Default Risk and Equity Returns

Default Risk and Equity Returns

- A comparison of the Z-score model and the Naïve EDF model

By

Kun Shan (1361465)

University of Groningen, Faculty of Economics Msc Business Administration (Finance)

E-mail: S. Kun@student.rug.nl

September 29th, 2006

Abstract:

In this paper, I examine the relationship between default risk and one year lead stock returns in the US stock market for the period from 2000 to 2005. Using the accounting based Z-score (Altman 1968) model and the market-based Naïve EDF model (Merton 1974), I test and compare the capacity of two different models to predict the expected stock returns. Results demonstrate that the Naïve EDF model provides significantly more information about the default probability than the Z-score model. In addition, the business cycle plays an important role for the relationship between default risk and equity returns. During the recession period, firms with higher bankruptcy risk earning lower stock returns, the relationship, however, is only at a 10% significance level. The result of firms with higher default risk earn higher stock returns is much more prominent and significant during the post-recession period. Moreover, the effects of firm size and book-to-market are powerful predictors of stock returns, but it is not clear how they could be related to some sort of a firm distress risk factors.

Key words: Default risk, Stock returns, Z-score, Naïve EDF, business cycle

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Table of contents

1. Abstract 1

2. Table of Contents 2

Chapter 1 Introduction 3

Chapter 2 Literature Review 6

2.1 The Z-score model vs. The Merton option price model…...6

2.1.1 The Z-score ………6

2.1.2 The Merton option price model………..7

2.1.3 Predictability of different default risk models………8

2.1.4 Bridging two approaches………..10

2.2 Empirical evidence………...11

2.3 Conclusion………..13

Chapter 3 Data Description and Methodology………...16

3.1 Data Description………..16

3.2 Methods and Hypotheses ………18

3.2.1 Z-score model (Altman 1968)………...18

3.2.2 Naïve EDF Model………20

Chapter 4 Results……….23

4.1: Estimation of the default risk………...23

4.2: Default probability and Equity returns………26

4.3: Regression analysis……….29

4.3.1 Regression analysis (Z-score and Stock returns)………...29

4.3.2 Regression analysis (Naïve EDF and Stock returns)……….31

4.4 Robustness checks………...33

4.4.1 Outlier adjustment ………33

4.4.2 Business Cycle………...35

4.4.3 Z’’-score (non-manufacturing firms)……… 39

4.4.4 Continuity and Spilt samples……… 41

Chapter 6 Discussion and Conclusion………....45

3. Reference. 46

CHAPTER ONE

-Introduction-

Default refers to various events of financial distress including missing debt payments, debt reorganization, filing for bankruptcy protection and liquidation (Garlappi Shu and Yan 2006). Distress (default) risk is a term in corporate finance used to indicate a condition when promises to creditors of a company are broken or honored with difficulty. It has long been argued in the empirical asset pricing literature that the cross-section of stock returns is related to risk factors associated with systematic financial distress, little attention has been paid to the effects of default risk on equity returns (Vassalou and Xing 2004). According to asset pricing theory, stock investors demand a premium for investing in firms with high risk of default as a compensation for bearing the non-diversifiable risk, consequently, high default risk should be associated with high expected returns in cross sectional tests (Vassalou and Xing 2004, Garlappi Shu and Yan 2006).

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(1973) for valuing European options. The equity of a firm is viewed as a call option on the firm’s assets, the strike price of which is the debt level. A firm goes bankrupt when the market value of its assets falls below its debt obligations to outside creditors.

The stock price of the firms with higher default risk should be discounted to enable the investors to earn higher expected returns. Using different measures of probability of default, the existing empirical literature has failed to produce consistent evidence to confirm the above conjecture. Recent papers show that companies with higher probability of default earn lower stock returns (Dichev 1998, Griffin and Lemmon 2002, and Campbell, Hilscher and Szilagyi 2005), the negative relationship between default risk and stock returns can be explained by a mispricing argument, which is due to a high degree of financial distress information asymmetry. On the other hand, another set of papers draw the conclusion that there might be no significant relationship between default risk and expected returns (Oplter and Titman 1994). Shumway (1996) and Vassalou and Xing (2004) use the distance to default based on the Merton (1974) model to conclude that default risk is systematic risk and positively priced in stock returns. All in all, the aforementioned studies generalize different results of the relationship between default risk and stock returns, with applying different default risk measures.

relationship between default risk and stock returns controlling for firm size and the book-to-market equity ratio.

In this paper, I find that firms with high default risk are not rewarded by high stock returns when using the Z-score model as a proxy for a firm’s probability to default. In fact, there is no significant relationship between Z-score and expected stock returns in the US stock market for the sample period between 2000 and 2005. This paper also finds that higher default risk firms, implied by NEDF model, earn higher returns than low default risk firms in the US market in the same sample period. The coefficient on NEDF is highly significant than the coefficient on Z-score in the multivariate regression. This result demonstrates that the market-based NEDF model provides significantly more information about the probability of default than the Z-score model. In addition, during the entire sample period, the US economy and stock market went through tremendous changes, so additional tests attempt to consider the business cycle effects, and in doing so I divide the entire sample period into two sub-periods - the recession period and the post-recession period. The post-recession period is based on the definition of the US National Bureau of Economic Research (NBER). Further investigation reveals that the business cycle is an important factor to determine the relationship between default risk and equity returns. During the recession period, firms with higher bankruptcy risk earn lower stock returns, the relationship, however, holds only at a 10% significance level. The result of firms with high default risk earning high stock returns is much more prominent and significant during the post-recession period at a 1% significance level. This result indicates that default risk is regarded as systematic risk in the post-recession period, but unsystematic during the recession period, it could signify that the market does not fully impound the available financial distress information. Thus, the most insolvent firms earn lower returns when this negative information is eventually embedded in prices (Dichev 1998).

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methodology and data used in this paper. In Chapter Four, I give the regression results of the relationship between default risk and stock returns, and report the robustness checks. I conclude in Chapter Five with a summary and discussion of my results.

CHAPTER TWO

-Literature Review-

The first part of this Chapter will present the review of the development of the Z-score model (Altman 1968) and the Merton option price model (1974) associated with their extensions. Then, the assessment of the performance of different models in bankruptcy prediction will be shown. This part will also discuss the possibility to improve predictive accuracy by bridging the Z-score and Merton models. Second, I will briefly discuss the existing empirical evidence on the relationship between default risk and stock returns. Finally, I will give a conclusion of this chapter.

2.1 The Z-score model vs. The Merton option price model

I focus exclusively on the scoring models and the structured models. The Z-score (Altman 1968) model and the Merton (1974) option pricing model have been widely applied in practice and academic research (for reviews see Altman 1993, Bharath and Shumway 2004 and Garlappi, Shu and Yan 2006).

2.1.1 The Z-score model

The early studies concerned with bankruptcy predication using financial ratios were ascended to the 1930’s1. The researches conclude that failing firms exhibit significantly different ratio measurements than continuing entities (Beaver 1967). However, the signal ratio is too simplistic to capture the complexity of financial failure. The combination of financial ratios analysis and statistical technique was pioneered in papers by Beaver (1967) and Altman (1968). The Z-score model, the first scoring model, was developed by Altman (1968), which is based on multiple discriminant analysis (MDA), selects five financial ratios, and is weighted differently to attribute a credit score to public listed firms. The five ratios are: working capital/total assets, retained earnings/total assets, earnings

1

before taxes and interest/total assets, market value of equity/book value of total liabilities, and sales/total assets. MDA is a statistical technique used to classify an observation into one of several a prior groupings (Altman 1968). MDA approach is the most appropriate technique for the bankruptcy study, and by far the largest numbers of multivariate accounting based credit-scoring models have been based on discriminant analysis models (Altman and Saunders 1998).

A limitation of Altman (1968) is that the firms examined in the paper were all publicly held manufacturing corporations. The subsequent studies have extended the model to private firms (Z’ model), to non-manufacturing entities (Z’’-model), and also refer to emerging markets (Altman et al 1995). In response to the increased size of business failures, new database setting, and new financial reporting standards, Altman, Haldeman and Narayanan (1977) construct a second generation model (ZETA-model) with seven variables, and test linearly and in a quadratic fashion. In general, the new ZETA model is shown to improve upon Altman’s earlier model (Altman 1998). However, ZETA is a proprietary model which is not publicly available. These models allow several ratios and financial data to be considered simultaneously and provide descriptive statistics for the estimated parameters. Table 1 gives a summary of the development of different forms of the Z-score model.

Table 1

The development of the different forms of Altman's Z-score model Model Target firms Formula

Z-Score(1968) Publicly manufacturing firms Z = 1.2*X1 + 1.4*X2 + 3.3*X3 + 0.6*X4 + 1.0*X5

Z' Private firms Z' = 0.72*X1 + 0.85*X2 + 3.11*X3 + 0.42*X4 + 1.0*X5

Z" (1995) Emerging markets FIRMS Z" = 6.56*X1 + 3.26*X2 + 6.72*X3 + 1.05*X4 ZETA (1977) Manufactures and retailers a proprietary effect, can not disclose the parameters X1: Working capital/ Total assets;

X2: Retained earnings/Total assets; X3: EBIT/Total assets

X4: Market value of equity/Book value of total liabilities (Z': Book value of equity instead) X5: Sales/Total assets

Notes: In a emerging market model, they added a constant term of 3.25 so as to standardize the score of zero (0) equated to a D(default) rated bond. The Z-Score is a well-known statistical predictor of

- 8 - 2.1.2 The Merton option pricing model

The market value of assets is a very powerful default predictor since it is an indicator of a firm’s economic prosperity and distress (Black and Cox 1976, Davydenko 2005, Bandyopadhyay 2005). Merton (1974) proposed a structural model for calculating probabilities of default from market data, which is a direct application of the Black-Scholes model (1973) for valuing European options. The equity of a firm is viewed as a call option on the firm’s assets. The reason is that equity holders are residual claimants on the firm’s assets after all other obligations have been met. The strike price of the call option is the book value of the firm’s liabilities. A firm goes bankrupt when the market value of its assets falls below its debt obligations to outside creditors (Saunders and Allen 2002). In the Merton model, the market value of a firm’s asset (A) and its volatility (σ) are not directly observable. Under the model’s assumptions both can be inferred from the value of equity, the volatility of equity and several other observable variables by solving two nonlinear simultaneous equations. Once this numerical solution is obtained, the distance to default (DD) can be calculated as the gap between the mean asset value and the value of the debt, normalized by the standard deviation of the asset value. The distance to default (DD) defines by how many standard deviations should the log of the ratio of the firm’s assets to its book value of debt deviate from its mean for default to occur. It means the shorter this distance, the greater the probability of default. The theoretical distribution implied by Merton’s model is the normal distribution. The corresponding theoretical probability of default, sometimes called the EDF, is

EDF = ( (ln( / ) ( 0.5 ) )) ( ) 2 DD T T D V V V =Ν − − + − Ν σ σ µ

A popular implementation of the Merton (1974) model was developed by the Moody’s KMV Corporation in the late 1980s, which we refer to as the KMV-Merton model until KMV was acquired by Moodys in 2002. In the KMV-Merton model, there are two key theoretical relationships; the first one is that the value of equity can be viewed as a call option on the value of a firm’s assets. Second is the theoretical link between the observable volatility of a firm’s equity value and its asset value volatility.

2.1.3 Predictability of different bankruptcy risk models

Academics and practitioners have recently discussed the ability of default risk models to capture default risk2. In general, there are two approaches to assess the probability of default in the default risk literatures. The first one relies on prediction-oriented tests to discriminate between firms that go bankrupt and firms that remain solvent within a particular (typically one-year) time horizon. Prediction accuracy is assessed by comparing the total Type I and II error rates for each alternative specification, and the model with the lowest total error rate is deemed the best (Scott 1981). Altman (1993) demonstrates that his Z-score model predicts correctly 24 out of 25 bankrupt firms and 52 out of 66 nonbankrupt firms. Bandyopadhyay (2005) reveals that the Merton model has the capacity to discriminate between the defaulted and solvent firms. The second approach is to compare the performance of alternative default measures using relative information content tests (Hillegeist et al 2004). The tests of Hillegeist et al, (2004) are based on how well each probability of default measure explains the variation in the actual probability of default using a discrete hazard model3. An important advantage of using a discrete hazard model to compare model performance is to allow us to determine whether differences in performance are statistically significant. Duffie and Singleton (2003) show that the KMV-Merton model has a significant predictive power in a model of default probabilities over time, and can generate a term structure of default probabilities. Moreover, some papers demonstrate that the market-based Merton model provides

2

The models are discussed in Duffie and Singleton (2003) and Saunders and Allen (2002).

3 β α β α t i it X t X t t i e e p , ) ( ) ( , 1 + + +

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significantly more information about the probability of default than the Z-score model (Bandyopadhyay 2005, Hillegesit et al 2004).

2.1.4 Bridging two approaches

This paper focuses on two default risk measures, the accounting-based Z-score model and the market-based Merton model, due to their widespread use in the existing literatures (see table 2).

Table 2

Empirical result summary of default risk and stock returns

No. Authors Market Period Model Control variable

1 Dichev (1998) US market 1981-1995 Z-score and O-score MV, B/M

2 Xu and Zhang (2003) Japan Market 1980-2000 Z-score and O-score MV, B/M, Beta

3 Griffin and Lemmon (2002) US market 1965-1996 O-score MV, B/M

4 Campbell, Hilscher, Szilagyi (2005) US market 1963-2003 Logit model CAPM B/M

5 Vassalou and Xing (2004) US market 1971-1999 Merton (1974) MV, B/M

6 Shumway (2001), US market 1962-1992 hazard ratio market size

7 Lorenzo, Tao and Hong (2005) US market 1969-2003 KMV (EDF) B/M H-index, beta

Results:

(1): High bankruptcy risk, High expected stock return. (No 2,3,5) (2): High bankruptcy risk, low expected stock return. (No.1,4,7) (3): no significance relationship. (No.6)

Shumway 2004). In table 3, I give a brief summary of comparing the difference of features, prediction performance, and problems of the two approaches.

<Table 3>

- 12 - 2.2 Empirical evidence

Plenty of research effort has been put toward default risk and corporate debt valuation and derivatives products (Evans and Giola 1991, Madan and Haluk 1994), yet little attention has been paid to the effects of default risk on stock returns. The effect that default risk has on equity returns is not obvious, since equity holders are the residual claimants on a firm’s cash flows and there is no promised nominal return in equity (Vassalou and Xing 2004). If default risk is systematic, basic economic intuition implies that investors would demand a premium for investing in firms with high risk of default and, consequently, high default risk should be associated with high expected returns in the cross section (Garlappi, Shu and Yan 2006). However, the existing empirical results on the relationship between default risk and stock returns have failed to produce consistent evidence to confirm the above conjecture. In fact, some papers imply that bankruptcy risk could be positively related to systematic risk, which means the firms with high default risk earn higher than average returns (Lang and Stulz 1992, Denis and Denis 1995, Shumway 1996). However, Oplter and Titman (1994) suggests that default risk is unrelated to systematic risk, and is mostly due to idiosyncratic factors. Interestingly, Dichev (1998) and Griffin and Lemmon (2002) are using accounting-based models, Ohlson’s O-score (Ohlson 1980) and Altman’s Z-score (Altman 1968) to proxy for the likelihood of default. They find that firms with a high probability of bankruptcy tend to earn low average returns and suggest that this evidence is indicative of equity markets mispricing distress risk. This result is confirmed by Chava and Jarrow (2002) and Campbell, Hischer, and Szilagyi (2005), using the resulting forecasting measure of default probability and hazard model approach to proxy for the default risk. However, Xu and Zhang (2003) show a positive relationship between default risk and stock returns in the Japanese stock market, using the same methodology as Dichev (1998) for the US stock market.

practice. Vassalou and Xing (2004) provide the first study to employ the Merton option pricing model to construct a metric for default probability to mimic the EDF measure. It provides evidence that default risk is systematic risk, and that stocks with higher default risk tend to command higher expected returns. Garlappi, Shu and Yan (2006) was the first paper to analyze the relation between bankruptcy risk and stock returns, using the market-based measure of Expected Default Frequency (EDF TM) constructed by Moody’s KMV, and they found that higher default probabilities are not necessarily associated with higher expected stock returns. This finding complements the existing evidence using alternative measures of default risk and it is suggestive of cross-sectional variations in the relationship. Moreover, an alternative source of information for calculating default risk measures is the bond market. Previous studies that examine the effect of default risk in equities focus on the ability of the default spread to explain or predict returns (Vassalou and Xing 2004). However, much of the information in the default spread is proven unrelated to default risk (Elton et al 2001). This paper will not discuss the details of this model.

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were rewarded by higher returns. Pre-1980 evidence suggests that there is no reliable relation between bankruptcy risk and returns that could explain the size effect in earlier years (Dichev 1998). To isolate the effect of firm size, book-to-market equity ratio on stock returns that might be correlate with our variables, this paper examine the relationship between default risk and stock returns controlling firm size (market value of equity) and book-to-market equity ratio in a multivariate regression analysis.

2.3 Conclusion

CHAPTER THREE

-Models and Hypotheses- 3.1.1 Z-score model (Altman 1968)

This study investigates the empirical relation between default risk and stock returns. Measures of default risk are derived from existing researches. For comparison and sensitivity analysis I use two different models of ranking firms on the probability of bankruptcy. The first measure is derived from Altman’s (1968) Z-score model, which is probably the most popular model of bankruptcy prediction and has been extensively used in empirical research and in practice4. The implicit concept of the Z-score model is a default probability forecasting model. The Z-score is calculated using fiscal year-end data and is used to measure the risk of bankruptcy over the twelve month period beginning four months after a firm’s fiscal year end (Hillegeist et al, 2004). As it turns out, the Z-score model gives investors a good snapshot of corporate financial health and can be the prior warning system for the operating conditions of borrowers on specific horizons.

The Z-score (1968) model based on multiple discriminant analysis, selects five financial ratios out of an initial out of twenty-two potential ratios, and is weighted differently to attribute a credit score to manufacturing firms. The ratios are chosen on the basis of their (1) observation of the statistical significance of various alternative functions; (2) evaluation of inter-correlations between the relevant variables; (3) observation of the predictive accuracy of the various profiles; and (4) judgment of the analyst (Altman 1968).

The discriminate function of Altman’s Z-score model is given by; Z = 1.2*X1 + 1.4*X2 + 3.3*X3 + 0.6*X4 + 1.0*X5

In which

X1 = Working capital/total assets, X2 = Retained earnings/total assets,

X3 = Earnings before interest and taxes/total assets, X4 = Market value equity/book value of total liabilities,

4

X5 = Sales/total assets, and

“Working capital/total assets”: Working capital is defined as the difference between current assets and current liabilities. Liquidity and size characteristics are explicitly considered. Therefore if a firm experiences operating losses this will shrink the ratio of current assets to total assets and in its turn lower the working capital.

“Retained earnings/total assets”: Retained earnings are the earnings flowing back into the company or in other words the total amount of reinvested earnings and/or losses of a firm. If a firm is in trouble it is likely to have negative earnings and thus retained earnings will diminish or become even negative.

“Earnings before interest and taxes/total assets” This ratio is calculated by dividing the total assets of a firm into its earnings before interest and tax reductions. Since a firm’s ultimate existence is based on the earning power of its assets, this ratio appears to be particularly appropriate for studies dealing with corporate failure.

“Market value equity/book value of total liabilities” Equity is measured by the combined market value of all shares of stock, preferred and common, while debt includes both current and long-term.

“Sales/total assets”: It is a standard financial ratio illustrating the sales generating ability of the firm’s assets. In fact, because of its relationship to other variables in the model, the ratio ranks high in its contribution to the overall discriminating ability of the model. Overall, these five accounting ratios combine to capture the firm characteristics related to bankruptcy such as liquidity, profitability, productivity, solvency and sales generating abilities (Altman 1968).

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stock returns by directly employing the Z-score (1968) model for the period from year 2000 to 2005. Since the bankruptcy risk is not the only variable that may predict future stock returns, I will also include two control variables, namely firm size and book-market equity ratio, which have been found to have predictive power of stock returns in the literature (Fama and French, 1992, 1993, Chen Roll, and Ross, 1986). The regression model is as follows: t i t i t i t i t i Z ME B M R,+1 =α1+α2 , +α3ln( ), +α4( / ), +ε ,

Based on the regression model, the following hypothesis is examined in this paper,

Hypothesis 1: Firms with higher probability of bankruptcy implied by the Z-score model

earn higher average stock returns in the US stock market from year 2000 to 2005.

3.1.2 Naïve EDF Model

In Merton’s (1974) model, the equity of a firm is viewed as a call option on the firm’s assets:

Value of a default option on a risky loan = f (A, B, r, σ, τ)

There are five factors. A is the market value of firm’s assets, B is the level of firm’s debt, r is the short-term interest rate, σ is the variability in future market value of assets, τ is the time horizon (default horizon) for the loan. In general, three variables (B, r, and τ) on the right side of above equation are directly observable. B, the default exercise point, is taken as the value of any proportion of total debt outstanding that is of interest of the user. r is a matched risk-free Treasury rate. The maturity variable (τ) can be altered according to the default horizon of the analyst; most commonly, it is set equal to one year. Symbolically, the Merton model stipulates that the equity value of a firm satisfies:

) ( ) ( 1 2 0 0 V N d De N d E = − −rT (1)

T T r D V d V V σ σ /2) ( ) / ln( 0 2 1 + + = , d2 =d1−σV T

Under Merton’s assumptions the value of equity is a function of the value of the firm and time, so it follows directly from Ito’s lemma that,

0 0 V V E E _V E σ σ ∂ ∂ = σEE₀ =N(d₁)σVV₀ (2)

The model makes use of two important equations. The first equation (1) is the value of a firm’s equity as a function of the value of the firm. The second one (2) relates the volatility of the firm’s value to the volatility of its equity. They need formulate a simulation equation combining equation (1) and (2) numerically for values of V and σ.

Bharath and Shumway (2004) construct a “feasible” Merton model, called the Naïve EDF model (NEDF) without solving the simultaneous nonlinear equations required by the KMV-Merton model. The NEDF model can be estimated and implemented by researchers that can not subscribe to Moody’s KMV. The feasible model avoids simultaneously solving any equations or estimating any difficult quantities in its construction. This model has also been employed by Vassalou and Xing (2004). A simple NEDF model captures the same information that the KMV Merton predictor uses, and has a reasonable chance of performing as well as the KMV-Merton predictor (Bharath and Shumway, 2004). In my empirical investigation I use the NEDF model, which adapts the Merton (1974) framework to make it suitable for practical analysis. To begin constructing the naive probability, they approximate the market value of each firm’s debt with the face value of its debt, Naïve D = F, and approximate the volatility of each firm’s debt as Naïve σD = 0.05 +0.25 * σE . 0.05 in this term to represent term structure volatility, and 0.25 times equity volatility to allow for volatility associated with default risk. The formula is estimated or optimized by the historical data.

An approximation to the total volatility of the firm of

) * 25 . 0 05 . 0 ( E E D E V F E F F E E Naive NaiveD E NaiveD NaiveD E E Naiveσ σ σ σ + σ + + + = + + + =

Next, they set the expected return on the firm’s assets equal to the firm’s stock return over the previous year,

- 20 - T Naive T Naive r F F E NaiveDD V V σ σ ) 5 . 0 ( ] / ) ln[( + + − 2 = , NaiveEDF=Ν( NaiveDD− )

This NEDF model is easy to compute-it does not require solving the equations simultaneously-yet it retains the structure of the KMV-Merton distance to default and the expected default frequency. It also captures approximately the same quantity of information as the KMV-Merton probability (Bharath & Shumway 2004).

In the topic of the relationship between default risk and stock returns, only few recent papers are using the market-based option pricing model as proxies for corporate bankruptcy risk. Vassalou and Xing (2004) is the first and most important paper, because their metric for default probability and is comparable and similar with the NEDF model. They provide evidence that default risk is systematic risk, and that stocks with higher default risk tend to command higher expected returns. My investigation adds to the body of evidence and helps clarify the empirical regularity on this issue. Investors would suggest a positive association between bankruptcy risk and subsequent realized returns. This paper examines the empirical relationship between default risk and expected stock returns by employing NEDF model for my sample year from 2000 to 2005. The regression model is as follows:

t i t i t i t i t i EDF ME B M R_,+1 =α₁+α_{2 ,} +α₃ln( )_, +α₄( / )_, +ε_, t i t i t i t i t i EDF ME B M R,+2 =α1 +α2 , +α3ln( ), +α4( / ), +ε,

Based on the regression models above, the following hypotheses are examined in this paper,

Hypothesis 2: Firms with higher probability of bankruptcy implied by the NEDF model,

earn higher average stock returns in the US stock market from 2000 to 2005.

increasing number of bankrupt firms may have changed the original coefficients. The model is thus likely to under predict certain sorts of bankruptcy. On the other hand, the Merton model provides guidance about the theoretical determinants of bankruptcy risk, and uses a measure of asset volatility, which is a critical variable in bankruptcy prediction. The assumptions in the Merton model may also introduce errors and biases in to the bankruptcy prediction, but, in the paper of Hillegeist et al (2004), they suggest that researchers should use the Merton model instead of the traditional accounting based measures as a proxy for the probability of bankruptcy. My following hypothesis is given as,

Hypothesis 3: The coefficient on NEDF is more significant (t-statistics) than the

coefficient on Z-score in the multivariate regression in explaining the relations between default risk and expected stock returns.

-Data Description and Methodology- 3.2 Data Description

This section presents the raw data and their sources, and explains how I construct my database for required variables in the models. The information on the firm’s accounting and market data are obtained from Value Line Database5, which tracks more than 7000 publicly listed firms in the US stock market. The stock price information is from both the COMPUSTAT Industrial File and Value Line Database. Prior studies stated that Altman’s Z-score model is derived for industrials (Altman 1993, Dichev 1998 etc), so I only include firms with Standard Industrial Classification (SIC) codes 1000 to 5910 and 7000-9975, excluding financial firms’ codes 6000 to 6730. The primary sample is all the non-financial firms listed on the US stock market for the period of 2000-2005. The research is concerned with the 2000-2005 years because, with the burst of the Internet bubble in the early 2000s and the recession period in 2001, the United States has witnessed a spate of personal and business bankruptcy filings not seen since the early 1990s. In 2002, the total number of bankruptcy filings reached a record 1.6 million, of which 37,548 were business bankruptcy filings. In 2002, the total asset value of the top ten business filings alone amounted to $291.7 billion, compared with slightly under $100

5

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billion in 1991 for all public company filings combined (Matthew 2003). The National Bureau of Economic Research (NBER) has declared the recession period from 2001 to 2002 in the US. Xu and Zhang (2003) divide the entire sample period into three subperiods: the pre-bubble period, the bubble period, and the post-bubble period. The six years period study in this paper can examine whether the relationship between default risk and stock returns evolves over time. On the other hand, I only can get the database from 2000 to 2005 due to the access limitation of database source. The 1980s and 1990s databases are only available with expensive payments. The final sample consists of 19833 firm-year observations representing an average of 3500 firms in six years (see table 5).

Table 4 Summary Statistics

This table shows sample statistics for all variables used in the predicting models, The sample has 19833 yearly observations and covers form 2000 to 2005. It reports the mean, median, min & max, and standard deviation of all variables at the Z-score, Naïve EDF and control variables.

Variables Model Mean Median Min Max Std

WC/TA Z-score 0,26 0,23 -0,61 0,99 0,23

RE/TA Z-score -0,03 0,02 -5,63 2,23 0,28

EBIT/TA Z-score 0,07 0,10 -3,79 1,56 0,22

MV/TL Z-score 104,05 4,01 0,00 36072 977,73

S/TA Z-score 1,09 0,91 0,00 17,80 0,94

Naive D Naive EDF 1235,83 69,71 0,10 275333 7854,45

NaiveσD Naive EDF 0,19 0,16 0,06 12,71 0,27

NaiveσV Naive EDF 0,45 0,35 0,03 40,99 0,86

Naive DD Naive EDF 2017,53 4,49 -20,23 2967748 54377,65

Ln(MV) Control 5,65 5,71 -3,42 12,78 2,42

B/M Control 3,64 0,53 0,00 5556,42 105,60

In most cases the mean and median are reasonably close, and it applies to four out of five financial ratios in the Z-score model, only MV/TL (Market value equity/book value of total liabilities) is different. The mean value is 104.05, but the median is only 4.01. The minimum and maximum are highly variable, suggesting the presence of significant outliers. The variables embedded in the NEDF model also have significant outliers’ problems. Variables with substantial outliers can distort relationships and significance tests. I use an outlier controlling method –transformations- in the robustness tests.

CHAPTER FOUR

-Results -

This paper tests these hypotheses in three ways. First, I will present the descriptive statistics and correlation matrix for the test variables, which offer preliminary evidence about the relations between the test variables. Second, I will give the time-series regressions of the stock returns on the measures of bankruptcy risk. Third, I carry out additional tests along four dimensions (outlier problem, business cycle, alternative models, and split samples) to check the robustness of my results.

- 24 -

Table 5 reports the summary statistics of the Z-score (1968) and naïve EDF measure in US stock market for the entire sample period from year 2000 to 2005. Each sample year I give descriptive statistics for the cross-sectional distribution: the mean, standard deviation (Std) and the quartiles of the distributions (first and third quart) of the risk measures.

Table 5. Descriptive statistics of the bankruptcy risk.

Table 5 presents descriptive statistics of the Z-score (1968) and NEDF, my sample period spans from year 2000 to 2005. The table reports the number of firms in my sample, the mean, standard deviation, median, first and third quartile of the Z-score and NEDF distribution. NEDF are expressed in percent units.

Panel A: Summary statistics of the Z-score (1968) measure (2000-2005)

Year # Firm Mean Std. median Quart 1 Quart 3

2000 3004 78,12 690,61 3,86 2,27 9,07 2001 3084 62,80 561,34 3,97 2,29 9,46 2002 2977 39,89 288,26 3,60 2,08 7,96 2003 3797 65,06 541,54 4,22 2,24 10,21 2004 3558 67,90 450,58 5,13 2,78 13,17 2005 3413 81,74 986,84 5,24 2,74 12,53 Total 19833 65,92 586,53 4,34 2,40 10,40

Panel B: Summary statistics of the EDF measure (2000-2005)

Year # Firm Mean Std. median Quart 1 Quart 3

2000 3004 5,71 0,11 0,14 0,00 5,80 2001 3084 6,20 0,12 0,13 0,00 6,04 2002 2977 7,60 0,14 0,24 0,00 8,80 2003 3797 3,18 0,09 0,00 0,00 3,05 2004 3558 2,28 0,08 0,00 0,00 0,04 2005 3413 2,76 0,10 0,00 0,00 0,06 Total 19833 4,62 0,11 0,09 0,00 3,97

lower probability of bankruptcy and a higher NEDF signifies a higher probability of bankruptcy, so both Z-score and NEDF illustrate that the probability of bankruptcy is relatively high during the period from 2000 to 2002 and relatively low during the period from 2003 to 2005.

Figure 1: Z-score & Naïve EDF

Figure 1 plots the time series of the average Z-score and NEDF measure from year 2000 to 2005. More significantly, the distribution of the Z-score is quite similar to the NEDF model. The correlation between the Z-score and NEDF is quite high at 63.6%, and it is significant at the 1% level. Moreover, Figure 1 also shows the probability of bankruptcy increasing from year 2000 to 2002, and decreasing from year 2003 to 2005.

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2003). The shaded areas on the graph report NBER recession periods. The absolute value of correlation coefficient between Z-score and business cycles is 76.4%, and that value is 81.2 % between NEDF and business cycles. It means that the probability of bankruptcy corresponds to business cycles, and during the economic recession period, both the Z-score and EDF appear to decrease, and recover after the recession period. This trend lends credence to the argument that default risk is systematic and should be priced in market securities (Garlappi and Shu, Yan 2006).

4.2 Default risk and Equity returns

In this part, descriptive statistics for the test variables are given. Since the default risk is not the only variable that may predict future stock returns, I will also include firm size and book-to market ratio to explain the stock returns. But as the main objective, our emphasis is on the relationship between the bankruptcy risk and stock returns when controlling for size and book-to market equity ratio.

Table 6: Descriptive Statistics and Correlation Matrix for the Test Variables

Panel A: Summary statistics of the Test Variables (2000-2005)

Variables Mean StdD P1 P5 P95 P99 Returns 0,18% 2,35 -45,57% -31,13% 123,33% 236,64% Z -(1968) 65,92 586,53 -0,10 1,05 162,53 1154,06 NEDF 4,60% 0,11 0,00% 0,00% 27,14% 48,40% MV 5,65 2,42 0,04 1,64 9,57 11,18 B/M 3,73 107,35 0,03 0,09 2,95 11,27

Panel B: Recession Period (2000-2002)

Variables Mean StdD P1 P5 P95 P99 Returns -14,29% 3.45 -56,78% -35,99% 134,99% 278,91% Z -(1968) 60,27 513,40 -0,17 0,96 131,34 996,42 NEDF 6,49% 0,12 0,00% 0,00% 35,49% 49,99% MV 5,55 2,34 0,67 1,87 9,46 11,18 B/M 6,03 199,23 0,04 0,11 4,03 13,08

Panel C: Post-Recession Period (2003-2005)

Panel D: Pearson Correlation Coefficients(2000-2005) Returns Z-(1968) NEDF MV B/M Returns 1,000 Z -(1968) -0,006 1,000 NEDF 0,031 -0,045 1,000 MV -0,060 0,063 -0,365 1,000 B/M -0,008 -0,016 0,254 -0,207 1,000

Table 6 presents the descriptive statistics and correlation matrix for the test variables. The t-statistics in the multivariate regressions provide the formal tests of statistical significance. Panel A in table 6 reports the mean, median, standard deviation, and percentiles (1st and 99th, 5th and 95th percentiles) of test variables. Stock Returns are the average annual returns for all sample firms listed in the US stock market. Probabilities of bankruptcy scores are denoted as Z and NEDF. Higher values of Z-score signify lower probability of bankruptcy and higher values of NEDF indicate higher probability of bankruptcy. Firm size (Ln (MV)) is the log of the fiscal-year-end price times the number of shares outstanding. B/M is book value of equity divided by fiscal-year-end price times number of shares outstanding. Panel B and Panel C illustrate the same descriptive statistics for the recession period (2000-2002) and the post-recession period (2003-2005). Panel D displays a Person correlation matrix for all test variables, which offer preliminary evidence about the relations between the test variables.

The average value of score is 65.92, which is an abnormal number. If the Altman Z-score is above 3.0, the company is considered “safe” based on financial figures only, and if the Z-score below 1.8, probability of financial catastrophe is very high (Altman, 1968). The average value of the Z-score in Dichev (1998) is 5.31 and, the huge gap is due to the accounting reporting standards and the significant outliers’ problem in the database. The standard deviation of the Z-score is 586.53, which is quite high. As expected, the Z-score and NEDF are negatively correlated (-0,045) as the Z-score is a measure of financial strength and NEDF is a measure of financial distress. However, this is a very small figure, hardly different from no-correlation. The correlation between the average yearly Z-score and average yearly NEDF from 2000 to 2005 is quite high at -0,6366. The correlations between Z, NEDF, MV and B/M are consistent with the size and the book-to-market

6

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effects being related to some form of firm distress captured in default risk: Firms with higher default risk tend to be smaller and have higher book-to-market. The correlation between Z and stock returns is negative, and NEDF and stock returns is positive, which in line with the higher default risk associated with lower than average stock returns.

Figure 2: Average Naïve EDF & Stock Returns

- 30 - 4.3 Regression analysis

To test whether the default risk plays a role in the time-series of returns by itself and with other variables, this paper runs the cross-sectional regressions of stock returns (in year t+1) on firm size, book-to-market equity ratio and the default risk measures, jointly and separately. The univariate regression illustrates the interdependencies among default risk measures, size effect and book-to-market equity ratio in explaining security returns. Table 7 presents the regression parameters with t-statistics for the entire sample period from 2000 to 2005, using the Z-score (Altman, 1968) and the Naïve EDF model (Merton, 1974) as measures of default risk.

Table 7 Cross-sectional regression of returns on Z-score, Naïve EDF, size and B/M

The table reports the coefficient estimates of the cross-sectional regression of returns on the default risk measures, size and B/M, where Z and NEDF are the measures of the default risk, Returns is the average yearly returns (in percent) at fiscal-year-end (t+1). The entire sample has 19833 yearly observations. Regressions are OLS regressions with six years cross sections. The t-statistic (numbers in parentheses) is the average coefficient dividend by its standard error.

Entire sample period (2000-2005)

Model Intercept Z-(1968) ln(ME) B/M NEDF R2

1 2,8992 -0,0002 0,0007 (7,24)*** (-0,38) 2 -1,0933 -0,0004 0,7086 0,0009 (-1,08) (-0,65) (4,32)*** 3 2,8999 -0,0002 -0,0002 0,0001 (7,24)*** (-0,38) (-0,11) 4 -1,0992 -0,0004 0,7095 0,0002 0,0009 (-1,09) (-0,65) (4,32)*** -0,12 5 3,219 -7,6681 0,0002 (7,49)*** (-2,08)* 6 3,219 0 -7,6687 0,0002 (7,49)*** -0,01 (-2,07)* 7 -0,7793 0,6659 -2,2654 0,0009 (-0,68) (3,79)*** (-0,57) 8 -0,7836 0,6668 0,0002 -0,2859 0,0009 (-0,69) (3,79)*** -0,13 (-0,58)

Notes: 10% significance level (*), 5% significance level (**), 1% significance level (***)

4.3.1 Regression analysis (Z-score and stock returns)

returns (score is a measure of financial strength). However, the coefficient of the Z-score is not significant in multivariate regression. The slope coefficient on Z-Z-score appears small, which is due to the large magnitude of these measures. In addition, the size effect (Ln (ME)) is positive and significant with B/M and Z-score to explain the stock returns at a 1% significance level in the multivariate regression. However, the book-to-market equity ratio is negative and insignificant in all the regressions. The multivariate regression results show that the relationship between one year lead stock returns and default risk, implied by the Z-score model, is insignificant during 2000 to 2005.

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returns. During the sample period I cover from year 2000 to 2005, the US economy and stock market went through tremendous changes. An official panel of senior economists has declared that the US entered recession in March 2001 (The National Bureau of Economic Research (NBER), 2003). In the following robustness tests, I will separate the sample to test the effect of business cycle on the relationship between default risk and stock returns.

Three possibilities are presented with different interpretations in the existing literature. If the relationship between the expected stock returns and default risk is found to be significant positive, the default risk is regarded as a priced systematic risk. If the relationship is found to be insignificant, the default risk is interpreted as being idiosyncratic and diversifiable. If the relationship between the expected stock returns and default risk is found to be significant negative, the only plausible interpretation is the market inefficiency (Xu and Zhang, 2003). This paper finds an insignificant relationship between default risk and stock returns for the US stock market from year 2000 to 2005, using Z-score model. Opler and Titman (1994) and Asquith, Gertner, and Sharfstein (1994) showing that there might be no significant positive relationship between default risk and expected returns. The insignificant association between default risk and returns could be explained by idiosyncratic factors, which suggests that default risk is unrelated to systematic risk. The idiosyncratic factors including large asset sells, including merger, composition of debt, are as the important determinant of the outcome of financial distress (Asquith, Gertner, and Sharfstein, 1994).

4.3.2 Regression analysis (Naïve EDF and stock returns)

The NEDF model is introduced by Vassalou and Xing (2004) and discussed by Bharatha and Shumway (2004). This method can be estimated and implemented by academic researchers or practitioners that can not subscribe to Moody’s KMV. Vassalou and Xing (2004) constructed default likelihood indicators (DLI) for individual firms using equity data, to assess the effects of default risk on equity returns. The Fama-MacBeth regressions results show that default risk is systematic risk, and that stocks with higher default risk tend to command higher expected returns from year 1971 to 1999. Default likelihood indicators are nonlinear functions of the default probabilities of the individual firms. They are calculated using the contingent claims methodology of Merton (1974). The NEDF method, in the paper, is a simplified KMV-Merton model with strict assumptions. Moreover, Vassalou and Xing (2004) get the daily market values for firms from the CRSP daily files, which is different than the Value Line database in this study. In addition, strictly speaking, both the NEDF and DLI method are not an accurate default probability because they do not correspond to the true probability of default in large historical samples. In contrast, the default probabilities calculated by KMV are indeed default probability because they are calculated using the empirical distribution of defaults. Garlappi, Shu and Yan (2006) using the market-based EDF database from Moody’s KMV found the higher default probabilities do not consistently lead to higher expected stock returns.

- 34 - 4.4 Robustness checks

4.4.1 Outlier adjustment

Variables with substantial outliers can distort relationships and significance tests. Outlier removal is straightforward in most statistical tests. However, it is not always desirable to remove outliers. The Analyses by Osborne (2001) show that removal of univariate and bivariate outliers can reduce the probability of Type I and Type II errors and distort accuracy of estimates. In this paper, I use an outlier controlling method which is known in many statistical textbooks as the “transformations” method. Dichev (1998) and Vassalou and Xing (2004) apply this method as well, when controlling for outliers. To abstract from the influence of extreme outliers, I set all observations higher than the 95th percentile of each variable to that value, and replace any observation below the 5th percentile with the 5th percentiles. Table 8 presents the new regression parameters after the outliers’ adjustment with t-statistics for the entire sample period from 2000 to 2005.

Table 8: Regression Results after controlling outliers

The table reports the coefficient estimates of the cross-sectional regression of returns on the default risk measures, size and B/M after controlling outliers. The outliers set at 5th percentile and 95th percentile. The entire sample has 19833 yearly observations. Regressions are OLS regressions with six years cross sections. The t-statistic (numbers in parentheses) is the average coefficient dividend by its standard error.

Entire sample period (2000-2005)

Model Intercept Z-(1968) ln(ME) B/M NEDF R2

1 0,3403 0,0004 0,0003 (45,93)*** (2,63)*** 2 0,2928 0,0004 0,0085 0,0008 (15,99)*** (2,40)** (2,84)*** 3 0,3902 0,0002 -0,0602 0,0025 (36,63)*** -1,19 (-6,51)*** 4 0,3987 0,0002 -0,0012 -0,0621 0,0024 (15,51)*** -1,18 (-0,36) (-5,86)*** 5 0,3475 0,0384 0,0001 (47,36)*** -0,47 6 0,397 -0,0846 0,4095 0,0034 (41,78)*** (-8,19)*** (4,39)*** 7 0,2797 0,0112 0,1529 0,0006 (13,41)*** (3,47)*** (1,73)* 8 0,3876 0,0014 -0,0829 0,4163 0,0034 (15,25)*** -0,4 (-7,42)*** (4,39)***

After controlling the outliers, the slope coefficients of the Z-score are positive in all of the regressions, and at a 1% significance level in the univariate regression. However, the coefficient of the Z-score is still not significant in multivariate regression. In addition, the size effect is positive and significant with Z-score to explain the stock returns at a 1% significance level, but it becomes negative and insignificant in the multivariate regression. The book-to-market equity ratio turns robust in all the regressions. The multivariate regression results confirm that the relationship between one year lead stock returns and default risk, implied by the Z-score model, is insignificant during year 2000 to 2005 after outlier controlling. This result rejects my hypothesis 1 of firms with higher probability of default implied by Z-score earns higher stock returns.

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the volatility of a firm’s assets in calculating its default risk. It contains forward-looking information, which is better suited for calculating the likelihood that a firm may default in the future.

The multivariate regression results show only the Book-to-market equity ratio explains the next year equity returns with a 1% significance level. This is confirmed in tests where only default risk measures and Book-market ratio are considered. The size effect is positive and significant with default measurements to explain the stock returns at a 1% significance level, but it becomes negative and insignificant in the multivariate regression. Fama and French (1996) observe that high book-to-market firms tend to be relatively distressed, coming from a persistent period of negative earning, suggesting that size and in particular book-to-market capture a firm’s level of financial distress: Firms with higher default risk tend to be smaller and have higher book-to-market equity ratio, earn higher stock returns. Vasslou and Xing (2004) also find that high-default-probability firms with a small market capitalization and a high book-to-market ratio earn high returns. My result confirms that firm size and B/M factors capture some of the default-related information.

4.4.2 Business cycle

of distressed firms are more sensitive to unexpected changes in relevant economy-wide factors. More distressed firms could be more severely affected by economy-wide factors. Denis and Denis (1995) and Vassalou and Xing (2004) show that default risk is related to macroeconomic factors and that it varies with the business cycle. For the sake of the analysis, we divide the entire sample period into two subperiods with in 2000 to 2005; first, the recession period from 2000 to 2002 and second, the post-recession period from 2003 to 2005.

Panel B and C in table 6 report the descriptive statistics for the two sub periods. During the recession period, the mean value of average returns is -14.29%. The average return sharply increased to positive 14.65% in the post-recession period. The default measurements are consistent with the trend of average stock returns. Both the Z-score and the NEDF illustrate that the probability of default is relative high during the period from 2000 to 2002 and relative low during the period from 2003 to 2005. It means, in the recession period, the firms in the US stock market were exposed to high default risk and earn low equity returns, likewise, firms exhibited low default risk with high stock returns in the post-recession period. The changing characteristics of the US economy motivate us to examine whether the relationship between default risk and stock returns evolves over time.

- 38 -

Table 9: Business cycle effects on the relationship between default risk and stock returns

The table reports the coefficient estimates of the cross-sectional regression of returns on the default risk measures, size and B/M after controlling outliers, where Z and NEDF are the measures of the default risk, Returns is average yearly returns (in percent) at fiscal-year-end t. The outliers set at 5th percentile and 95th percentile. The recession period (Panel A) has 9064 yearly observations. The post-recession period (Panel B) has 10769 yearly observations. Regressions are OLS regressions with six years cross sections. The t-statistic (numbers in parentheses) is the average coefficient dividend by its standard error.

Panel A: Recession Period (2000-2002)

Model Intercept Z-(1968) ln(ME) B/M NEDF R2

1 0,5101 0,0001 0,0001 (36,63)*** (0,39) 2 0,2707 0,0004 0,0441 0,0063 (7,83)** (1,21) (7,56)*** 3 90,783 0,0008 -0,1322 0,008 (8,46)** (2,31)* (-8,55)*** 4 _{0,4797 0,0008 0,0239 -0,0973 0,0093} (9,11)** (2,24)* (3,42)*** (-7,14)*** 5 0,5563 -0,8715 0,0047 (38,01)*** (-6,53)*** 6 0,6235 -0,0100 -0,3984 0,0081 (33,02)*** (-5,61)*** (-2,53)** 7 _{0,3552 0,0328 -0,5196 0,0074} (8,31)** (5,00)*** (-3,45)*** 8 0,4773 0,0212 -0,0761 -0,2835 0,0091 _{(9,01)** (2,95)*** (-3,89)*** (-1,75)*}

Panel B: Post-Recession Period (2003-2005)

Model Intercept Z-(1968) ln(ME) B/M NEDF R2

1 0,1901 -0,0012 0,0066 (29,46)*** (-8,43)*** 2 0,2668 -0,0012 -0,0135 0,0091 (16,81)*** (-8,70)*** (-5,29)*** 3 0,245 -0,0009 -0,0835 0,0132 (26,92)*** (-6,63)*** (-8,53)*** 4 0,4365 -0,0009 -0,0282 -0,1306 0,0224 (20,67)*** (-6,29)*** (-10,04)*** (-12,08)*** 5 0,2004 0,6349 0,0048 (32,92)*** (7,20)*** 6 _{0,2716 -0,135 10,521 0,0208} (33,64)*** (-13,28)*** (11,32)*** 7 0,2468 -0,0078 0,5595 0,0056 (14,53)*** (-2,93)*** (6,09)*** 8 0,4333 -0,0244 -0,1706 0,9249 0,0276 _{(21,04)*** (-8,62)*** (-15,60)*** (9,86)***}

Panel A of Table 9 presents the regression results for the recession period. During the recession period, the Z-score is positively related to stock returns and the NEDF is negatively related to stock returns in the multivariate regressions. Because a high Z-score signifies low probability of default and a high EDF signifies high probability of default, so this result indicates firms with higher default risk earn lower stock returns in the recession period, however, the result is only significant at a 10% significance level. In fact, the 10% significance level of Z-score in the multivariate regressions is disappeared without the control variables. On the other hand, there is a significant and negative relationship between the NEDF and stock returns in the univariate regression, but the t-statistics of NEDF become somewhat weaker when combined with all other variables. In addition, both size effect and B/M ratio are significant at the 1% significance level in all tests. This indicates that the size effect and B/M contain the default risk information. For the post-recession period, the regression results in Panel B of table 9 tell a different story. The positive relationship between the default risk and stock returns is much more prominent during this sub-period. When the default risk measures are combined with other firm-specific variables in the regression model, the average slope of absolute value on Z-score is 0.0009 with a t-statistics of 6.29, and the average slope on NEDF is 0.9249 with a t-statistics of 9.86. Both of them are significant at a 1% significance level. This result indicates firms with higher default risk earn relative higher stock returns during the post-recession period. During the sub-periods, the size effect and book-to-market effect are all strong and robust in all tests. Overall, the default risk measures, the size and the book-to-market ratio are all helpful in explaining the expected stock returns in post-recession period.

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time-series variation seems to correspond to business cycles, and during the economic down cycles the distribution of the EDF measure appears to widen. In this paper, although the relationship between default risk implied by Z-score model and expected stock returns is insignificant for the entire sample period, the sub-periods analysis indicates that the entire sample is generally a weighted average of the results for the two sub samples. The post-recession regression result, the positive relationship between the NEDF and expected stock returns, is much more prominent for the entire period. In fact, this is an important finding. It is based on the observation that default probabilities are linked to the economy. When the economy worsens, default risk increase; when the economy becomes stronger, default decrease. In other words, default risk follow business cycles closely. One possible explanation of firms with higher default risk earning a lower stock return in the recession period can be the market inefficiency: Market efficiency suggests that, at a given time, prices fully reflect all available information on a particular stock and/or market. It could signify that the market does not fully impound the available financial distress information to explain the stock returns. Thus, the most insolvent firms earn lower subsequent returns when this negative information is eventually embedded in prices (Dichev, 1998). On the other hand, the positive relationship in the post-recession period means that when anticipating the default risk of some firms, investors should expect higher stock returns for compensation. However, the sub-period results are inconsistent with a distress explanation for the size and the book-to-market effects, the relationship between default risk and book to market and size effect are not monotonic.

4.4.3 Z’’-score (non-manufacturing firms)

control for this industry effect to capture the business risk. The X5 (Sales/Total Assets) ratio in the Z-score model (1968) is believed to vary significantly by industry. It is likely to be higher for merchandising and service firms than for manufacturers, since the former is typically less capital intensive (Eidleman, 1995). Consequently, nonmanufacturers would have significantly higher asset turnover and Z scores. The model is thus likely to underpredict certain sorts of bankruptcy. To correct for this potential defect, Altman recommends the following correction that eliminates the X5 ratio:

Z" = 6.56*X1 + 3.26*X2 + 6.72*X3 + 1.05*X4

In this part, I carry out an additional test to check the robustness of my result, which using Z’’ instead of Z-score (1968). This is an important concern because my sample data contains 88 industries, including the non-manufacturer industries, like Internet and Advertising. Panel A of Table 10 presents the regression parameters with t-statistics for the entire sample period from 2000 to 2005.

Table 10: Industry and business control

The table reports the coefficient estimates of the cross-sectional regression of returns on Z’’, size and B/M. The entire sample (Panel A) has 19833 yearly observations. The recession period (Panel B) has 9064 yearly observations. The post-recession period (Panel C) has 10769 yearly observations. Regressions are OLS regressions with six years cross sections. The t-statistic (numbers in parentheses) is the average coefficient dividend by its standard error.

Panel A: entire period (2000-2005) with outliers (0,05,0,95)

Model Intercept Z'' ln(ME) B/M R2

1 328,479 13,399 0,0003 (62,14)*** (2,53)** 2 0,2933 0,0002 0,0085 0,0007 (16,03)** (2,30)** (2,84)*** 3 0,3909 0,0001 -0,0604 0,0025 (36,82)*** (1,09) (-6,53)*** 4 _{0,3994 0,0001 -0,0013 -0,0622 0,0025} (15,56)** (1,08) (-0,37) (-5,89)***

Panel B: Recession Period (2000-2002)

Model Intercept Z'' ln(ME) B/M R2

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_{(9,12)** (2,31)** (3,43)*** (-5,27)***}

Panel C: Post-Recession Period (2003-2005)

Model Intercept Z'' ln(ME) B/M R2

1 0,1909 -0,0007 0,0064 (29,72)*** (-8,35)*** 2 0,2678 -0,0007 -0,0135 0,009 (16,89)*** (-8,64)*** (-5,30)*** 3 0,2458 -0,0005 -0,0836 0,0131 (27,10)*** (-6,56)*** (-8,54)*** 4 0,4375 -0,0005 -0,0283 -0,1308 0,0223 _{(20,75)*** (-6,25)*** (-10,06)*** (-12,10)***}

Notes: 10% significance level (*), 5% significance level (**), 1% significance level (***)

In the multivariate regressions for the entire sample period, the sign of the coefficient of Z” is positive, though not significant; it is only significant in the univariate test and with the size effect variable. The sub-periods analysis in Panel B and C of Table 10 uncovers certain patterns of the relationship between default risk and stock returns using the Z-score model. There is a positive relationship between Z’’ and stock returns in the recession period with a 5% significance level, and a negative relationship in the post-recession period with a 1% significance level. In fact, the relationship of firms with high default risk earn low returns is more significant than when using the Z-score model during the recession period. Dichev (1998) finds that firms with high default risk earn significantly lower than average returns since 1980 in the US market, indicating the most insolvent firms earn lower subsequent returns when this negative information is eventually embedded in prices during the recession period.

4.4.4 Continuity and Random selections

corporation on a particular stock market. For most stock symbols, the letters are simple identifiers. One-or two- letter symbols always trade on the New York Stock Exchange (NYSE), three letter codes may trade on either the NYSE or American Stock Exchange (AMEX), Four- and five-letter codes trade on the NASDAQ. This paper chooses the sample firms by random ticket symbol selecting in the US stock market. By using random sampling, the likelihood of bias is reduced. Each individual firm is chosen entirely by chance and each firm of the population has an equal chance of being included in the sample. Table 11 presents the regression parameters with t-statistics for the first 300 randomly selected sample firms. The other two samples are reported in the Appendix.

Table 11: First 300 firm’s sample

The table reports the coefficient estimates of the cross-sectional regression of returns on Z-score, Naïve EDF, size and B/M. The entire sample (Panel A) has 1500 yearly observations. The recession period (Panel B) has 750 yearly observations. The post-recession period (Panel C) has 750 yearly observations. Regressions are OLS regressions with six years cross sections. The t-statistic (numbers in parentheses) is the average coefficient dividend by its standard error.

Panel A: Entire period (2000-2005)

Intercept Z-(1968) ln(ME) B/M NEDF R2

0,0547 -0,0023 0,0103 (5,36)** (-3,95)*** 0,1816 -0,0021 -0,0201 0,0247 (6,29)** (-3,49)*** (-4,69)*** -0,0527 -0,0009 0,1689 0,0218 (-1,26) (-1,48) (5,65)*** -0,0527 -0,0009 0,0012 0,1576 0,0611 (-1,26) (-1,48) (0,25) (7,62)*** 0,0065 0,8479 0,0265 (0,69) (6,39)*** -0,0739 0,1461 0,4010 0,0647 (-5,35)** (7,81)*** (2,82)*** 0,0961 -0,01317 0,6918 0,0318 (2,94)* (-2,88)*** (4,83)*** -0,0916 0,0023 0,1501 0,4156 0,0648 (-2,22) (0,45) (7,26)*** (2,85)***

Panel B: Recession Period (2000-2002)

Intercept Z-(1968) ln(ME) B/M NEDF R2