, 2008; Brown et al., 1983; Clinch et al., 2012; Gaunt, 2004).
Table 2 also reports the averages and standard deviations of returns for the VW and EW micro, small and big portfolios, as well as the market portfolio of all sample stocks. Because the big stocks represent on average more than 90% of market capitalisation, the VW market portfolio is similar to the VW big portfolio in average returns (0.84% and 0.83% per month, respectively) and volatilities (3.84% and 3.80% per month, respectively). However, the EW market average return and volatility (1.28% and 5.90%, respectively) are much higher than those of the VW market portfolio, since 70% of the number of stocks in the market portfolio are micro stocks and these have the highest EW average returns and volatilities (1.47% and 6.71%, respectively). It is interesting to note that the VW small stocks portfolio has higher returns and lower volatilities (1.00% and 5.02%, respectively) than those of the EW small stocks portfolio (0.75% and 5.06%, respectively), indicating that the bigger market cap stocks outperformed the smaller cap stocks in the small size group. The VW big portfolio has similar average returns (0.83%) compared to the EW returns (0.84%). Nevertheless, its volatility is lower than the EW big portfolio by 0.37%.
Table 2 also presents the time-series averages and standard deviations of the annual cross-sections of returns and the anomaly variables we use to predict returns. The eight anomaly variables, which are used to predict the monthly returns for January of year t + 1 to December of year t + 1 are defined and constructed as:
Similar to Fama and French (2008), the cross-sectional dispersion is generally largest for micro, and declines from micro to small and then to big stocks for returns and all anomaly variables, except Size, Mom and Con. This result further implies that micro stocks have stronger influence in testing the explanatory power of anomaly variables on stock returns.
It is interesting to note that the average EW returns for Mom and Con are quite large for small and big stocks, but not for micro stocks. This can be attributed to the stocks’ migration effect. To illustrate, stocks experienced extremely large positive (negative) returns in the previous years are more likely to move from micro (big or small) to small or big (micro) size categories. Because of this migration effect, the one-year (five years for Con) ahead returns are biased upward for big and small stocks and downward for micro stocks and, hence, result in the larger (smaller) returns for small and big (micro) stocks.
3. Empirical results
3.1. Sorts
Table 3 shows average monthly VW and EW returns for quintile portfolios formed using sorts on each anomaly variable for micro, small and big stocks, from January 1992 to December 2010. In December of each year from 1991 to 2009, sample stocks are sorted into quintile portfolios within each size group according to their ranks in each variable in December of year t. 5 The portfolios’ EW and VW returns are then computed for year t + 1.
Average returns for portfolios formed using sorts on anomaly variables, 1992–2010.
In December of each year from 1991 to 2009, sample stocks are sorted into quintile portfolios within each size group according to their ranks in each variable in December of t. The portfolios’ equally and value-weighted returns are then computed for year t + 1. All returns are reported in percentage form. SMB is the returns on the lowest market cap portfolio minus the returns on the highest market cap portfolio. HML for BM (ROA) is the returns on the highest book-to-market (Return on Assets) ratio portfolio minus the returns on the lowest book-to-market (Return on Assets) ratio portfolio. SWML (LLMW) is the returns on the short-term winners’ (long-term losers’) portfolio minus the returns on the short-term losers’ (long-term winners’) portfolio. LMH for EG (AG, Acc) is the returns on the lowest earnings growth (asset growth, accrual) portfolio minus the returns on the highest earnings growth (asset growth, accrual) portfolio. The t-statistics are shown in parentheses.
To avoid look-ahead bias, we ensure the accounting data are available to the public at the time of portfolio formation. For portfolios formed in December of year t, accounting variables used (book equity, earnings, total assets and cash flows from Aspect Huntley) are those for the fiscal year ending in calendar year t (t − 1) if companies’ fiscal year end is between January and August (September and December) of year t. The one year changes/averages are calculated as changes/averages from the fiscal year ending in calendar year t − 1 (t − 2) to the fiscal year ending in calendar year t (t − 1) if companies’ fiscal year end is between January and August (September and December) of year t. This ensures a minimum three months, and in most cases six months, difference between portfolio formation and report date. 6
Size, momentum and contrarian, which relies on the SPPR data, are measured in a more timely fashion than accounting-based variables. Size is measured at each December year end. Our methodology in forming momentum and contrarian portfolios slightly differs from what is commonly used in the previous literature. 7 That is, at the December end of year t, the momentum variable is the 12-month buy-and-hold returns preceding December. Similar to De Bondt and Thaler (1985), the Contrarian variable is the 60-month buy-and-hold returns preceding December of t. We skip the returns in December to account for illiquidity and market microstructure considerations associated with portfolio implementation. Momentum and contrarian variables are then updated each year.
As discussed in Table 2, micro stocks are more influential in EW returns and big stocks matter more in VW returns; the EW returns on quintile portfolios for all stocks reported in Table 3 are typically closer to those on micro stocks than those on small and big stocks. This is because micro stocks represent 70% of stocks and, hence, they have a large influence not only on the equal weightings but also on the portfolio sorting of stocks. However, the VW returns on quintile portfolios for all stocks are not necessarily more similar to those on big stocks than those on micro and small stocks. This is because even though big stocks represent on average 90% total market capitalisation, and they absolutely dominate the value weightings, they are however dwarfed on the portfolio sorting of stocks. That is, micro stocks have higher cross-sectional dispersion in anomaly variables, therefore they are more likely to be in the extremes than big stocks. The composition of extreme portfolios for all stocks might be dominated by micro stocks, coupled with few big stocks and, thus, the VW returns would be distorted by returns on this limited number of big stocks in the portfolio. This is particularly evident on portfolios sorted on ROA, where the average VW returns on the bottom ROA portfolio for all stocks (−0.36% per month) is more different to those for big stocks (1.08%) than those for micro and small stocks (0.11% and 0.41%, respectively).
Previous studies on anomalies tend to focus on the absolute returns of long and short stock positions at different extremes of anomaly variables. Table 3 also shows the difference in returns between bottom and top quintile portfolios. Whether the spread for a particular anomaly is shown as bottom minus top or top minus bottom depends on what it is empirically documented for this anomaly. For example, according to empirical evidence, one would expect the bottom quintile portfolio sorted on Size to outperform the top quintile portfolio; therefore, the spread is calculated as the bottom quintile minus the top quintile. If the spread is positive (negative), then the evidence is consistent (inconsistent) with what empirically suggested. Spreads for Size, Con, EG, AG and Acc are calculated as bottom minus top and denoted with SMB, LLMW, LMH, LMH and LMH, respectively. Spreads for BM, Mom and ROA are calculated as top minus bottom and denoted with HML, SWML and HML, respectively.
Previous studies tend to emphasise the use of EW hedge returns using all stocks. Table 3 supports the existence of five anomalies. That is, when all stocks are included, they generate statistically significant EW hedge returns. Mom, ROA and EG are the exceptions. In particular, EW hedge returns for EG are significantly negative and the evidence contradicts the extrapolation explanation of Lakonishok et al. (1994). On the other hand, all anomalies generate statistically significant VW hedge returns using all stocks except Con and EG. If size group partition is not considered, one would conclude that at least four anomalies (Size, BM, AG, Acc) are strong and robust to different weighting methodologies in the Australian stock market.
Which anomalies produce statistically significant average EW and VW hedge returns across all three size groups? Table 3 shows that not a single anomaly passes the test. Although AG and Acc anomalies show statistically significant EW hedge returns for all size groups, all anomalies fail to prove their existence across all three size groups using VW hedge returns. Anomalies tend to be stronger in micro and small stocks than in big stocks. This indicates that the anomalies often documented using all stocks’ EW returns are largely attributable to the empirical irregularities of micro stocks. 8
Size and BM, the two variables that can explain the cross-sectional US stock returns (Fama and French, 1992), fail to generate positively significant hedge returns, especially for Australian big stocks. Within big stocks, the smallest size quintile outperforms the largest size quintile by 0.15% (0.29%) per month on an EW (VW) basis, but this is statistically insignificant. The EW returns on the highest quintile ranked on BM even slightly underperform the EW returns on the lowest BM quintile (−0.03%). The evidence also suggests that the majorities of the size and value premia (2.20% and 1.44% per month, respectively) come from the lowest size quintile (average returns = 3.39%) and highest BM quintile (average returns = 2.07%) of the micro stocks.
Although constructed differently, the evidence on momentum returns is largely consistent with Brailsford and O’Brien (2008), who find the momentum returns to be negative for the smallest size quintile stocks and positively strongest for mid-cap stocks. In Table 3, the average momentum returns for micro stocks are negative for EW returns but positively significant for VW returns, indicating that momentum exists primarily in larger Australian stocks. However, momentum returns for big stocks are significant for EW but not significant for VW returns. Contrary to the momentum evidence, contrarian hedge returns are significantly positive for extremely small ‘micro’ stocks and extremely large ‘big’ stocks. This is illustrated by the evidence that the EW hedge returns (0.88%) are much larger than VW hedge returns (0.01%) for micro stocks and EW hedge returns (0.51%) are smaller than VW hedge returns (0.61%) for big stocks.
Hedge returns based on ROA show that the profitability anomaly is evident in micro and small stocks. However, the spread is negative for big stocks. In particular, returns on the lowest ROA quintile stocks generated the highest returns among big stocks on both an EW (0.95%) and VW (1.08%) basis. This may indicate that Australian investors overly extrapolate the past level of earnings of big firms. The evidence on earnings growth, as discussed, contradicts the extrapolation explanation of Lakonishok et al. (1994). This is because Lakonishok et al. (1994) eliminate stocks with negative earnings. We do not delete stocks with negative earnings because they are so common in Australia (almost half of stocks have negative earnings), primarily due to small and unprofitable Australian mining companies. 9 The negative spreads are primarily attributable to the low returns on the lowest EG quintile. This evidence supports an under-reaction to historical earnings growth rather than an excessive extrapolation of EG.
Our evidence on AG is in general consistent with Gray and Johnson (2011). The VW hedge returns are not strong for micro and big stocks, however. Similar to Clinch et al. (2012), the accruals anomaly exists when EW hedge returns are calculated for all stocks. However, VW accruals hedge returns are no longer significant for micro and big stocks.
3.2. Correlations, volatilities and cross-sectional regressions
In this section, we firstly examine to what degree the hedge returns on different anomalies in different size groups are correlated with each other across time. This exercise gives insight on what anomalies are similar and how Australian investors could diversify assets among different anomalies using variance and covariance information. We then use Fama and MacBeth (1973) (FM) regressions to show which anomalies offer information in predicting returns and which do not for each size group.
Table 4 shows the correlations and volatilities of the VW hedge returns based on the anomalies. Due to the hedging nature, none of the hedge returns are strongly correlated with the market. ROA and AG are the two strategies that mostly negatively correlated with the market. However, the beta neutral strategies generate much higher volatilities than the market (12.55% per annum). The volatilities are on average higher for strategies based on ROA and Con, and lower for strategies based on Size and Acc.
Correlations and volatilities of long-short portfolios formed on anomaly variables, 1992–2010.
This table reports the monthly correlation coefficients and annualised volatilities for the value-weighted market returns of all stocks and long-short portfolios reported in Table 3. Values reported on the diagonals of the correlation matrices are annualised volatilities. me-smb is the returns on the lowest market cap portfolio minus the returns on the highest market cap portfolio. bm-hml (roa-hml) is the returns on the highest book-to-market (Return on Assets) ratio portfolio minus the returns on the lowest book-to-market (Return on Assets) ratio portfolio. mom-swml (con-llmw) is the returns on the short-term winners’ (long-term losers’) portfolio minus the returns on the short-term losers’ (long-term winners’) portfolio. eg-lmh (ag-lmh, acc-lmh) is the returns on the lowest earnings growth (asset growth, accrual) portfolio minus the returns on the highest earnings growth (asset growth, accrual) portfolio. Correlation coefficients greater than 0.5 or less than −0.5 are shown in bold and italic.
The correlation matrix reviews some interesting stylised empirical facts. Contrarian strategies are strongly correlated with a number of anomalies, most evidently with Size (0.64 for all stocks) and BM (0.35 for all stocks). This is in line with the argument of De Bondt and Thaler (1985), who claim that contrarian profit is a result of long-run overreaction of small stocks. This is also illustrated by the evidence that contrarian profit does not covary much (−0.05) with the size premium for big stocks. Hedge returns on ROA appear to offer some sources of diversification, as they are negatively correlated with returns on other strategies (−0.75 with Size, −0.16 with BM, −0.55 with Con and −0.21 with EG for all stocks). It is interesting to note that the hedge returns on ROA are highly negatively correlated with hedge returns on EG (−0.61) for big stocks. Because hedge returns on ROA are high minus low and hedge returns on EG are low minus high, the negative correlation implies that ROA and EG capture similar sources of market anomalies, possibly the investors’ extrapolation of past earnings. It is also important to note that, in Table 4, value and momentum are not only different in nature, but also operate in different directions. The negative correlation between returns on Mom and BM is pervasive across size groups. This empirical feature of value and momentum is both interesting and yet to be explained, and therefore warrants future research.
Similar to Fama and French (2008), we estimate FM regressions separately for micro, small and big stocks, because micro stocks are influential in a market-wide regression test. We also measure the difference-of-means to see whether the relations between anomaly variables and stock returns vary across size groups. The regressions are estimated monthly, using all eight anomaly variables at the December of year t as the independent variables and returns for year t + 1 as the dependent variables. The returns are updated monthly and anomaly variables are updated once a year. Table 5 shows average slopes and t-statistics for anomaly variables from monthly cross-section regressions.
Average slopes and t-statistics from monthly cross-section regressions, 1992–2010.
The table shows average slopes and their t-statistics from monthly cross-section regressions to predict stock returns. The variables used to predict returns for January of t + 1 to December of t + 1 are: Size, the natural log of market cap in December of t; BM, the ratio of book equity for the last fiscal year-end t divided by market equity in December of t; Mom (momentum), the 12-month buy-and-hold returns preceding December of t; Con (contrarian), the 60-month buy-and-hold returns preceding December of t; ROA (Return on Assets), the earnings before interest and taxes (EBIT) in t divided by the average of total assets for t and t − 1; EG (earnings growth) the trailing three-year average of changes in EBIT from t − 1 to t scaled by the average book equity for t and t − 1; AG (asset growth), natural log of total assets in t divided by total assets in t − 1; Acc (accruals), the difference between EBIT and cash flow from operations in t, scaled by average total assets in t and t − 1. Each regression includes all the anomaly variables. Int is the average regression intercept and the average regression R2. adjusted for degrees of freedom. The t-statistics for the average regression slopes (or for the differences between the average slopes) use the time-series standard deviations of the monthly slopes (or the differences between the monthly slopes) and are shown in parentheses. All regression coefficients are multiplied by 100.
Table 5 shows that no anomalies demonstrate statistically significant explanatory power on stock returns consistently across all size groups. Size only explains the average returns of micro stocks. The average slope on Size is even positive (0.08, t = 1.03) for big stocks, which means bigger stocks slightly outperform the smaller stocks in the top 10% of market cap stocks. BM and ROA have the strongest explanatory power over returns of both micro (0.37, t = 4.42 and 1.87, t = 4.54, respectively) and small stocks (0.56, t = 4.25 and 4.57, t = 4.56, respectively). However, like the sorts, they do not show significance in explaining big stock returns. Only Mom and AG predict average returns of big stocks, with average slopes of 0.66 (t = 2.25) and −1.07 (t = −3.39), respectively. However, Mom fails to explain micro stocks average returns. Unlike sorts, AG however does not offer additional information in predicting small stocks, possibly due to the positive correlation with hedge returns on BM shown in Table 4. The explanatory power on Con is weak due to its correlation with Size and BM. Similar to sorts, regression results show that EG does not provide information in predicting stock returns. Nevertheless, in the small stock group, a significantly negative coefficient on EG indicates some degree of extrapolation of earnings for small stocks. Acc appears to be a micro-cap anomaly only.
On a market-wide basis, four anomaly variables (BM, ROA, AG and Acc) offer useful information in predicting stock returns. Five variables can explain the average returns of micro stocks; however, the eight variables together only explain 4% of variations in stock returns. A large and positively significant alpha (8.69, t = 5.56) for micro stocks is still unpredictable, but perhaps also not exploitable due to transaction costs. However, for big stocks, although only two variables show explanatory power, the eight variables on average explain 17% cross-sectional variations of stock returns. Alpha is not only insignificant, but also slight negative, indicating that the big stocks more efficiently price in these variables than micro stocks.
4. Anomalies, regimes and risk
In this section, we investigate the performance of anomalies in different times, in particular in different market regimes. The motivation for this analysis is two-fold. Firstly, from a portfolio management perspective, investors need to understand in what market conditions an anomaly-based strategy is likely to succeed or fail. Secondly, and more importantly, from an asset pricing perspective, it is important to examine whether any of the eight anomaly variables are risk factors. Although our size grouping analysis in Section 3 shows that none of these anomalies are robust across size categories, it is difficult to draw inferences on the future existence of these anomalies based on findings from a specific sample period. If an anomaly variable indeed captures additional information about risk, it is likely to exist in the long term and across different size categories. Lakonishok et al. (1994) state that if the superior returns to an anomaly-based strategy are due to greater risk exposure, the strategy should underperform in some states of the world, particularly, in the ‘bad’ states, in which the marginal utility wealth is high, therefore making risky assets unattractive to risk-averse investors. While it is difficult to either prove or reject a risk-based explanation, the non-parametric approach of Lakonishok et al. (1994) is a simple and logical methodology in examining whether excess returns are due to risk or mispricing. 10 We therefore examine the success of anomalies in different market regimes.
We follow Lakonishok et al. (1994) by examining the performance of the anomalies in various market states. Table 6 reports the performance of the eight anomalies in each of three regimes of the Australian market: a bear regime with the 25 worst stock return months, a bull regime with the 25 best stock return months and a normal regime with the remaining 178 normal stock return months based on the VW Australian market portfolio returns from 1992 to 2010. 11 The average difference in EW and VW returns between the highest and lowest quintile portfolios sorted on each anomaly variables, along with the t-statistics, are calculated for each size category under each regime. A negative return difference or hedge return indicates an underperformance of the anomaly strategy.
Anomalies’ hedge returns under three regimes, 1992–2010.
All months in the sample (228 in total) are divided into the 25 worst stock return months (W25), 25 best stock return months (B25) and remaining 178 normal stock return months (N178) based on the value-weighted market portfolio returns from 1992 to 2010. Equally weighted (Panel A) and value-weighted hedge returns (Panel B) for each anomaly are calculated separately for the three regimes. me-smb is the returns on the lowest market cap portfolio minus the returns on the highest market cap portfolio. bm-hml (roa-hml) is the returns on the highest book-to-market (Return on Assets) ratio portfolio minus the returns on the lowest book-to-market (Return on Assets) ratio portfolio. mom-swml (con-llmw) is the returns on the short-term winners (long-term losers) portfolio minus the returns on the short-term losers (long-term winners) portfolio. eg-lmh (ag-lmh, acc-lmh) is the returns on the lowest earnings growth (asset growth, accrual) portfolio minus the returns on the highest earnings growth (asset growth, accrual) portfolio. The t-statistics are shown in parentheses.
The EW hedge returns shown in Panel A of Table 6 indicate that, on average, short-term momentum winners and low earnings growth stocks underperform the losers (−0.64% per month, t-stat = −0.63) and high earnings growth stocks (−1.22% per month, t-stat = −2.63) during the worst 25 months period, primarily attributable to micro stocks. In line with the results in the previous section, the low earnings growth stocks do not outperform the high earnings growth stocks in other periods. The growth extrapolation story of Lakonishok et al. (1994) is only found in big stocks during the bear market, where big stocks with lower earnings growth significantly outperform the higher earnings growth counterpart by 2.50% per month. The underperformance of the momentum strategy in bear markets is insignificant. However, the micro losers’ stocks significantly outperform the micro winners’ stocks in the bull market. Therefore, it is difficult to argue that any of these anomaly variables have additional information about risk.
What about the size and value anomalies, the two risk factors along with the market factor that is widely used in Fama–French three-factor model? The size and value premia are in fact the strongest during the bearish states, at least for the micro and small stocks. However, the big value stocks underperform the big growth stocks in the most bullish market by −1.25% per month. This evidence is inconsistent with risk-based explanations for size and value effects.
Profitability, asset growth and accruals all appear to be more like bear market strategies rather than bull market strategies. It is particularly interesting to note that although high-profitability stocks significantly outperform in the bear market (2.64% per month), they significantly underperform the low-profitability stocks in the bull market (−2.98% per month). There is no significant difference in returns between high- and low-profitability stocks during the normal period. Within the big stocks, the high-profitability stocks underperform the low-profitability stocks not only during the bear market (−0.43% per month), but also significantly during the bull market (−1.13% per month). Contrarian profit is more evident in bull market for micro stocks; however, the opposite holds true for big stocks.
The VW hedge returns provided in Panel B of Table 6 show similar implications. None of the anomalies experience significantly negative returns consistently across size groups in bear market. Again, most of anomalies (value, profitability, asset growth, accruals and, to a lesser extent, contrarian) have superior returns skewed towards negative market return months rather than positive market return months. The profitability anomaly is the only one that generates significantly negative returns during the bull market.
In summary, not only do the anomaly variables not appear to proxy for systematic risk, but also portfolio strategies based on these anomalies provide some degree of downside risk protection. The evidence provided is therefore not consistent with a risk-based explanation. This also, to some extent, explains why certain anomalies are found in some size groups but not in others.
5. Conclusion
This study is the first to examine the existence and pervasiveness of eight well-documented stock market anomalies together in Australia. While previous anomaly studies in Australia produce some inconsistent and, at times, controversial findings, there are also methodological issues in some of these studies, primarily the use of EW returns computation on decile or quintile portfolios and the market-wide cross-sectional regression test. Because micro stocks in Australia are so numerous and influential in EW returns and market-wide regression tests, we further partition all stocks into micro, small and big stocks and examine the anomalies in each size group separately.
We find that none of these eight anomalies are pervasive across size groups in sorts and cross-sectional regressions. In sorts, the existence of size, value, profitability, asset growth and accruals anomalies is mostly attributable to micro-cap stocks, which are generally considered not investable by Australian institutional investors and therefore are difficult to exploit. While asset growth and accruals generate significantly positive EW hedge returns for all size categories, the VW counterparts are insignificant for micro and big stocks. Momentum returns are significantly positive for big stocks using EW returns, but are negative among micro stocks. Contrarian returns are only significantly positive in EW hedge returns for micro stocks and VW hedge returns for big stocks. The hedge returns on earnings growth are all negative, which contradict the findings of Lakonishok et al. (1994). In cross-sectional regressions, only momentum and asset growth predict the expected returns of big stocks. However, momentum does not predict returns on micro stocks and asset growth does not matter for small stocks. Contrarian returns are largely explained by size and value.
Our Australian results are quite different from those of the US, as reported by Fama and French (2008), which find pervasiveness in some of anomalies (e.g. value, momentum and net stock issues). This difference is perhaps due to a different market capitalisation distribution or industry composition between the two markets. For example, the Australian market is dominated by Financials and Resources sectors in both market value and number of stocks. This domination is likely to dictate both EW and VW returns. On the other hand, the US market is much less concentrated, and has a more dispersed industry composition. 12 In addition, this study employs a relatively short sample period compared to most of the US studies on market anomalies. Nevertheless, we cannot exclude the possibility that these anomalies could be spurious in the Australian context.
In an attempt to examine whether any of these anomalies are risk factors, this study finds that most of the anomalies (except momentum and earnings growth) tend to outperform in the bear rather than in the bull market. Lakonishok et al. (1994) argue that high-risk assets must underperform in those states of the world where the marginal utility of wealth is high and investors are risk-averse, such as the bear market state. Our evidence therefore does not lend support to risk-based explanations of anomalies.
This study provides implication to academic research on Australian fund managers’ performance. Given the results concerning anomalies in this study, and other empirical evidence showing fund manager skill in active Australian equities (see, e.g., Chen et al., 2010; Fong et al., 2008), it would appear that fund managers are generating alphas in areas beyond the mainstream anomalies. If this is the case, then active Australian fund managers are providing genuine value-added services. This issue warrants further research.
Footnotes
Acknowledgements
The authors are indebted to the valuable comments and suggestions made by John Pearce and Dennis Sams.
Funding
This work was supported by UniSuper Management Limited and Capital Markets CRC Limited.
Date of acceptance of final transcript: 2 July 2012.
Accepted by Associate Editor, Karen Benson (Finance).