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«Equity Style Investing RONG, WU How to cite: Equity Style Investing, Durham theses, Durham University. RONG, WU (2013) Available at Durham E-Theses ...»

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The theoretical style investing model of Barberis and Shleifer (2003) proposes that investors chase a particular style with higher relative returns in a market with positive feedback style-level investors (switchers) and fundamental traders (arbitrageurs), The trading behaviour of style-chasing investors would bid stock prices away from fundamentals and subsequently prices revert to fair value. Thus the style-switching trading behaviour plays an important role in the return generating process and affects the cross-sectional variations of stock returns. Hence the evolution of equity style cycles conveys useful information in predicting future stock returns.

The style investing model of Barberis and Shleifer (2003) predicts some interesting and empirically testable results. One of which is that style-level momentum strategy is profitable. A growing number of studies have provided evidence that is consistent with the predictions of Barberis and Shleifer (2003). For example, on country level, Chan et al. (2000) find significant excess momentum returns for a sample of 38 countries as well as a subsample of 16 developed countries, indicating that momentum exists if treating country as investable assets 16. Haugen and Baker (1996) track returns on a number of investment styles and show that a strategy that tilts to styles with relative good performance could earn higher risk-adjusted returns.

Moskowitz and Grinblatt (1999) and O’Neal (2000) show the evidence of momentum strategies based on the industry categorisation. They also assert that a large portion of individual price momentum of Jegadeesh and Titman (1993) is attributed to the industry momentum effect17. Lewellen (2002) examines the momentum strategies based on the sorting of industry, size and book-to-market ratios (BM). The author finds that the well-diversified size and BM portfolios exhibit momentum effect as strong as the individual price and industry momentum. Chordia and Shivakumar (2002) also find significant industry momentum and Swinkels (2002) finds evidence for the industry momentum in Europe. Using weekly data, Pan et al. (2004) find industry momentum generates significant profits for short horizons of less than 4 weeks. More closely relates to this chapter, Chen (2003) investigates the profitability of momentum strategies based on firm characteristics of market value (MV), BM and dividendyields (DY). It is found that a hedged strategy of buying past winner characteristic portfolio and selling past loser characteristic portfolio yields 0.782% per month in the following three months after portfolio formation. Such profits are distinct from price and industry momentum. Moreover, Chen and De Bondt (2004) uncover evidence of

Richard (1997) investigates momentum and contrarian strategies at the country

index level. The author finds that the momentum return of 0.57% per month at the 6-month holding period but it is not statistically significant. Asness et al. (1997) also successfully apply momentum strategy for country portfolios. The findings of Bhojraj and Swaminathan (2001) are qualitatively consistent with the results of Chan et al.


Several other studies have come to different conclusions. For example, Grundy and Martin (2001) argue that price and industry momentum are two separate phenomena.

style momentum effect within S&P-500 index. Their study covers all firms within the S&P-500 index since 1976 and finds that winner style continues to outperform loser style for periods up to 12 months or probably longer, and style momentum is a unique phenomenon that is different from price and industry momentum documented in the literature.

Chapter 4 is motived by the dynamic U.K. relative equity style returns found in Chapter 3 and the potential success of systematic active style rotation strategies documented in the context of U.S. market data in the literature. This chapter builds on the methodology in papers of Chen (2003), and Chen and De Bondt (2004) to test the characteristicbased equity style momentum strategies in the U.K. stock market. It is recognised that so far there are very limited relevant research for the U.K. market in the current literature. Chapter 4 therefore contributes to the literature by offering comparison test results in a different institutional and market environment relative to the U.S. data. The

objective of Chapter 4 is to answer the following questions:

1) Do equity style cycles exist in the U.K. stock market?

2) If style cycles do exist, can investors profit from the information of style cycles?

3) Are the return patterns of equity style momentum investing unique? Namely, is style momentum effect distinct from price momentum of Jegadeesh and Titman (1993) and industry momentum of Moskowitz and Grinblatt (1999) documented in the literature?

To pursue these questions, during sample period of 1980-2003 and on the annual basis, all U.K. non-financial stocks with meaningful firm characteristics of PC, BM and DY are partitioned alone two dimensions of the market value and the value-growth axis. For each characteristic this two-way independent sorting yields 9 style portfolios for the style momentum strategy. The 9 style portfolios are ranked according to their previous 3- to 12-month returns. The empirical results in this chapter suggest that stocks in current infavour (winner) styles continue to outperform those in out-of-favour (loser) styles for periods up to 12 months or possibly longer.

Specifically, a monthly average return differential between the extreme styles for (3, 3) PC-based style portfolios is 0.48%, and the spreads for BM- and PC-based style portfolios are 0.57% and 0.74%, respectively. 18 In contrast, a typical (12, 6) strategy yields average monthly profit of 0.62%, 0.27% and 0.62% for PC-, BM- and DY-based portfolios, respectively. Style momentum payoffs generally increase with longer ranking periods and decrease with longer test periods, suggesting that the outperformance of winner styles are more persistent once more information is added in the ranking period.

However, style spreads reverse at longer horizon.

While Chapter 4 documents the profitability of style momentum strategies in the U.K. market, one may argue that such profit is simply the miracle of price momentum of Jegadeesh and Titman (1993) or industry momentum documented by Moskowitz and Grinblatt (1999).

This is because stocks in current in-favour (out-of-favour) styles may also be categorised into the winner (loser) portfolios based on past individual stock returns, or winner (loser) industries according to the industry performance. Thus the style continuations observed may be due to a concentration of winner (loser) stocks within winner (loser) A (J, K) style momentum strategy means that style portfolios are ranked according to past J-month performance and then the strategy is tested for the following K months period.

styles whose returns persist in test periods. To disentangle the style, price and industry momentum effects, three methods are applied.

First, style momentum payoffs are recalculated after adjusting for the price or industry momentum effects on individual stock level. Next, a two-way independent sorting is used to avoid the problems criticised by Berk (2000) when distinguishing the explanatory ability for future returns from two variables that are perceived to be correlated. Finally, monthly Fama-MecBeth (1973) cross-sectional regressions are fitted to examine the explanatory power of three momentum effects. The results suggest that, consistent with the literature, style momentum has strong independent explanatory power for the future individual stock returns, and style momentum is distinct from price and industry momentum.

The profitability of style momentum poses challenge to traditional financial theories based on rational agents and frictionless markets.

Conventional risk-based approach such as Fama and French (1993) three-factor model does not capture all the variations in the returns of firm characteristic-based style momentum in this study. It is shown that differences in market risk (betas) of long and short side of the hedge portfolios do not cause style momentum profits. The threefactor model appears to strengthen, rather than explain, the style momentum returns. The intercept of the regression suggests that riskadjusted return differentials between the winner and loser styles are in some cases larger than raw return spreads, and controlling for the factors exposures can actually increase style momentum returns.

Based on this, it is argued that from a conventional risk-adjusted sense, style momentum strategy may not be necessary risky.

The structure of Chapter 4 is organised as follows. The next section discusses the theoretical framework for momentum strategy. Section 3 describes the sample data and methodology. Section 4 explains the characteristics of equity style portfolios based on firm attributes PC, BM and DY. Section 5 reports the payoffs of style momentum strategy.

Section 6 analyses the interaction of style, price and industry momentum and examine whether style momentum is distinct from price and industry momentum. Section 7 evaluates the performance of style momentum trading using Fama and French (1993) three-factor models. Finally, section 8 summaries and concludes.

4.2 General framework of momentum trading

It is useful to first begin with a general framework to understand the nature of the risks and the source of the rewards to momentum investing on individual stock level. The momentum effect is typically defined as a positive relation between the return of the underlying stock in a certain period of time with its lagged return, both relative to cross-sectional sample average returns. Mathematically, momentum exists if

–  –  –

where ri,t is the return of stock i in period t, rm,t is the average return of the sample and N is the number of stocks in the sample.

A momentum strategy based on individual stocks ranks stocks according to their past returns. There are several research methods in the literature aiming to capture the momentum effect but they differ somewhat in their implementations, and hence may affect the empirical outcomes. Papers such as Jegadeesh and Titman (1993) use the decile-based method to include only top (bottom) 10% of the stocks in the ranking on past returns from the winner (loser) portfolio in the analysis. The advantage of using decile strategy is that portfolio weights of the stocks are equal for both top and bottom performers, thus extreme weighting schemes are excluded. Arguably the decilebased strategy is more consistent with the concept of style investing because style-based investors make asset allocations along style level instead of individual stocks level. Hence they do not distinguish between stocks in the style regarding the weightings.

Studies such as Lo and MacKinlay (1990) use a different approach often referred as WRSS to detect momentum effect. Analogue of Equation (1), the zero-investment hedge portfolio longs stocks that outperform the sample mean and financed by the short positions of stocks that underperform relative to the sample average. The portfolio weights of WRSS depend linearly on the absolute value of deviations of the stock’s return from the cross-sectional mean, and momentum effect can be estimated by calculating the excess portfolio returns based on time-series stock returns. The average excess return of s WRSS strategy is

–  –  –

The WRSS strategy invests most in the stocks with the most extreme performance, capturing the belief that extreme price movements are often followed by extreme movements. Despite the smooth weighting patters, WRSS could potentially lead to long and short positions that contain only smallest stocks listed, resulting in large idiosyncratic components in the momentum portfolios.

This chapter uses the decile-based strategy throughout the analysis but the following discussion is based on WRSS scheme. Prior studies suggest that the two methods yield empirical outcomes that are highly correlated. For example, Jegadeesh and Titman (1993) note that the correlation between the momentum effect based on their decile scheme and that of WRSS strategy is 0.95. Unlike the decile-based strategy, the WRSS weighting scheme in Equation (3) can be conveniently used to decompose the profit of momentum trading strategy, and hence provides useful insight in the understanding of the mechanism of style momentum strategy.

In the context of WRSS, consider an economy containing 2N stocks for simplicity and assume investors buy or sell stocks at time t based on their performance from time t-2 to t-1. Assume that the performance of a stock i is determined relative to the average performance of all stocks in the sample. Following Lehmann (1990), Lo and MacKinlay (1990), the expected return of the stock-level momentum strategy in the next period t+1 is given by

–  –  –

where i is the unconditional expected return of stock i and  m is the mean return (unconditional) of the market portfolio containing N stocks.

Equation (4) suggests that the stock-level momentum profit may be driven by three factors: the serial correlation of the underlying stock i, the serial (cross) correlations between stock i and its peers, and the cross-sectional dispersion in unconditional expected returns. There is no general consensus as which factor dominants because different papers assume different assumptions to stock price dynamics and in turn the return generating process. For example, Conrad and Kaul (1998) assume a random walk with drift for stock price. The authors provide empirical evidence to hypothesise that the dispersion in unconditional expected stock returns explains momentum profit.

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