A leverage-augmented tree factor model and default risk pricing:

Evidence from France

Taher HAMZA

1

Institut Supérieur de Gestion, Université de Sousse.

Laboratoire Orléanais de Gestion (LOG) – Université d‟Orléans.

e-mail : tahahalim2000@yahoo.fr

Olfa BEN MDALLA2

Institut Supérieur de Gestion, Université de Sousse.

e-mail : benmdalla_olfa@yahoo.fr

Abstract

We investigate a central and controversial research issue: is the default risk a systematic risk? We analyse 12

size, B/M and leverage sorted portfolios as well as the portfolio of distressed firms over the period 1995-2009

and test the explanatory power of the risk factors that best capture the default risk. First, we find robust

evidence that the portfolio return requires systematically both size and value premium and that HML and

SMB capture an additional risk missed by the market portfolio. Second, the leverage premium is positive for

highly leveraged firms and vice versa. Third, we show a non significant effect of both momentum and relative

distress factors. Lastly, the distress risk premium is robustly significant only for the distressed firm‟s

portfolio. Our results advocate for researchers and practioners, a leverage-augmented three factor model to

price accurately assets and to implement efficient portfolio strategies.

Keywords: Systematic risk factors, Augmented FF three factors model, Financial Distress, Value premium,

Size premium, Leverage premium.

JEL classification: G11, G12, G33, E44.

1. Introduction

The CAPM as a single risk factor model has been considered for decades as an asset pricing

benchmark. 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), as well

as other multifactor approaches have been controversed in terms of empirical significance and

robustness. However, these models argue that the return covariation is a linear function of a

set of risk factors that Cochrane (2001) links to macroeconomic variables or the ones that

anticipate the macroeconomic events. In reference to the linear models, the return covariation

1 Taher HAMZA, PhD, Institut Supérieur de Gestion, University of Sousse, Tunisia, and a fellow researcher, Laboratoire Orléanais de

Gestion (LOG) – University of Orléans, e-mail: tahahalim2000@yahoo.fr. 2 Olfa ben mdalla, Institut Supérieur de Gestion, University of Sousse, Tunisia, e-mail: benmdalla_olfa@yahoo.fr

2

is mainly due to the changes in premiums related to systematic risk factors as related to the

expected cash flows. Accordingly, Fama and French (FF-1993) argue that HML and SMB

contribute to an additional explanatory power and that they capture the distress risk. Thus, the

academic literature raises a central and controversial empirical research question: is the

default risk a systematic risk? Three propositions are available in literature: the first one

assumes that after controlling for the market premium, HML and SMB are robust proxy of the

distress risk (FF-1993; 2006). The second one emphasizes that HML and SMB are

insufficient to capture all the distress risk. The last stream of research suggests that alternative

risk factors subsume HML and SMB to capture the distress risk.

The main goal of our study is to identify the risk factors that best capture the default risk in

France over the period 1995-2009. We analyse 12 size, book-to-market and leverage sorted

portfolios as well as the portfolio of distressed firms and test the explanatory power of the risk

factors specified by this study. We find robust evidence that these 12 portfolios require

systematically size and value premiums. We conclude that FF (1993) tree factor model

outperform the CAPM and that HML and SMB capture an additional risk missed by the

market portfolio. Second, relative leverage portfolio is significant for all study portfolios

except for the one of highly leveraged firms with high book to market (B/M). The leverage

premium is positive for highly leveraged firms and negative for lowly leveraged ones. Third,

we find a non significant relationship between both momentum and relative distress factor,

and the portfolio return comovement. We conclude and confirm through the Davidson and

MacKinnon (1981) that, in the French context, the FF (1993) three factor model augmented

by leverage premium is relevant which indicate that the additional factors capture default risk.

Lastly, the distress risk premium is robustly significant only for the distressed firm 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

3

and portfolio return. Section 3 presents the sample and methodology, followed by results,

discussion and implications. The last section concludes the paper.

2. Augmented vs. alternative distress risk pricing model: Literature review.

The pricing of default risk focuses on the identification of the risk factors that determine

systematically the portfolio return. Dichev (1998) and Piotroski (2007) argue that firms with

low B/M have a high level of intangibles assets synonymous with high financial distress.

Hussain et al. (2002) support the relevance of the B/M as a proxy of the financial distress risk

and underline that the value premium is characteristic of potentially failing firms3. These

authors concluded that the FF (1993) three-factor model is an improvement of the CAPM. We

present hereafter the available literature regarding the different distress risk model

specification.

2.1. Value and size premiums and the FF three factor model: According to FF (1993),

HML and SMB risk factors capture equity distress risk and contribute to significant additional

informational content to the popular CAPM. This adhoc model assumes a negative

relationship between size and default risk and a positive one between book-to-market and

default risk. The authors 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" (Graham &

Dodd, 1934; Basu, 1977; Chan and Lakonishok, 2004) require systematically a risk premium

i.e. a value premium (see FF, 1998; 2008). Besides, small firms require systematically a risk

premium i.e. a size premium. A wide debate of literature has focused on the explanatory

power of FF (1993) three factors model. Studies such as those of Liew and Vassalou, (2000)

3 The financial distress selection process focused on O-score Olhson more than the Altman Z-score. Others (Ferguson and Shockley, 2003; Agarwal and Poshakwale, 2006) use options to discriminate distressed companies. Alternatively, Campbell et al. (2007) use a new set of

variables to predict future bankruptcy and concludes that their model contribute to a better prediction power than the previous models. A last

stream of empirical research (FF, 2007; O‟Doherty, 2008) considers the delisted companies as an indicator to predict firm bankruptcy.

4

and Hussain et al. (2002) confirm that SMB and HML constitute systematic risk factors. Chan

and Zhao (2009) support that the FF (1993) model has become the benchmark model for

estimating expected returns with a profound impact on financial economics and industry

practice. In the French context, Molay (2000) and Malin and Veeraraghavan (2004) empirical

results 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 economic cycle (Perez-Quiros and Timmermann, 2000). Accordingly, Gulen et al.

(2008) highlight the inflexibility of firms with high B/M to economic cycle‟s change that

generate an additional risk.

Several studies supporting the CAPM consider size and value premium as firm fundamental

characteristics and plead for market anomalies4. 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 actor‟s irrationality (Daniel and Titman, 1997). La Porta et al.

(1997) consider that the value premium is not induced by a higher systematic risk. Gharghori

et al. (2007) show that SMB and HML do not capture the default risk and 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 difference in performance between firms with high

vs. low B/M. They add that B/M effect is consistent with mispricing argument. Lastly, Dichev

(1998) argues that the size effect has disappeared since the 80s when it was effective in the

60s and 70s and that the default risk do not generates high performance. Based on this

theoretical and empirical supports, we predict that:

H1: HML and SMB constitute systematic risk factors that capture firm distress risk.

2.2. Additional vs. alternative’s risk factors: Chan et al. (1998) propose a typology of risk

factors: market, fundamental, macro-economic, technical and statistics. In literature, three

4Kothari et al. (1995), Moskowitz (1999), Schwert (2003), Agarwal and Taffler (2008).

5

contrasted research stream are developed, that of FF (1993) who consider, as exposed above,

that SMB and HML are risk factors that systematically capture default risk. This thesis was

empirically corroborated by several research (see Table 1). The second research stream

considers that SMB and HML do not represent systematic risk factors and propose alternative

risk factors that capture the missing beta risk. Among these studies, that of Hahn and Lee

(2006) who propose two macroeconomic variables: default spread and term spread5,

alternatives to HML and SMB. The authors6 provide evidence that, in the U.S. market, these

two factors best capture systematic risk. Chen et al. (1986) underlined that macroeconomic

variable innovations are sources of risk that must be rewarded. For his part, Liu (2006) tested

an alternative model and underlined the existence of a liquidity risk premium that captures the

market portfolio 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 stream

of research proposes additional risk factors to the three factors specifications to better capture

the default risk (see table 1). The main streams of literature for pricing default risk support FF

(1993) augmented model, which leads us to propose the following prescription:

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

2.2.1. Relative leverage portfolio and the leverage premium: The financial literature has

for long supported the virtues of debt policy (tax deductibility, conflict resolution, disciplinary

mechanism toward the CEO, free cash flows reduction...). In such case, Séverin et al. (2000)

underline that it acts positively on the operating performance, then it is good source of stress.

Authors such as Altman (1968) and Wruck (1990) show that excess of debt leads to

bankruptcy and generates direct and indirect costs. However, the debt influence on firm value

5 Fama and French in 1989 as well as Chan et al. (1998) have introduced these two variables and show that SMB and HML capture these two

effects. 6 According to Hahn and Lee (2006) and in an economic downturn/favourable context, the default risk premium is relatively high/low and

thus explains partially the return variation of stocks and bonds. As for the maturity premium which reflects the agent expectations on future

growth, it is high in a case of anticipation of increased activity? Value firms are viewed with positive and strong correlation to this factor.

6

depends on several factors such as the economic context, ownership structure; competence

and reputation of the management (Roll, 1986) or the industry (Opler and Titman, 1994). In

this case, it affects negatively the operating performance especially for cyclical activity where

the return on investment is unstable. The relationship between debt, performance and value

remains an open question. Indeed, debt does not lead to financial distress in case of positive

free cash flows. Conversely, low debt and high free cash flow volatility can lead to financial

distress. Thus, the debt policy is likely to affect the relationship between the state of the

economy and asset returns7. Empirically, Bhandari (1988) finds a positive relationship

between equity returns and debt because of its strong impact on systematic risk (Ferguson and

Shockley, 2003) and its contribution to a high bankruptcy risk (Mossman et al. 1998). Roll

(1977) highlights the debt effect on asset pricing explained by the CAPM anomaly due to an

irrelevant market portfolio choice. The latter do not takes into account the investment

opportunities related to debt. Lajili (2005), replicating the Ferguson and Shockley approach

(2003) in France, shows a significant explanatory power of the debt on equity returns. Fallon

and Sarmiento (2005) compare the betas of leveraged and non leveraged firms and find that

debt is a systematic risk factor. Penman et al. (2007) show that the HML factor captures only

the operating risk, while the financial risk is captured by leverage that constitutes a systematic

risk factor. With regard to the existing works, we suggest the following hypothesis:

H3: Relative leverage is a systematic risk factor and captures distress risk.

2.2.2. Relative distress portfolio and distress premium: Does the distress premium

contributes to price assets and explains return comovement? In such case, this risk must be

systematically rewarded. The other question is whether this factor subsumes both size and

HML premiums. According to several studies (see table 1), the default risk requires a risk

7 Séverin et al. (2000) proposed a typology of debt effects on firm value according to the economic context. The authors emphasize that at

the beginning of a recession, low (high) leverage and low (high) free cash flows affect slightly firm performance. In a second case, low level

of debt with high free cash flow permits a best resistance to an economic crisis. In a last case, high leveraged firms with low level of free

cash flows may lead to financial distress.

7

premium and constitutes a systematic risk factor. Griffin and Lemmon (2002) support this

argument and state that HML and SMB are not able to explain financial distress. For these

authors, the default risk factor captures a significant proportion of systematic risk missed by

the market portfolio. The investors may not seek for distressed firm equity which requires an

additional risk premium, especially in economic downward cycle. In contrast, many other

studies (see table 1) support the thesis that default risk is not a systematic risk and that it

represents an idiosyncratic factor. Others argue that the fundamental and/or macroeconomic

factors capture the default risk and a specific factor for this risk is not justified. Insofar as most

work in this area support a non-systematic risk factor, we develop the following hypothesis:

H4: Relative distress is not a systematic risk factor.

2.2.3. Momentum, systematic risk factor or anomaly? In literature, a crucial question is if a

continuation historical return is related to risk or market underreaction to new informations.

Jegadeesh and Titman (1993, 2001a) and Hong et al. (2000) argue that momentum is driven

by market underreaction to information. Chan et al. (1998) find poor evidence that technical

variables generate large spread returns but do not constitute common risk factors. Similarly,

Liew and Vassalou (2000) as well as Griffin et al. (2003) underline that momentum factor is

not a systematic risk factor and that is unable to predict economic growth. Conversely,

Grundy and Martin (2001) show that Buying recent winners and shorting recent losers,

guarantees time-varying factor exposures in accordance with the performance

of common risk

factors. Similarly, Yao (2008) finds that momentum is a systematic-return phenomenon and

that its profits are primarily due to stock return response to a small number of dynamic

systematic factors. L‟Her et al. (2004) research underline that momentum is an augmented

risk factor to FF (1993) tree factor model. Recently, Agarwal and Taffler (2008) document

that momentum is proxying for distress risk and is largely subsumed by distress risk factor.

Finally and based on a study of long period (1940-2002), Hwang and Rubesam (2008) find

that momentum explain positively and significantly the return covariation only during certain

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periods (1940-60; 1970-90) and that momentum has disappeared since the late 1990s. The

preceding developments and discussions leads to our next hypothesis:

H5: Momentum is not a systematic risk factor

In reference to major theoretical and empirical contributions previously developed, two

conflicting streams of research are raised: the default risk is or not a systematic risk factor.

Table 1 shows the literature‟s contribution about the pricing of the distress risk.

Table 1: Literature contribution’s review

Authors

Study context

Study

period

Model specification

Systematic risk factors

Default risk is not a systematic risk factor

FF (1993) USA 1963-1991 FF (1993) three factors model

SMB, HML. SMB, HML.

Hahn and Lee (2006)

USA

1963-2001

Alternative model

Default spread, Term spread

Default spread, Term spread

Hussain et al. (2002)

Great Britain

1974-1994

FF (1993) three factor model

SMB, HML.

SMB, HML.

Liew and Vassalou

(2000)

Australia, , Europe

and USA. 1957-1998

Augmented FF (1993) three factors model

SMB, HML, Momentum. SMB, HML.

Molay (2000) French market 1987-1997 FF (1993) three factor model

SMB, HML.

SMB, HML.

Dichev (1998) USA 1981-1991 Augmented FF (1993) three factors model

SMB, HML, Default risk SMB, HML

Chan, Karceski and

Lakonishok (1998)

Japan, Great Britain and USA.

1968-1993

Augmented FF (1993) three factors model Fundamentals, technical, statistical and

macroeconomic variables.

Fundamentals variables (SMB,

HML, dividend, earning) Macroeconomic variables

(Default spread, Term spread).

L‟Her, Masmoudi and

Suret (2004) Canada 1960-2001

Augmented FF (1993) three factors model

SMB, HML, Momentum.

SMB, HML, Momentum.

Lajili (2005) French market 1984-2001 Augmented FF (1993) three factors model

.SMB, HML, leverage SMB, HML, Leverage

Griffin and Lemmon (2002)

USA 1965-1996 FF (1993) three factor model

SMB, HML.

SMB, HML.

Penman, Richardson

and Tuna (2007) USA 1962-2001

Augmented FF (1993) three factors model

SMB, HML. et endettement. SMB, HML, Leverage.

Default risk is a systematic risk factor

Vassalou and Xing

(2004) USA 1971-1999

Augmented FF (1993) three factors model

SMB, HML, Default SMB, HML, Default

Ferguson and

Shockley (2003) USA 1964-2000

Alternative model

Default, Leverage Default, Leverage

Agarwal and Taffler

(2008) Great Britain

Augmented FF (1993) three factors model

SMB, HML, Momentum, Default SMB, HML, Default

Agarwal and

Poshakwale (2006) Great Britain 1979-2002

Augmented FF (1993) three factors model

SMB, HML, Default SMB, HML, Default

Zaretzky and

Zumwalt (2007) USA 1985-1994

Augmented FF (1993) three factors model

SMB, HML, Default SMB, HML, Default

O'Doherty (2008) :

USA 1963-2006

Augmented FF (1993) three factors model

SMB, HML, Default SMB, HML, Default

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3. Methodology and results

We investigate the explanatory power of the risk factors that best capture the default risk. To

this end, we analyse 12 size, book-to-market and leverage sorted portfolios as well as the

portfolio of distressed firms over the period 1995-2009 to identify the risk factors that

determine systematically these portfolio‟s return.

3.1 Sample selection: Our sample includes all the French listed companies (832 firms). We

eliminated the financial and banking firms (SIC codes between 6000 and 6999) given that

they have different financial, operating and risk characteristics (129 financial firms). We also

remove firms with missing financial data (138 firms) and those with negative B/M (63 firms).

The final sample includes 502 firms. To sort portfolios by size, B/M and leverage and to

calculate Altman Z-score we use accounting and financial data collected from Thomson One

Banker database. We obtained historical stock prices from Datastream database over the

period from 1995 to 2009. The study period choice takes into account the fact that this period

was characterized by different macroeconomic conditions and industry shocks: (1995-1999)-

(2000-03)-(2003-07)-(2007-09) to provide relevant analysis of firm financial distress and to

stress the robustness of the risk factors. Table 2 reports the descriptive statistics of financial

and market characteristics of the sample firms without the distressed ones.

Table 2: Descriptive statistics of firm financial and market characteristics 1995-2008. WKTA: working capital scaled by total assets; EBITTA: Earnings Before Interests and Taxes scaled by total assets; DTA:

total debts scaled by total assets; GPM: Gross Profit Margin, FCFTA: Free cash flow scaled by total assets, OPM: Operating

Profit Margin; MTB: Market to Book ratio (market value of capital stock/Book value of capital stock); ROA : return on

assets, ROE : return on equity; ATURN: Asset Turnover; TA: total assets; MC: Market capitalization or firm market value.

WKTA EBITTA DTA GPM FCFTA OPM MTB ROA ROE ATURN TA

(millions €)

MC

(millions €)

Mean 0,24 0,11 18,54 15,23 0,01 5,16 3,05 6,13 11,57 1,26 1500,61 1444,55

Median 0,22 0,08 17,17 11,05 0,01 5,89 2,04 5,75 12,47 1,18 101,63 82,31

Std Dev. 0,21 0,49 14,13 19,14 0,14 18,82 3,94 10,07 42,18 0,60 5661,29 6156,58

Max 0,86 7,61 90,56 83,34 1,02 57,58 36,08 90,25 250,61 4,97 60608,35 72614,50

Min -0,40 -0,79 - -110,90 -0,77 -219,38 -11,67 -47,59 -374,35 -0,02 2,54 1,75

10

Table 2 provides descriptive statistics and presents firm characteristics based on the last fiscal

year. It reports that our sample is diversified in terms of firm size (average total assets: 1500

millions € from 2.54 millions € to 60608.35 millions €). Firm‟s market to book is on average

equal to 3.05 > 1 («glamour firms”). These firms present a moderate level of financial debt

(18.54 percent the total assets) with a low level of standard deviation. In addition, sample

firms present a low level of free cash flows of 1 percent the total assets on average which

indicate that they do not previously overinvest and signal a low level of agency cost of free

cah flows (Jensen, 1986). Besides, these firms are profitable with a high level of returns

(ROA = 6.13%, ROE = 11.57%, OPM = 5.16 and EBIT = 11 percent the total assets on

average) and corollary a high level of asset turnover. Lastly, we find that firm‟ activities

generate a high level of working capital (24% of total assets). We present hereafter the

different model specifications supporting the methodological process of empirical validation.

3.2. Model specifications: In a distress risk pricing context, we support the argument of Roll

(1977) regarding the market portfolio composition that prices assets. Ferguson and Shockley

(2003) argue that this portfolio ignores the economy‟s debt claims. In reference to Fama and

MacBeth (1973) approach and that of Vassalou and Xing (2004), we propose additional risk

factors for SMB and HML to price the missing distress risk. Table 3 presents hereafter the

definitions and measurements of dependent and independent variables.

Table 3. Summary of variable definitions Variable name Description

Dependent variables

(RPi-Rf)

(RPD-Rf) Return in excess of risk free rate of 12 portfolios sorted by size, book-to-market and leverage.

Return in excess of risk free rate of distressed firm portfolio.

Independent variables

(Rm-Rf)

Rm

Rf

Market risk premium.

Return of market portfolio.

Return of risk free rate estimated from Treasury bills 1 month (July 1995-August 2009).

SMB Represents the size premium: This variable expresses the difference in monthly returns between

portfolio of small capitalizations and that of large sizes: SMB = [1/3 (RS/L + RS/M + RS/H)] – [1/3

(RB/L + RB/M + RB/H)]. The arbitrage strategy is to buy the portfolio of high size firms and to sell

the one of low size firms.

HML Represents the value premium: This variable expresses the difference in monthly returns between

portfolios of firms with high B/M and those with low B/M. Based on the B/M ratio, the stocks are

11

divided into three classes: Low (30%), Medium (40%) and High (30%). HML is measured as

follows: [1/2(RB/H + RS/H)] – [1/2(RB/L + RS/L)]. The arbitrage strategy is to buy/sell the portfolio

of firms with high/low B/M.

RD Represents the financial risk premium and expresses the difference in monthly returns between

portfolios of firms with high and low leverage. Based on the ratio of total debt scaled by total

assets in December of year t-1, the stocks are divided into 3 classes: low (30%), medium (40%)

and high (30%). Each month of the year t, the average monthly returns of the 3 classes of stocks

are calculated. The arbitrage strategy is to buy/sell the portfolio of firms with high/low debt level.

WML Represents the momentum risk premium: This variable expresses the difference in monthly

returns between “Losers” and “Winners” portfolios. Losers are portfolios of stocks with lowest

last period's average return (20%). “Winners” are portfolios of stocks with the highest last period's

average return (20%). “Medium” are the remaining 60% of the stocks.

Rz Represents the distress risk premium: This variable expresses the difference in monthly returns

between portfolio of distressed and the one of non distressed firms. Based on accounting data of

December of year t-1, the stocks are divided into 2 classes based on their Z-score. Each month of

the year t, the average monthly stocks returns are calculated. The distress risk premium is

calculated from the difference in returns between the portfolio of distressed (Z-score< 2,675) and

the one of non distressed firms (Z> 2,675). To obtain a more relevant discrimination in France, Z

> 3 is the score for non distressed and Z <1.8 is the one for distressed firms. The arbitrage strategy

is to buy the portfolio of distressed firm and to sell the one of non distressed firm.

Table 4 presents the risk factors specified by our study and the theoretical prescriptions about

the sign of their correlation with the return of the different portfolios.

Table 4: Risk factors and correlation with portfolio return. The following portfolios are those of firms with SLHD: small size, low B/M and high leverage. SMHD: small size, medium

B/M and high leverage, SHHD: small size, high B/M and high leverage. BLHD: big size, low B/M and high leverage.

BMHD: big size, medium B/M and high leverage, BHHD: big size, high B/M and high leverage, SLLD: small size, low B/M

and low leverage, SMLD: small size, medium B/M and low leverage, SHLD: small size, high B/M and low leverage. BLLD:

big size, low B/M and low leverage, BMLD: big size, medium B/M and low leverage, BHLD: big size, high B/M and low

leverage.

Explanatory variables

Risk factors

Market

portfolio SMB

portfolio HML portfolio Relative

leverage

portfolio

Momentum

portfolio

Relative

distress

portfolio (Ri – Rf) (Rm-Rf) SMB HML RD WML Rz

Theoretical prescriptions

12 size, book-

to-market

and leverage

sorted

portfolios

HD

HS

(+)

(+) (+)

(+) NS NS

MS (+) LS (+) (-) HB (-) (+)

MB (-) LB (-) (-)

LD

HS

(+)

(+) (+)

(-) NS NS

MS (+)

LS (+) (-)

HB (-) (+)

MB (-) LB (-) (-)

Portolio of distressed firms

(+)

(+)

(+)

(+)

NS

(+)

3.3. The dependent variables: The returns of the 12 portfolios sorted by size, book-to-

market and leverage8 (HSHD, HBHD, HSLD, HBLD, MSHD, MBHD, MSLD, MBLD,

LSHD, LBHD, LSLD, LBLD) are regressed on the risk factors. These 12 portfolios eliminate

8 Firm number is insufficient to form the 25 portfolios formed through the FF (1993) study, which prevent poorly diversified portfolios.

12

the distressed firms stocks which then form the portfolio of distressed firms. We present

hereafter the monthly returns of these 12 portfolios and their Sharpe performance index.

Table 5: Descriptive statistics of 12 size, book-to-market and leverage sorted portfolios

1995/2009. The following portfolios are those of firms with SLHD: small size, low B/M and high leverage. SMHD: small size, medium

B/M and high leverage, SHHD: small size, high B/M and high leverage. BLHD: big size, low B/M and high leverage.

BMHD: big size, medium B/M and high leverage, BHHD: big size, high B/M and high leverage, SLLD: small size, low B/M

and low leverage, SMLD: small size, medium B/M and low leverage, SHLD: small size, high B/M and low leverage. BLLD:

big size, low B/M and low leverage, BMLD: big size, medium B/M and low leverage, BHLD: big size, high B/M and low

leverage.

Leverage

HD LD

Size

S B S B

Book to market

Mean monthly returns in excess of risk free rate

H -3,46% -3,69% -3,66% -3,44%

M -3,14% -3,05% -3,25% -2,94%

L -2,91% -3,01% -2,73% -2,64%

Standard deviation of monthly returns in excess of risk free rate (%)

H 7,45% 8,36% 7,39% 8,01%

M 5,84% 6,58% 6,48% 6,95%

L 5,73% 6,97% 5,68% 6,01%

Sharpe ratio

H -46,49 -44,10 -49,51 -42,95

M -53,79 -46,36 -50,11 -42,35

L -50,86 -43,24 -48,22 -44,10

Table 5 shows that, over the period 1995-2009, the average monthly returns in excess of risk

free rate of the 12 size, book-to-market and leverage sorted portfolios, are negative. This

indicates that the 12 portfolio strategy as well as that of the market portfolio underperforms

the French Treasury bills-1 month as a risk free rate. We underline also that, when leverage

level is high, the average return of small firm‟s portfolio is higher than the one of big firm‟s

portfolio, after controlling for B/M and size. We obtain the opposite result with lowly

leveraged firms. Furthermore, the portfolios of firms with high B/M have low returns and

high volatility. The Sharpe ratio indicates that these portfolios outperform the other portfolios

when they are, of small and high leverage, and big and low leverage.

3.4. Independent variables: Table 6 presents the monthly returns of risk factors. These

arbitrage portfolio‟s returns are calculated with simple average stock return9. They indicate

the risk premium related to the different risk factors as explanatory variables.

Table 6: Descriptive statistics of monthly returns of explanatory factors (2000/2008). Rf, Rm: Return of risk free rate and that of market; (Rm-Rf): Market risk premium; SMB: Size premium; HML: value

premium; RD: Financial risk premium, WML: momentum risk premium, Rz: distress risk premium.

9 Weighting returns by market capitalization as shown by Molay (2000), leads to more weight for large capitalization profitability. However,

the Fama and French portfolios control for size and book to market, which requires an equally weighted securities.

13

Monthly returns in excess of risk free rate

Rm-Rf HML SMB RD WML RZ

Mean -3,25% -0,82% -0,30% 0,003% -0,71% 1,09%

Std deviation 6,09% 4,08% 3,85% 2,58% 9,61% 6,81%

Correlation matrix Rm-Rf 1

HML 0,250** 1

SMB -0,330** -0,033 1

RD -0,139 -0,521** -0,077 1

WML -0,170* 0,004 0,175* 0,042 1

RZ -0,039 -0,313** 0,061 0,281** -0,589** 1

***, **, * denote two-tailed statistical significance levels at the 1%, 5% and 10%, respectively.

We underline that the risk premiums related to the portfolios of relative leverage (0,003%)

and relative distress (1,09%) are positives contrary to those of market (-3,25%), HML (-

0,82%), SMB (-0,30%) and momentum (-0,71%) portfolios. The highest volatility level of

risk premiums are those of momentum (9,61%), relative distress (6,81%) and market (6,09%)

portfolios. Moreover, arbitrage strategies based on relative leverage and relative distress

appear to be most efficient. We also note low correlations between the different risk factors

which is in line with the results of Molay (2000) and Malin and Veeraraghavan (2004) studies

in the French context. Table 7 shows the VIF test results and indicates the absence of

colinearity between the explanatory variables. They are thus all orthogonolized and permit to

adopt an OLS specification with 6 explanatory factors.

Ri – Rf = i + βmi (Rm-Rf) + βSi SMB + βHi HML+ βDiRD + βWMLiWML + βZiRz + i

With, Ri, Rf, Rm: Return of portfolio i, risk free return and market portfolio return.

Regression intercept of portfolio i.

βmi, βSi, βHi, βDi βWMLi, βZi: regression coefficients of the different risk factors.

(Rm-Rf), SMB, HML, RD, WMLRz: represent respectively market, size, value, financial,

momentum and distress risk premium.

Table 7: VIF-test and Multicoliniarity Rf, Rm: Return of risk free rate and that of market; Regression intercept of portfolio i; 1, 2, 3 and 4: regression

coefficients associated to risk factors: market; (Rm-Rf): market risk premium; SMB: size premium; HML: value premium;

RD: Financial risk premium, WML: momentum risk premium, Rz: distress risk premium.

Dependent variables Regression equation VIF-test

Rm-Rf

SMB

HML

RD

WML

Rz

Rm-Rf = 0 + 1SMB + 2HML + 3RD + 4Rz + 4WML +

SMB = 0 + 1(Rm-Rf) + 2HML + 3RD + 4Rz + 4WML +

HML = 0 + 1(Rm-Rf) + 2SMB + 3RD + 4Rz + 4WML +

R = 0 + 1(Rm-Rf) + 2SMB + 3HML + 4Rz + 4WML +

WML = 0 + 1(Rm-Rf) + 2SMB + 3HML + 4RD + 5Rz +

Rz = 0 + 1(Rm-Rf) +2SMB + 3HML + 4RD + 4WML +

1.57

1.58

1.23

1.50

1.87

2.07

14

3.5. Regression tests of the 12 portfolios sorted by size, book-to-market and leverage:

The returns of these 12 portfolios are regressed on the 6 risk factors specified by our study

(see table 8). Initially, we tested respectively the CAPM and the three-factor model of FF

(1993). Panel A shows that the return of these 12 portfolios has a positive and strong

significant relationship with the market portfolio return. By controlling beta, B/M and

leverage effect, the portfolio return of small10

/big firms11

have a positive/negative and strong

significant relationship with the SMB factor (see Panel B). Thus, portfolios of small/big firms

are rewarded with a positive/negative size premium. These results provide robust evidence

about the size effect on portfolio return. As argued by Chan and Zhao (2009), “size premium

is as robust as ever”. Besides, the portfolio return of firms with high B/M is positively and

significantly with the HML factor and vice versa for the portfolios with low B/M. Thus, firms

"value firms" require systematically a risk premium i.e. a value premium. The previous results

confirm our theoretical prescription (H1) and join those of FF (1993) and the most empirical

studies (see Table 1). However, they contrast with those of Hahn and Lee (2006) and

Ferguson and Shockley (2003) who find that other fundamental and/or macroeconomic

factors subsume the SMB and HML effect. On the French market, Molay (2000), Lajili

(2005) and Hamza (2009) confirm that portfolios with low size and/or high B/M outperform

the other portfolios. In addition, Malin and Veeraraghavan (2004) confirm the previous

French studies but only for strategy based on the size factor. They shows that the strategy

based on B/M outperform weakly the other strategies. In reference to Panel B results, we

conclude that FF (1993) tree factor model outperform the CAPM (see the two model adjusted

R2). We can then stress that HML and SMB are systematic risk factors and capture a

significant additional distress risk. These results assume that, in the French context, the

CAPM augmented by size and value premium is relevant.

10 These portfolios are SLHD, SMHD, SHHD, SLLD, SMLD, SHLD. 11 These portfolios are BLHD, BMHD, BHHD, BLLD, BMLD, BHLD.

15

In what follow, we proceed to test a model that specifies alternative risk factors to see

whether they subsume HML and SMB factor and best capture the distress risk. Panel C

indicates that momentum as well as relative distress factors are not significant. On the other

side, relative leverage is significant for all portfolios, except for portfolio of highly leveraged

firms with high B/M. Besides, leverage premium is positive/negative and significant for

highly/lowly leveraged firms. We conclude that firm‟s lowly leveraged experience a low level

of risk and than a low level of cost of capital. This means that their value is highest which

corroborate the trade off theory. Indeed, firms lowly leverage i.e. with high debt capacity and

a low probability of bankruptcy, take advantage from debt insofar tax benefits outweigh

bankruptcy costs (Harris and Raviv, 1991). The same negative and significant correlation is

found by Penman et al. (2007) who argue that HML do not capture the financial risk but only

the operational risk. In sum, relative leverage is considered as a systematic risk factor which

Table 8: OLS regression results of monthly returns of 12 size, book-to-market and leverage sorted portfolios 1995/2009. SLHD: small size, low B/M and high leverage. SMHD: small size, medium B/M and high leverage, SHHD: small size, high B/M and high leverage. BLHD: big size, low B/M and high leverage.

BMHD: big size, medium B/M and high leverage, BHHD: big size, high B/M and high leverage, SLLD: small size, low B/M and low leverage, SMLD: small size, medium B/M and low leverage,

SHLD: small size, high B/M and low leverage. BLLD: big size, low B/M and low leverage, BMLD: big size, medium B/M and low leverage, BHLD: big size, high B/M and low leverage. Rf, Rm:

Return of risk free rate and that of market; (Rm-Rf): Market risk premium; SMB: Size premium; HML: value premium; RD: Financial risk premium, WML: momentum risk premium, Rz: distress risk

premium. 12 size- and book-to-market-sorted portfolios

HD LD

S B S B

H M L H M L H M L H M A

Panel A: CAPM model

αi

-0,001

(-0,40)

-0,004

(-1,66)

-0,003

(-1,25)

0,003

-1,090

0,002

-0,830

0,002

-0,620

-0,001

(-0,36)

-0,001

(-0,24)

-0,002

(-0,86)

0,004

-1,310

0,005

(2,45)***

-0,001

(-0,44)

βMi

1,023

(19,73)***

0,842

(23,82)***

0,794

(20,38)***

1,241

(27,26)***

0,996

(30,81)***

1,023

(19,73)***

1,096

(27,16)***

0,984

(31,38)***

0,769

(18,89)***

1,182

(26,61)***

1,068

(34,33)***

0,771

(16,27)***

Adjusted R2

69.68%

77.02%

71%

81,45%

84.87%

74.17%

81.34%

85.34%

67.80%

80.70%

87.45%

60.95%

T-Fisher 389.36 567.44 415.16 743.25 949.11 486.26 737.51 984.42 356.80 707.84 1178.61 264.75

Panel B: FF (1993) tree factors model

αi

0,002

-0,620

-0,002

(-0,83)

-0,002

(-0,86)

-0,001

(-0.62)

-0,001

(-0.65)

-0,002

(-0,80)

0,001

(-0,51)

0,001

(-0,7)

0,000

(-0,18)

0,002

(-0,73)

0,003 (-1,43)

-0,004 (-1,33)

βMi

1,040

(19,56)***

0,936

(27,00)***

0,924

(27,59)***

1,047

(30.89)***

0,985

(32.60)***

1,007

(25,49)***

1,084

(26,55)***

1,032

(31,45)***

0,921

(27,39)***

0,999

(31,19)***

1,048

(32,86)***

0,822

(18,21)***

βSMBi

0,287

(3,53)***

0,282

(5,31)***

0,276

(5,37)***

-0,604

(-11.62)***

-0,248

(-5.36)***

-0,272

(-4,49)***

0,162

(2,58)***

0,212

(4,20)***

0,402

(7,81)***

-0,418

(-8,51)***

-0,198

(-4,04)***

-0,121

(-1,75)*

βHMLi

0,257

(3,43)***

-0,207

(-4,23)***

-0,430

(-9,12)***

0,406

(8.49)***

-0,242

(-5.70)***

-0,459

(-8,25)***

0,274

(4,77)***

-0,026

(-0,57)

-0,410

(-8,66)***

0,571

(12,64)***

-0,127

(-2,83)***

-0,456

(-7,16)***

Adjusted R2

73.42%

81.60%

82.16%

91.42

88.98%

83.81%

84.07%

86.60%

81.66%

91.63%

89%

70.44%

T-Fisher 156.57 250.76 260.48 601.07 455.93 280.17 298.30 364.91 251.77 617.59 456.74 135.23

17

HD LD

S B S B

H M L H M L H M L H M L

Panel C: Alternative model to FF (1993) tree factors model αi

0,001

-0,160

-0,003

(-1,41)

-0,002

(-1,03)

0,003

-0,930

0,003

-1,410

0,002

-0,800

-0,002

(-0,93)

-0,001

(-0,46)

-0,003

(-1,00)

0,004

-1,360

0,006

-2,590

-0,001

(-0,38)

βMi 1,050

(20,11)***

0,882

(25,70)***

0,838

(25,17)***

1,192

(26,67)***

1,020

(38,1)***

1,014

(25,870)***

1,058

(29,41)***

0,971

(30,65)***

0,797

(19,77)***

1,136

(28,60)***

1,075

(33,77)***

0,794

(16,93)***

βDi

0,091

-0,700

0,232

(2,72)***

0,654

(7,92)***

-0,084

(-0,76)

0,612

(9,24)***

0,697

(7,17)***

-0,648

(-7,27)***

-0,243

(-3,10)***

0,147

(-1,470)

-0,572

(-5,81)***

0,193

(2,45)***

0,408

(3,51)***

βWMLi 0,087

(2,07)**

0,083

(3,00)***

0,012

(-0,460)

-0,137

(-3,81)***

-0,040

(-1,83)*

-0,056

(-1,77)*

-0,002

(-0,06)

0,004

(-0,160)

0,050

(-1,550)

-0,026

(-0,80)

-0,014

(-0,55)

-0,010

(-0,25)

βZi

-0,045

(-0,74)

0,101

(2,53)***

0,042

-1,080

-0,178

(-3,42)***

-0,018

(-0,58)

0,022

(-0,490)

0,001

(-0,010)

0,007

(-0,190)

0,146

(3,11)***

-0,116

(-2,51)***

-0,018

(-0,49)

0,043

(-0,78)

Adjusted R2 71.17% 79.70% 80.19% 83.25% 90.30% 81.44% 86.12 85.97% 70.39% 85.53% 87.69% 64.14%

T-Fisher 105.32 166.87 172.03 210.96 394.45 186.41 263.10 259.89 101.43 250.69 301.90 76.57

Panel D: Augmented Fama and French three factor model

αi

0.004

(1.44)

-0.0008

(-0.37)

0.0001

(0.09)

-.0017

(-0.78)

0.0002

(0.13)

-0.001

(-0.49)

-0.0006

(-0.27)

0.0006

(0.30)

0.00002

(0.01)

0.0004

(0.22)

0.003

(1.53)

-0.003

(-1.25)

βMi

1.06

(20.84)***

0.94

(27.93)***

0.93

(31.75)***

1.03

(30.48)***

0.99

(37.23)***

1.005

(26.68)***

1.07

(28.26)***

1.02

(32.08)***

0.91

(26.93)***

0.99

(33.58)***

1.050

(32.41)***

0.82

(17.90)***

βSMBi

0.37839

(3.73)***

0.28

(5.21)***

0.33

(7.25)***

-0.58

(-10.82)***

-0.206

(-4.89)***

-0.225

(-3.85)***

0.12

(2.11)**

0.205

(4.06)***

0.404

(7.50)***

-0.46

(-9.91)***

-0.194

(-3.79)***

-0.11

(-1.72)*

βHMLi

0.30

(4.36)***

-0.10

(-1.93)*

-0.26

(-5.46)***

0.39

(6.98)***

-0.078

(-1.78)*

-0.319

(-5.02)***

0.09

(1.66)*

-0.13

(-2.58)***

-0.39

(-6.94)***

0.44

(8.94)***

-0.111

(-2.06)**

-0.42

(-5.62)***

βDi

0.43126

(3.26)***

0.24

(2.77)***

0.57

(7.55)***

-0.0003

(-0.09)

0.49

(7.10)***

0.41

(4.18)***

-0.54

(-5.48)***

-0.27

(-3.24)***

0.0086

(0.10)

-0.41

(-5.39)***

0.057

(0.68)

0.084

(0.70)

βWMLi 0.06

(1.66)*

0.045

(1.70)*

-0.03

(-1.64)

-0.051

(-1.94)*

-0.017

(-0.86)

-0.041

(-1.40)

-0.012

(-0.44)

-0.026

(-1.04)

-0.013

(-0.52)

0.048

(2.07)**

0.004

(0.19)

-0.0135

(-0.38)

βZi

-0.03

(-0.66)

0.04

(1.06)

-0.05

(-1.49)

-0.028

(-0.72)

0.003

(0.10)

0.012

(0.29)

-0.005

(-0.12)

-0.045

(-1.25)

0.024

(0.6)

0.022

(0.66)

-0.003

(-0.10)

-0.002

(-0.05)

Adjusted R2 75.83% 83.29% 86,57% 91.49% 91.60% 85,53% 86.52 87.97% 81.54% 92.90% 88.84% 70.02%

T-Fisher 89.39 135.46 182,54 303.86 308.40 160,55 181.86 198.67 125.44 369.82 225.18 66.79

***, **, * denote two-tailed statistical significance levels at the 1%, 5% and 10%, respectively.

is in line with Bhandari (1988), Chan and Chen (1991) and Ferguson and Shockley (2003)

works and confirms our theoretical prescription (H3). In France, Lajili (2005) and Hamza

(2009) show that the leverage factor provides a significant additional explanation about the

portfolio‟s variance of returns. Besides, the explanatory power of the alternative model is

slightly lower than that of the FF (1993) three factor model. Furthermore, we introduce

leverage, momentum and relative distress to test the augmented or the alternative model

specification form. We find a non significant relationship between the momentum factor and

the portfolio return which leads us to assume that this factor do not capture distress risk (H5).

Moreover, we find, contrary to Vassalou and Xing (2004), Zaretzky and Zumwalt (2007) and

O'Doherty (2008), that the relative distress factor is not a significant explanatory variable of

the return covariation, except for the portfolio of firm with high B/M. This result joins our

theoretical prescriptions presented above (H4) and is line with several studies (see table 1).

Overall, and across the different tests, we show an extremely high level of adjusted R2

(between 70% and 93%) and of overall significance model (T-Fisher) synonymous of an

important informational content of these specifications. Ultimately, SMB, HML and leverage

factors provide an additional contribution to price the CAPM missing distress risk. The

systematic nature of the risk premium associated to these 3 factors permits to price with more

accuracy the return portfolios volatility. We check hereafter the robustness of our study

models to identify the final specification of the explanatory model of financial distress.

3.6. Robustness check: the Davidson and MacKinnon (1981) J-test. We address here a

robustness issue by performing a Davidson and MacKinnon (1981) J-test. This test is applied

on the three specifications proposed by the theoretical and empirical literature: three factors,

alternative and augmented model. Based on several empirical results, this procedure aims to

infer the direction of the true model relative to the rejected non-nested alternatives (Davidson

and MacKinnon, 1981) and thus to identify the most robust model specification. Besides, the

19

J-test ensures the stability of the explanatory factor significance and permits to optimize the

information content of the different proxy factor model. Lastly and to overcome the problem

of residual autocorrelation due to the added or eliminated variables, we applied generalized

least squares (GLS). The 7 competing models are presented hereafter.

Basic model: RPti = 0 + 1 RMt + 2 SMBt + 3HMLt + 4RDt + 5WMLt + 6RZt + t

Model 1: RPti = 0 + 1RMt + 2SMBt + 3HMLt + t

Model 2: RPti = 0 + 1 RMt + 2RDt + 3WMLt + 4RZt + t

Model 3 : RPti = 0 + 1 RMt + 2 SMBt + 3HMLt + 4WMLt + 5RDt + t

Model 4 : RPti = 0 + 1 RMt + 2 SMBt + 3HMLt + 4WMLt + 5RZt + t

Model 5 : RPti = 0 + 1 RMt + 2 SMBt + 3HMLt + 4RDt + 5RZt + t

Model 6 : RPti = 0 + 1 RMt + 2 SMBt + 3HMLt + 4RDt + t

Model 7 : RPti = 0 + 1 RMt + 2 SMBt + 3HMLt + 4RZt + t

The J-Test procedure (see table 9) provide strong evidence that the Four factor model 6 is the

most robust compared to the other model‟s specification. The relative distress factor as well

as the momentum factors are rejected by this test insofar they do not contribute to capture the

portfolio return comovement (H4 and H5). Hence, our findings advocate a leverage-

augmented three factor model that permits a robust explanation of the portfolio return in

excess of the risk free rate which validates our previous prescription (H2).

3.7. Regression and results of distressed firm’s portfolio: We regress hereafter the

distressed firm portfolio returns (excluded from the 12 previous portfolios) on the 6 risk

factors (see Table 11). Previously, we present financial characteristics of distressed firms and

therefore their specific profile. Table 10 shows that distressed firms are on average of medium

size (median 415,88 millions €) with wide differences (from 3,59 to 134767 millions €) and

expect growth opportunities (MTB = 1,93). They are highly leveraged (financial debts =

30,67 percent of total assets) with negative free cash flows (-6 percent of total assets) even if

their working capital is negative, which indicate a financial distress and a lack of liquidity to

pay the short term debts. The other important feature is that all the profitability indicators are

negative over the study period (ROA = -6,20%, ROE = -13,03%, Asset‟s turnover = 0,72,

EBIT = -13 percent of total assets an OPM = -6,08%).

Table 9: GLS regression results of monthly returns of 12 size, book-to-market and leverage sorted portfolios 1995/2009. SLHD: small size, low B/M and high leverage. SMHD: small size, medium B/M and high leverage, SHHD: small size, high B/M and high leverage. BLHD: big size, low B/M and high leverage.

BMHD: big size, medium B/M and high leverage, BHHD: big size, high B/M and high leverage, SLLD: small size, low B/M and low leverage, SMLD: small size, medium B/M and low leverage,

SHLD: small size, high B/M and low leverage. BLLD: big size, low B/M and low leverage, BMLD: big size, medium B/M and low leverage, BHLD: big size, high B/M and low leverage. Rf, Rm:

Return of risk free rate and that of market; (Rm-Rf): Market risk premium; SMB: Size premium; HML: value premium; RD: Financial risk premium, WML: momentum risk premium, Rz: distress

risk premium.

HD LD

S B S B

H M L H M L H M L H M L

αi

0.0046

-0.0009

0.0001

-0.0019

0.0002

-0.0006

-0.0010

0.0004

0.0004

0.0006

0.0032

-0.0039

βMi 1.0657*** 0.9414*** 0.9344*** 1.0383*** 0.9903*** 1.0151*** 1.0843*** 1.0265*** 0.9213*** 0.9993*** 1.0506*** 0.8221***

βSMBi 0.2901*** 0.3022*** 0.3157*** -0.5909*** -0.2053*** -0.2422*** 0.1201** 0.1896*** 0.4024*** -0.4601*** -0.1956*** -0.1214*

βHMLi 0.3827*** -0.1169** -0.2532*** 0.4094*** -0.0798* -0.3274*** 0.095* |-0.1234** -0.4102*** 0.4353*** -0.1098** -0.455***

βDi 0.4132*** 0.2774*** 0.5457*** 0.4963*** 0.4062*** -0.6256*** -0.2994*** -0.4066***

βWMLi 0.0835* 0.051* -0.0394** 0.0381**

βZi

Adjusted R2 75.92% 82.59% 86.48% 91.57% 91.66% 84.76% 86.55% 87.55% 81.66% 92.93% 88.91% 70.44%

J-Test (0.00)*** (0.00)*** (0.00)*** (0.00)*** (0.00)*** (0.00)*** (0.00)*** (0.00)*** (0.00)*** (0.00)*** (0.00)*** (0.00)***

***, **, * denote two-tailed statistical significance levels at the 1%, 5% and 10%, respectively.

Table 10: Descriptive statistics of distressed firm: financial and market characteristics 1995-2008. WKTA: working capital scaled by total assets; EBITTA: Earnings Before Interests and Taxes scaled by total assets; DTA: total debts scaled by total assets; GPM: Gross Profit Margin, FCFTA: Free

cash flows scaled by total assets, OPM: Operating Profit Margin; MTB: Market to Book ratio (market value of capital stock/Book value of capital stock); ROA : return on assets, ROE : return on

equity; ATURN: Asset Turnover; TA: total assets; MC: Market capitalization or firm market value.

WKTA EBITTA DTA GPM FCFTA OPM MTB ROA ROE ATURN TA MC

Mean -0,02 -0,13 30,67 5,99 -0,06 -6,08 1,93 -6,20 -13,03 0,72 7119,90 2475,38

Median -0,01 -0,01 28,87 8,00 -0,02 -1,10 1,12 -1,27 -2,72 0,64 415,88 71,79

StdDev. 0,27 0,59 22,14 32,14 0,18 28,66 6,01 15,64 34,09 0,46 21087,98 9459,41

Max 0,54 0,98 111,54 68,75 0,20 43,73 38,70 30,16 49,66 2,61 134767 67385,84

Min -1,06 -5,00 0,22 -118,8 -0,93 -90,98 -10,75 -61,57 -124,4 0,03 3,59 1,09

Table 11 hereafter summarizes the market performance of the distressed firm‟s portfolio.

Table 11: Descriptive statistics of returns of distressed firm’s portfolio

Mean monthly returns in

excess of risk free rate (%) Stand dev. of monthly returns in

excess of risk free rate (%) Sharpe ratio

Distressed firm portfolios

-1,37%

8,86%

-15,463

Table 11 shows that even if the average return of this portfolio is negative, it experiences

highest level of return compared to the 12 size, book-to-market and leverage sorted portfolios

(see table 5). The volatility of the distressed firm‟s portfolio is highest except for the portfolio

with high B/M. The Sharpe ratio shows that the distressed firm‟s portfolio outperforms widely

all these 12 portfolios. Table 12 presents the results of the OLS regression that tests the

specified model presented previously on portfolio of distressed firms.

Table 12: OLS regression results of monthly returns of distressed firm portfolios

1995/2009 and J-test. Rf, Rm: Return of risk free rate and that of market regression intercept of the portfolio i; (Rm-Rf): Market

risk premium; SMB: Size premium; HML: value premium; RD: Financial risk premium, WML: momentum risk

premium, Rz: distress risk premium.

Distressed firm portfolio

OLS regression

GLS regression

Augmented model

Eq1

Alternative model Robustness test

J-Test Eq2 Eq3

αi

0.0116

(6.61)***

0.0109

(5.88)***

0.0130

(5.60)***

0.0117***

βMi

1.013

(37.65)***

1.0439

(38.10)***

1.093

(32.56)***

1.0158***

βSMBi

-0.0093

(-0.22)

βHMLi

0.254

(5.70)***

0.2547***

βDi

-0.437

(-6.21)***

-0.6068

(-8.93)***

-0.4349***

βWMLi

-0.041

(-1.96)**

-.0527031

(-2.38)***

-0.0425**

βZi

0.858

(27.76)***

0.8196

(25.60)***

0.8011

(26.69)***

0.8569***

R2 ajusté

Test de Fisher

95.25%

565.66

94,37%

709,42

91,11%

855,44

95.28%

J-Test (0.00)*** ***, **, * denote two-tailed statistical significance levels at the 1%, 5% and 10%, respectively.

22

Table 12 shows a positive and significant relationship between the performance of distressed

firm‟s portfolio and both market portfolio and HML factor. In addition, the size effect is non

significant joining the fact that distressed firms are of medium size (Banz, 1981) on average

(see table 10). Besides, we underline a strong and negatively significant relationship between

the distressed firm‟s portfolio return and the relative leverage factor (RZ). Such result is

paradoxical insofar it joins the one of the lowly leveraged portfolio while distressed firms are

highly leveraged (see table 10). Thus, it appears that HML captures the distress risk but

insufficiently. Lastly, distressed firm portfolio experience a strong and significant relationship

vis-a-vis the relative distress factor, contrary to the 12 previous portfolios. The growth of firm

failure rate generates a higher risk premium for distresses firm portfolio return. Relative

distress factor constitutes therefore a significant risk factor that operates essentially for

distressed firms and provides an additional risk premium (Adjusted-R2 coefficient between

91,11 and 95,25%). Furthermore, the distressed firm portfolio outperforms the 12 previous

portfolios (model constant is statistically significant at the 1%). We could hypothetically

argue that, as a risk factors, market, SMB, HML and RD does not totally capture the default

risk for distressed firm‟s portfolio contrary to that of non distressed firms. Table 12 shows

also that the explanatory power of alternative models (eq2 and eq3) are almost equal to the

augmented three factor‟s model one as shown by the Adjusted-R2 coefficient (95.25% vs.

94,37 and 91,11%). In reference to eq 2, the alternative variables best capture the distress risk

than SMB and HML factors. In addition, after eliminating the relative leverage factor (eq3),

the adjusted-R2 is slightly different (91,11 vs. 94,37%) which indicates his weak explanatory

power. The J-Test procedure, as a robustness test, rejects the augmented three factor model.

Besides, this test provides robust evidence that the relative distress factor constitutes the

major determinant factor of the distressed firm portfolio return but does not seem to be a

systematic risk factor insofar it explains only the return of the distressed firm‟s portfolio (H4).

23

4. Conclusions and implications

Extensive and controversial literature has focused on a central question: the default risk is

there a systematic risk? Some authors assume that HML and SMB are robust proxies that

capture the beta missing distress risk. A second stream of research emphasizes that these risk

factors are insufficient to capture all the distress risk. The last one suggests that alternative

risk factors subsume HML and SMB to capture the distress risk. The main goal of our study is

to identify the risk factors that best capture the default risk on the French context. We analyse

12 size, book-to-market and leverage sorted portfolios as well as the portfolio of distressed

firms and test the explanatory power of the risk factors specified by this study. We find robust

evidence about both size and value premium. We conclude that FF (1993) tree factor model

outperform the CAPM and that HML and SMB are systematic risk factors. In addition,

leverage premium is significantly and positively/negatively correlated with highly/lowly

leveraged firms. Furthermore, a non significant relationship between both the momentum and

the relative distress factors, and the portfolio‟s return comovement. We conclude and confirm

through the Davidson and MacKinnon (1981) J-test that, in the French context, the FF (1993)

three factor model augmented by leverage premium is relevant which indicate that the

additional factors capture default risk. Lastly, the distress risk premium is robustly significant

only for the distressed firm‟s portfolio.

In terms of managerial implications, our results suggest that B/M, size and debt risk factors

affect the cost of capital and than the investment decision and the firm value. In the other

hand, everything else remaining constant, portfolio strategy based on SMB, HML and

leverage leads to high level of return. Insofar this strategy is rewarded by these risk

premiums, it outperforms the market portfolio strategy. Lastly, in a context of long term event

study, the valuation of abnormal returns must take into account the risk factors previously

specified, to make more accurate, the event specific impact. Overall, our results help

24

researchers and practioners to price with more accuracy assets and to implement efficient

portfolio strategies. Our research has certain limitations including the fact that the study

period is not sufficiently long to provide efficient findings and could be extended to better

understand the impact of different economic cycle. Besides, the Altman Z-score can be

associated to Olson O-score to better select the distressed firms. Future research can focus on

testing the contribution of the regime-switch model in the French context. Indeed, differences

persist because of contingency of risk factors related to economic cycle variations. Finally,

future research could also compare the French case with the other European markets, to

identify empirically evidences on any contextual features.

25

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