India
University of Groningen
Faculty of Organization and Management Msc in Business Administration
Student: Zhe Nie
Number: 1504096
The first supervisor: Prof. Dr. B.W. Lensink
The co-accessor: Dr. I. J. Naaborg
First draft: June 2006
Second draft: August 2006
Acknowledgements
During my study period, I was strongly interest in the area of credit risk analysis. The interest for this subject resulted in the main research question of this thesis: what is the relationship between default risk and equity returns for the companies?
First, I am very grateful to Prof. Dr. B. W. Lensink for being my supervisor. He inspired me to connect the issue of credit risk with the context of group-affiliation, and provided me the data source. After each our meeting, his detailed comments and valuable suggestions helped me to improve my thesis significantly.
Further, I would like to thank my friends Marten Poutsma and Hans Schoonman for their useful comments and insightful suggestions.
Finally, I would like to thank my parents for supporting me to study in Groningen University so that I can improve myself in a new academic level.
Groningen, August 24, 2006 Zhe Nie
Group affiliation, Default risk and equity returns in
India
Abstract
This paper investigates the relationship between default risk and stock returns in the Indian stock market. Using the default probability measure Expected Default Frequency (EDF) based on an alternative KMV model, the results indicate that the expected stock returns are positively related to default probability for non-group-affiliated firms. However, the relationship between equity returns and default risk for group-affiliated firms is not statistically significant. Analysis indicates that the controlling shareholders’ debt renegotiation power and the internal market of business group plays an important role in explaining the different risk-return relationship between group-affiliated firms and stand-alone firms. The financially constrained group firms, in which controlling shareholders have strong power in debt negotiation, can resolve financial distress by means of out-of-court. Therefore, the default probabilities EDF do not adequately represent the true default risk for the group-affiliated firms. The results also show that although Fama-French factors SMB and HML contain some default-related information, this is not the reason that they can explain the cross section of equity returns.
Table of Content
1. Introduction ...5
2. Literature review ...7
2.1 The relationship between default risk and equity return...7
2.2 The risk-return relationship vis-à-vis group-affiliation ...8
3. Methodology and empirical model...10
3.1 Methodology ...10
3.2 The alternative KMV-Merton model ...12
4. Data and summary statistics ...14
4.1 Data collection and description ...14
4.2 Fitch rating results ...16
4.3 Fama-French Factors ...16
4.4 The overview of the portfolios ...18
5. Results ...20
5.1 Default probability and variation in equity return: sub-portfolio analysis...20
5.2 The result for the CAPM model ...21
5.3 The result of Fama-French model...23
5.4 Interpretation of the results...25
6. Conclusion...28
1. Introduction
Default is an important aspect of every firm’s life. Default refers to various events of financial distress including missing debt payments, debt reorganization, filing for bankruptcy protection and liquidation in the future (Garlappi et al 2006). It is important to know whether default risk is systematic. If default risk is systematic, one would expect a positive association between default risk and subsequent realized returns (Dichev 1998).
A widely held view among researchers is that the investors would demand a premium for investing in firms with high default risk. Indicating a positive relationship between default risk and equity returns. This is the so-called “risk-return trade-off” argument. On the other hand, the “market mispricing” argument suggests a negative relationship between default risk and equity returns. The common interpretation of this argument is that markets are less capable to fully assess the true risk embedded in a company when it faces default, so they do not require a high default risk premium to compensate for this risk. (Garlappi et al 2006)
One of the most important recent studies by Vassalou and Xing (2004) supports the view of “risk-return tradeoff”, and argues that default risk is systematic risk. Using Merton’s (1974) model, they compute monthly “default likelihood indicators” (DLI) for individual firms, and examine whether default risk is systematic through an asset-pricing test. Their results show that stocks with a high default risk likelihood earn significantly large positive abnormal returns. Even after controlling for the systematic risk by using Fama-French’s (1993) three-factor model, they find similar results. They argue that default risk is a variable worth considering in asset-pricing test, above and beyond size and BM.
In light of the study by Vassalou and Xing (2004), the aim of this paper is to follow their method of study to examine the relationship between default risk and equity returns in the Indian stock market. This study is the first attempt to provide empirical evidence about the effect of default risk on equity returns in an emerging country.
The relationship between default risk and equity return is more complex in the emerging countries. In the emerging economies, many private companies are affiliated to a business group (Lensink and Van der Melon 2005). Claessens et al. (2002) show that in nine Asian countries, there are on average 70 percent of all firms are affiliated to group. A group can be described as a corporate organization where a number of firms are linked through cross-ownership or where a
single individual, family or coalition of families owns a number of different firms (Claessens et al 2002). The main reason for the pattern of business group is that the market is less efficient in less developed countries, so the group’s practice of choosing new investments stems from an effort to alleviate risk and uncertainty (Leff 1978).
There are two reasons for choosing India as the subject of analysis. Firstly, the Indian economy is well developed compared to other emerging countries. The Bombay Stock Exchange (BSE) has been established in 1875, and is perhaps one of the oldest stock exchanges in Asia. The Indian stock markets have also demonstrated remarkable stability and resilience in general (Poshakwale 1996). Secondly, data is available. The database used can distinguish the group-affiliated companies and stand-alone companies clearly.
In this paper, I estimate the monthly default probability of Indian listed firms by using an alternative KMV model1 from the period 1998 to 2004. To investigate how default risk varies with equity returns for the firms with different characteristics, the stocks are sorted into portfolios based on size, book-to-market value and whether they are group-affiliated. Furthermore, an asset-pricing model is used to test whether default risk is systematic.
The results do not appeal to “the market mispricing” argument, and are in fact consistent with “the risk-return trade-off” argument. The default risk and equity returns are positively related for stand-alone firms. However, for group-affiliated firms, we do not find a statistical significant relationship between default risk and equity returns. The analysis suggests a crucial role of controlling shareholders of group-affiliated firms in debt negotiation, who can bargain with the creditors to resolve bankruptcy out-of-court when the member firms face financial distress; hence the default probability EDF does not adequately reflect the true risk embedded in group companies. On the other hand, for the stand-alone firms, whose shareholders do not have debt renegotiation power, the default probability is positively related to equity returns. The findings illustrate that the observed patterns are in fact consistent with the “risk-return trade-off” argument. In addition, by using the Fama-French model, the paper investigates whether
1 KMV is a trademark of KMV Corporation that was founded in 1989. The KMV model calculates the
Expected Default Frequency (EDF) based on the firm’s capital structure, the volatility of the assets returns and the current asset value. This model best applies to publicly traded companies for which the value of equity is market determined. http://www.ronalddomingues.com/index.php?lang=&s=risk&id=36
Fama-French factors SMB and HML2 proxy for default risk. The results show that they appear
to contain other significant price information that is unrelated to default risk.
The rest of the paper proceeds as follows. Section 2 gives a review about the existing empirical evidence on the relationship between default probability and stock returns. Moreover, the literatures about how default-risk relationship interacts with group-affiliations in emerging economies are also shown in this section. Section 3 describes the methodology of how to estimate the expected default frequency (EDF) by using an alternative KMV model. The construction of the data set and some descriptive statistics of the data are reported in Section 4. Section 5 presents the results of the regression analysis, and section 6 concludes.
2. Literature review
2.1 The relationship between default risk and equity return3
Several studies argue for a “risk return trade-off relationship”. Implying investors would demand a “risk premium” for investing in firms with higher default risk. Using Merton’s (1974) model, Vassalou and Xing (2004) mimic KMV’s EDF measure for default probability. Their results show a positive relationship between stock returns and default probability in the U.S. However, Da and Gao (2005) argue that some of the very high returns earned by small stocks with high default risk and a high book-to-market ratio are due to the illiquidity of these stocks. Garlappi et al. (2006) examine the relationship between default probability and stock returns by using a database of EDF produced by Moody’s KMV. Their results are consistent with “the risk return trade-off” argument. Moreover, they argue that the level of shareholder advantage has a strong impact on the relationship between default risk and equity return. They define the shareholder advantage as the combination of shareholders’ bargaining power and efficiency gained through bargaining. They argue that when the firm faces high default risk, the ability of shareholders with a stronger advantage to extract value from debt-holders leads to lower risk for equity, hence lower returns.
2 Fama-French factors SMB and HML stand for “small (cap) minus big”, and “high (book-to-market
value) minus low”, they measure the historic excess returns of small caps and “value” stocks over the market as a whole. More detail can be seen: http://www.moneychimp.com/articles/risk/multifactor.htm
3 The summary of the literatures about the relationship between default risk and equity returns can be seen in Table 1 in Appendix A
Contradictory to these previous studies there are also those who argue that when a firm experiences default, markets seem to be less capable of fully assessing the risk embedded in a company. And hence, do not demand a sufficiently high premium to compensate for the risk of default (Garlappi et al. 2006). Therefore suggesting a negative relationship between default risk and equity returns. For example, Dichev (1998) examines the relationship between bankruptcy risk and stock returns by using Ohlson’s (1980) O-score4 and Altman’s (1968) Z-score5 to
proxy for the default probability. Dichev (1998) finds that firms with high default risk earn lower than average returns. Concluding that the size and Book-to-market value effects are unlikely to proxy for a distress factor related to bankruptcy. Griffin and Lemmon (2002), also use Olson’s model and reach a similar result. Shumway (2001) estimates the bankruptcy probability by using a hazard model approach. Shumway finds that firms with a high default probability tend to earn a low average return. While the mispricing argument seems plausible, there are several concerns about the use of accounting models in estimating the default risk of equities. Hillegeist, Keaing, Cram and Lundstedt (2004) argue that both Z-score and O-score model are limited in their forecasting power. The information of accounting models is derived from financial statements, since financial statements aim to report a firm’s previous performance rather than future prospects, the information herein is inherently backward looking. More importantly, accounting models do not take into account the volatility of a firm’s assets in estimating its risk of default (Vassalou and Xing 2004).
2.2 The risk-return relationship vis-à-vis group-affiliation
Since this paper is the first attempt to investigate the relationship between default risk and equity returns in an emerging economy, there are no previous studies that examine this issue
4 The O-score model is a bankruptcy prediction model, which was developed by Ohlson in 1980. This
model identifies a company’s financial condition. It includes nine variables: size, total liabilities to total assets, working capital to total assets, current liabilities to current assets, dummy if total liabilities exceeds total assets, net income to total assets, operational funds to total liabilities, dummy if income was negative for the last two years and the change in net income.
5 The Z-score model is a multivariate formula for a measurement of the financial health of a company,
which was developed by Altman in 1968. This model combines five common business ratios: wording capital to total assets, retained earnings to total assets, market value of equity to market value of total liabilities and sales to total asset.
directly. However, through many previous literatures that focus on default risk and economic performance of group-affiliated firms, this relationship can be inferred indirectly.
The traditional view supports the idea that group-affiliation provides the benefit of risk-sharing to the member firms, hence the group-affiliated firms will have lower default probability than stand-alone firms. There are three reasons, which explain why business groups can provide risk-sharing to their member firms. The first explanation is that business groups enable member firms to share risks by smoothing income flows and reallocating money from one member firm to another. For example, Nakatani (1984) shows that the variance of operating profitability is lower for group-affiliated firms than unaffiliated firms in Japan. The second explanation is that diversification of business groups provides themselves with varied sources of income and allows them to spread their risks. Claessens et al (1999) study how corporate diversification policy interacts with the group affiliation in nine East Asian economies. They find that group-affiliated firms are more likely to diversify than independent firms, particularly in less-developed economies. The last explanation for this risk-sharing is that the ownership structure affects the resolution of firm financial distress. The controlling shareholders of group-affiliated firms have stronger debt renegotiation powers than that of stand-alone firms. When group-affiliated firms face financial distress, their controlling shareholders can renegotiate with creditors to resolve financial distress by out-of-court agreement. The study by Claessens et al. (2003) show that for the informational advantage of controlling shareholders and high legal cost in emerging countries, group-affiliated firms are less likely to file for bankruptcy then stand-alone firms in five Asian countries.
The complex ownership structures of group-affiliation may lead to great agency cost, which will negatively affect firm performance and firm value. As Johnson et al (2000) pointed out; controlling shareholders have an incentive to tunnel assets from group companies where they have low cash-flow rights to firms where they have high cash flow rights. In general the complicated owner structures of group-affiliated firms may lead to more severe agency conflicts. This “tunneling” argument is supported by a number of scholars. For instance, Bertrand et al. (2002) test the tunneling hypothesis by examining whether shocks propagate between firms in a business group in accord with the controlling shareholder’s ownership in each firm. They apply the methodology in Indian data and find a significant amount of tunneling, much of it occurring
via non-operating components of profit. Lensink and Van Der Molen (2005) examine the effect of group-affiliation in the Indian market. They find that the stock returns on group-affiliated firms are significantly lower than that of stand-alone firms, on average.
From the above literature, we know that group-affiliation can help member firms to alleviate financial distress, so the group firms may have lower default risk than stand-alone firms. On the other hand, the conflict between controlling shareholders and minority shareholders for group-affiliated firms can give rise to large agency costs, which may reduce firm value. The lower default risk and lower equity returns for group-affiliated firms may suggest that there is a positive linear relationship between default risk and equity returns.
3. Methodology and empirical model 3.1 Methodology
First, an estimate of the credit risk measurement EDF (expected default frequency) based on the alternative KMV model suggested by Bharath and Shumway (2004) will be given. This alternative is much easier to compute than the original KMV model. In order to verify the accuracy of the model, the default probability estimates are compared to the credit rating results of 45 Indian firms from the professional credit rating agency Fitch (the result can be seen in appendix A). It is expected that group-affiliated firms have lower default probability EDF than stand-alone firms, since group-affiliation provides risk-sharing to their member firms.
Hypothesis 1: group-affiliated firms have lower default probability than their independent counterparties in the Indian stock market.
Second, to give a clear overview of the relationship between default probabilities and stock returns for group-affiliated firms and stand-alone firms, a sub-portfolio analysis is performed. In the end of each year, the stocks are divided into portfolios sorted by their different characteristics: size, book-to-market-ratio, whether they are group-affiliated and their default probabilities. The equally weighted monthly returns are then presented.
Third, in order to test whether default risk is systematic risk, an asset-pricing model (CAPM) that includes the default risk measures EDF is estimated. An asset-pricing model, which includes only default risk factors would be miss-specified. Since even if default risk is priced, it is unlikely that
the default risk factor is the only factor that can explain equity returns. For this reason, a CAPM model, which includes the excess return on market portfolio and the expected default frequency (EDF), is used. From “the risk-return tradeoff” argument we know that the investors would demand a “risk premium” to compensate for the higher default risk they bare. Thus,
Hypothesis 2: In general, higher default probability would be associated with higher equity returns for all companies in Indian stock market.
In emerging countries, group-affiliation accounts for a large part of the economic activity, so it is important to examine the risk-return relationship for these group-affiliated firms. As mentioned in Section 2.2, group-affiliation provides risk-sharing to their member firms. They have lower default risk than their stand-alone peers. On the other side, the agency costs of group affiliation lowers firm value. Therefore, group-affiliated firms have lower equity returns than stand-alone firms. The lower default risk associated with these lower equity returns suggests that there is a positive risk-return relationship for Indian group-affiliated firms.
Hypothesis 3: Higher default probability would be associated with higher equity returns for group-affiliated companies in Indian stock market.
The stand-alone firms, who mainly rely on the external market, are more easily affected by external factors, such as the business cycle and the financial market. Thus, they have a higher default risk than group-affiliated firms. The shareholders of stand-alone firms do not own other firms, they do not have the ability to expropriate funds from one firm to another. As a result, stand-alone firms have higher default risk and higher economic performance than group-affiliated firms do. This suggests that there is a positive relationship between default risk and equity returns for Indian stand-alone firms.
Hypothesis 4: Higher default probability would be associated with higher equity returns for stand-alone companies in Indian stock market.
Finally, Since Fama and French (1996) argue that SMB and HML proxy for financial distress, this paper will examine whether the Fama-French factors, SMB and HML, do proxy for default risk. The Fama-French model including the default risk measures EDF are used. If SMB and HML include only default-related information, it is expected that in the presence of EDF, the
SMB and HML will lose their ability to explain equity returns because all default-related information is captured by the default risk factor EDF.
3.2 The alternative KMV-Merton model
The KMV model is based on the idea of Merton’s (1974) model, that the equity of the firm is regarded as a call option on the underlying value of the firm, with a strike price of the firm’s debt. When the value of the firm drops below its debt, the firm will default on its obligations. The expected default frequency (EDF) can be calculated from the option-pricing model based on the normal probability distribution assumption.
The KMV model has been accepted and is widely used by financial institutions. However, in this model neither the market value of the asset, nor the volatility of the firm can be observed directly. These two variables can be inferred from two non-linear simultaneous equations. A complicated iterative numeric procedure is required. Due to the complexity of solving these two simultaneous equations, it is difficult to be applied by most non-professionals. Bharath and Shumway (2004) introduced an alternative default probability model and it has been proven more accurate for forecasting default probability than the general KMV model
This simple alternative KMV model has the advantage that it does not need to solve the equations, thus, no iterative procedure is required. Furthermore, the study by Bharath and Shumway shows that the alternative model captures both the functional form and the basic inputs of the KMV-Merton model. Due to its simplicity and ease of use, this model is used to estimate the EDF for the sample firms.
Some additional assumptions are required for this alternative model. The first assumption is the market value of the firm’s debt equal to the face value of its debt:
Naïve D 6 = F (1)
The second assumption assumes there is an approximate relationship between the volatility of firm’s debt and firm’s equity. Since firms with higher proportion of debt have higher default risk, and the risk of their debt is correlated with the risk of the firm’s equity.
Naive
D = 0.05 + 0.25*
E (2)6 Since the alternative KMV model is also called naïve KMV model, so following the paper of Bharath
In equation (2), the magnitude of five percent volatility in the first term represents term structure volatility, the twenty-five percent times equity volatility is to allow for volatility associated with default risk (Bharath and Shumway 2004). It is worth to note that since Bharath and Shumway estimate the default risk probabilities for American firms, the coefficients might not be appropriate for the Indian firms. This problem may lead to less accurate results for estimating the default risk probabilities for the Indian firms.
An approximate total volatility of the firm’s asset is:
D E v Naive NaiveD E NaiveD NaiveD E E Naive
E
E
F E F F E E
* 25 . 0 05 . 0 (3)The naïve distance to default is:
T Naive T Naive r F F E NaiveDD v v t
2 5 . 0 / ln (4) Since the Merton model estimates the risk-neutral probability of default, another assumption is made. The underlying asset return (change in asset value) process has a mean return equity to the risk-free rate (Saunders and Allen 1999). In equation (4) rtequals risk-free rate in year t.The corresponding implied probability of default, the expected default frequency is then:
T Naive T Naive r F F E NaiveDD N EDF v v t
2 5 . 0 / ln ) ( (5) In equation (5),E= market value of the firm’s equity
F= face value of the firm’s debt measured by current liability plus half the long-term liability rt= risk-free rate
NaiveσV= the volatility of firm’s market value, calculated by equation (3)
T= time-to-maturity, in this paper T is set by one N () = the standard normal distribution
In the rest of this paper, I will use this alternative KMV model to estimate the default probability of listed Indian companies.
4. Data and summary statistics 4.1 Data collection and description
In my empirical investigation the main data sources are obtained from the Prowess dataset from the Center for Monitoring the Indian Economy (CMIE). This dataset contains detailed company profiles and financial information of over 8,000 Indian firms. The information on monthly average stock returns, monthly market capitalization, monthly return variance and firms’ liability information is used.
Following the method of the KMV model introduced by Saunders and Allen (2002), which uses the “current liability” plus half the “long-term liability”, is used as the book value of debt. According to Vassalou and Xing (2004), there are two reasons to include long-term liability in the calculations. The first reason is that firms need to service their long-term debt, and these interest payments are part of their shot-term liabilities. The second reason is that the size of the long-term liability affects the ability of firm to roll over its short-term liability, hence reduce its risk of default.
Book-to-market ratio is calculated as the inverse of the price-to-book ratio. Prowess identifies a company as affiliated to a group based on an analysis of company announcement and a qualitative assessment of the behavior of the firm in relation to the rest of the group7. As the
risk-free rate the monthly observation of the 1-year Indian Treasury Bill rate obtained from the DataStream is used.
All stocks listed on the Bombay Stock Exchange are classified into four categories (A, B1, B2 and Z) from most frequently traded stocks (A) to the least frequently traded stocks (Z). This paper will use only shares in the categories A and B1, to avoid detecting a spurious relationship between EDF and stock returns. Because, Da and Gao (2005) argue that the high returns earned by small stocks with high default risk and a high book-to-market ratio are due to the illiquidity of the stocks.
These two categories include 421 group-affiliated firms and 354 stand-alone firms. However, there are many missing observations in different variables, the stocks with missing observations are excluded from the dataset. To ensure that the statistical results are not heavily influenced by outliers, the observations higher than the 99th percentile of each variable are eliminated. After
the exclusion of these stocks, there are 234 group-affiliated firms and 160 stand-alone firms left in the dataset. The sample period is seven years from 1998 to 2004.
Table 1 in Appendix B presents the summary statistics for each variable of the sample. The average market capitalization of stand-alone firms is 1,829.898 with a median value of 767.895, both values are higher than that of group affiliated firms. Stand-alone companies also have higher debt value than their group-affiliated peers, for both average and maximum value. Group firms on average have lower debt value than that of stand-alone firms. This can be interpreted as such, that the group-affiliated firms can finance themselves more easily by using their internal financial channel, so the debt burden of group-affiliated firms is much lower than that of stand-alone firms.
The average book-to-market value for stand-alone firms is 1.455, which is lower than that of group-affiliated firms (1.955). Since the book-to-market value is calculated as the inverse of the P/B ratio, and the P/B ratio is similar to the Tobin’s Q ratio. In other words, the group-affiliated companies have on average a lower Tobin’s Q than stand-alone firms, which is consistent with the finding by Tarun Khanna and Krishna Palepu (2000).
The average equity return for all stand-alone firms is 17%, which is higher than 15.7% for group affiliated firms. Noticeable is that stand-alone firms also have higher equity return volatilities than group firms. The range of equity returns for stand-alone firms is from –9.12% to 54.55%, which is much larger than that for group-affiliated firms (from –7.98% to 14.7%.). The interpretation of this finding is that the less profitable group-affiliated firms can obtain financial assistance from other more profitable member firms, good performing group-affiliated firms share some of their fortune with their lesser successful group members, so the return difference between good performing firms and bad performing firms for group-affiliated firms is not as high as stand-alone firms.
The mean value of default probability EDF is 5.8% for stand-alone firms, which is slightly higher than the estimate of 5.7% for group-affiliated firms. It is surprisingly to note that although the theory states that group-affiliation provides risk-sharing, we cannot find significant differences in default probability EDF between group-affiliated firms and stand-alone firms.
4.2 Fitch rating results
In order to compare the default risk between group-affiliated firms and stand-alone firms from the point of view of professional credit rating agencies, Table 2 in Appendix B presents the credit rating results from Fitch for both group firms and stand-alone firms. Prowess provides the credit rating results of 85 debt issue companies (including 53 group-affiliated firms and 32 stand-alone firms) published by Fitch. After exclusion of all the financial firms8, only 45 firms
in Fitch’s rating overlap with the sample used in this paper, including thirteen stand-alone firms and thirty-two group-affiliated firms. The credit rating results are represented by different credit rating classifications, and these results are published at different points in time when the companies issue debt. The credit rating classification of Fitch ranges from AAA (the best creditworthiness) to D (the default category), totally twenty-four risk levels are being included. A corresponding score is assigned to each category. The AAA rating is assigned the score of one and since the lowest debt rating in the sample is BB-, the maximum score is 12 (the corresponding score for each credit rating classification can be seen in Table 2 of Appendix A). The higher the rating score, the higher the default risk of the debt issued by the companies. Table 2 also presents the corresponding EDF and stock returns of the companies.
Table 2 shows that the average Fitch credit rating score for stand-alone firms is 4.077, which is higher than that of group firms (3.563). This result indicates that stand-alone firms on average have higher default risk than group firms. The average EDF of stand-alone firms is also higher than the EDF of group-affiliated firms (0.052 against 0.04), which is consistent with the result from the Fitch’s rating. The average stock return of stand-alone firms is lower than the average stock return of group-affiliated firms by 0.7 percent.
4.3 Fama-French Factors
In order to conduct the subsequent asset-pricing test by using the Fama-French model, the Fama-French factors are constructed. The studies of Fama-French (1992, 1995 and 1996) show that the expected equity returns are related to firm’s characteristics, like size and book-to-market value. Fama and French’s three-factor model can successfully explain many
8 Since most financial firms are featured by high leverage ratio and low default risk, I exclude all financial firms in order to avoid spurious results.
abnormal returns that cannot be explained by the CAPM. The model states that the expected excess return of a portfolio can be explained by: 1) the excess return on market portfolio; 2) the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks; and 3) the difference between the return on a portfolio of high book-to-market stocks and the return on a portfolio of low book-to-market stocks. Since Fama and French (1996) argue that SMB and HML proxy for financial distress, this paper will examine to what extent the Fama-French factors are related to the default risk measure EDF.
There are in total 394 firms that are involved in the construction of FF factors, including 234 group-affiliated firms and 160 stand-alone firms. There are two reasons to why this paper constructs Fama-French factors by using the data sample of 394 firms instead of using the credit rating results from Fitch. Firstly, there is only credit rating information of 83 firms provided by Fitch, and some of the firms are not listed companies or illiquid stocks. Such a small sample size is not sufficiently enough to represent the whole Indian market. The second reason is that the credit rating results from Fitch were published at different points in time, when the firms issued debt. Therefore, they cannot be used to construct time-series data. Since the Fama-French factors are constructed by time series data, it is impossible to construct FF factors by using the credit rating results from Fitch. The 394 firms used are the most liquid stocks listed in the Indian market, and the time-series data of their different variables are calculated. It is therefore very convenient to calculate Fama-French factors by using the data sample.
The paper will follow the same procedure as Fama and French (1992). First, all the stocks in the sample are allocated into two categories, based on whether they are group-affiliated or not (the group-affiliated firm category and stand-alone firm category). At the end of each year from 1998 to 2004, for each category, the stocks are independently sorted into three equally populated groups according to their market capitalization (small size, middle size and large size). In each size group, the stocks are then sorted into three equally populated groups based on their book-to-market ratio (low B/M, middle B/M and high B/M). Therefore, 18 portfolios in total will be formed, based on the intersections of the group-affiliation, size and book-to-market ratio. SMB is the monthly difference between the average of the returns on the six smallest-stock portfolios (S/L, S/M and S/H for both group-affiliated firms and stand-alone firms) and the average of the returns on the six biggest-stock portfolios (B/L, B/M and B/H for
both group-affiliated firms and stand-alone firms). HML is the difference between the average of the returns on the six highest book-to-market portfolios (S/H, M/H and B/H for both group-affiliated firms and stand-alone firms) and the average of the returns on the six lowest book-to-market portfolios (S/L, M/L and B/L for both group-affiliated firms and stand-alone firms). The market excess return EMKT is calculated as the value-weighted return of whole stocks in the sample over the risk-free rate. The correlation coefficients between average default probabilities EDF and the Fama-French factors are presented in Panel A of Table 3 in Appendix B. The correlation coefficients of EDF with the EMKT and HML are very low. However, the correlation coefficient of EDF between SMB is positive and significant at the 10% level, this suggests that SMB contains potentially significant default-related information whereas EMKT and HML do not.
Panel B of Table 3 provides the results of time series regression between default probability EDF and the three Fama-French factors. We can see, although EDF has statistically significant positive relationship with SMB at the ten percent level, the adjusted R squares for all regressions are very low, which indicates that default probability EDF cannot explain a substantial portion of the time-variation in EMKT, SMB and HML.
4.4 The overview of the portfolios
Table 4 in Appendix B presents the descriptive statistics based on the sorted portfolios. In general, the firms seem to exhibit decreasing stock returns when the firm size increases. In each size category, average returns increase when BM ratio increases. The difference between stand-alone firms stock return and group-affiliated firms stock return is less clear. The stock returns of stand-alone firms outperform group-affiliated firms only in the small-cap portfolios. Stand-alone companies also have slightly higher average returns than group-affiliated firms in the highest BM portfolio within median and large cap categories.
The default likelihood measure EDF exhibits a similar trend as the stock returns. Small cap firms have the highest default probabilities on average, and EDF decreases as the firms’ size increases. In each size category, the highest EDF portfolio is associated with the highest B/M ratio, consequently if the EDF increases the BM ratio will also increase. However, in small cap category, stand-alone firms exhibit lower default probabilities than group firms. In the large cap
category, stand-alone firms show higher default probabilities than group firms.
This paper will follow the method by Lensink and Van der Molen (2005), to verify whether the differences of stock returns and EDF between stand-alone firms and group-affiliated firms are significant. First, the difference between the equally weighted average monthly returns for the two types of stocks (group-affiliated and stand-alone) at each point in time is calculated. The result is a time-series of differences in return. This can be seen as the return on holding a long position in group-affiliated firm shares and a short position in stand-alone firm shares (Lensink and Van der Molen 2005). In table 5, this portfolio is denoted as GRMINSA. The same method is also applied for comparing the EDF differences between group affiliated and stand-alone firms. To investigate return and EDF differences between group-affiliated and stand-alone firms in more detail. This paper not only compares the return and EDF differences between all group-affiliated firms and all stand-alone firms, but also compares these differences within each size category.
Second, the differences in return between group-affiliated firms and stand-alone firms are compared based on the 18 constructed portfolios. The differences between group-affiliated firms and stand-alone firms are computed as the differences between average returns and EDF on the nine group-affiliated portfolios and the average returns and EDF on nine stand-alone portfolios. There is a time-series difference again, which is denoted by GMS.
In Table 5 in Appendix B, Panel A shows the differences in stock return between group-affiliated firms and stand-alone firms. For all firms, the mean value for both GMS and GRMIMSA are less than zero, these differences are not statistically significant. Therefore it cannot be concluded that the stock returns of all stand-alone firms are on average higher than that of all group-affiliated firms. However, in the small-cap category, the mean value of both GMS and GRMINSA are less than zero and these differences are significant at the 10 percent level, which means that the return of group-affiliated firms are lower than that of stand-alone firms in the small cap category.
Panel B demonstrates the difference on default probability EDF between group-affiliated firms and stand-alone firms in the whole sample and in different size categories. For all firms, the EDF mean value of GMS is negative and statistically significant, implying that group-affiliated firms have lower default probability than stand-alone firms when they are sorted into portfolios.
The mean value of GRMINSA is only -0.001 percent and it is not statistical significant. Although the result of GRMINSA may imply that the default probabilities of group-affiliated firms is not statistically different from that of stand-alone firms, I also conclude that the group-affiliated firms in overall have lower default probability than stand-alone firms. The first reason for this conclusion is that in section 4.2, the group-affiliated firms also have lower default risk than stand-alone firms when default risk is measured by Fitch credit rating results. The second reason is that default probability measure EDF cannot capture some risk-sharing information of business group, so its result cannot adequately represent the true risk embedded in group-affiliated firms. The further explanation will be given in section 5.2.
In the small cap category, the mean value of EDF on the GMS and GRMINSA are all significantly higher than zero, which means group-affiliated firms have a higher default probability than stand-alone firms in the small cap category. While the mean value of EDF on GMS and GRMINSA is significantly lower than zero in the medium and the large cap categories, which indicates that group-affiliated firms have lower default probability than stand-alone firms in the medium and the large cap category.
The results presented in Table 4 and Table 5 is really interesting. On one hand, we can see that in general the higher stock returns are associated with the higher default probability. This result seems consistent with the “the risk return trade-off” argument. On the other hand, in the small cap category, the group-affiliated firms have lower expected return than stand-alone firms, but they have higher default risk than stand-alone firms. Due to these contradictory results some questions arise: is this result violating the risk-return trade-off relationship? Since I sort portfolios by the firm size, does the size effect bias the results? To answer these questions, I will give further insight in the next section by sub-portfolio analysis.
5. Results
5.1 Default probability and variation in equity return: sub-portfolio analysis
To investigate the relationship between default probability and equity return for group-affiliated firms and stand-alone firms in more detail, portfolios of stocks according to each firm’s EDF in each year will be analyzed. At the end of each year in the period 1998 to 2004, the stocks are sorted into portfolios based on their most recent monthly default probabilities (EDF).
Table 6 in Appendix B presents the average equity returns, EDF values, size and Book-to-market ratio’s of the portfolios that are sorted based on the default probability measurement EDF, the lower the average EDF the lower the default risk. First, the EDF difference in panel A (for stand-alone firms) and panel B (for group-affiliated firms) will be examined. In panel A, the EDF difference between high-default-risk portfolios and low-default risk portfolios is 0.218 percent. This is a little bit higher than the high-low EDF difference of group-affiliated firms (0.205) in panel B. The high-low EDF differences for both stand-alone firms and group-affiliated firms are all statistical significant at the one percent level. Second, the equity return differences of the portfolios in Panel A and Panel B will be examined. In Panel A for stand-alone firms, the equity return difference between the equally weighted high-default-risk portfolio and the low-default-risk portfolio is 20.8 percent per month. This difference is statistically significant at the one percent level. However, this is not the case for the group-affiliated firms in Panel B, whose equity return difference is only 7.8 percent per month, which is not statistically significant.
From the results in Table 6, it can be seen that the EDF difference between the high-risk-portfolio and the low-risk-portfolio for stand-alone firms is similar to that of group-affiliated firms (0.218 versus 0.205). However, the equity return difference between the high-risk-portfolio and the low-risk-portfolio for stand-alone firms is much higher than that of group-affiliated firms (0.208 versus 0.078). It seems that the stock return and default risk vary monotonically for stand-alone firms, but not for group-affiliated firms. Table 6 also shows that the average BM increases when the default risk of the portfolio increases, and that the average size increases when the default risk of the portfolio decreases. These results imply that the size and BM effect might be linked to the default risk of stocks.
5.2 The result for the CAPM model
In the section above, the results indicate that the stock returns seems positively related to the default risk of stand-alone firms, however this relationship is not automatically true for the group-affiliated firms. The sub-portfolio analysis presents a non-parametric examination of the cross-sectional differences in the relationship between default probability and stock returns (Garlappi et al. 2006). It is necessary to give a structural and multivariate view, by means of
regression analysis; of whether the relationship between equity returns and default risk is statistically significant for both group-affiliated firms and stand-alone firms. First, consider the CAPM model which includes the factors of excess return on the market portfolio (EMKT) and the default risk measure (EDF). The asset-pricing model is given below:
Rt = α +β1*EMKTt +β2*EDFt + εt (6)
Where Rt is the excess return of the portfolio over the risk-free rate at month t, EMKTt is the
excess return on the market portfolio at month t, and EDFt is the default probability of the firms
at month t. In order to give a more specific view, the equation (6) is estimated for all firms, all stand-alone firms and all group-affiliated firms. Furthermore, it is also estimated for the risk-return relationship of the 18 equally weighted portfolios based on their size, BM ratio and whether they are group affiliated. In total, there are 21 results for equation (6).
The results from estimating equation (6) of all 21 portfolios are presented in Table 7 in Appendix B. Panel A shows the results of equation (6) for all firms, all stand-alone firms and all group-affiliated firms. Panel B and C display the corresponding results of the 18 sub-portfolios sorted by size, B/M ratio and whether they are group-affiliated. The market factors are statistically significant at the one percent level in all cases, and the coefficients are all close to one. Although in Panel A the relationship between stock returns and default risk is positive and significant for all firms, the situation is changed when the stocks are split into group-affiliated firms and stand-alone firms. Panel A indicates that the statistically significant positive relationship between stock returns and default risk only exists within stand-alone firms and this relationship is significant at the 5% level. However, this relationship does not hold for the group-affiliated firms. Panel B and Panel C show more detailed information on respectively the stand-alone firms and the group-affiliated firms. As is seen in Panel B six out of nine portfolios of the stand-alone firms have significant positive relationship between stock returns and default probabilities. However, in Panel C, none of the portfolios has a significant relationship between the stock return and default probability.
Moreover, in Panel B, the coefficients of EDF in the small-cap portfolio are much higher than the coefficients of EDF in the large-cap portfolio. Since Fama and French (1996) argue that the size factor proxy for financial distress it can be inferred that, when a stand-alone firm faces high distress risk, the positive relationship between default probability and equity return is more
prominent than that when they face low distress risk. However, for the group-affiliated firms, higher default risk probabilities are not always associated with higher expected stock returns. Carlappi et al. (2006) also find similar results. Their results show that for the distressed firms with low shareholder advantage, the relationship between default probability and equity return is upward slopping. Nevertheless, for the distressed firms with high shareholder advantage, this relationship present non-linear pattern. They define shareholder advantage as the combination of shareholder’s bargaining power and the efficiency gained through bargaining—in the determination of equity returns. They suggest that since the firms have a stronger shareholder advantage in their debt renegotiation power, their default probability (EDF) does not adequately represent the true risk of default.
Another explanation is that the group-affiliated firms are characterized by complex ownership structures. These complex ownership structures allow a small number of controlling investors to expropriate the benefits from the minority owners. In particular, deviations of voting from cashflow rights-through stock pyramids, cross shareholdings and dual-class shares—will often be used to allow a controlling shareholder behind the group to gain effective control of a firm (Claessens et al. 2002).
5.3 The result of Fama-French model
Fama and French (1996) argue that SMB and HML proxy for financial distress. However, Lakonishok, Shleifer, and Vishny (LSV 1994) and Haugen (1995) argue that the premium for relative distress is irrational. The reason for the irrational distress premium is due to investors’ overreacting. If the stocks are priced irrationally, then the FF factors may not contain sufficient information of default of these firms. Table 3 shows that the default probability EDF is not highly correlated with SMB and HML factors, Since the EDF measure represents the firms’ default probability it seems that some default information is not captured by the FF factors. In order to test to what extent the default information is subsumed in the SMB and HML factors, and how much the default probability EDF can explain of the equity return for Indian firms, the Fama-French three-factor model including the default probability measure EDF will be used. The empirical specification is given by:
Rt = α +β1*EMRTt +β2*SMBt +β3*HMLt+ EDFt + εt (7.2)
Where Rt is the excess return of the portfolios over risk-free rate at month t, EMRTt is the
excess returns on the market portfolio at month t, SMBt is the size effect at month t, HMLt is the
BM effect at month t and EDFt is the default probability of the firms at month t. If indeed all the
priced information SMB and HMl is related to financial distress, then it is expected that in the second equation the default risk factors EDF will loose their explanatory power.
The stocks are still classified into 21 portfolios as mentioned before. By comparing the coefficient and R-square of these portfolios, it is possible to find out whether the high return of the stand-alone firms is due to their high default risk. If true then the coefficient of the default risk factor on stand-alone portfolios will be higher than that of group-affiliated portfolios. It is expected that the explanatory power of the model will increase by including the default risk factor (EDF) in equation (7.2). The equation (7.2) will be compared with the equation (7.1) which is the FF model without the default risk factor and which acts as a benchmark.
The results of equation (7.1) is reported in Table 8 in Appendix B. The market factor is statistically significant in all portfolios, and the coefficients of the portfolios are all below unity except for one portfolio (small-cap, low BM). Most portfolio coefficients are in the range of 0.8 to 0.9. In Panel A, The excess equity returns are regressed against FF factors for all firms, all stand-alone firms and all group-affiliated firms. The coefficients of all Fama-French factors are statistically significant. Panel B and Panel C present the effects of FF factors on the equity returns of stand-alone firms and group-affiliated firms in more detail. Panel B presents the results of nine sub-portfolios for stand-alone firms. The size factor SMB is significant in 8 of out 9 portfolios, and the book-to-market factor HML is significant in 6 out of 9 portfolios. In panel C for group-affiliated firms, the size factor is significant in 8 out of 9 portfolios, and the book-to-market factor is significant in 7 out of 9 portfolios. The average explanatory power of Fama-French three-factor model is 0.739, which is slightly lower than the result of Connor and Sehgal (2001). They test the Fama-French model in India, and find that the average explanatory power is about eighty percent. The results in this paper show that all three Fama-French factors, market, size and book-to-market ratio, have a pervasive influence on the returns in the Indian stock market. Table 9 in Appendix B presents the result of equation (7.2). Similar to the results in Table 7, the coefficient of the default risk factor EDF are significant for most stand-alone portfolios, while
none of the EDF coefficients is significant for the group-affiliated portfolios. In panel A, it is seen that the coefficients of the EDF factor are not significant for both overall firms and group-affiliated firms. However, they are positively significant for the stand-alone firms, which confirm that the stock returns of stand-alone firms are positively related to their default risk. Panel B and panel C provide more detailed information of the 18 sub-portfolios for stand-alone firms and group-affiliated firms. In panel B for the stand-alone firms, the default risk factor EDF is statistically significant in 5 out of 9 portfolios, the size factor SMB is significant in 8 out of 9 portfolios and value factor HML is significant in 6 out 9 portfolios. In comparison to the Fama-French model in Table 8, the adjusted R square improves in 6 out of 9 portfolios. This suggests that the Fama-French model includes the default risk factor and does a better job in explaining the cross-section of returns for stand-alone companies. Again, this is not the case for group-affiliated firms. Panel C shows that none default risk factors EDF is significant. The SMB factor is significant in 7 out of 9 portfolios and the HML factor is significant in 8 out of 9 portfolios. The model fit increases only in three out of nine portfolios. These results indicate that the equity returns of Indian stand-alone firms are positively related to the default risk factor. While for the group-affiliated firms, the higher default probabilities are not associated with higher expected stock returns.
It is interesting to note that once SMB and HML are included in the asset-pricing model, the loadings of EDF are reduced substantially for all portfolios. This suggests that SMB and HML include important default-related information. However, for most portfolios, SMB and HML still remain statistically significant when EDF is included in the model. This result implies that although SMB and HML contain some default-related information, they also contain other significant information unrelated to default risk, which is not included in the EDF.
5.4 Interpretation of the results
There are three important findings in the results. First, the default probability measure EDF of group-affiliated firms is overall lower than that of stand-alone firms when the stocks are sorted into portfolios. Furthermore, from the credit rating results provided by Fitch, the group-affiliated firms also share lower default risk and stand-alone firms. This result is consistent with the first hypothesis, which stated that group-affiliated firms have lower default
probability than their independent counterparties in the Indian stock market.
Secondly, the default risk is not systematic for the whole Indian stock market. Although the default risk factor is significant in the equation (6), when the Fama-French factors SMB and HML add into the model, the default risk factor is not significant anymore. This indicates that the default effect is less influential than the size and BM effect in the overall Indian market. The second hypothesis can be rejected (higher equity returns are associated with higher default risk in the Indian market). However, for the stand-alone firms, the stock returns are positively related to their default probabilities in both CAPM and Fama-French equations. This result is consistent with the third hypothesis (higher equity returns are associated with higher default risk for Indian stand-alone firms). For the group-affiliated firms, there is no linear relationship between equity returns and default risk, the forth hypothesis can be rejected (higher equity returns are associated with higher default risk for Indian group-affiliated firms).
Third, comparing with the results of the equation (6), when the Fama-French factors SMB and HML are present in the equation (7.2), the loadings of EDF are reduced dramatically for all portfolios, suggesting that SMB and HML indeed share some default information that are included in the default factor EDF. On the other side, although the loadings of default risk factor EDF are reduced, most of them still remain statistical significant in most stand-alone firms’ portfolios. This indicating that although SMB and HML contain some default-related information, they also contain other significant information unrelated to default risk, which is not included in the EDF
The first results support the view that the group-affiliation enables group-affiliated firms to share lower default risk than stand-alone firms. There are mainly two reasons can explain why group-affiliated firms have lower default risk than stand-alone firms. The first reason is the controlling shareholder’s debt renegotiation power of business group can help to alleviate the firms’ debt burden. The study by Claessens et al (2003) shows that since the legal costs of bankruptcy is higher and judicial efficiency is lower for the emerging countries than the developed countries, so the creditor are less willing to fill bankruptcy in the emerging countries. For example, the longer time it takes to render a bankruptcy judgment and the lower the priority of secured creditors, the less likely creditors are to use formal bankruptcy proceedings. As a result, the controlling shareholders of group-affiliated firms have the advantage to negotiate
with creditors. Their high bargaining power leads creditors to internalize the opportunity costs of filing for bankruptcy through conducting out-of-court negotiations. Therefore, for the group-affiliated firms, the higher default probability is associated with a potential reduction in debt burden, hence leads to the lower risk for equity and lower expected returns.
Another reason is the business group can serve as an internal market that can help their member firms financially during the period of distress. For the group-affiliated firms, the group structures are associated with greater use of internal markets and financial markets (Claessens, et al. 2002). Through their internal financial market, groups can allocate capital among firms within the group that can lead to lower outside debt obligations for the group member firms than their independent counterparties.
The second result is the most important one of this study. The non-linaer relationship between default probability and equity returns for group-affiliated firms can be explained by the fact that since the default probability measure EDF cannot capture the risk-sharing information provided by business group, so it does not adequately represent true default risk level of group-affiliated firms. As a result, this result does not reflect the true relationship between default risk and equity returns for group-affiliated firms.
As mentioned above, when the group-affiliated firms face financial distress, they can reduce their default risk by means of their internal market and the controlling shareholder’s renegotiation power. However, the default probability measure EDF is mainly driven by the firm’s capital structure and its asset volatility, which does not take account of business group’s internal market and the controlling shareholder’s debt renegotiation power. Therefore, the default probability EDF does not adequately represent true default risk of the group-affiliated firms, especially for the financial distressed firms. For instance, when a group-affiliated firm has a very high leverage ratio and high asset volatility, the default probability EDF will indicate that there is a very high default probability of the firm. However, as mentioned above, due to the controlling shareholder’s renegotiation power with creditors and the internal financial market of business group, the true risk embedded in this group firm is not as high as it indicated by default probability measure EDF. Therefore, this group-affiliated firm who has high default probabilities do not need to provide a high risk premium to their investors to compensate for
this risk, hence its return is not as high as the stand-alone firm who has the same default probability EDF.
Another important finding in the results is although FF factors SMB and HML contain some default related information, they also contain other significant information unrelated to default risk, which is not included in the EDF. In other words, the reason that SMB and HML can explain cross-sectional return is not just because they proxy for default risk. As suggested by Lakonishok, Shleifer, and Vishny (LSV 1994), the premium for the FF factors is too large to be explained by rational pricing. They argue that the premium is due to investors’ irrational pricing. There are two arguments that can explain this investors’ irrational pricing. The first one is; since investors do not understand that the low earnings growth of high-B/M stocks and the high earnings growth of low-B/M stocks quickly revert to a normal level, therefore they over-react in respect to these stocks. The second argument is; the premium arises simply because investors dislike distressed stocks and therefore cause them to be underpriced.
6. Conclusion
In this paper, the alternative KMV model is used to compute monthly EDF measures as an indicator of default probability. The relationship between default risk and equity returns in Indian stock market is examined by using the CAPM model and the Fama-French model. My study is the first to examine the relationship between default risk and equity returns in the context of group-affiliation in an emerging country.
In this paper, I find that in general, group-affiliated firms have lower default risk than stand-alone firms when they are sorted into portfolios. The most striking result of this paper is that, when testing the risk-return relationship with the CAPM model which includes the default risk factor, the expected returns are positively related to default probability for stand-alone firms. However, for the group-affiliated firms, a higher default probability is not associated with a higher stock return. The Fama-French model including the default risk factor is used in order to test whether size and value factors capture all the default information. The results show that, although SMB and HML contain some default-related information, this is not the only reason that it can explain the cross-sectional returns.
The results suggest that the nature of group affiliation has a substantial impact on the relationship between default risk and equity returns. Group affiliation can alleviate member firms’ financial distress through their internal financing channel. Even when the group firms face bankruptcy risk, the controlling shareholder can use their bargaining power to resolve this risk by means of out-out-court agreement with creditors. Therefore the default probability measure EDF cannot adequately represent the true risk of the group-affiliated firms. As a result, the high EDF firms do not always provide “risk premium” to their investors. For the stand-alone firms the default probability is positively related with equity returns, this is consistent with the original intuition that default risk should be compensated by the return premium.
This paper shows that when analyzing the risk and return relationship of firms in emerging countries. It is not only important to choose an appropriate default risk measurement to estimate the default risk of the firms, but also, and more essentially, to acknowledge the special nature of the group-affiliated companies and properly account for the negotiation power in distress situations.
The limitation of this paper is that the alternative KMV is designed to measure the default risk for the American firms. It is unclear whether some of its coefficients can also be applied in the Indian stock market. In addition, since EDF cannot capture some risk-sharing information of business group, so it is difficult to examine the risk-return relationship of group-affiliated firms more accurately. Further research is needed to develop a more sophisticated credit risk measurement model to take account of the special features of group-affiliation.
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