Augmented three factor model and default risk pricing: Evidence from France

• Author: Taher HAMZA, Olfa BEN MDALLA

Introduction

The CAPM as a single-risk-factor model has been considered for decades as an asset pricing benchmark, and several studies have highlighted the limitations related to its explanatory power. The inter-temporal model (ICAPM) of Merton (1973), the APT model of Ross (1976), and other multifactor approaches have been controversial in terms of empirical significance and robustness. However, these models argue that return co-variation is a linear function of a set of risk factors that Cochrane (2001) links to macroeconomic variables or those that anticipate macroeconomic events. In reference to the linear models, return co-variation is due mainly to the changes in premiums related to systematic risk factors as related to expected cash flow. Accordingly, Fama and French (FF-1993) argue that HML and SMB contribute to an additional explanatory power and that they capture distress risk. Thus, the academic literature raises a central and controversial empirical research question: is the default risk a systematic risk? The literature suggests three propositions: 1) that after controlling for the market premium, HML and SMB are robust proxies of distress risk (FF-1993; 2006); 2) that HML and SMB are insufficient to capture all distress risk; and 3) that alternative risk factors subsume HML and SMB to capture distress risk.

The main goal of our study is to identify the risk factors that best captured the default risk in France from 1995-2009. We analysed 12 size-, (B/M)-, and leverage-sorted portfolios as well as the portfolio of distressed firms and tested the explanatory power of the risk factors specified by this study. We found robust evidence that these 12 portfolios systematically required size and value premiums. We concluded that the FF (1993) model outperforms the CAPM and that HML and SMB capture an additional risk missed by the market portfolio. Second, the relative leverage portfolio is significant for all study portfolios except for the one of highly leveraged firms with high B/M. The leverage premium is positive for highly leveraged firms and negative for lowly leveraged. Third, we found a non-significant relationship between both momentum and relative distress factors and portfolio return co-movement. We conclude and confirm, through the Davidson and MacKinnon (1981) test that, in the French context, the FF (1993) three-factor model augmented by leverage premium is relevant, which indicates that the additional factors capture default risk. Lastly, the distress risk premium was robustly significant only for the distressed firms’ portfolio.

The remainder of this paper is organized as follows: Section 2 presents the theoretical framework and the literature review regarding the relationship between distress risk factors and portfolio return; Section 3 presents the sample and methodology, followed by results, discussion and implications; and the last section concludes the paper.

Augmented vs alternative distress risk pricing model: Literature review

The pricing of default risk focuses on identifying the risk factors that systematically determine portfolio return. Several studies (Liew and Vassalou, 2000; Hussain et al. 2002, ,…) support the relevance of the B/M as a proxy of financial distress risk and suggest that the value premium is characteristic of potentially failing firms.1>/FN> These authors conclude that the FF (1993) three-factor model is an improvement of the CAPM. In contrast, Dichev (1998) argue that the relationship between the distress risk and the B/M is not monotonic and that the most distressed firms have low B/M. We present the available literature regarding the different distress risk model specifications.

Value and size premiums and the FF three-factor model:

According to FF (1993), HML and SMB risk factors capture equity distress risk and provide significant additional informational content to the popular CAPM. This ad hoc model assumes a negative relationship between size and default risk but a positive one between B/M and default risk. FF (1993) conclude that HML and SMB are systematic risk factors that price the beta missing distress risk. Hence, firms with high B/M (i.e., "value firms") (Basu, 1977; Chan and Lakonishok, 2004) systematically require a risk premium (i.e., a value premium) (see FF, 1998). In addition, small firms systematically require a risk premium (i.e., a size premium). A large debate in the literature focuses on the explanatory power of the FF (1993) three-factor model. Studies such as those of Liew and Vassalou (2000) and Hussain et al. (2002) confirm that SMB and HML constitute systematic risk factors. Chan and Zhao (2009) support the idea that the FF (1993) model has become the benchmark for estimating expected returns with a profound impact on financial economics and industry practice. In France, the empirical results of Molay (2000) and Malin and Veeraraghavan (2004) parallel the studies previously presented. Finally, Denis and Denis (1995) show that HML and SMB price default risk but depend on macroeconomic factors with variability related to the economic cycle (Perez-Quiros and Timmermann, 2000). Accordingly, Gulen et al. (2008) highlight the inflexibility of firms with high B/M to an economic cycle’s change that generates additional risk.

Several studies supporting the CAPM consider size and value premium as firm fundamental characteristics and plead for market anomalies ². The behavioural approach argues that HML and SMB effects are due to extrapolation of past trends (DeBondt and Thaler, 1985; Lakonishok et al. 1994) and the actor’s irrationality (Daniel and Titman, 1997). La Porta et al. (1997) consider that the value premium is not induced by higher systematic risk. Gharghori et al. (2007) show that SMB and HML do not capture default risk but fail to identify the nature of risk captured by these factors. In turn, Griffin and Lemmon (2002) show that the three-factor model is unable to explain the differences in performance among firms with high versus low B/M, and add that the B/M effect is consistent with the mispricing argument. Lastly, Dichev (1998) argues that the size effect, effective in the 60s and 70s, disappeared in the 80s and that default risk does not generate high performance. Based on these theoretical and empirical supports, we predict that H1: HML and SMB constitute systematic risk factors that capture a firm’s distress risk.

Augmented vs alternative Fama and French risk factors:

Chan et al. (1998) propose a typology of risk factors: market, fundamental, macro-economic, technical, and statistical. In the literature, three contrasting research streams are developed: FF (1993), who considers, as discussed, that SMB and HML are risk factors that systematically capture default risk, a thesis empirically corroborated by other research (Table 1 - SEE IN ATTACHED PDF). The second considers that SMB and HML do not represent systematic risk factors and proposes alternative risk factors that capture the missing beta risk. Among these studies is that of Hahn and Lee (2006), who propose two macroeconomic variables: default spread and term spread ³, alternatives to HML and SMB. The authors ⁴ provide evidence that, in the U.S. market, these two factors best capture systematic risk. Chan et al. (1998) emphasize that macroeconomic variable innovations are sources of risk that must be rewarded. Liu (2006) tested an alternative model, highlighting the existence of a liquidity risk premium that captures the market portfolio’s missing risk. Ferguson and Shockley (2003) propose two alternative risk factors represented by the relative leverage portfolio and the relative distress portfolio and show that these factors represent a robust alternative to SMB and HML factors. A final arm of research proposes additional risk factors to the three-factor specifications to better capture default risk (Table 1). The primary literature for pricing default risk supports the FF (1993) augmented model, which leads us to propose the following:

H2: Augmented models are more relevant than the alternative ones to capture distress risk.

Relative leverage portfolio and leverage premium:

The corporate finance theory has long supported the virtues of debt policy (tax deductibility, conflict resolution, disciplinary mechanism toward the CEO, free cash flow reduction, etc.). Séverin et al. (2000) suggest that debt policy is positive for the operating performance and a good source of stress. Altman (1968) and Wruck (1990) show that excess debt leads to bankruptcy and generates direct and indirect costs. However, the debt influence on firm value depends on several factors: the economic context; ownership structure; competence and reputation of the management (Roll, 1986); or the industry (Opler and Titman, 1994). Debt policy negatively affects operating performance, especially for cyclical activity where the return on investment is unstable. The relationship among debt, performance, and value remains open. Indeed, debt does not lead to financial distress in the case of positive free cash flow. Conversely, low debt and high free cash flow volatility can lead to financial distress. Thus, the debt policy is likely to affect the relationship...