Academic journal article Journal of Economics and Finance

Are Standard Asset Pricing Factors Long-Range Dependent?

Academic journal article Journal of Economics and Finance

Are Standard Asset Pricing Factors Long-Range Dependent?

Article excerpt

(ProQuest: ... denotes formulae omitted.)

1Introduction

In recent decades, the identification and deeper analysis of exploitable crosssectional stock market effects has received considerable attention in both practice and academia (see Chordia et al. 2014). Among the vast number of revealed phenomena, the size, book-to-market, momentum and beta effects can be considered the most important because related arbitrage portfolios have become important components of modern investment products and/or benchmark variables in standard asset pricing models. According to Fama and French (1992), the size (book-to-market) effect implies that returns are negatively (positively) related to firm size (the bookto-market ratio). Jegadeesh and Titman (1993) show that stocks exhibit momentum behaviour such that buying past winners and selling past losers can lead to substantially high returns. Finally, Frazzini and Pedersen (2014) document that high-beta stocks earn significantly lower returns than low-beta stocks.

The properties of the arbitrage portfolio returns exploiting these effects (hereforth, factor returns) have been the subject of numerous empirical studies.1 For example, they have been shown to be predictors of economic growth (see Liew and Vassalou 2000), to proxy for variables that describe investment opportunities (see Petkova 2006) and to have strong co-movement across asset classes (see Asness et al. 2013b). However, one important question has not yet been answered: Do factor returns show signs of long-range dependence (LRD)? This issue is especially salient because the presence of LRD in factor returns would have significant impact on many applications in modern financial economics. First, as size, book-to-market, momentum and beta portfolios are typical components of financial products (see, for example, AQR Capital Management, www.aqr.com), optimal consumption/savings and portfolio decisions involving these products would become extremely sensitive to the investment horizon if the factor returns were LRD (see Lo 1991). Second, problems would arise in the pricing of derivative securities (where the arbitrage portfolios are the underlyings) with martingale methods since the class of continuous time stochastic processes most commonly employed is inconsistent with long-term memory (see Maheswaran and Sims 1993; Ohanissian et al. 2004). Finally, traditional tests of capital asset pricing models and the arbitrage pricing theory, in which factor return factors have become standard explanatory variables, are no longer valid since the usual forms of statistical inference do not apply to time-series exhibiting such persistence (see Lo 1991).2

In economics and finance, LRD has a long history (see Mandelbrot 1997). It is a specific departure from random walk behaviour because LRD time-series exhibit an unusually high degree of persistence so that observations in the remote past are nontrivially correlated with observations in the distant future, even as the time span between the two observations increases. Thus, the defining characteristic of LRD has been taken by many to be a slow (hyperbolic) decay of the autocorrelation function (see Grau-Carles 2000).3 To detect LRD, various estimators have been proposed in the literature (see Baillie 1996; Kantelhardt 2009; Fernandez 2011). In this article, we focus on the 'fractal class' of estimators. Specifically, we use rescaled range analysis (RRA; also often called Hurst R/S analysis) and the detrended fluctuation analysis (DFA) to gain insights into the dynamics of factor returns. These two methods (and their modifications) are the most popular ones in the field and have been extensively applied in recent studies of the return properties of equities (see Cajueiro and Tabak 2004a,b, 2005a,b; Kristoufek and Vosvrda 2013; Hull and McGroarty 2014; Sensoy and Tabak 2015), exchange rates (see Ausloos 2000; Ivanova and Ausloos 2002; Norouzzadeh and Rahmani 2006), commodities (see Tabak and Cajueiro 2007; Alvarez-Ramirez et al. …

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