Asset pricing methodologies

3.2.4.1 Two stage cross-sectional regressions (2SCSR)

This research uses the standard two-stage cross-sectional regressions (2SCSR)

methodology, a prominent framework to explore a risk-based explanation for return

anomalies. This methodology has been developed by Black et al. (1972) and Fama and

MacBeth (1973) for CAPM testing along with others (Grauer and Janmaat, 2009, 2010).

116 CAPM, Campbell and Vuolteenaho (2004) for the two-beta model, and Huang and Wang

(2009) for an investment-based asset pricing model. Recently, the 2SCSR has been used for

testing the accrual quality factor, and alternative three-factor model beyond the US market

for risk-based explanations (Core, et al., 2008; Kim and Qi, 2010; Ogneva, 2012;

Walkshäusl and Lobe, 2011).

Cochrane (2001) explains the procedure of two-stage cross-sectional regressions.

The cross-sections of average returns are run on the betas, in order to distinguish whether a

factor is a return or not. Intuitively, the risk premium should be directly related to the betas,

where betas proxies risk exposures; thus, higher returns are expected for higher beta of

assets to factors, which bear high risk premiums. Under 2SCSR methodology first time-

series regressions of the following form are run, to get the betas on average future returns.

Rit− Rft = α + βi,MKT_RFMKT_RFt+ βi,SMBSMBt+ βi,HMLHMLt+ βi,FLEXFLEXt+ εit (2)

Where, (R_it− R_ft) are excess future returns for a portfolio of firms; (MKT_RFt), (SMBt), and (HMLt) are Fama and French (1993) risk factors that are representing the

market, firm size, and book-to-market ratio premiums. The Fama and French (1993) risk

factors are used by extensive asset pricing literature (Aboody et al., 2005; Francis, et al.,

2005; Petkova, 2006; Stambaugh, 2003). The FLEX represents the new return factors that

are constructed by going long on financial flexibility characteristics ranked in the bottom

117 Then, under the second step we estimate the factor risk premium γ from cross- sectional regression, with betas on the right-hand side as independent variables and γ as regression coefficients, and ν_i are the cross-sectional regression residuals (pricing errors) as shown in equation (3).

Rit− Rft = γ0+ γ1bi,MKT_RF+ γ2bi,SMB+ γ3bi,HML+ γ4bi,FLEX+ νit (3)

Apart from Fama and French’s (1993) three risk factors, this research adds a

momentum (UMD) factor as given in Ken French’s data library and Pastor and

Stambaugh’s (2003) liquidity factor (LIQ). In this case, the coefficient magnitude on γ₄ determines whether there is a statistically significant premium on the FLEX factor loading

or not. If there is a significant premium then the factor is categorised as a risk factor (Core,

et al., 2008; Gray and Johnson, 2011); otherwise it would be the characteristics that derive

the returns.

In particular, for asset pricing tests based on using a two-stage cross-sectional

regressions (2SCSR) approach, three types of portfolios are used as test assets. These are 25

LSIZE-LBTM portfolios; 100 FIN_FLEX portfolios, and 64 LSIZE-LBTM-FIN_FLEX

portfolios, where the portfolio returns are value-weighted monthly returns. Kim and Qi

(2010) note that the use of portfolios as test assets helps induce variations in returns and

118 3.2.4.2 Characteristics versus covariance test

Daniel and Titman (1997) argue that characteristics dominate the covariances. For

example, the book-to-market ratio characteristic remains a significant determinant for

subsequent returns even after controlling for the covariances. The authors prove this by a

characteristic versus covariance test that make it possible to distinguish whether

characteristics or factor loadings predict returns. DT finds that as expected returns do not

positively correlate with the factor loadings after controlling for characteristics; factor

loadings do not predict returns. Thus, it is characteristics that predict the returns and this

effect is due to investor mispricing of stocks. However, there is wide criticism over DT’s

approach being biased against covariances. For example, Zhang (2005) and Lin and Zhang

(2013) argue that the measurement errors in covariances (betas) are responsible for their

demise against the characteristics. The covariances are generally estimated using rolling

regressions of 36 or 60 months that induce the time-lag between the covariances and

portfolio formation and lead to the reduction of covariances’ ability to predict returns.

Moreover, Lin and Zhang (2013) argue that the reversal of sorting order in the DT test from

first characteristics and then covariances to first covariances and then characteristics, would

weaken the characteristics’ substantially and relatively enhance the predictive power of

covariances.

3.2.4.3 Fama and MacBeth’s (1973) cross-sectional regressions

To further investigate the properties of both characteristics and corresponding factor

loading and to strengthen arguments in favour of either the risk-based or characteristics-

119 regressions. First of all, it tests both characteristic and factor loading separately to examine

whether they significantly predict the subsequent excess returns or not. Second, including

both of them together in one regression, helps in observing whether characteristics subsume

the factor loading return predictive power (supporting the mispricing doctrine) or factor

loading survives the test and remains significantly positive (supporting the risk doctrine).

Finally, keeping control variables in place that are the FF3 risk factors and past six month

return characteristic BHRET6; the factor loading is estimated through time-series

regressions over 60 months or requiring at least 24 months, using a four-factor model that

is Fama and French’s (1993) three-factor model augmented with the financial flexibility

factor (FLEX) (see equation 2).

3.2.4.4 Financial flexibility and information uncertainty

The interpretations about a certain factor’s candidature as a risk factor or merely a

mispriced characteristic may vary based on the nature of the information environment. The

risk doctrine asks for no effect of risk environment on return generating pattern. On the

contrary, the mispricing doctrine documents that the variation in return generation is

expected with a variation in the quality of the environment. Precisely, the cost of capital

increases with the degradation of the information quality (Easley and O'hara, 2004).

Consistently, Armstrong et al. (2011) find a positive relationship between firms’ cost of

capital and information asymmetry. The degradation of information quality also magnifies

120 In the case of this study, the greatest reduction (increase) in financial flexibility is

coupled with higher (lower) expected returns. If FLEX echoes the risk, this particular trend

should persist irrespective of the changes in the information environment. On the other

hand, the FLEX premium would amplify (reduce) in an (a) opaque (transparent)

information quality environment, if FLEX echoes the mispricing. Current literature echoes

mispricing more than risk when information is uncertain. Time information is highly

uncertain the longer underreaction to analyst forecast revision and the momentum effect is

observed (Zhang, 2006), investor sentiments effect the assets that are difficult to arbitrage

and if they are valued subjectively (Baker and Wurgler, 2006). Because, the information

uncertainty poses substantial impediments to arbitrage and corrective trades (Hirshleifer,

2001).

To test the information uncertainty effects on FIN_FLEX, this research presents the

mean returns and the factor model regression alphas on the portfolios ranked on various

information uncertainty measures and the FIN_FLEX. It borrows four information

uncertainties from Zhang (2006) and Durate and Young (2009), literature that include

inverse of market value of equity (1/MV), inverse of firm age (1/AGE), the probability of

informed trading (PIN), and the firm cash flow volatility (CFVOL).

3.3 Descriptive statistics, correlation matrix, and relationship of financial