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Data, Portfolios, and Performance: How We Test the Strategies

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Abstract

In this chapter, the authors reviewed the methods, then tested and implemented particular strategies. They presented the data sources and explained how they had prepared the samples. Having demonstrated how they had formed the portfolios and implemented the strategies, the authors specified both the methods and indicators used to evaluate the strategies.

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Notes

  1. 1.

    This approach was used in numerous studies of the cross-section of stock returns. Examples include Liu et al. (2011), Bekaert et al. (2007), Brown et al. (2008), Rouwenhorst (1999), Barry et al. (2002), Griffin (2002), Bali and Cakici (2010), Chui et al. (2010), Hou et al. (2011), de Groot et al. (2012b), de Moor and Sercu (2013a, b), and Cakici et al. (2013).

  2. 2.

    Waszczuk (2014a, b) indicates that the discrete-time asset pricing theory provides no information on the relevant interval of expected returns (Fama 1998). Thus, we choose monthly intervals, which are also the most widely used in similar studies. The reasons are twofold. On the one hand, it offers a sufficient number of observations to ensure power of the conducted tests. On the other hand, monthly intervals avoid excessive exposure to the micro-structure issues (de Moor and Sercu 2013a). Lower frequency could be adequate for the estimation of capital cost but not for asset pricing tests, for which shorter time intervals markedly improve their quality. In practice, it is used rather rarely, mainly when the research additionally encompasses macroeconomic data. The paper by Avramov and Chordia (2006), who investigated the Consumption CAPM , may serve as an example. Some of the methods and their description in this book are analogous and sourced from Zaremba and Shemer (2017).

  3. 3.

    The filters applied in this book are similar to plenty of asset pricing studies on international equities. For instance, de Moor and Sercu (2013a, b) set the minimum market value at $100 million on the international sample and additionally limit the examinations to stocks with monthly trading volume larger than $100,000, identically as in this book. Brown et al. (2008) include only equities belonging to the intersection of top 50% market liquidity and top 50% market capitalization. van der Hart et al. (2005) set the lower boundary for the firm capitalization at $100 million for the last month of the study sample and Burghof and Prothmann (2011) use the limit of GBP20 million. Considering the price of the stock , most of the studies rely on the SEC definition, implying that penny stocks priced below $5 (Jegadeesh and Titman 2001; Gutierrez and Kelley 2008; Bhootra 2011).

  4. 4.

    The type of quantile portfolios highly depends on the number of available constituents, and it is a trade-off between the number of assets available and the grid resolution (Waszczuk 2014b). The most widely considered alternatives are quintiles, for example, Banz (1981) and Chan et al. (1998), and deciles, for example, Jegadeesh and Titman (1993, 2001) and Lakonishok et al. (1994). We decided that 78 diversified index portfolios are sufficient for the 20th and 80th breakpoints but insufficient for the 10th and 90th breakpoints. Among alternative approaches, Bauman et al. (1998) considered quartile grouping, Achour et al. (1998) worked with tertile portfolios, and Brav et al. (2000) used the 50% cut-off. In our case, due to a relatively small number of assets in the portfolios, we mostly rely on tertile portfolios.

  5. 5.

    For stocks, see, Arnott et al. (2005), Tamura and Shimizu (2005), Hsu and Campolo (2006), Walkshausl and Lobe (2010), and Zaremba and Miziołek (2017a). For comprehensive literature surveys, see Chow et al. (2011), Amenc et al. (2012), and Bolognesi and Pividori (2016); for country equity indices, see Estrada (2008), Yan and Zhao (2013), and Zaremba and Miziołek (2017b).

  6. 6.

    In the literature, by default the term volatility means a yearly standard deviation of returns. Both terms are used in this book in the same meaning.

  7. 7.

    In financial studies, we have two main methods of converting prices to returns: the arithmetic (simple) and logarithmic return approach. The latter is usually preferred for three basic reasons: (1) better arithmetical properties (including compounding over time), (2) return distributions that represent a larger degree of normality than arithmetic returns, and (3) reduced heteroscedasticity in logarithmic returns series (Waszczuk 2014b). This type of returns are not fully additive over assets, but the bias is rather small, especially for the short time intervals; so they are also used in the cross-sectional studies (e.g., Liew and Vassalou [2000], Diacogiannis and Kyriazis [2007]). In the calculations used in this book, for the sake of simplicity, we use arithmetic returns. For further discussion on the return calculation for financial studies, see Roll (1984) or Vaihekoski (2004).

  8. 8.

    The Sharpe ratio was later frequently revised and modified by many authors, including its inventor; across this book, however, we rely on the simplest and most intuitive definition described by Sharpe (1966). For more examples of the modifications and revisions of the Sharpe ratio, see Sharpe (1994), Vinod and Morey (1999), Dowd (2000), Israelsen (2005), or Le Sourd (2007).

  9. 9.

    The detailed characteristics of the Sharpe model were extensively presented in a number of financial textbooks, for example, Francis (1990), Elton and Gruber (1995), Campbell et al. (1997), Cochrane (2005), or Wilmott (2008).

  10. 10.

    Treynor (1961, 1962), Lintner (1965a, b) and Mossin (1966) developed a similar model at the same time, so all four—including Sharpe (1964)—are now considered to be the fathers of the CAPM model. See also French (2003).

  11. 11.

    For simplicity, in the book we use the Jensen’s alpha in its most basic form. Nonetheless, this performance measure has been frequently updated and modified over time (Zaremba 2015). For example, Black (1972) suggested using a portfolio with a beta coefficient equal to zero instead of a risk-free return. Brennan (1970), on the other hand, constructed a model taking into account taxes. Elton and Gruber (1995) suggested using a total risk instead of a systematic one. Many papers also suggested putting additional attention to the way the profit was earned and how the alpha coefficient was decomposed in respect of its origin (e.g., Treynor and Mazuy 1966, McDonald 1973, Pogue et al. 1974, Merton 1981, Henriksson and Merton 1981, Henriksson 1984, Grinblatt and Titman 1989). Furthermore, a substantial body of research attempts to improve the measure of systematic risk . There are several basic strands in this line of studies. The first uses conditional betas taking different values for growing and declining markets (Ferson and Schadt 1996; Christopherson et al. 1999). The second approach incorporates other risk factors and macroeconomic variables (e.g., Ross 1976; Fama and French 1996; Carhart 1997; Amenc and Le Sourd 2003). Example of different types of systematic risk could be found in the models of Connor and Korajczyk (1986), based on the arbitrage pricing theory, the index model by Elton et al. (1993), or the management style analysis according to Sharpe (1992).

  12. 12.

    In particular, we source the market factor returns from Kenneth R. French’s website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

  13. 13.

    All the regression parameters in this book were estimated using the OLS method. This approach has been employed, among many others, by Fama and French (2012). Furthermore, all the t-statistics were estimated using the bootstrap standard errors to avoid any distributional assumptions. Under our null hypothesis, all of the intercepts equal zero whereas the alternative hypothesis assumes the contrary. The bootstrap simulations are performed with the use of 10,000 random draws. All the statistical analyses are performed in R.

  14. 14.

    Further details could be found in basically any statistical textbook, for example, Aczel (2012).

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Zaremba, A., Shemer, J.“. (2018). Data, Portfolios, and Performance: How We Test the Strategies. In: Price-Based Investment Strategies. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-91530-2_1

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