Momentum Strategies in the Portuguese Stock Market

Momentum Strategies in the Portuguese Stock Market por Cátia da Mota Lopes Tese de Mestrado em Finanças Orientada por: Professor Doutor Júlio Fernando Seara Sequeira da Mota Lobão 2012 ii Biographical Note Cátia da Mota Lopes was born in Vila Nova de Gaia, Portugal, on the 2 nd of December, 1987. In 2005, she entered to Faculdade de Economia do Porto where she graduated in 2009 in Economics. In the same year she joined the Master in Finance at the Faculdade de Economia do Porto, where she improved her knowledge and qualifications in subjects as portfolio management, financial theory, project management, risk management, among others. Within the professional scope, she started her career in 2009, as credit analyst in Banco Português de Negócios. Then, in the end of 2010, she was invited by Ernst & Young to work in the assurance division. There, she had the opportunity to work with several national companies and improve her audit skills. Since September 2011, she has been working in Galp Energia, SA, in the Lisbon headquarters, in the Oil and Gas Trading department. iii Acknowledgments First of all, I want to give a word of gratitude to Professor Júlio Lobão, for his guidance and the constant encouragement in times of need and for helping me to grow as a student, and as a person. I am also very grateful to my family: my parents, Américo e Quitéria, my grandparents, my brother, Ricardo, my little sister Raquel and my supportive fiancé, Miguel, along with his family, for all the support and love that I needed to continue my work. Last but not least, to all the friends who have given me their warmth and encouragement: thank you. iv Momentum Strategies in the Portuguese Stock Market Cátia da Mota Lopes MF, FEP-UP [email protected]p.pt Abstract Over the last decades, the Efficient Market Hypothesis (EMH) has been one of the dominant topics in financial research literature. Inspired by cognitive psychology studies, “overreaction” and “underreaction” are one of the most important challenges to the EMH. The main purpose of our study is to explore the existence of return continuation in the Portuguese Stock Market, thus investigating its efficiency at the weak form level (Fama, 1970). We demonstrate that strategies which buy stocks that have performed well in the past and sell stocks that have poor performances previously – momentum strategies – can generate significant positive returns over three to twelve months holding periods. As in Jegadeesh and Titman (1993), we found that the profitability of momentum strategies is not satisfactorily justified by delayed stock price reactions. When comparing the momentum strategy profits with the profitability of the equally weighted market portfolio, we verified that it is possible to obtain higher returns through this relative strength strategy. We also analyze the momentum profits over long horizons. In this matter, our results seem to support the underreaction hypothesis, but our outcomes are not conclusive, since there is no sufficient statistic evidence. Keywords: Overreaction; Underreaction; Momentum; Market Efficiency; Behavioral Finance. JEL: G1; G11 and G14. v Momentum Strategies in the Portuguese Stock Market Cátia da Mota Lopes MF, FEP-UP [email protected]p.pt Resumo Nas últimas décadas, a Hipótese de Eficiência de Mercado (HEM) tem sido um dos temas dominantes na literatura financeira. Com base na psicologia cognitiva, as hipóteses de “sobre-reação” e “sub-reação” dos preços colocam-se como um dos mais importantes desafios à HEM. Assim, o principal objetivo do nosso trabalho é explorar a existência de continuação dos retornos no mercado de capitais português, investigando a sua eficiência na forma fraca (Fama, 1970). De acordo com os resultados obtidos, estratégias que compram ações com boas performances no passado e que vendem ações com performances fracas – estratégias de momentum – geram retornos positivos significativos, para períodos de manutenção de três a doze meses. Tal como em Jegadeesh e Titman (1993), descobrimos que a rendibilidade das estratégias de momentum não é satisfatoriamente justificada pela reação tardia dos preços das ações. Quando a rendibilidade das estratégias de momentum é comparada com a rendibilidade do portefólio de mercado igualmente ponderado, verificamos que é possível obter retornos mais elevados através da estratégia estudada. A rendibilidade das estratégias de momentum foi, também, analisada no longo prazo, tendo sido encontrada evidência que suporta a hipótese de “sub-reação”. No entanto, os resultados alcançados neste domínio não são conclusivos, uma vez que não possuímos evidência estatística suficientemente significativa. Palavras-chave: Sobre-reação; Sub-reação; Momentum; Eficiência e Finanças Comportamentais Códigos JEL: G1; G11 e G14. vi Index of Contents 1. Introduction ............................................................................................................... 1 2. Literature Review ...................................................................................................... 4 2.1. Trading Strategies – Market (In)Efficiency ....................................................... 4 2.1.1. Contrarian Strategies ................................................................................... 5 2.1.2. Momentum Strategies ................................................................................. 7 2.1.2.1. Seasonality and Size Effect ................................................................... 10 2.1.2.2. Momentum Strategies over Long Horizons .......................................... 11 2.2. Causes of Momentum Profits ........................................................................... 12 2.2.1. Momentum profits as a Compensation for Risk ....................................... 13 2.2.2. The Behavioral Models ............................................................................. 15 3. Data and Methodology ............................................................................................ 18 3.1. Data .................................................................................................................. 18 3.2. Methodology .................................................................................................... 19 4. Main Findings .......................................................................................................... 23 4.1. Returns of Relative Strength Portfolios ........................................................... 23 4.2. Causes of Relative Strength Profits.................................................................. 27 4.3. Performance of Relative Strength Portfolios in Long Horizons ...................... 29 5. Conclusions ............................................................................................................. 33 6. Bibliographic References ........................................................................................ 36 vii Index of Tables and Charts Table I – Returns of Relative Strength Portfolios .......................................................... 24 Table II – Relative Strength Portfolios and Market Portfolio ....................................... 26 Table III – Betas and Market Capitalizations of Relative Strength Portfolios ............... 28 Table IV – Performance of Relative Strength Portfolios in Long Horizons ................. 30 Chart I – Evolution of the monthly and cumulative average returns in long horizons …31 1 1. Introduction Over the past decades, the Efficient Market Hypothesis has been one of the dominant topics in financial research literature. According to Fama (1970, p.383), in an efficient market, prices “always fully reflect available information”. Therefore, prices could be considered an unbiased estimate of the true value of an investment at any given moment. The concept of Efficient Market Hypothesis reached such a height of dominance around the 1970’s that any deviation in financial markets has been called anomaly. Subsequently, the 1980’s has witnessed the proliferation of reported anomalies, in which are included, among others, “underreaction” and “overreaction” (Wang, 2008): “If stock prices either overreact or underreact to information, then profitable trading strategies that select stocks based on their past returns will exist.” Jegadeesh and Titman (1993, p.68) According to these anomalies, investors may be able to conceive profitable strategies based on past returns’ observation. Considering the existence of this possibility, the Efficient Market Hypothesis can be seriously questioned. For that reason, the investigation of these anomalies has attracted the interest of many financial researchers and market professionals that want to explore this inefficiency. The seminal works by De Bondt and Thaler (1985, 1987) and Jegadeesh and Titman (1993), about overreaction and underreaction, respectively, were the first to show that it was possible to consider that stocks returns are related to their past performances. De Bondt and Thaler (1985, 1987) based on the overreaction hypothesis, analyzed the profitability of contrarian strategies (buy the past losers and sell the past winners), concluding that stocks with poor performances in the last three to five years earn higher average returns than stocks that perform well. On the other hand, based on underreaction hypothesis, Jegadeesh and Titman (1993) report medium-term continuation of equity returns. The authors suggested that momentum strategies (buy the past winners and sell the past losers) result in profits of about 1 percent per month in the year following the portfolios’ formation. 2 The main base of momentum strategies is the continuation of existing trends in the market. The basic idea is that investors will buy winner and sell loser stocks, because it is more likely that a rising asset price continues to rise further than the opposite, at least in the short-term (Jegadeesh and Titman, 1993). For the Portuguese stock market, few studies analyzed, exclusively, the predictability of Portuguese stock returns based on their past performances and even fewer have focused on the profitability of momentum strategies. Alves and Duque (1996) studied the performance of contrarian strategies over the period of 1989 to 1994, but their results were inconclusive. Soares and Serra (2005), beyond analyzing the contrarian strategies with an extended sample 1 , also investigated the existence of momentum returns. However, some of their results lack statistical significance. More recently, Pereira (2009) also focused on this issue, studying the profitability of momentum and contrarian strategies; similarly to Soares and Serra (2005) most of the obtained results are not statistically significant. Thus, we verify that the lack of statistically significant results, that prove or disprove the existence of return predictability based on past returns in Portuguese stock market, is transversal to the studies done so far. Reason why, we decided to focus our study in this thematic, more specifically in the momentum strategies, in order to provide additional evidence to what has already been found in this regard. Our study present some differences from the precedent studies for the Portuguese stock market, as we use an extended sample (approximately 24 years), similarly to the sample periods used in the main international studies. We will follow the Jegadeesh and Titman (1993) methodology, with the division of the sample into deciles, and, finally, our study will be the first to focus exclusively in the performance of momentum strategies. Additionally, by examining the profitability of several momentum strategies, our work intends to investigate the efficiency of the Portuguese stock market at the weak form level, according to Fama (1970). In case this market is efficient in its weak form, current prices will fully reflect all historical information. Consequently, abnormal 1 Soares and Serra (2005) sample period goes from 1988 to 2003 (16 Years). 9 best performances of “traditional” Momentum (without any adjustments for the market beta exposure) close to Denmark, Australia and Canada. On the other hand, Griffin, Ji and Martin (2003) have also considered Portugal in their international sample. However, they found that there were no statistical significant momentum profits, at a five percent level, for the Portuguese stock market. Specifically for this stock market, Soares and Serra (2005), that also studied contrarian strategies, demonstrated the profitability of momentum strategies for short-term horizons. The authors considered a sample of 82 stocks, from 1988 to 2003 (16 years), which are ranked into quintiles. They concluded that momentum effects persist even after the risks have been accounted for. Nevertheless, most results lack statistical significance. Recently, Pereira (2009) examined the existence of momentum and contrarian profits in the Portuguese stock market, from January 1997 until December 2008. The author found that, for formation and holding periods of one to twelve months, the monthly average returns of the top winners’ portfolio are 0.97 percent; while the top losers’ portfolio’s monthly average returns are about -0.16 percent, thus concluding that a momentum strategy can provide returns of approximately 1 percent. However, similarly to Soares and Serra (2005), most of these results are not statistically significant. Considering the popularity and visibility of this market “anomaly”, according to the Efficient Market Hypothesis (Fama, 1970), the profitability of momentum strategies should cease to exist. However, Jegadeesh and Titman (2001b) show that momentum profits have continued in the 90’s 11 , demonstrating that the original results were not a product of data snooping bias, as noted by Lo and MacKinlay (1990). After Jegadeesh and Titman’s (1993) revolutionary work, this thematic has attracted substantial research, which documents more details about this “anomaly”. In the next subsections, we will present some of these studies that attempts to correlate momentum profits to stock characteristics. 10 The Portuguese sample was constituted by 267 monthly observations (about 22 years), being one of the smallest samples used on Chaves' (2012) study. 11 Jegadeesh and Titman (1993) use a sample period from 1965 to 1989 and in their 2001 study use a sample period from 1965 to 1998. 10 2.1.2.1. Seasonality and Size Effect Some researchers demonstrated that momentum strategies can exhibit an interesting pattern of seasonality, especially in January. Jegadeesh and Titman (1993) pointed out that, between 1965 and 1989, momentum strategy lost about 7 percent on average in January months, but generated positive returns in each of the other months. More recently, Grundy and Martin (2001) found that only 15 of the 69 January months’ returns, from 1926 to 1995, are positive. In January, the average return of momentum strategies is -5.85 percent. In contrast, 491 of the 759 non-January months’ returns are positive, with a mean of 1.01 percent, over the same period. The momentum strategy implemented on Jegadeesh and Titman’s (2001a) sample earns a return of -1.55 percent in January and positive returns in every other calendar month. Therefore, the authors conclude that much of the size effect and long horizon return reversals are concentrated in January, while the momentum effect is entirely a nonJanuary effect. Then again, Jegadeesh and Titman (1993), as well as Grinblatt and Moskowitz (2004), show that momentum profits tend to be stronger in December, followed by April and November. Several studies focus on the relation between momentum profits and stock characteristics, giving a special emphasis to the firm size. Most of them found that momentum profits are negatively correlated to the firm size (Jegadeesh and Titman, 1993, 2001b; Rouwenhorst, 1998; and Hong et al., 2000). However, some texts conclude otherwise (Israel and Moskowitz, 2012). Jegadeesh and Titman (1993, 2001b) found that both winners and losers tend to be smaller than the average firm size of the sample. In the authors’ opinion, smaller firms are more likely to be in the extreme return decile portfolios, since they have more volatile returns. Yet, the average size of the winner’s portfolio tends to be larger than the loser’s. Baker and Wurgler (2007) associate the high-volatility to low capitalization and unprofitable stocks, affirming that these stocks tend to be disproportionately sensitive to 11 investor sentiments. This occurs as small stocks are harder to arbitrage and more difficult to evaluate, “making the biases more insidious and valuation mistakes more likely” (Baker and Wurgler, 2007, p. 130). According to Rouwenhorst (1998) return continuation is negatively related with the firm size, but it is not limited to small firms. Similarly, Hong et al. (2000) found that the profitability of momentum strategies tends to decline sharply with the increase of firms’ size. In contrast, the results of Chui et al. (2000), for some Asian stock markets, provide weak evidence that support the negative relation mentioned above. Israel and Moskowitz (2011) found that significant momentum returns are present across size categories. According to these authors, there is no considerable evidence that sustain the higher momentum returns among small firms’ stocks. In conclusion, there are no consensual results on these matters. 2.1.2.2. Momentum Strategies over Long Horizons In the long run, De Bondt and Thaler (1985) supported that losers tend to outperform winners. As a result, momentum strategies should not be profitable in such horizons. Their conclusion attracted momentum researchers’ attention in order to study what usually happens with this type of profits in the long-term period. Jegadeesh and Titman (1993) documented that momentum profits slowly dissipate over long horizons. For instance, a zero-cost portfolio strategy 12 , based on the past six months, generates a cumulative return of 9.5 percent over the first year, but loses more than a half of this return in the following two years. Lee and Swaminathan (2000) confirmed these results and found significant price reversals between the third and the fifth year. Additionally, the authors demonstrated that past trading volume is related with both the magnitude and the persistence of price 12 A zero-cost portfolio strategy consists on buying the winner’s portfolio and selling the loser’s portfolio (Rouwenhorst, 1998). 12 momentum, concluding that stocks with higher past transaction volume tend to experience faster return reversals. Jegadeesh and Titman (1999) examined the returns in each of the 60 months following the portfolios’ constitution date (formation date), founding significant positive returns in the first 12 months. However, when they considered the 13-60 months period, the returns were negative. By the end of the 60 st month, the cumulative momentum returns have declined to -0.44 percent. On the other hand, George and Hwang (2004) showed that future returns, estimated using a 52-week high criterion, don’t reverse in the long run. Therefore, they suggest that short-term momentum and long-term reversals are not likely to be components of the same phenomenon. 2.2. Causes of Momentum Profits While the momentum profitability in short horizons have been well accepted, financial economists are far from reaching consensus on the causes of momentum profits. Jegadeesh and Titman (2001a) considers the underreaction to new information as a natural explanation for those profits. “(…) if a firm releases good news and stock prices only react partially to the good news, then buying the stocks after the initial release of the news will generate profits. However, this is not the only source of momentum profits.” Jegadeesh and Titman (2001a, p.7) In case momentum profits are indeed driven by underreaction, the good performance of a winner portfolio will continue until all the news is incorporated in prices. Chan et al. (1996) and Hong et al. (2000) found evidence consistent with this explanation. As we have already referred, some authors documented that momentum profits revert on long horizons. Lee and Swaminathan (2000) and Jegadeesh and Titman (2001b) interpreted this long term reversion as a consequence of, not only underreaction, but delayed overreaction. Good news in the pre-formation date period pushes postformation prices above fundamental value. Consequently, strategies that buy winners and sell losers will be profitable in the short-run. However, these deviations from 13 fundamental values are only temporary and cumulative momentum profits will disappear or even turn negative in the long-run. “Continuation and contrarian theories say that prices underreact and overreact, respectively; the efficiency theory allows neither” Ray et al. (1995, p.54) While some have argued that these results provide strong evidence of “market inefficiency,” others affirmed that the returns from these strategies are either a compensation for risk (Chan, 1988; Fama and French, 1996), a product of size/seasonal anomalies (Zarowin, 1989), or a product of biases in the way that investors interpret information (Barberis, Shleifer and Vishny, 1998; Hong and Stein, 1999; and Daniel Hirshleifer and Subrahmanyam, 1998). 2.2.1. Momentum profits as a Compensation for Risk According to the Efficient Market Hypothesis , investors cannot earn extra returns without bearing extra risk (Fama, 1970). Therefore, momentum and contrarian strategies present a challenge to the efficient market theory, by providing abnormal returns. Some researchers identify the existence of patterns, typically called anomalies, in average stocks returns that Capital Asset Pricing Model (CAPM) cannot explain. In consequence of this limitation, Fama and French (1996) present their Three-Factor Model. This model seams to capture much of the cross-section variation. Nevertheless, it was not able to explain the returns continuation over short-term periods. “The main embarrassment of the three-factor model, (is) its failure to capture the continuation of short-term returns documented by Jegadeesh and Titman (1993) and Asness (1994)” Fama and French (1996, p.81) Some authors tested whether cross-sectional differences in risk may explain momentum profits, by examining risk adjusted returns under specific asset pricing models. For example, Jegadeesh and Titman (1993) adjusted their results for risk using the CAPM 13 , while Fama and French (1996) and Jegadeesh and Titman (2001b) used the Three13 Jegadeesh and Titman (1993) shows that momentum profits can’t be explained by the market risk. The authors find that the best performers appear to be no more risky than the worst performers. Therefore, standard risk adjustments tend to increase rather than decrease the return spread between past winners and past losers. 14 Factor Model. Their results indicate that the cross-sectional differences in expected returns under the two asset pricing models cannot explain momentum profits. “However, it is possible that these models omit some priced factors and hence provide inadequate adjustments for differences in risk.” Jegadeesh and Titman (2001a, p.10) Conrad and Kaul (1998) admitted that it is premature to reject the rational models and have suggested a momentum risk-based interpretation. According to the authors, momentum profits could be entirely due to cross-sectional variations in mean returns rather than to any predictable time-series variations in stock returns. They started with the hypothesis that stock prices follow random walks with drifts that vary across stocks. The differences in these unconditional drifts explain momentum profits. Consequently, winner portfolios should continue to significantly outperform loser portfolios by the same magnitude, in any post-holding period. However, as we have already referred, Jegadeesh and Titman (1999) concluded that, in the long run (13-60 months), momentum profits, not only tended to disappear, but also turned negative. This evidence clearly rejects the Conrad and Kaul (1998) hypothesis which suggests that the winners will continue to outperform the losers outside the momentum strategy holding period. Even Jegadeesh and Titman (1999) referred their surprise, as they reached very different conclusions after examining essentially the same data as Conrad and Kaul (1998). To reconcile these conflicting findings, the authors reexamined Conrad and Kaul (1998) procedures to better understand why their conclusions were so different. They found that Conrad and Kaul (1998) had a small sample bias, which allowed extreme observations to be drawn in two, biasing momentum profits upwards. Therefore, Jegadeesh and Titman (1999) concluded that the momentum profits observed were not generated by cross-sectional variation in returns, but due to the stocks returns time-series properties. Grundy and Martin’s (2001) evidence also contradicts the risk-based explanations. The authors found that, between 1926 and 1995, the risk adjusted profitability of momentum strategies is more than 1.34 percent per month (with an associated t-statistic of 12.11). 15 In summary, current risk-based explanations fail to fully account for the momentum effect. Contrasting Conrad and Kaul (1998) results, the behavioral models suggest that the post-holding period returns of the momentum portfolio have a propensity to be negative. “Although the negative post-formation returns of the momentum portfolio appear to support the predictions of the behavioral models, based on our further analysis, we suggest that this support should be interpreted with caution.” Jegadeesh and Titman (1999, p.13) 2.2.2. The Behavioral Models Given the limitations of risk-based explanations for momentum profits, some researchers have turned their attentions to behavioral models in order to clarify this occurrence. The behavioral models attempt to explain the momentum profits through investors’ overconfidence or by the way that investors interpret firm’s specific information. These models are based on the idea that momentum profits arise because of inherent biases (Jegadeesh and Titman, 2001a). In Barberis et al.’s (1998) model, there is a representative investor who suffers from a conservatism bias and does not sufficiently update his beliefs when he observes new public information. As a result, prices will slowly adjust to information and, once the information is fully incorporated in prices, there is no further predictability about stock returns. The authors argued that the representative heuristic 14 may lead investors to mistakenly conclude that a winner portfolio will continue to win in the future. Although the conservatism bias in isolation leads to underreaction, this behavioral tendency, in conjunction with the representative heuristic, can lead to price overshooting. Therefore, in the long-term, prices will readjust to their fundamental values, causing returns reversals. 14 Representative heuristic is the tendency of individuals to identify “an uncertain event, or a sample, by the degree to which it is similar to the parent population.” Tversky and Kahneman (1974, p.1124) 16 “What causes intermediate-term momentum but long-term overreaction?”[...] “The answer is heuristic-driven bias." Shefrin (2000, p.103) Daniel et al. (1998) proposed a model that is also consistent with the short-term momentum and the long-term reversals (overreaction). They suggested that the behavior of informed traders can be characterized by two psychological biases: “(…) investor overconfidence about the precision of private information; and biased self-attribution, which causes asymmetric shifts in investors' confidence as a function of their investment outcomes”. Daniel et al. (1998, p.1839) According to their model, an overconfident investor overestimates his ability to generate information or to identify the significance of existing data that others neglect. The overconfident investors perceive themselves as more able to value stocks than they actually are, so, they underestimate their forecast error variance. Due to self-attribution bias, when investors receive a confirming public information, their confidence rises, but the inverse causes confident to fall only modestly, if at all. For example, investors attribute ex-post winners to their stock selection skills and the ex-post losers to external noise or bad luck. Based on their increased confidence in their signals, they push up the prices of the winners above their fundamental values, causing momentum in security prices (Daniel et al., 1998). The authors concluded that overconfidence leads to negative long-run autocorrelations while biased self-attribution results in positive shortrun autocorrelations. Hong and Stein (1999) do not directly appeal to any behavioral biases, but they consider two types of investors who trade based on different sets of information. The informed investors or the “news watchers” obtain signals about future cash flows but ignore information in historical prices. The other investors, the “momentum traders”, make forecasts based on history of past prices and, in addition, do not observe fundamental information. The authors assume also that information diffuses gradually across population. The information obtained by the “news watchers” is transmitted with delay and, hence, is only partially incorporated in the prices (underreaction). The “momentum trader” bases his trade only on the price changes over some prior interval and tends to push prices of past winners above their fundamental values (Hong and Stein, 1999). This model accepts the existence of return reversals when prices, eventually, revert to their fundamentals. 17 Using Hong and Stein (1999) example, in case we have good news at the moment t and no change in fundamentals after all, the “news watchers” will push the prices up, but not enough. At moment t+1, the “momentum traders” will buy these stocks, pushing the prices up again. This round of momentum trading creates a further price increase leading to a further round of momentum trading, and so on. When “momentum traders” implement “naive momentum strategies” based on past price trends, their trades will finally lead to overreaction in long horizons. As we can see, behavioral models present a number of different interesting facts to explain the existence of momentum profits. However, financial investigators are far from reaching consensus on what generates momentum profits, turning this subject into an interesting area for future research. 18 3. Data and Methodology This section intends to expose the data used in this study and the methodology adopted. In the following subsection (3.1), we will present the main data that we have collected for constitute our sample and in the subsequent subsection (3.2) we will detail the methodological steps that we have followed in order to reach our final results, including all the assumptions and tests made. 3.1. Data Our study is centered in the Portuguese stock market – NYSE 15 Euronext Lisbon, more specifically in the stocks that integrate the PSI 16 Geral. The sample period runs from January 1988 to April 2012 (about 23 years), in order to meet the needs of data required by this kind of empirical studies. For instance, Rouwenhorst (1998) considered 17 years (from 1978 to 1995) and Jegadeesh and Titman (1993) used 24 years (1965 to 1989) in their samples. Thus, our study provides the most extensive sample used for the analysis of momentum profitability in the Portuguese stock market. For a specific stock to be included in our sample, it must belong to the PSI Geral and must have been traded continuously at least for 25 months, since one of our strategies needs 12 months as observation period (J), 1 month of delay between the observation and the formation of the portfolio and 12 months of holding period (K). Using Datastream database, we have collected the Total Return Index (TRI) instead of daily prices. Thereby, we can obtain the stock returns adjusted for stock splits, dividends and right issues. All stocks, except one, comply with the limitations established for our sample. Thus, we have not included the “Teixeira Duarte” data, since, in the analysis period, this stock only had 20 months of negotiation. Therefore, although we could use this stock data for some strategies, with smaller observation and holding periods, we decided to consider 15 NYSE - New York Stock Exchange 16 PSI - Portuguese Stock Index 25 As in Rouwenhorst (1998) we verified that, independently of the interval used for ranking, the average monthly returns tend to fall for longer holding periods. In Table I, we report, as a reference, the average monthly return of an equally weighted market portfolio. When compared, the average monthly returns of the zero-cost portfolios, for each of the 32 strategies, are higher than the average monthly returns of the market portfolio. We can conclude, from the results of Table I, that relative strength strategies are on average quite profitable, as in Jegadeesh and Titman (1993). For each of the ranking and holding periods, we can observe that past winners have outperformed past losers by about 1.1 percent per month. The monthly return ranges from 0.58 percent, in the 12month/12-month Panel B strategy, to 1.84 percent, in the 3-month/3-month Panel B strategy. In Table II, we report the differences between the relative strength portfolios and the market equally weighted portfolio, for the different K holding periods. As mentioned in the last section, many of the studies on small capital markets divided the stock data into quintiles instead of deciles. Nevertheless, we have decided to rank the data into five portfolios for all the holding periods, in order to verify whether the obtained results were significantly altered. Thus, we present the average monthly returns in accordance with the portfolio construction suggested by Soares and Serra (2005) for the Portuguese stock market and we have also compared them with the average returns of the market equally weighted portfolio. Although, for all the holding periods, the quintile zero-cost portfolios presented smaller average returns than the decile zero-cost portfolios, the main findings are the same and the difference between the monthly average returns is not significant. Thus, we have continued to use the decile portfolios in the remainder of our study, continuing to follow the portfolio construction presented by Jegadeesh and Titman (1993). 26 The hypothesis test performed to determine whether the zero-cost strategy had significant different average returns from those achieved by the market portfolio, allows us to conclude the existence of abnormal returns based on this trading strategy. Table II Relative Strength Portfolios and Market Portfolio The relative strength portfolios are formed based on six-month lagged returns and held for K months, with no delay in the portfolio formation. The values of K for the different strategies are indicated in the first column. In the second column the stocks are ranked into deciles and in the last column the stocks are ranked into quintiles. For each holding period, we conduct a hypothesis test to determine the difference between the average monthly returns of the relative strength portfolio and the market portfolio. All t-stat are significant at 1 percent level. Holding Period (K) Average Return Deciles Average Return Quintiles 3 Winner 0,0052 0,0051 Loser -0,0121 -0,0096 Winner - Loser 0,0174 0,0147 Average Monthly Returns of a Equally Weighted Market Portfolio -0,0010 -0,0010 T-stat 4,5570 4,6341 6 Winner 0,0033 0,0036 Loser -0,0112 -0,0089 Winner - Loser 0,0145 0,0125 Average Monthly Returns of a Equally Weighted Market Portfolio -0,0008 -0,0008 T-stat 5,0487 5,2061 9 Winner 0,0020 0,0024 Loser -0,0096 -0,0078 Winner - Loser 0,0116 0,0102 Average Monthly Returns of a Equally Weighted Market Portfolio -0,0006 -0,0006 T-stat 4,8390 4,9607 12 Winner 0,0008 0,0016 Loser -0,0087 -0,0064 Winner - Loser 0,0095 0,0079 Average Monthly Returns of a Equally Weighted Market Portfolio -0,0003 -0,0003 T-stat 4,4334 4,2578 27 We can verify that, for the quintile strategies, the zero-cost portfolio have positive average returns, i.e., the six-month past winners outperformed the six-month past losers, for each of the K holding periods. In conclusion, for all the K holding periods, the winners minus losers portfolios significantly outperformed the equally weighted market portfolio. This market portfolio, for the different holding periods presented negative monthly average returns (although near zero), while the monthly average returns of the “buy past winners and sell past losers” strategies were positive. 4.2. Causes of Relative Strength Profits The rest of our study concentrates on portfolios formed on six-month ranked returns basis, formed at the end of the ranking period and held for six months (6-month/6month strategy), following the main literature (Jegadeesh and Titman, 1993, 2001b; Rouwenhorst, 1998; etc.) In this subsection, we analyze the average returns and standard deviations of the ten relative strength portfolios (P1 to P10, being P1 the loser Portfolio and P10 the winner), connecting the obtained results with the two most common indicators of systematic risk: Betas and Market Capitalization. Focusing on the average returns, we can verify that the lowest past returns portfolios (from Loser Portfolio to P5) continued to have the worst performances in the six subsequent months and the ninth decile portfolio (P9) had the higher average return. Accordingly, the first column shows that higher past six-month returns is on average associated with stronger future six-month returns. Similarly to Rouwenhorst (1998) we have performed an F-test, that strongly rejected the equally hypothesis between the monthly average returns of the 10 relative strength portfolios. Rouwenhorst (1998) found a U-shaped standard deviation of decile portfolios. In our sample, the standard deviations were not perfectly U-shaped, although the winner and loser portfolios had higher standard deviations than the portfolios in the middle deciles. 28 Portfolios with higher standard deviations, caeteris paribus, are more likely to show more volatile performances (Rouwenhorst, 1998). The standard deviation of the excess return of winners over losers is about 2.4 percent per month. Table III Betas and Market Capitalizations of Relative Strength Portfolios The relative strength portfolios are formed based on six-month lagged returns and held for six months. The equally weighted portfolio of stocks in the lowest past return decile is the P1 or Loser Portfolio, the portfolio in the next decile is P2, and so on, being P10 the Winner Portfolio. The average returns of the ten portfolios and their standard deviation, average Beta and Market Capitalization (as a proxy of firm size) are reported here. The F-Statistic test for equality of average returns of the ten relative strength portfolios and it is significant at 1 percent level. The sample period is January 1988 to April 2012. In the third column, we report the average betas for the ten portfolios. Accordingly to the Jegadeesh and Titman’s (1993) results, the extreme decile portfolios have higher betas than the average beta (for the full sample). Since the beta of the losers’ portfolio is higher than the winners’ portfolio beta, the zero-cost portfolio has a negative beta not statistically different from zero, i.e., not significant. This leads us to conclude that the excess returns of winners over losers is unlikely explained by their covariance with the market, since, according to Average Return Standard Deviation Beta Market Capitalization (m€) Loser -0,0112 0,0425 1,0203 496,6 P2 -0,0061 0,0400 0,8162 2621,2 P3 -0,0014 0,0369 0,7747 2301,2 P4 -0,0015 0,0344 0,8039 2590,6 P5 -0,0017 0,0378 0,7897 2778,2 P6 0,0013 0,0327 0,8104 2933,8 P7 0,0016 0,0353 0,8176 3101,2 P8 0,0018 0,0331 0,8327 3405,5 P9 0,0040 0,0337 0,8861 3007,4 Winner 0,0033 0,0389 0,9409 2586,5 Winner - Loser 0,0145 0,2401 -0,0793 Average 0,8492 2582,2 F-Test 4,4962 29 Rouwenhorst (1998), it would be necessary for the beta of the winners to exceed the beta of the losers by about two, so that market risk could explain a continuation effect of 1 percent per month. In the last column, we report the average market capitalizations of the decile portfolios. The findings are not surprising: as in Rouwenhorst (1998), the losers’ portfolio presents the lowest average size and both (winners and losers) are, on average, smaller than the mean. We did not examine the profitability of the 6-month/6-month relative strength strategies within size and beta subsamples, as in Jegadeesh and Titman (1993), due to the reduced number of stocks in the Portuguese stock market. As we have already mentioned, this kind of analysis would allow us to examine whether the profitability of the strategy is confined to any particular subsample stocks, since extent empirical evidence indicates that size and beta are related to expected returns. Although this limitation, we can conclude that the deciles used in the winners-losers strategy are usually constituted by small-firms stocks. We can also suggest that the excess momentum returns cannot be explained by their portfolios’ betas. 4.3. Performance of Relative Strength Portfolios in Long Horizons As in all the other studies on this subject, we could not fail to analyze the performance of Relative Strength Portfolios in each of the 36 months following the portfolio formation date. This analyzes can also provide additional insights about whether the profits are due to overreaction or to underreaction. Table IV reports the average monthly and the cumulative returns of the zero-cost portfolio over 36 months after the formation date. The average monthly returns in the first year are positive, but, only in the first four months after the portfolio formation date, they show significant positive returns. The average monthly returns are both positive and negative during the second and the third year, which does not happen in the first year. 30 Table IV Performance of Relative Strength Portfolios in Long Horizons The relative strength portfolios are formed based on six-month lagged returns. The equally weighted portfolio of the stocks in the bottom decile (lowest previous performance) is the sell portfolio and in the top decile (highest previous performance) is the buy portfolio. This table reports the average returns of the zero-cost, Winners minus Losers, portfolio in each month t following the formation period and the cumulative average returns. The sample goes from January 1988 to April 2012. We also present the tstatistic for the monthly returns. The marked t-statistics are significant at a 1(*), 5(**) and 10 (***) percent level. tMonthly Return Cumulative Return tMonthly Return Cumulative Return tMonthly Return Cumulative Return 1 0,0129 0,0129 13 0,0007 0,1111 25 -0,0054 0,1134 t-stat 2,1737 ** t-stat 0,1228 t-stat -1,1174 2 0,0236 0,0364 14 0,0040 0,1151 26 0,0033 0,1166 t-stat 3,6444 * t-stat 0,6732 t-stat 0,6841 3 0,0177 0,0542 15 0,0024 0,1174 27 -0,0006 0,1160 t-stat 2,7567 * t-stat 0,4410 t-stat -0,1331 4 0,0118 0,0659 16 0,0049 0,1224 28 0,0028 0,1188 t-stat 1,8769 ** t-stat 0,9076 t-stat 0,6526 5 0,0095 0,0754 17 0,0036 0,1260 29 -0,0042 0,1146 t-stat 1,4764 *** t-stat 0,7114 t-stat -0,8588 6 0,0073 0,0828 18 -0,0021 0,1239 30 0,0047 0,1193 t-stat 1,2197 t-stat -0,3693 t-stat 0,9962 7 0,0042 0,0870 19 -0,0039 0,1201 31 -0,0078 0,1115 t-stat 0,7161 t-stat -0,6969 t-stat -1,3304 *** 8 0,0094 0,0964 20 -0,0017 0,1184 32 0,0045 0,1160 t-stat 1,4964 *** t-stat -0,2665 t-stat 0,7456 9 0,0036 0,1000 21 -0,0021 0,1163 33 -0,0035 0,1125 t-stat 0,6442 t-stat -0,3591 t-stat -0,5553 10 0,0046 0,1046 22 -0,0013 0,1149 34 0,0007 0,1133 t-stat 0,8438 t-stat -0,2329 t-stat 0,1176 11 0,0021 0,1068 23 0,0000 0,1149 35 0,0048 0,1181 t-stat 0,3782 t-stat -0,0030 t-stat 0,8325 12 0,0037 0,1104 24 0,0038 0,1188 36 -0,0008 0,1173 t-stat 0,6574 t-stat 0,7820 t-stat -0,1451 31 The cumulative returns reach a maximum of 12.6 percent at the end of 17 months. However, we verified that, in the following months, this cumulative return does not reverse, standing approximately in 11 percent, which is a small decrease in relation to the maximum cumulative return reached. Figure I Evolution of the monthly and cumulative average returns in long horizons Figure I present the monthly and cumulative average returns of the zero-cost portfolio reported in Table IV. In the monthly returns we can observe significant positive returns and the graphics show perfectly the mixture of positive and negative returns verified specially in the third year. The line for the cumulative returns shows the inexistence of momentum return reversals over the 36 months period, especially when compared with the Jegadeesh and Titman (1993)’s cumulative returns. -2,0000 0,0000 2,0000 4,0000 6,0000 8,0000 10,0000 12,0000 14,0000 -1,0000 -0,5000 0,0000 0,5000 1,0000 1,5000 2,0000 2,5000 3,0000 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Cumulative Average Returns(%) Montly Average Returns (%) Monthly Return Cumulative Return Jegadeesh and Titman (1993)´s Cumulative Return In their sample, Jegadeesh and Titman (1993) observed negative returns beyond the 12 th month, suggesting that the positive returns over the first 12 months may not be permanent. Contrarily to their findings, we did not observe consistently negative average monthly returns in the months beyond the holding period, but a mixture of, non-significant, positive and negative returns. Through our results, we are led to conclude that momentum strategies for the Portuguese stock market do not show any return reversal over long horizons. However, we cannot rule out that the positive returns in the first 12 months are due to overreaction or underreaction, since our results are a mixture of positive and negative 32 returns and, moreover, we did not find significantly different from zero monthly returns, at a 5 percent level, beyond the fourth month. Nevertheless, our results seem to draw some clues indicating underreaction as the main cause of the momentum profitability in this market, in line with the non-reversal returns in the long-term. 33 5. Conclusions By challenging the notions of Efficient Market Hypothesis, momentum strategies have attracted financial researchers to, not only, study the momentum profitability in different stock markets, but also to study different causes and explanations for these profits. Although several studies found evidence of momentum profitability, specifically for the Portuguese stock market, the studies done so far didn’t found statistically significant results that prove or disprove the existence of return predictability based on past returns. Therefore, our purpose was to explore, with an extended sample period, the existence of return continuation, as well as investigate the Portuguese stock market efficiency at the weak form level (Fama, 1970). As we have reported in the last section, the main findings of our study indicate the existence of momentum profitability in the short-run, confirming, thus, most of the results found in the main international literature, for large and liquid markets. Following Jegadeesh and Titman (1993) methodology, we analyzed 32 different momentum strategies. For all of them, past winners significantly outperform the past losers portfolio in about 1.1 percent per month, for each ranking and performance periods. For instance, a strategy that selects stocks based on their past 6-month returns and holds them for 6 months presents a 1.45 percent monthly return. Therefore, we were led to conclude that it is possible to predict future returns based on past performance, at least in the short run. Our findings seriously call into question the Market Efficiency Hypothesis in the Portuguese stock market, since, according to this assumption, there is no possibility to conceive profitable strategies based on past returns’ observations. Although the main findings of our study point to the existence of momentum profits in the Portuguese stock market, the momentum causes are not, yet, fully ascertained. Due to the reduced number of stocks, we are not able to perform size and beta subsamples, as in the Jegadeesh and Titman (1993). Nevertheless, following the Rouwenhorst (1998) 34 example, we characterized all the deciles’ portfolios regarding to their volatility, their beta and firms size. Through this characterization, we could verify that winner’s and loser’s portfolios presented higher volatility than the portfolios in the middle deciles, and both winner’s and loser’s portfolios are constituted by small stocks on average, being the losers smaller than the winners. Concerning to the most common risk factor, our portfolios’ betas seem to suggest that momentum profits are unlikely explained by risk, since the winners’ beta are even lower than the losers’. However, it should be noted that these findings were obtained through a portfolios' characterization and we didn’t performed statistical tests that allow us to obtain conclusive results. Therefore, especially the risk explanations could be an interesting matter for further investigations. Lastly, concerning to the performance of momentum profits over long horizons, we found that there is no significant return reversals over long horizons, contrarily to Jegadeesh and Titman’s (1993) findings. After reaching maximum cumulative return, at the 17 th month, the return reversals are very low (about 1 percent). However, we cannot rule out that the positive returns in the first 12 months are due to overreaction or underreaction, since our results are not consistent, in the long run. Moreover, we did not find monthly returns significantly different from zero, at a 5 percent level, beyond the fourth month. Nevertheless, our findings seem to draw some clues indicating underreaction as the main cause of the momentum profitability in this market, in line with the non-reversal returns in the long-term. The explanations for the existence of underreaction can be extracted from behavioral models. However, these models consider both short-term momentum and long-term reversals (overreaction). Therefore, the evidence of underreaction found can be associated to a slowly adjustments from the investors, as in the Barberis et al. (1998) model, for instance. According to this, investors suffer from a conservative bias and do not update their beliefs after observing new public information, causing the prices to underreact. This model also admitted the possibility of price overshooting due to