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Motivated by the time-varying nature of relative style performance and the potential benefit of tactical style rotation in the stock market, Chapter 4 explores a dynamic trading strategy to select stocks based on its in-favour or out-of-favour style category. In doing so, a set of firm characteristic variables PC, BM and DY is used to categorise different stock groups. The use of such firm characteristics is justified partly by prior studies such as Fama and French (1993, 1996), Kothari and Shanken (1997), and Chan et al. (1998) who suggest that these variables are important fundamentals relating to the variations in expected stock returns. It is argued that as assets perform differently during various stages of a market cycle, style momentum strategies to buy asset groups that perform well and to sell asset classes that do poorly in the past could generate positive returns up to 12 months and possibly longer. Given the perceived interaction amongst style momentum and the price and industry momentum effects, three methods are analysed to disentangle style, price and industry momentums. The procedure includes doing the price and industry effect adjustment on the individual level, the independent two-way sorting and the application of Fama-MacBeth (1973) crosssectional regressions. The empirical results in this study shows that consistent with the literature, style momentum in the U.K.
The profit of style momentum based on firm characteristics seems to pose challenge to financial theories based on rational agents and frictionless markets. Prior studies provide mixed evidence for riskbased models in explaining asset-level momentum. For example, Jegadeesh and Titman (1993) show that differences in market risk of long short side of the hedge portfolios do not cause momentum profits.
Fama and French (1996) fail to price momentum returns using their unconditional three factor model (1993). Jegadeesh and Titman (2001) find that risk-adjustment tends to increase rather than decrease the momentum profits. Other studies such as Conrad and Kaul (1998), Johnson (2002) and Lewellen (2002) contend that momentum effect relates to the cross-sectional and time-series variations in risks.
Motivated by the lack of straightforward risk-based explanation for the momentum profits on individual stock level, recently, an increasing number of studies focus on the role investors’ behaviour plays in affecting asset pricing. Studies such as Daniel et al. (1998), Barberis et al. (1998), Hong and Stein (1999, 2000), Lee and Swaminathan (2000) are only a few examples. These studies suggest that the profit of asset-level momentum arise form a delayed overreaction to news.
The existence of style momentum strategy may be explained by the findings of Berk et al. (1999) on the rational basis or the behavioural model of Barberis and Shleifer (2003). Berk et al. (1999) argue that firms with same characteristics are affected by the same state variables relating to the systematic risks and expected returns. The payoffs of momentum strategies are compensation for systematic risks that changes in predictive ways over the periods comparable to the average life of firm’s investment project. Barberis and Shleifer (2003) propose that in an economy with two heterogeneous investor groups, i.e. switchers and fundamental traders, style-based noisy traders allocate their money on the style level based on relative style performance, causing some styles becoming popular and others, often regarded as the “twin style”, being disliked. The arbitrageurs (fundamental traders) ensure that the irrational style-based investors do not push asset prices too far away from its fundamental values.
The model of Barberis and Shleifer (2003) predicts that style momentum strategies are as profitable as asset-level momentum.
Empirical studies such as Lewellen (2002), Chen (2003), Chen and De Bondt (2004) all provide evidence which are consistent with the prediction of Barberis and Shleifer (2003).
While this Chapter find significant raw style momentum payoffs, the risk-adjusted performance evolution based on the Fama-French threefactor model suggests that such strategy should be implemented with caution. When measured against the Fama and French three-factor model, the style-level misspricing is insignificant for BM- and DYbased style sorting. However, stocks classified by characteristics PC still remain significant misspricing. This suggests that the information content of characteristics PC, BM and DY may differ. On the other hand, due to its regular rebalancing nature, equity style momentum strategy could introduce non-trivial transaction cost. Hence financial practitioner should assess whether style momentum can generate positive returns after accounting for the transaction cost. Arguably, style momentum strategy is best implemented to enhance passive investing such as indexation strategy. The relative fixed composition nature of market index results in constant overall style exposures which is inefficient under the changing market environment. Style momentum strategies based on ETF (Exchange Traded Funds) of style benchmarks can be used to enhance index returns. Since the style momentum hedge portfolios are generally market neutral thus are free of market risk. Given that the transaction cost for ETFs is low and its liquidity is high, arguably the long-short style momentum hedge portfolio can be designed to overlay with the underlying index to eliminate its least attractive style exposures. Hence index hedging based solely on the equity style momentum would be possible and be an interesting subject to explore.
Chapter 5 Optimal Multi-Style Investing Parameterising on Business Cycle Predictors
5.1 Introduction There is substantial evidence in empirical finance suggesting that the distributions of stock returns are time-varying and predictable using business cycle variables. Prior studies such as Fama and French (1996) show that company characteristics of size (firm capitalisation), book to market ratios and lagged past performance are related to the variations on expected stock returns of both time-series and crosssectional level. The expected stock returns are also related to the variance and covariance structure with other stocks (e.g. Chan et al.
(1998)). These findings yield fresh insights into portfolio management in the investment practice. A number of recent studies have addressed the issue of portfolio choice problem when incorporating the stock predictability to capture the changing investment opportunities and enhance portfolio returns. For example, Kandel and Stambaugh (1996) show that from an ex ante perspective variables predicting the distributions of moments of stock returns have significant impact on a myopic portfolio setting. Brennan and Schwartz (1996), Brennan et al.
(1997) and Barberis (2000) numerically study the impact of myopic versus dynamic portfolio choice problem. Ferson and Siege (2001) derive the optimal portfolio weights for mean-variance investors assuming that the moments of stock returns are known functions of state variables. More recently, Avramov and Chordia (2006a, 2006b) find that a real-time optimising investor benefits from incorporating business cycle information to the asset allocation between stocks and cash or investment strategies of ‘fund of mutual funds’. These studies, amongst others, develop a general framework to study dynamic portfolio choice implications of return predictability and provide further evidence on the value of active portfolio management over the business cycles.
While previous studies have made contributions to our understanding regarding the impact of predictability of the first and second moments of stock returns on the portfolio selection process, their empirical
approaches generally arise one or two of the issues:
First, on the one hand, the analysis of portfolio choice with the timevarying investment opportunity set has generally focused primarily on the well-diversified market portfolio (or all stocks in the investment universe) plus cash and bonds. Such arrangement is not designed to help investors who hold multiple equity asset classes like ‘fund of funds’ asset managers. In today’s investment industry, institutional investors such as mutual funds and pension funds are generally structured around different asset classes to follow some predefined investment styles (e.g. Brown and Goetzmann (1997), Fung and Hsieh (1997), Chan et al. (2002)). This is even predominant in the hedge fund industry where mangers generally have expertise in and focus solely on some specific asset classes. Hence investors of ‘fund of funds’ equivalently exposes themselves to specific asset class within the market segments. Meanwhile, large institutional investors such as pension and endowment funds generally delegate their investment to different managers who are specialised in a single asset class. Sharpe (1981) argues that such ‘centralised decision’ may be motivated by the desire to exploit managers’ specialisation or to diversity among managers. Barry and Starks (1984) also contend that risk-sharing may be a motivation to hire multi-managers. Given these situations, it is reasonable to assume that in addition to cash and bonds, investors would hold multiple equity asset classes instead of accessing to only one domestic equity portfolio (i.e. market index). Arguably, investing in a market index or all the stocks in the market is neither attractive nor technically applicable simply because such strategy cannot satisfy investors’ different return-risk preferences.
On the other hand, when considering business cycle predictability in the asset allocation process, focusing on market portfolio alone may hamper our understanding of the underlying mechanism as how the economic exogenous forces affect equity returns in a changing environment. For example, the divergent returns between value and growth stocks are well recognised but the underlying driving forces for such return differentials are not fully explained yet. Campbell and Vuolteenaho (2004) recently study the risk characteristics of the two styles and find that growth stocks have larger conditional correlation of returns with variables that proxy for time variation in aggregate stock market discount. In contrast, value stocks have higher conditional correlation of returns with changes in aggregate stock market cash flows news. Indeed, from the perspective of a longhorizon risk-averse investor who holds the market portfolio, value stocks are riskier than growth stocks because aggregate cash flow shocks tend to be permanent while aggregate discount rate shocks appear to be transitory. Similarly, small and large stocks also demonstrate different risk-return characteristics during different phase of business cycles (c.f. Chan and Chen 1991). Obviously investing in a market index is by definition not optimal because of the different risk-return characteristics for value-growth and small-large stocks within the index constitution. Such different return-risk profiles of different styles would induce hedging demand as suggested by Merton (1973) for multi-period style investors. Lynch (2001) also argues that such hedging demand can affect not just the weights allocated to equities but the composition of equity portfolio as well.
Hence optimal portfolio selection problem is perhaps best framed in the context of multi styles allocation because multi-asset investors require style timing when the return distribution or the covariance structure of different equity classes changes corresponding to change of economic states.
Second, although academic researchers have developed a variety of theoretical solutions to solve the theoretical optimal portfolio choice problem based on return predictability, most techniques are out of reach for ordinary market practitioners and hence are not practically useful for real-world investment. Investment optimisation has always been a challenging job since most often the close-form solutions are not available. Over the years the Markowitz (1952) mean-variance framework is the workhorse of portfolio optimisation in the investment industry. As Brandt and Santa-Clara (2006) states that prior studies incorporating the predictability of asset returns generally solve the optimal portfolio choice problem by first solving optimal portfolio of Arrow-Debreu securities that pays state prices, and then replicate the optimal portfolio by dynamically trading basis assets. Some papers also first specify the conditional moments with state variables and then apply the traditional Markowitz approach to characterise the portfolio choice. These methodologies could raise a number of concerns. For this approach to work, the rigid assumption that market is complete must be satisfied so Arrow-Debreu securities can exist, or ad hoc distributional assumptions must be applied between moments of returns and state variables to guarantee the positive definiteness of the variance-covariance matrix. There is a major problem of being not parsimonious – there are a large number of moments (e.g. parameters of expected returns and covariance) to be estimated. Such ‘curse of dimensionality’ could inevitably cause notoriously noisy and unstable test results (c.f. Michaud (1989)). Since a portfolio manager’s livelihood depends largely on the outcome of the investment decisions, the traditional two-step econometric approaches for optimal portfolio choice offers little help if there is any in the realworld investment management practice.