Momentum in Australian stock returns.

Abstract: Medium-term momentum, or the tendency of investment strategies based on buying past winning stocks while selling past losing stocks to maintain above normal performance over a period, has been a well-documented feature of stock returns in the US. We investigate the performance of momentum investment strategies in portfolios of Australian stocks and examine some of the common explanations and empirical features of momentum. The paper establishes the presence of a strong medium-term momentum effect, which cannot be completely accounted for by any of the possible explanations considered in this paper.

Keywords: STOCK RETURNS; MOMENTUM PORTFOLIOS; RISK ADJUSTMENT

1. Introduction

Within the context of investment strategy, two interesting challenges to the debate on market efficiency have emerged in recent years. DeBondt and Thaler (1985, 1987) argued that past losers outperform past winners over an investment horizon of three to five years. The profitability of this contrarian investment strategy is attributed largely to the fact that investors over-react to good or bad news. It is generally true to argue, however, that most investors have investment horizons which are shorter than those required for the contrarian approach to yield acceptable returns (De Long, Shleifer, Summers & Waldmann 1990; Shleifer & Vishny 1990). As a consequence, a result which has received relatively more recent attention is due to Jegadeesh and Titman (1993) who demonstrate that past winners outperform past losers over the intermediate horizon of three to twelve months. A momentum strategy, therefore, involves buying past winners and selling past losers. Using returns of individual stocks, Jegadeesh and Titman (1993) established that this strategy produced abnormal returns over horizons of 3 to 1 months. Since this influential work a number of other studies have confirmed and extended this result. Moskowitz and Grinblatt (1999) show that momentum exists in industry-based portfolios while Llewellyn (2002) demonstrates that momentum is also present in size and book-market sorted portfolios. Grundy and Martin (2001) take a longer-term historical perspective and show that a momentum strategy has been profitable in the US since the 1920s. There is thus a solid body of literature documenting that momentum is a robust and pervasive feature of US stocks and there is emerging evidence (Rouwenhorst 1998) to suggest the presence of momentum in European markets.

A number of explanations have been suggested to account for momentum. Some authors have suggested that momentum profits are solely due to data-snooping bias. Jegadeesh and Titman (2001), using data over a sample period subsequent to their earlier paper, show that a momentum strategy continues to be profitable, this result may be taken as evidence against the data-snooping argument.

Conrad and Kaul (1998) argue that the cross-sectional dispersion in mean returns of individual stocks can be an important determining factor in generating momentum profits. One prediction of this explanation would be that the return to a momentum strategy would be positive, on average, for all the post-ranking period. Evidence to the contrary in the US is provided by Jegadeesh and Titman (2001), who show that the performance of momentum portfolios 13-60 months post-formation is negative.

Another popular explanation of momentum is provided by Chan, Jegadeesh and Lakonishok (1996), who attribute momentum to firm-specific events in that investors either under-react to information or that positive feedback trading causes a delayed over-reaction to information. Llewellyn (2002), on the other hand, interprets the profitability of momentum strategies for size and book-market sorted portfolios as evidence against the first-specific behavioural explanations since these portfolios may be regarded as fairly well diversified and therefore reflecting systemic risk. Llewellyn (2002) also provides an alternative view of the behavioural story by focusing on the possible influence of patterns of correlation and autocorrelation in returns as a possible explanation for momentum. In particular, it appears that lead-lag correlations among stocks are stronger than autocorrelations, with a possible behavioural rationale for this phenomenon being that investors mistakenly believe that news about one firm contains news about another.

Given the scale of the recent interest in momentum and the fact that no single persuasive explanation for the phenomenon has emerged, it is perhaps surprising that more has not been written on this score in the Australian context. As a consequence, this paper aims to fill the gap in the literature by investigating the profitability of a momentum investment strategy implemented using the top 200 Australian stocks by market capitalization. The results are then examined further to explore possible alternative explanations for the presence of momentum in Australian stock returns.

The rest of the paper is structured as follows. Section 2 describes the dataset employed and deals with various methodological points related to the construction of the stock returns which are used to examine momentum. In section 3 the basic momentum strategy is outlined and the results from implementing this strategy with Australian stocks are presented. Section 4 tries to interpret these findings in terms of popular explanations of the momentum phenomenon. Of particular importance here will be the role of risk adjustment of the returns of individual stocks. Conclusions and suggestions for further research are contained in section 5.

2. Data and Measurement

The data are sourced from the AGSM database containing monthly observations on prices, returns, dividends and capital reconstructions for the period from December 1973 to December 1998. A particular feature of the Australian stock market is the low liquidity encountered for small stocks. To limit the effect of this feature on the results, the analysis in the first part of the paper was limited to the top 200 stocks by market capitalization. (1)

The analysis is performed on simple monthly returns defined as the sum of the capital gain and dividend yield, taking into account any capital reconstructions. Over the period covered by the sample, a substantial number of stocks were delisted and exited the database. To avoid the effects of survivorship bias, it is assumed that any such occurrence resulted in a 100% capital loss for shareholders. (2)

Even having restricted the analysis to the largest stocks, the resultant dataset has a considerable number of periods when a particular stock was not traded and hence no price record exists. A number of alternative methods for dealing with missing data are tried.

2.1 Simple Approach

This is the approach adopted by the AGSM database in recording price observations to be included in index construction. A similar convention is adopted by the ASX for constructing stock market indices. If no trade occurs in a particular month, the last recorded price is used for calculating the return. It should be noted that this price is not adjusted for dividends or capital reconstructions. Effectively, it implies that all missing gross returns are imputed with the value of 1.

2.2 Unconditional Mean Approach

Sample mean returns are computed for each stock using all valid monthly total return observations (a return observation is considered valid if the stock was traded both in the current and the previous months). Any missing return observations during the period when it was listed on the stock exchange are replaced with the sample estimate of the unconditional mean return.

2.3 Regression Approach

Returns are assumed to have been generated by the factor model:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [R.sup.i.sub.t] is the return on stock i, [f.sub.j,t]'s are factors yet to be determined and the e's are stock specific errors uncorrelated across time-periods and stocks. In the regression approach, missing returns are replaced with the predicted return obtained from this regression equation. Of course the practical implementation of this approach relies crucially upon the identification of the appropriate factors to include and the method by which the factors were determined is now spelled out.

The first attempt at identifying the appropriate factors to include in this regression involved a principle-component analysis of size-sorted portfolio returns. All listed stocks in the database were ordered on size and the 200 largest companies were sorted into 10 portfolios, each containing the same number of stocks. The remaining stocks were arranged into 5 equal value portfolios. (3) The results of the principle-component analysis suggested that a three-factor model was appropriate and the scores of the 3 largest principle components of the unconditional variance-covariance matrix of the returns to these size-sorted portfolios were then computed. (4) Interestingly enough, the first and second factors obtained from the principle--component analysis can easily be interpreted--on the basis of correlations as the market and the size factors commonly encountered in the empirical asset pricing literature. It would perhaps have been desirable to be able to interpret the third factor as the excess return on value stocks or the Fama-French (1996) HML factor. Unfortunately, this is not possible as the information necessary to construct value portfolios for the entire period of our dataset was not available. (5)

Recognizing that all factors in these empirical asset-pricing models are proxies for underlying economic sources of risk, the following pragmatic approach was adopted to construct the factors used in the regression model. Given the overwhelming theoretical importance of the market factor, the return on the equal-weighted market index was constructed from all listed ordinary stocks to serve as the first factor. (6) Two additional factors were then obtained from a principle-component analysis of the residuals of the size-sorted return regressions on the market factor. To capture any additional variation in returns due to industry-specific influences we also included a collection of returns on equal-weighted industry portfolios. To sum up, the missing returns are interred from the regression

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [R.sub.m,t] is the return on the market portfolio, [f.sub.j,t] are the scores of the PCA factors and [R.sup.Industry.sub.k,t] are the returns on stock portfolios organised by industry.

3. Momentum

Momentum is investigated within three separate value bands. Stocks are sorted on their current market capitalisation and momentum portfolios are constructed from the 200 top value stocks, and then separately for the top 50 and the remaining 150 stocks.

Within a given value band, the construction of momentum portfolios follows closely the method described in Jegadeesh and Titman (1993):

1. Sort the stocks on the cumulative return over the past 6 months.

2. Split the sorted stocks into three groups with equal numbers of stocks.

3. Form an equal-weighted arbitrage portfolio at time t by buying the group of best performing stocks and short-selling the group comprising the worst performing stocks.

4. Keeping the composition of the arbitrage portfolio fixed, the return for holding the portfolio for one month, or from h-1 to h months after the date of portfolio construction is computed, for the investment period h ranging between 1 and 36 months.

5. Repeat steps 1 to 4 for every time period.

Figure 1 reports the average holding return for the different investment periods under alternative treatments for missing data outlined in section 2 and contrasts them with a strategy based on the random selection of stocks within a given value band. A striking feature of the panels A to C is the positive return to a momentum strategy over the short- to medium-term investment horizon. Profits to the random sort in panel D of the figure display no apparent regularities suggesting that the momentum profits are not a statistical artefact. The conclusion is robust to the choice of the method for inferring missing data, although the simple approach generates momentum profits that are about 3 basis points less than both the unconditional and factor approaches. This result suggests that the simple approach introduces a bias by underestimating the unconditional mean of returns of individual stocks. Panels C and D are very similar and give no reason to select between unconditional and factor approaches. The factor approach however fits the cross-sections of stock returns reasonably well (regression [R.sup.2] of about 35%-40% for individual stocks) and the results reported in the rest of the paper were obtained from the dataset generated using this method.

[FIGURE 1 OMITTED]

The cumulative returns to a momentum strategy reported in table 1 indicate that profits from holding the momentum portfolio in the first year after formation range from 4.79% to 7.13% for the raw returns. In addition, momentum appears strongest in the larger stocks. The preliminary evidence provided by the random sort in panel C of figure 1 is confirmed by the t-statistics reported on the holding returns to momentum portfolio. (7) The null hypothesis of zero expected returns is rejected for all size bands for holding periods between 1 and 12 months.

Another interesting feature of the results is that once momentum profits abate, there is no conclusive evidence to suggest that a contrarian investment strategy becomes profitable. Recall that the major explanation of the profitability of contrarian investment is that the stock market overreacts to news, so winners tend to be overvalued and losers undervalued (De Bondt & Thaler 1985, 1987). As a result, any investor that exploits this inefficiency will profit when stock prices revert to fundamental values. This explanation of contrarian profits has been the subject of criticism on two main fronts. Chan (1988) and Ball and Kothari (1989) argue that if the risk of the value portfolio is properly measured, then the abnormal return to contrarian investment is low, while Zarowin (1989) and others have argued that the apparent profits earned by such a strategy are attributable to other well-known asset pricing anomalies (the size and January effects). Despite this criticism, the hypothesis that contrarian investment produces abnormal returns has stood up reasonably well to empirical scrutiny in US markets (Chopra, Lakonishok & Ritter 1992; Lakonishok, Shleifer & Vishny 1994). The results reported in table 1, however, indicate that contrarian investment is not a viable longer-term strategy in the Australian market at least over the three-year investment horizon. The returns to short-selling the momentum portfolio over this horizon are not significantly different from zero.

4. Explanations

This section examines the contribution of unconditional means, risk premia and industry factors to momentum profits. Behavioural explanations for momentum (see Jagadeesh & Titman 2001, for a summary) and the effect of cross and autocorrelations in stock returns (Llewellyn 2002) are not investigated here because they are not easily accommodated within the scope and method of this study.

4.1 Cross-Sectional Dispersion in Unconditional Mean of Returns

Conrad and Kaul (1998) argue that momentum strategies that involve buying winners and selling losers are by construction tilted towards stocks with high unconditional mean returns. According to this view momentum profitability can be explained completely by the cross-sectional dispersion of unconditional mean returns. To examine the validity of this argument in the Australian context we re-estimate the mean holding return for the momentum strategy after removing the effect of the unconditional means from the returns series. Figure 2 shows holding returns for a momentum strategy where stocks are sorted into portfolios on the basis of their cumulative returns over the sorting window, but with profits over holding periods computed using centred returns.

[FIGURE 2 OMITTED]

It appears that the adjustment for the unconditional mean does not eliminate medium-term momentum profits or longer-term contrarian profits, although it dampens momentum in the short term (1 to 6 months). To confirm this tentative conclusion, table 2 reports the cumulative returns, with associated HAC t-statistics, to a momentum strategy based on the returns once their unconditional mean has been removed.

It is now apparent that the statistically significant abnormal profit, experienced in the first month post-formation of the momentum portfolio and also in the 6-12 month period, has disappeared. Another noteworthy feature is the fact that the momentum profits in the top 50 stocks are now very similar to those for all 200 stocks and the bottom 150. This would lead to the conjecture that the Conrad and Kaul proposition is responsible for the apparent difference in the profitability of the momentum in the top 50 and bottom 150 stocks observed in figure 1 and confirmed in table 1. The argument is reinforced by observing that after about 2 years any apparent regularity in momentum returns seem to dissipate and the profits of the two portfolios oscillate around the levels determined by their respective long-term means which contrasts with figure 1 where mean-reversion in returns drives a reduction in further momentum.

4.2 Risk Adjustment

Another potential source of momentum is the time-varying risk exposure to economy-wide factors. To explore this possibility we examine momentum profits after risk-adjusting returns for factor exposure. Instead of adjusting returns on individual stocks for their factor exposure (Grundy & Martin 2001), we perform risk adjustment of portfolio returns. There are two reasons for proceeding in this manner: First, the pricing model, (1), which is used to effect the risk adjustment has better explanatory power for portfolios than for individual stocks due to a high degree of idiosyncratic variation in the latter; and Second, the model based on portfolios is likely to be more robust in the presence of time-variation in individual stock factor loadings.

The momentum portfolio returns are adjusted for risk on a period-by-period basis. As in the original momentum strategy construction, stocks are ordered in each time-period on their cumulative raw returns over the previous 6-month period. The portfolio composition is then fixed and the full-sample estimates of the loadings of the momentum on the factors at time t are estimated by simple OLS. The risk-adjusted returns are then given by the regression residuals between t and t + h. This procedure is then repeated for all t, in effect this approach to risk adjustment is aimed at capturing any time variation in factor exposure for the momentum portfolio.

The factors used to adjust portfolio returns for risk require a little further explanation. The three factors used to infer the missing data in terms of the regression approach outlined previously are again used in the risk adjustment. It should be noted, however, that returns to industry portfolios are not included in this regression. This decision reflects our assumption that this kind of industry-specific risk is not priced. (8)

Figure 3 shows that adjusting for factor risk does not change the basic story, both momentum and contrarian profits are still clearly present.

[FIGURE 3 OMITTED]

The results reported in table 3 reinforce some of the patterns observed in table 2. It has already been established that the removal of the unconditional means of individual stocks reduces the significance of momentum profits in the first month after the formation of the momentum portfolio. The process of risk adjustment further erodes the profitability of the momentum strategy at very short horizons. Indeed, the most significant result reported in table 3 is that momentum profits are only significant in the 6-12 month holding period. This result is consistent with that reported by Grundy and Martin (2001) who show that exposure to factors correlated strongly with momentum returns, which accounts for some but not all abnormal momentum returns.

4.3 Industry Factors

Moskowitz and Grinblatt (1999) suggest that momentum is primarily driven by industry factors. To prove this point they compared momentum profits from investing in industry portfolios adjusted for individual stock momentum and the momentum in excess returns on individual stocks above the industry index.

To explore industry momentum in the Australian context, profits from a momentum strategy implemented using industry returns were computed as follows. Equal-weighted industry indices were reconstructed from the database and the algorithm for the construction of the momentum portfolio was then applied to industry returns instead of individual stocks. The first row of table 4 reports the result of this construction. It is clear that industry momentum appears to be strongest at the very short horizon (up to 6 months), a result that differs from that observed for size sorted stocks. This is consistent, however, with the results reported with Martin and Grundy (2001) and Llewellyn (2002) that momentum in industry returns is strongest in the very short term. Although not reported in this paper, short-term industry momentum survives risk adjustment, another feature of industry momentum that is contrary to the results reported earlier for individual stocks.

The remainder of table 4 refers to intra-industry momentum, computed from individual stocks sorted by industry. It should be noted that some industries do not contain sufficient data for the construction of a momentum portfolio. Table 4 only reports results for industries that have greater than 50 stocks. In addition, unlike the results for size-sorted stocks table 4 utilises information on all listed stocks to keep the number of excluded industries to a minimum. As a result, the magnitudes of momentum profits reported in table 4 are not directly comparable with those in tables 1 to 3. The general tenor of the intra-industry results appears to be very similar to momentum computed from industry indices. A reasonable conclusion, therefore, is that momentum cannot solely be attributable to industry factors.

5. Conclusion

The paper establishes the existence of short- to medium-term momentum in Australian stocks. Momentum profits for the yearly holding period post formation are statistically significant and range from 4.79% to 7.13% for portfolios formed from the largest 200 stocks and are even stronger for portfolios based within individual industries. These figures are consistent with momentum in stock returns reported in international markets. Unlike previous US studies however there does not appear to be any abnormal profitability in following a contrarian investment strategy at least over the investment horizons we consider.

Three common reasons for momentum namely cross-sectional dispersion of unconditional mean returns, adjustment for the exposure to market-wide risk factors and industry-driven momentum, were also investigated with a view to explaining this phenomenon in the Australian context. Results are broadly consistent with those reported in the US in that there appears to be no single factor that offers a complete description of momentum. Risk adjustment tends to reduce the size of the momentum profits for individual stocks at the very short end of the investment horizon quite considerably. The medium-term profitability of a momentum strategy, however, persists. Recent explanations for momentum have emerged based on lead-lag relationships between adjusted stock returns. The dynamics of momentum in Australia identified in this paper suggest that this avenue may be a fruitful one for future research in this area.

This research was supported by are ARC SPIRT grant C00107709 in collaboration with the Queensland Investment Corporation. Financial assistance from these sources is gratefully acknowledged. The authors would particularly like to thank Neill Colledge and Mark Thompson of QIC for help with establishing the database and for useful discussions on investment strategies in the Australian context. We are also grateful to two anonymous referees for useful comments.

Table 1
Mean Returns (%) On Holding The Momentum Arbitrage
Portfolio for Different Holding Periods

                                Size Band
Holding Period    Top 200         Top 50          51-200
(Months)                      Raw Returns (%)

                   0.60           0.86            0.53
0-1               (2.36 *)       (2.88 *)        (1.99 *)
                   2.73           3.21            2.27
1-6               (4.97 *)       (4.36 *)        (4.02 *)
                   2.42           3.05            1.99
6-12              (4.01 *)       (3.69 *)        (3.08 *)
                   5.75           7.13            4.79
1-12              (2.49 *)       (2.01 *)        (2.16 *)
                   0.84           3.94           -0.32
12-24             (0.35)         (0.97)         (-0.15)
                   1.75           4.56            0.67
24-36             (0.89)         (1.22)          (0.44)

Note: The numbers in parenthesis are t-statistics;

* = 5% level of significance.

Table 2
Cumulative Mean Returns (%) on Holding the Momentum
Arbitrage Portfolio for Different Holding Periods After Removing
Sample Means From Individual Stocks

                                       Size Band
                           Top 200       Top 50       51-200
Holding Period (Months)   Returns Adjusted for Unconditional Mean (%)

                            0.40          0.49        0.39
0-1                        (1.47)        (1.62)      (1.36)
                            1.70          1.40        1.56
1-6                        (2.33 *)      (1.62)      (2.00 *)
                            1.19          0.87        1.15
6-12                       (1.31)        (0.80)      (1.15)
                            3.29          2.76        3.10
1-12                       (0.87)        (0.63)      (0.76)
                           -1.62         -0.42       -2.02
12-24                     (-0.37)       (-0.08)     (-0.45)
                           -0.71          0.19       -1.02
24-36                     (-0.19)        (0.05)     (-0.27)

Note: The numbers in parenthesis are t-statistics;

* = 5% level of significance

Table 3
Cumulative Mean Returns (%) on Holding the Momentum
Arbitrage Portfolio for Different Holding Periods After
Adjusting for Risk

                                       Size Band
                           Top 200       Top 50       51-200
Holding Period (Months)   Risk-adjusted (%, 3-Factor Model)

                           -0.10         0.21        -0.15
0-1                       (-0.57)       (0.88)      (-0.79)
                            0.46         0.73         0.26
1-6                        -1.11        (1.17)       (0.62)
                            1.81         1.29         1.88
6-12                       (4.51 *)     (2.05 *)     (4.13 *)
                            2.16         2.23         1.98
1-12                       (1.17)       (0.81)       (1.08)
                           -1.49         1.24        -2.50
12-24                     (-1.00)       (0.42)      (-1.84)
                           -1.20         2.23        -2.14
24-36                     (-1.08)       (0.84)      (-2.02 *)

Note: The numbers in parenthesis are t-statistics;

* = 5% level of significance

Table 4
Industry Momentum Returns (%)

                                   Investment Period (Months)
Industry            No. of
                    Stocks     0-1        1-6       6-12       0-12

                             1.23        3.71       0.30       5.23
All                         (5.14)      (5.83)     (0.39)     (2.03)
                             0.74        4.12      -1.85       3.01
Gold                 428    (1.45)      (3.35 *)  (-1.41)     (0.64)
                             1.95        7.34       1.90      11.19
Other Metals         217    (4.11 *)    (5.48 *)   (1.36)     (1.79)
                             0.92        4.16       1.77       6.85
Energy               153    (2.03 *)    (3.29 *)   (1.45)     (1.21)
Developers &                 2.32       11.72      10.07      24.12
 Contractors         151    (8.49 *)   (15.13 *)  (12.93 *)   (5.49 *)
                             1.22        6.53       7.22      14.97
Building Materials   124    (5.46 *)   (11.56 *)  (13.12 *)   (5.44 *)
Food & Household             1.12        5.34       5.06      11.53
 Goods               114    (5.97 *)   (12.62 *)  (10.57 *)   (7.39 *)
                             1.21        5.72       6.14      13.07
Engineering          150    (5.46 *)    (9.78 *)   (9.95 *)   (4.43 *)
                             1.46        4.93       3.09       9.48
Retail               114    (6.24 *)    (9.37 *)   (6.22 *)   (5.67 *)
                             2.11        9.03       5.74      16.88
Media                 98    (7.96 *)   (13.57 *)   (6.98 *)   (5.21 *)
Investment &                 2.39       12.42      10.49      25.30
 Financial           433    (10.08 *)  (16.88 *)  (13.58 *)   (5.99 *)
Miscellaneous                 1.62       7.43       4.51      13.56
 Industrials         635    (8.66 *)   (16.27 *)   (7.82 *)   (5.39 *)
Diversified                  2.39       10.36      10.37      23.11
 Industrials          57    (7.28 *)   (13.93 *)   (9.32 *)   (5.79 *)

(1.) Preliminary results indicate that the main thrust of the results is unaltered by the inclusion of all the listed stocks.

(2.) Discussions with industry analysts suggested that in the overwhelming majority of all cases, stock exists from the database were associated with a full loss for original stockholders. In any event, repeating the analysis under the alternative extreme assumption of no loss on exits does not alter the paper's conclusions in any material way.

(3.) This strategy was adopted because the usual convention of splitting size-sorted returns into equal value bands is not practical here due to the concentration of the Australian market. A number of different divisions were tried without any material differences to the results being evident.

(4.) Scores are defined as projections of the data into the space of principle components. They are computed by taking cross-products of returns and principle components.

(5.) We had a number of measures for shorter periods provided by industry sources, but these appealed to be inconsistent with our PCA score and in tact with each other.

(6.) For all the calculations in this paper equal weighting is preferred to the customary practice of weighting by value. This is necessary because of the concentration problems encountered when dealing with Australian stocks related to the dominance of a small number of very large companies. It is the contention here that weighting on value results in poorly diversified portfolios.

(7) Note that the t-statistics are corrected for both heteroskedasticity and autocorrelation using the procedure suggested by Newey and West (1987).

(8.) While we do not investigate this assumption further, but it is indirectly supported by the results of the principal components analysis, which indicates that a three-factor model is sufficient to explain the cross-sectional dispersion of expected returns on diversified size-sorted portfolios. Some evidence that industry specific risk factors do not attract a risk premium can be found in Moskowitz and Grinblatt (1999).

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(Date of receipt of final transcript: June 24, 2003. Accepted by Michael E. Drew, Stan Hum & Garry Twite, Special Issue Editors.)

Stan Hurn ([dagger]) Vlad Pavlov ([dagger])

([dagger]) School of Economics and Finance, Queensland University of Technology. Email: [e-mail]