1
Amsterdam Business School
The Interrelationship between Credit and Market risk:
Does Expected Shortfall as a Market Risk Measure Plays a
Significant Role in Credit Rating Risk Analysis on the European
Stock Market?
Author: Suin Lee
Student number: 11400374 Supervisor: Fons van Overbeek Date: 29 June 2020
BSc Economics and Business, Finance and Organization University of Amsterdam
2
Statement of Originality
This document is written by Suin Lee who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
3
Abstract
This paper examines the interconnection between credit risk and market risk through credit rating event study with an application of expected shortfall as a measurement of market risk. The event study examines the impact of Moody’s credit rating change on the European stock price subject to the STOXX 500 listed firms over a period between 1990 and 2020. The statistical result of the event study shows that negative credit rating changes have a significant impact on abnormal returns. Using two quantitative models, this study found evidence of the mutual interconnection between credit rating and market risk. One of the main findings of the study is that higher market risk firms draw out more sensitive stock price reactions due to the credit rating change. Moreover, credit risk factors, for example, a low credit quality rating, contribute to higher market risk to some degree. Liquidity risk is expected to deteriorate both credit and market risk, but the result did not present any evidence on this.
4
TABLE OF CONTENT
1. INTRODUCTION ··· 5
2. THEORETICAL BACKGROUND & HYPOTHESIS DEVELOPMENT ··· 6
2.1 Efficient Market Hypothesis ··· 6
2.2 Information Content Hypothesis ··· 6
2.3 The factors related to Abnormal return performances ··· 8
2.4 Value-at-Risk ··· 10
2.5 Credit rating and market risk ··· 11
3. DATA ··· 12
4. METHODOLOGY ··· 13
4.1 Event study ··· 13
4.2. Value-at-risk calculation ··· 15
4.3 Ordinary Least Squares (OLS) regression ··· 17
4.4 Ordered Logistic regression ··· 19
5. EMPIRICAL RESULTS ··· 21
5.1 Event study statistical results ··· 21
5.2 Ordinary Least Squares (OLS) regression results ···24
5.3 Ordered Logistic regression results ···27
6. CONCLUSION ··· 29
7. REFERENCE ··· 31
5
1. Introduction
The informational value of credit rating has been controversial for decades. Many studies in the U.S and Europe have been researched before the financial crisis, and researchers could not draw out a clear
conclusion since the results are not consistent among them (Amin et al., 2018). Particularly, after experiencing the financial crisis in 2007-2009, the role of the Credit Rating Agencies (CRA) became more important to reflect the informational value of credit rating to markets. The CRAs announce credit rating change as either upgrade or downgrade depends on their current evaluation of a firm.
There are four types of risk in Finance that are credit risk, operational risk, liquidity risk, and market risk (Wolke, 2017). During the financial crisis, a heightened credit risk immensely affected market risk exposure inflicting deterioration of liquidation issues, which partly contributed to the financial crisis. Among the four risks, the Basel Committee on Banking Supervision (BCBS) confirmed the connection between credit risk and market risk owing to the severely worsened liquidation issue by the interaction between credit risk and market risk while experiencing the financial crisis. Before the financial crisis, market risk and credit risk have been dealt with separately because of its vague concept distinction. However, while experiencing the financial crisis, the empirical results suggest that the two risks may affect each other and worsen liquidity further (Basel Committee on Banking Supervision, 2009). Moreover, Jarrow & Turnbull (2000) explained that an
unexpected change of a market value of a firm could generate market risk, and this affects the probability of default, which means heightening credit risk. Jarrow & Turnbull (2000, p.271) wrote that “Economic theory tells us that market and credit risk are intrinsically related to each other and, more importantly, they are not separable.”
As an assessment of market risk, a value-at-risk methodology is widely used and representative as a market risk measurement (Ho & Lee, 2004). From the Basel II Accords which is a recommendation on
banking laws and regulations published by the Basel Committee, the banks are required to adopt a 10-day value-at-risk estimate at a 1% significance level for the measurement of market risk (Trading Book Group of the Basel Committee on Banking Supervision, 2009).
European stock market focused studies on credit rating have been less elucidated than credit rating researches in U.S. In this paper, I apply an event study methodology to test the informational value of credit rating change in Europe, by statistically testing the European stock returns whether they are abnormal or not during the period leading up to the event. Furthermore, even if the interrelationship between credit risk and market risk has been studied by the Basel Committee, there are still a few studies that have been researched on this topic. Moreover, the concept of credit risk and market risk is vague and broad. Accordingly, a contribution of this paper is to examine the correlation of credit risk and market risk but explicitly focusing on credit rating change for the credit risk factor and value-at-risk methodology for a market risk factor. By
6
introducing a practical application of two models, a regression model, and a classification model, a value-at-risk methodology is applied to show the connection between credit value-at-risk and market value-at-risk. It is expected to extend the understanding of this topic through this contribution. This study is meaningful in that it is not only limited to credit rating risk analysis but bridge this analysis to market risk for a further interlinkage effect of each other.
The rest of the paper is structured as follows. Section 2 gives the backgrounds of the study, including previous literature and a derivation of hypotheses. In section 3, the data description will be explained. Subsequently, the methodologies are introduced in section 4. The empirical results are discussed in section 5, and lastly, a conclusion will be provided in section 6
2. Literature review & Hypothesis development
2.1 Efficient market hypothesis
The efficient market hypothesis indicates that security prices fully reflect available information in a market (Fama, 1970). Based on this hypothesis, since a market fully reflects the available information, investors and firms can receive accurate signals from the market for their resource allocation decision (Fama, 1970).
There are three forms of the efficient market model varying in the sources of information that they consider. Firstly, in weak form of efficient market, security prices only reflect past historical information (Fama, 1970). Second, in semi-strong form of efficient market, security prices reflect not only the past historical information but also the publicly available information, for instance, announcements of share repurchase or credit rating (Fama, 1970). Lastly, strong form of efficient market concerns privately available information that has a
monopolistic position (Fama, 1970). Based on the efficient market hypothesis concept, this paper is expected to show that the credit rating announcement information is reflected in the stock price to some degree.
2.2 Information content hypothesis
Several studies had been conducted concerning the credit rating agency’s role in information asymmetry reduction. Information asymmetry could be minimized when the market reflects the information of the credit rating change announcements. If the credit rating announcement information can be exclusively accessible by the only announcement itself, it is assumed that a significant reaction of investors to an announcement of credit rating change is expected according to the ‘Information content hypothesis’ (Amin et al., 2018).
Many U.S-oriented studies on credit rating change impact have been done. Most of the papers suggest that downgrade announcements contribute to a minimization of information asymmetry, but upgrade announcements have less incremental information content. Matolcsy & Lianto (1995) examined evidence on
7
the information content of bond revisions using annual accounting information and found that bond
downgrade announcements have more information content to affect market reaction significantly. This result is very consistent with the study of Holthausen & Leftwich (1986) in that they found significant negative abnormal returns after bond rating downgrades while they found no significant positive abnormal return detected after bond rating upgrades. Additionally, from the Standard & Poor’s CreditWatch (Watch for Moody’s) data, they found significant abnormal returns corresponding with either downgrade or upgrade announcements (Holthausen & Leftwich, 1986. Goh and Ederington (1993) also concluded that statistically significant negative abnormal performances were shown after the downgrade announcements and no significant relationship with the upgrade announcements and abnormal returns. However, they pointed out that there are types of rating downgrade announcements which could draw out different reactions of shareholders. The credit rating downgrade due to the deterioration of the firm’s financial future has significant informational content drawing out a significant negative abnormal return, on the other hand, the credit rating downgrade announcements due to the leverage do not cause significant shareholder’s negative reaction (Goh and Ederington, 1993). Contrary to Holthausen & Leftwich's (1986) study, Followill & Martell (1997) found that shareholders do not react significantly to the actual downgrade announcements, whereas the information of watch being negative has a significant impact on abnormal returns. Kliger & Sarig (2000) investigated bond, stock, and option prices before and after Moody’s finer rating classification change. They found bond prices’ and the stock prices’ adjustments corresponding to Moody’s fine-rating change decision, which represents the value of rating information
Europe-oriented empirical researches also have been studied. Abad & Robles (2006) reported
contradictory results compared to the abovementioned U.S studies. The study documented that significantly negative abnormal returns were observed after upgrade announcements, and no significant abnormal return earnings after downgrade announcements (Abad &Robles, 2006). Barron et al. (1997) studied the relationship between U.K stock returns and bond rating changes. They identified the significant abnormal returns which are corresponded with credit rating changes of a downgrade and positive watch announcements.
Even though many studies have dealt with the effect of credit rating change on securities (stocks, bonds, or Credit Default Swap (CDS), etc.), still no clear conclusions have been drawn. In terms of Behavioral Economics, Tversky and Kahneman (1979) proposed ‘prospect theory’ as an alternative theory of expected utility theory. According to the prospect theory, the value function has a reference point, and the value functions toward gains or losses are different (Tversky and Kahneman, 1979). The function is concave toward gains, and on the other hand, the function for losses is convex and has a steeper slope than the value function for gains. In another paper by Tversky and Kahneman (1991), they defined the concept of “loss aversion” that a certain amount of the value losses outweighs the same amount of gains. Based on this theory,
8
this psychological concept supports the fact that many previous studies pointed out that the stock markets tend to react more to negative news but not to positive news. Here the first hypothesis is derived.
Hypothesis1: Stock markets react more strongly to negative credit rating news than positive credit rating news
2.3 The factors related to abnormal return performance
Size
Creighton et al. (2007) scrutinize the effects of credit rating changes on financial prices for both bond and stock prices in Australia. To test the firm size effect on the security prices, they used market capitalization to divide them into two equal-sized groups. As a result, they found that credit rating change announcements largely affect the stock price of relatively small-sized firms but not the stock price of large-sized firms. This result might be drawn out because larger firms are relatively more likely to release their information than smaller firms so that the informational value of credit rating agencies’ ratings is diluted (Creighton et al., 2007).
Vassalou & Xing (2003) argued that stock returns in credit rating events are influenced by the firm’s size, book-to-market ratio, and default risk factors. They observed that stock prices vary extremely after the announcement when the firm has a high book-to-market ratio and is a small-sized company, which leads to higher default risk (Vassalou & Xing, 2003). They used market capitalization as a measure of the size of companies.
Leverage
Kliger & Sarig (2000) explored the relationship between firms’ leverage and the effects of Moody’s fine-rating information announcements to check the informational value of credit rating change. The ratio of debt to debt plus equity is used for the leverage variable. They predicted that stock price reaction to higher leverage would be negative, and bond price reaction to higher leverage would be positive (Kliger & Sarig, 2000). The reverse trend is predicted for lower leverage. Their paper concluded that the estimated coefficients in their regression model for both bond prices and stock prices are as predicted. In terms of the reaction of bond prices, it is statistically significant but not for stock prices (Kliger & Sarig, 2000). This result could be
explained by a wealth distribution perspective that announcements of a bond downgrade due to an increase in leverage will burden bondholders, but its profitability will be transferred to shareholders by leveraging (Goh and Ederington,1993). Hence the reluctancy of leverage for bondholders results in significant reactions toward the downgrade announcements but not for stockholders. Conversely, if the downgrade decision is caused by a downturn of future financial profit, the market reaction is negatively significant, according to Goh and Ederington (1993).
9 Uncertainty index & The financial crisis (2007-2009)
In the book of Berk & DeMarzo (2017), the VIX index (volatility index) from the Chicago Board Options Exchange is illustrated as a measure of investor uncertainty, and it is referred to so-called “fear index.” The VIX index measures the volatility of S&P 500 option prices. Not surprisingly, during the time of the financial crisis, the level of uncertainty heightened dramatically to 80% of the VIX index while the normal average VIX level is around 20%. In the study of Finnerty et al. (2013), a market volatility dummy variable is used to measure investor’s uncertainty level to test the impact of credit rating changes on credit default swap (CDS) spread. Concerning downgrade announcements, market volatility dummy variables are significant as they expected but not for upgrade announcements (Finnerty et al., 2013).
During a financial recession period in 2007-2009, investors’ uncertainty of the market is expected to increase with market volatility based on the VIX index. In spite of the expectation that the CDS spread widens after downgrade announcements in this period, only upgrade announcements have a significant result in the recession period, according to Finnerty et al., (2013).
Credit quality
Investment grade refers to the investible quality of a company’s credit rating, which has a relatively low risk. On the other hand, non-investment grade or speculative-grade represents a company’s credit rating
accompanied by high risk. From Moody’s credit rating table, In between Aaa and Baa3 is considered as investment grade and otherwise considered as non-investment grade. The detailed Moody’s credit rating table can be found in Appendix I.
Steiner & Heinke (2001) built a ‘price pressure hypothesis’ that predicts a considerably stronger bond price reaction when the credit rating is downgraded from investment grade to non-investment grade. The price pressure hypothesis assumes a phenomenon where the downgrade announcements to non-investment grade push institutions and regulators to sell their bond massively (Steiner & Heinke, 2001). It turned out that the bond price reaction for downgrades into the non-investment class was twice or four times stronger than for downgrades within the non-investment or investment classes (Steiner & Heinke, 2001).
Finnerty et al. (2013) also investigated the effect of credit quality on cumulative abnormal returns of CDS spreads. The magnitudes of CARs are mostly larger for non-investment grade’s downgrade
announcements than for investment-grade’s downgrade announcements (Finnerty et al., 2013). Nevertheless, the security type is different for CAR; this outcome is very similar to the study done by Hand, Holthausen & Leftwich (1992) that they found the average bond returns are significantly higher for non-investment grade than investment-grade bonds in terms of downgrade announcement.
10
As an Australian study concerning the impact of investment-grade and non-investment grade on CAR of equities, Creighton et al. (2007) reported that CAAR earned after the credit rating changes to non-investment grade are substantially larger for all the event windows compared to the investment grade.
Liquidity ratio
The Basel Committee research group (2009) emphasized that “liquidity” plays a significant role in the interaction between market risk and credit risk while executing risk management strategies for banks. If the liquidity deteriorates, banks are forced to extend this horizon, and this leads to higher overall risk exposures. The Basel Committee (2009) predicted that a company with a low liquidity ratio is exposed to higher credit risk and following market risk and caused a significant reaction regarding downgrade announcements. Financial industry
Several studies analyzed the dependence of excess returns on different types of issuers. ‘Issuer hypothesis’ assumes a low-price fluctuation is observed on bank bonds, whereas corporate bonds show a strong price fluctuation, according to Steiner & Heinke (2001). In particular, both abnormal returns are substantially significant for downgrade events with the price change of −0.344% and −0.096% for corporate bonds and bank bonds respectively in Steiner & Heinke’s (2001) results. Compared to non-financial firms, higher availability of credit information on account of the prudential regulation requirement for banks results in trivial reactions toward downgrade credit rating changes (Steiner & Heinke’s, 2001). Based on the efficient market hypothesis, it is presumed that the available information has already been reflected. Therefore, an announcement on an event date may not have a substantial influence on investor’s expectations of the firm.
Additionally, Finnerty et al. (2013) gave a result that cumulative abnormal returns for financial industry firms were not statistically significant for both upgrade and downgrade announcements, while cumulative abnormal returns for the other industry firms showed its significance to some degree. Based on the abovementioned researches, the second hypothesis is derived.
Hypothesis 2: Non-financial sector companies are more sensitive to the credit rating change of announcement than the financial sector companies.
2.4 Value-at-risk
Traditionally, volatility or so-called beta in Capital Asset Pricing Model (CAPM) has been used as a default measurement for market risk. Volatility captures the average deviations of the expected upwards and downwards fluctuation of assets (Wolke, 2017). However, volatility has a few disadvantages that volatility does not indicate a potential loss in monetary units since it is a relative measure of risk exposure (Wolke, 2017). For this reason, a problem arises when comparing the risk of different securities like stocks and bonds
11
together (Ho & Lee, 2004). To remedy this problem, “value-at-risk (VaR)” is introduced as a unified measurement (Ho & Lee, 2004). Value-at-Risk (VaR) is a potential loss-oriented risk measure at a certain confidence level q ∈ (0,1) (for instance, 95% or 99%) or its significance level being α = 1- q over a given time horizon t. (Ho & Lee, 2004). Therefore, VaR can be explained as “a given time horizon t and a confidence level, VaR is given by the smallest return 𝑦q such that the loss 𝑌t+1 at time t+1 will fall below 𝑦q with a
probability of q” (Chang et al., 2019). As a market risk measurement, it is used widely by financial institutions. As mentioned in the introduction, the Basel Committee on Banking Supervision (BCBS) recommended using value-at-risk (VaR) as an internal model-based approach for financial institutions. In 2012, the Basel Committee published a consultative document to propose revised capital requirement policies. According to their publication (Basel Committee on Banking Supervision, 2012), it turned out that VaR has drawbacks with regard to determining regulatory capital requirements owing to its incapability to capture “tail risk.” Hence Basel Committee on Banking Supervision (2012) proposed to replace VaR at a 95% confidence level with Expected Shortfall (ES) at a 97.5% confidence level for the internal model-based approach and the revised market risk standardized approach. The Basel Committee (2013) believes that using a 97.5% confidence level of expected shortfall model is a better measure than VaR in that expected shortfall is less sensitive to extreme outlier observations generating more stable output and captures a similar level of risk of VaR at a 95% confidence level. Expected shortfall is also known as Conditional value-at-risk (CVaR).
2.5 Credit rating and market risk
Among factors that cause credit risk, this paper specifically focuses on the credit rating change, which implies the credit risk change to test the connection between the credit risk and market risk. Some papers have been written about the correlation between credit rating change and market risk.
Seetharaman et al. (2017), explored the impact of different types of risk on other types of risk and the performance management of credit rating agencies (CRA). The interrelation between credit risk and market risk results in a significant positive coefficient, with a 99% confidence level (Seetharaman et al., 2017). In the paper of Hirk et al. (2019), they considered a multivariate ordinal regression model to assess a firm’s credit quality based on firm-level variables and market information to assign the credit ratings like what the CRAs do. They concluded that firms with higher both idiosyncratic and systematic risk are prone to receive worse credit ratings (Hirk et al., 2019). Abad & Robles (2014) also researched the net effects of credit rating actions on risks, both idiosyncratic and systematic risk using beta/volatility as a measurement of systematic risk. Their results suggest that credit quality improvement is related to lower risk and vice versa for credit quality deterioration (Abad & Robles, 2014). Furthermore, the credit quality improvements reduce the idiosyncratic risk, whereas the deteriorations of credit quality influence both risks, but especially a significant amount
12
toward the systematic risk (Abad & Robles, 2014). Based on the literature, the other two hypotheses derived as:
Hypothesis 3: Higher market risk firms tend to react more to credit rating changes than the less risky firms no matter the sectors (The relationship between the degree of market risk exposure and credit risk (1)).
Hypothesis 4: Firms that experience a change to low investment-grade rating have a higher probability of high value at risk loss. (The relationship between the degree of market risk exposure and credit risk (2)).
3. Data description
To acquire the European firm dataset, firm samples that are listed in the STOXX Europe 600 index
components were collected, which were rated by Moody’s. The total number of companies that satisfied this condition was 268. The number of financial companies and non-financial companies among 268 companies is 70 and 168, respectively. In this paper, the analysis only considers Moody’s actual credit rating change
announcements and watch rating change announcements. Since the issuer credit rating is accessible, histories of long-term issuer rating data for each firm are gathered on Moody’s website*. This credit rating history period spans in between 1990/1/1 and 2020/3/31. Along with credit rating data, announcement date and rating action are collected on Moody’s website. Conducting the methodology of an event study requires a data match between credit rating data, stock data, and the other regression variables. Some of the stock data or the other regression variables are omitted due to various reasons, for instance, a firm closed their stock market during some periods, or just a firm started Initial Public Offering (IPO) later than 1990. After all the sorting and cleaning the dataset, the total number of credit rating events is 1233, and the number of events per rating action category is as follows:
Table 1 Rating change event observations 1990 until 2020
Upgrade Downgrade Watch**
Upgrade Downgrade Watch** Total The number of observations
used for analysis 313 442 67 411 1233
Firms’ stock price data from the period of 1990/1/1 until 2020/3/31 is gathered from FactSet database. As a benchmark, MSCI Europe Index data is collected from FactSet as well for estimation of expected returns in estimation periods for this event study. The data for further regression analysis, such as size (market capitalization), leverage (debt to equity ratio), liquidity ratio (current ratio) are also collected from * Moody’s website: https://www.moodys.com/
** An expected credit rating change in the short term is called a review. For Moody’s, ratings on review are called “Moody’s watchlist” or “On watch.”
13 the FactSet database with the same period.
From the previous literature review section, the VIX index was introduced. However, there is a limitation in that the VIX index represents the volatility of the U.S option market. Therefore, it does not apply to this paper since this paper covers the European stock market.As a market volatility/uncertainty measurement, World Uncertainty Index (WUI) is used as the uncertainty proxy. Ahir et al. (2018) developed the World Uncertainty Index (WUI) that is quarterly indices of economic uncertainty for 143 countries from 1996 based on Economist Intelligence Unit (EIU) country reports. The index is positively correlated with higher economic policy uncertainty (EPU), stock market volatility, risk, and lower GDP growth. For this reason, the use of the WUI complements the limitation in that WUI provides the time-series data of
uncertainty index at the regional level (Europe, Asia, North America, etc.). Similar to the VIX index, the WUI spikes at events such as the 9/11 attacks, the SARS outbreak, the Euro debt crisis, and the UK’s Brexit.
4. Methodology
4.1 Event study
To test hypothesis 1, An event study is performed following De Jong’s (2007) paper. De Jong (2007) demonstrated an empirical event study methodology divided into three steps:
i. Identify the event of interest and, in particular, the timing of the event. ii. Specify a "benchmark" model for normal stock return behavior. iii. Calculate and analyze abnormal returns around the event date.
Figure 1 Event study windows
4.1.1 Structure of event study
The event date is defined as the announcement date of the credit rating change by Moody’s. The event study has an estimation window and an event window which do not overlap each other. The length of windows differs among the studies. MacKinlay (1997) mentioned that the estimation window should be at least 120
14
days or more. As an example, MacKinlay (1997) used the 250 days as the estimation window, and several studies used 250 days as an estimation window ([T1, T2] in figure 1). Accordingly, this analysis used 250 days as the estimation window. In this analysis, the event window has several lengths ([-20, +20], [-10, +10], [-1, +1], [-2, +2], [-1, +5]) to see the different degrees of the effects over the observation periods ([t1, t2] in the figure 1). Additionally, calendar time is not considered as the time index t in the event study but the number of periods (days here) from the event. (De Jong, 2007).
4.1.2 Specifying a "benchmark" model
Abnormal Returns (AR) are computed to analyze the stock return behavior of investors before and after the event, and it is defined as follows:
𝐴𝑅𝑖𝑡 = 𝑅𝑖𝑡 – 𝑁𝑅𝑖𝑡
where 𝑅𝑖𝑡 is an actual stock return and 𝑁𝑅𝑖𝑡 is a normal return or so-called expected return (E(𝑅𝑖𝑡|𝑋𝑡)). For the
market model, 𝑋𝑡 is the market return that is used as conditioning information for the normal return
(MacKinlay, 1997). To start with the analysis, a “benchmark” model for the estimation period should be chosen. As a “benchmark” model of a short-term event study, the market model is selected in this analysis, which is the most representatively used in the credit rating event study. The use of CAPM has been disappeared because the potential problem of sensitivity can be avoided by using the market model
MacKinlay (1997). Furthermore, the Fama-French three-factor model is used for longer horizon event studies to calculate expected returns (De Jong, 2007).In order to get parameters for the estimating normal return, the following regression is run:
𝑅𝑖𝑡 = α𝑖 + β𝑖𝑅𝑚𝑡 + ε𝑖𝑡
The normal return is calculated as the following equation: 𝑁𝑅𝑖𝑡 = α̂𝑖 + β̂ 𝑅𝑖 𝑚𝑡
where α̂𝑖 and β̂ are the ordinary least squares (OLS) estimates of the regression coefficients. The market 𝑖
model is estimated over the estimation period, which does not include the event study. 4.1.3 Calculating and analyzing abnormal returns
Checking the abnormal return earned on the event date at t = 0 is the simplest way to analyze abnormal returns. By this, each firm’s abnormal return data for each event could be tested separately. However, De Jong (2007) pointed out that analyzing an event for a firm loses the informativeness since a lot of stock price could fluctuate due to information unrelated to the event (the possibility of the data is contaminated). Accordingly, by averaging the information over a number of firms improves the informativeness of the
15
analysis (De Jong, 2007). As same as the abnormal return, getting a cross-sectional average abnormal return (AAR) that is largely deviated from 0 indicates an abnormal performance (De Jong, 2007).
But since we use event windows to see the performance spread of the announcement across the nearest days of the event date, the typical way to analyze performance over more extended periods around the event date is by cumulative abnormal returns (CAR), where the abnormal returns are summated from the start of the event window, 𝑡1, up to the time 𝑡2. In a similar way of calculating AAR, the separately calculated CARs are aggregated over the cross-section of events to calculate cumulative average abnormal returns (CAAR). 4.1.4 Testing the significance of abnormal performance
A simple t-test is used to answer the question of whether the earned CAARs are significantly different from 0 at a given significance level. The hypothesis is given as:
𝐻0 : E(AARi) = 0 & 𝐻1 : E(AARi) ≠ 0
𝐻0 : E(CAARi) = 0 & 𝐻1 : E(CAARi) ≠ 0
As an important assumption for the simple t-test, stock returns should follow a normal distribution. According to the empirical findings from Fama’s (1976, p. 21) book, the extreme ends of the frequency distribution of the daily returns have fatter tails than the normal distribution. This means that extreme observations exist more than predicted by the normal distribution. This shape of the distribution is widely observed in almost all stock return series and is called as leptokurtosis or a fat-tailed distribution (De Jong, T2007). The Central Limit Theorem (CLT) is applied to solve a fat-tailed distribution problem. If some of the assumptions that the abnormal returns are independent and have the same mean and variance can be
maintained with the large samples (CLT), then the distributions of stock returns follow an approximately normal distribution (De Jong, 2007). In this event study analysis, the number of sample observations is mentioned in table1. Consequently, the data set satisfied the conditions for the t-test.
Along with testing the AARs, the significance of abnormal performance of events over a more prolonged event period (within the event window) is also interesting to analyze. Similarly, if each CAR is mutually uncorrelated/independent, the test statistic is approximately normally distributed for a large dataset of N based on the Central Limit Theorem (CLT). Based on this CAARs are also tested to check its
significance within the event windows
4.2 Value-at-risk calculation
There are three methods to calculate value-at-risk, such as delta-normal methodology, historical simulation, and Monte Carlo simulation. The historical simulation method is chosen for the value-at-risk calculation because many banks use this method as a default for market risk, according to the Basel Committee (2009).
16
This method has advantages compared to the other introduced method in that it is easier to understand the concept when calculating than Monte Carlo simulation, and it results in more accurate values and makes fewer errors than delta-normal methodology. The first two methodologies are introduced below to give an insight into how this value-at-risk calculation works.
4.2.1 Delta-normal methodology
Delta-normal methodology is a parametric approach. The most important assumption for the delta-normal method is that stock prices follow a normal distribution and the price itself indicates its risk (Ho & Lee, 2004). Therefore, simply the standard deviation of the stock volatility represents the uncertainty of the stock value over a given time (Ho & Lee, 2004). According to Chang et al. (2019), value-at-risk of 𝑌𝑡 is given by:
𝑉𝑎𝑅𝑡𝑞 (𝑌𝑡+1) = μ𝑡+1 + σ𝑡+1Ф−1(q)
where μ𝑡+1 and σ𝑡+1 are a mean and a standard deviation of the normal distribution of 𝑌𝑡+1. Assuming that
𝑌𝑡 follows the standard normal distribution, Ф−1(q) is the inverse cumulative distribution function of a
standard normal variable, which is the q quantile of the standard Student-t distribution (mean 0 and variance 1) and also denoted as Z𝑞, a critical value of the one-tail confidence level of standard normal distribution. The
confidence level depends on the preferred power of the tests. As a simple model, it has a disadvantage in the sense that the application of assumption is hard due to the fat-tailed distribution and the parameters drawn by the rough normal distribution assumption is rather subjective (Wolke, 2017).
4.2.2 Historical simulation
Historical simulation methodology is a non-parametric approach, unlike the delta-normal methodology. It is one of the most used methods for VaR analysis among 85% of large banks, according to the McKinsey report (2012). To begin with, the normality distribution assumption is needed similar to the delta-normal
methodology. As mentioned in the event study section, the stock return series tend to have fat-tail
distribution, but this problem could be settled by the Central Limit Theorem (CLT). Since the time horizon of VaR calculation is chosen to use 250 days before the event date for this analysis (same as the length of the estimation window), approximately normal distribution of the stock return series is assumed.
For the VaR calculation, the following steps should be taken, according to Ho & Lee (2004). Firstly, sort the stock return series from the worst return to the highest performance in the given period. Then, find the VaR value, which is the α% percentile value of the sorted distribution from the left-tail. These steps are described in figure 2.
17
Figure 2 Sorted data and finding the percentile for historical simulation methodology
The expected shortfall or conditional value-at-risk is introduced in the literature section. Because the methodology of VaR turned out not to reflect the market risk accurately, according to the Basel Committee, the expected shortfall or conditional value-at-risk (CVaR) at a 97.5% significance level is used in this analysis to represent the market risk. The expected shortfall at significance level α% (or a confidence interval of q) is the expected or averaged value at time t of the sorted loss in the next period, 𝑌𝑡+1, conditional on the loss in the left tail of the distribution exceeding 𝑉𝑎𝑅𝑡+1
𝑞 (Chang et al., 2019). Speaking differently, an average of 2.5% worst loss performance that has been earned during the given period. According to Chang et al., (2019), the expected shortfall is numerically defined as follows:
𝐸𝑆𝑡+1q (𝑌𝑡+1) = 𝐸𝑡[𝑌𝑡+1|𝑌𝑡+1> 𝑉𝑎𝑅𝑡+1 𝑞
]
4.3 Ordinary Least Squares (OLS) regression
The least-squares regression is applied to see the relationship between abnormal returns and the other variables as hypothesized in hypotheses 2 and 3. In particular, hypothesis 3 will be addressed by checking the relationship between market risk and credit risk with the calculated expected shortfall variable in this
regression. The regression model was built with the variables that are possible determinants of CAR based on the literature. According to Stock & Watson (2015), OLS regression is a linear regression model that the marginal effect of each variable is measured to test the relationship between independent and dependent variables while all the other variables are held constant. The complete regression model is formed as below: 𝐶𝐴𝑅[𝑡1,𝑡2]= 𝛽0 + 𝛽1*ES+ 𝛽2*Inv_grade_low + 𝛽3*Inv_grade_medium + 𝛽4*Non-fin_industry +
𝛽5*Uncertainty_index + 𝛽6*ln(size) + 𝛽7*Leverage +𝛽8*Fin_crisis +𝛽9*Downgrade + 𝛽10*Watch up +
𝛽11*Watch down + 𝛽12* Low *ES + 𝛽13*Down*ES + 𝛽14*Wat down*ES + 𝛽15*Down*Unc + 𝛽16*Wat
down*Unc + 𝜀𝑖
18
To prevent the dummy variable trap, the following dummy variables were dropped as reference categories: investment-grade high variable, financial industry firm variable, the non-financial crisis period variable, and upgrade events variable. Not only the main explanatory variables are included in the regression model to discuss hypotheses 2 and 3, but control variables and interaction terms are included as well to improve an omitted variable bias of the model. The main explanatory variables are the calculated expected shortfall (conditional value at risk), the dummy variable of low and medium credit quality rating, the dummy for non-financial industry firms. The regression model considers control variables that are correlated to the dependent variable, which mentioned in the literature. Furthermore, the model includes interaction terms that extend understandings of possible relationships between two variables that influence the dependent variable as together. By the first interaction term, it is anticipated to test whether a combination effect of higher credit risk (low credit quality) and the degree of market risk does exist on CAR. The market risk variable and uncertainty index variable are used for a further interaction terms analysis with all the negative credit rating actions, respectively.
Table 2 Variables for the OLS regression
Variable Description
CAR Cumulative abnormal return during the event window between 𝑡1 & 𝑡2 ES Expected shortfall or conditional value-at-risk (% of loss)
Inv_grade_low A dummy variable, 1 for low investment-grade category 0 for otherwise Inv_grade_medium A dummy variable, 1 for medium investment grade category 0 for otherwise Non-fin_industry A dummy variable, 1 for the non-financial industry firms (if not in banks,
real estates, financial services, insurance) 0 for otherwise
Uncertainty_index Percentage change of European uncertainty index from World Uncertainty Index
ln(size) Natural log of market capitalization value Leverage Total debt to equity ratio
Fin_crisis A dummy variable, 1 for the announcement date is in [2007, 2008, 2009] 0 for otherwise
Downgrade A dummy variable, 1 if the credit rating downgraded Watchup A dummy variable, 1 if the watch credit rating upgraded Watchdown A dummy variable, 1 if the watch credit rating downgraded Low * ES An interaction term between Inv_grade_low and ES Down*ES An interaction term between Downgrade and ES Watdown*ES An interaction term between Watch down and ES
Down*Unc An interaction term between Downgrade and Uncertainty_index Watdown*Unc An interaction term between Downgrade and Uncertainty_index The variance of the error term is expected to differ among the observations, which indicates “heteroskedasticity” (Stock & Watson, 2015). To adjust this problem, the OLS model was fit with
19
heteroskedasticity-robust standard error. Concerning a multicollinearity problem as a multiple regression model, none of the variables have high correlation coefficients (an absolute correlation coefficient > 0.7 as a rule of thumb) that are possible to severely affect the estimation of the OLS model.
4.4 Ordered Logistic regression
A non-linear probabilistic model applied to test the last hypothesis, which explores the direct interaction between the degree of market risk exposure and credit risk. As mentioned in the literature section, Hirk et al. (2019) used a multivariate ordinal regression model for a firm’s credit quality assessment based on
independent variables such as firm-level financial data and macroeconomic information. Inspired by the study of Hirk et al. (2019), ordered logistic regression is used to test how much firm-level financial variables, macroeconomic variables, and credit rating risk variables contribute to the degree of market risk.
To test the effect of other variables including investment-grade variables toward the degree of the expected shortfall (or market risk), the dependent variable, the expected shortfall is categorized into three parts as “High,” “Medium,” or “Low.” If the expected shortfall is lower than 5%, then the variable is categorized as “Low.” In the case of the expected shortfall being between 5% and 10%, it is classified as “Medium,” otherwise as “High” (over 10%). Since the dependent variable is multinomial (three categories) but ordered (high to low), “ordered” logistic regression is chosen to capture the extra information implicit in the ordinal nature of the dependent variable (Baltagi, 2008). Additionally, ordered probit regression is expected to conclude a very similar result, but here only ordered logistic regression is considered.
According to Williams (2019), the observed ordinal variables are represented as Yi and 𝑌𝑖∗ is a
continuous, unmeasured latent variable that has various threshold points. κ1 and κ2 will be estimated by
fitting the model with the variables that contribute to the classification of the dependent variable. Yi is
categorized as following:
Yi = 0, if 𝑌𝑖∗ ≤ κ1
Yi = 1, if κ1≤ 𝑌𝑖∗ ≤κ2
Yi = 2, if 𝑌𝑖∗ ≥ κ2
Since the continuous latent variable 𝑌𝑖∗ is not observed in this stage, we estimate this by making the latent
continuous variable model. The model of 𝑌𝑖∗ is given by:
𝑌𝑖∗= ∑ 𝛽𝑘𝑋𝑘𝑖+ 𝐾
𝑘=1
20 and the model is :
𝑌𝑖∗ = 𝛽0 + 𝛽1* Uncertainty_index + 𝛽2* ln(Size) + 𝛽3* Leverage + 𝛽4* Liq_ratio + 𝛽5* Inv_grade_low
+𝛽6* Inv_grade_medium + 𝛽7* Fin_crisis+ 𝛽8* Non-fin_industry + 𝛽9* Downgrade + 𝛽10* Watchup +
𝛽11* Watchdown + 𝜀𝑖
where 𝛽𝑖 is the coefficient to be estimated, and 𝑋𝑘𝑖 is observed explanatory variables and 𝜀𝑖 is the error term.
A detailed explanation of the variables is described in table 3 below. Table 3 Variables for the ordered logistic regression
Variable Description
𝑌𝑖∗ (ES) An ordinal variable of expected shortfall or conditional value-at-risk (High, Medium, Low)
Uncertainty_index Percentage change of European uncertainty index from World Uncertainty Index ln(Size) Natural log of market capitalization value
Leverage Total debt to equity ratio
Liq_ratio Liquidity measurement, current ratio of the firm
Inv_grade_low A dummy variable, 1 for low investment-grade category 0 for otherwise Inv_grade_medium A dummy variable, 1 for medium investment grade category 0 for otherwise Fin_crisis A dummy variable, 1 for the announcement date is in [2007, 2008, 2009] 0 for
otherwise
Non-fin_industry A dummy variable, 1 for the non-financial industry firms (if not in banks, real estates, financial services, insurance) 0 for otherwise
Downgrade A dummy variable, 1 if the credit rating downgraded Watch up A dummy variable, 1 if the watch credit rating upgraded Watch down A dummy variable, 1 if the watch credit rating downgraded
By using the estimated two cutoff terms, the probability that Yi will fall into a specific category can be
predicted (Williams, 2019). In the case of three ordinal dependent values, the probabilities of the ordered logistic model are as follows:
Pr(Yi= 0) = 1 1+𝑒−(κ1−∑𝐾𝑘=1𝛽𝑘𝑋𝑘𝑖 ) Pr(Yi= 1)= 1 1+𝑒−(κ2− ∑𝐾𝑘=1𝛽𝑘𝑋𝑘𝑖 )
−
1 1+𝑒−(κ1− ∑𝐾𝑘=1𝛽𝑘𝑋𝑘𝑖 ) Pr(Yi= 2) = 1 − 1 1+𝑒−(κ2− ∑𝐾𝑘=1𝛽𝑘𝑋𝑘𝑖 )21
Figure 3 Ordered logistic regression cut-offs and prediction zones.
As the coefficient estimation method, maximum likelihood estimation is used. The maximum likelihood estimation chooses the coefficient parameters that maximize the likelihood of a function that follows the joint probability distribution (Stock & Watson, 2015).
Unlike the linear OLS model, the coefficients 𝛽𝑘 does not represent marginal effects. Instead, the
marginal effects of each probability for each independent variable are calculated by differentiating the probability of the dependent variable in terms of an independent variable that needs to be investigated. The marginal effects of each dependent variable category are as follows (Baltagi, 2008):
∂Pr(Yi= 0)/∂Xi = −𝛽[ 1 1+𝑒−(κ1− ∑𝐾𝑘=1𝛽𝑘𝑋𝑘𝑖 )] ∂Pr(Yi= 1)/∂Xi = 𝛽[ 1 1+𝑒−(κ1− ∑𝐾𝑘=1𝛽𝑘𝑋𝑘𝑖 ) − 1 1+𝑒−(κ2− ∑𝐾𝑘=1𝛽𝑘𝑋𝑘𝑖 ) ] ∂Pr(Yi= 2)/∂Xi =𝛽[ 1 1+𝑒−(κ2− ∑𝐾𝑘=1𝛽𝑘𝑋𝑘𝑖 )]
The results will be analyzed in the subsequent chapter using the estimated OLS coefficients and calculated the probabilistic marginal effect of the ordered logistic model.
5. Empirical Results
5.1 Event study statistical results
5.1.1. Upgrade
CAAR is tested whether it is significantly different from 0. According to the statistical analyses of cumulative average abnormal returns (CAAR), all the windows CAAR for each window are insignificant for the upgrade rating action (see table 4). This result is well-aligned with hypothesis 1 that assumed that investors might not react substantially to the credit rating change of upgrade. The CAARs obtained during the upgrade
22
+20], [-10, +10], [-1, +5]). This consequence might happen because there was another firm-related event that happened during the event window; in other words, the results do not purely contain the effect of the credit rating change.
Table 4 CAARs and their p-values for upgrade
Event window [-20, +20] [-10, +10] [-2, +2] [-1, +1] [-1, +5]
CAAR -0.5% -0.494% 0.079% 0.124% -0.137%
CAAR t-stat -1.039 -1.475 0.440 0.865 -0.680
p-value 0.299 0.141 0.660 0.388 0.497
The table shows the cumulative average abnormal return and their p-value for different event windows. * p<.1, ** p<.05, ***p<.01
5.1.2. Downgrade
The regression results of the downgrade announcement are shown in table 5. CAARs in each window are all negative due to the downgrade announcement. The CAARs earned during the event window [-10, +10] and [-2, +2] are significant at a 5% level, and CAAR is significant at a 1% level in [-1, +1] window. The test accuracy of the window [-20,+20] is expected to be less than the other shorter-term windows in that there is a possibility that the result is affected by other factors and is not purely based on the credit rating change. However, it is meaningful to see the longer-term effect before and after the event. Nevertheless, significant abnormal performances were shown in relatively shorter-term windows. Window [-1, +5] does not give a significant result. This could mean that shareholders may already have some information about the companies’ worsened performance before the credit rating change announcement and react to the
information just after the announcement. Consequently, there is less informational value on further days after the announcement than before the announcement date and just one or two days after the announcement date.
Clearly, the downgrade statistical analysis shows its alignment with the previous studies (Matolcsy & Lianto, 1995; Holthausen & Leftwich, 1986; Goh and Ederington, 1993). As assumed in hypothesis 1, the result proves that investors reacted to the downgrade announcements more significantly than to the upgrade announcements.
Table 5 CAARs and their p-values for downgrade
Event window [-20, +20] [-10, +10] [-2, +2] [-1, +1] [-1, +5]
CAAR -0.409% -1.519% -1.107% -0.917% -0.769%
CAAR t-stat -0.419 -1.974 -2.414 -2.609 -1.540
p-value 0.675 0.049** 0.016** 0.009*** 0.124
The table shows the cumulative average abnormal return and their p-value for different event windows. * p<.1, ** p<.05, ***p<.0
23 5.1.3. Watch Upgrade
As a similar result of the upgrade announcement, CAARs earned after watch upgrade announcements are all positive, which implies that investors reacted positively toward the watch upgrade announcements during the event window (see table 6). Furthermore, as another evidence of hypothesis 1, the analysis for watch upgrade results in not significant CAARs for four of the event windows except that CAAR is weakly meaningful for [-10,+10] window.
Table 6 CAARs and their p-values for watch upgrade
Event window [-20, +20] [-10, +10] [-2, +2] [-1, +1] [-1, +5]
CAAR 0.091% 1.424% 0.245% 0.116% 0.646%
CAAR t-stat 0.089 1.679 0.399 0.258 1.241
p-value 0.929 0.0951* 0.691 0.797 0.217
The table shows the cumulative average abnormal return and their p-value for different event windows. * p<.1, ** p<.05, ***p<.01
5.1.4. Watch Downgrade
For the watch downgrade announcement, similar results are drawn out with the downgrade CAAR analysis. The CAARs were all negative for all the event windows and strongly significant at a 1% level (see table 7). It is interpreted that shareholders strongly reacted in a negative way toward the downgrade of watch
announcements. This outcome is well-aligned to Followill & Martell’s (1997) paper, where it showed an evidence that the abnormal return performances were very significant for watch downgrade announcements compared to the actual downgrade announcements.
Table 7 CAARs and their p-values for watch downgrade
Event window [-20, +20] [-10, +10] [-2, +2] [-1, +1] [-1, +5]
CAAR -3.051% -3.403% -2.145% -1.990% -1.648%
CAAR t-stat -2.906 -4.014 -3.899 -3.853 -2.685
p-value 0.004*** 0.000*** 0.000*** 0.000*** 0.007***
The table shows the cumulative average abnormal return and their p-value for different event windows. * p<.1, ** p<.05, ***p<.01
24
5.2 Ordinary Least Squares (OLS) regression results
Table 8 Ordinary Least Squares regression result on cumulative abnormal returns
The table shows the regression results of predicted coefficients and standard errors (in parentheses) for different windows. The independent variable is Cumulative Abnormal Returns (CARs). The first column regressions for each window (1), (4), (7), (10), and (13) are results of models with only explanatory variables. On top of the first column regression, control variables are added to the second column regressions for each window, (2), (5), (8), (11) and (14). The last column regressions for each window includes the interaction terms on top of the previous variables. *,** and *** indicate the significance level of 10%, 5%, 1% respectively.
[-20, +20] [-10, +10] [-2, +2] [-1, +1] Variable (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Constant -0.013 (0.020) (0.051) 0.013 (0.054) 0.005 (0.017) 0.016 0.082** (0.041) (0.042) 0.032 (0.013) 0.023* (0.029) 0.013 (0.025) -0.014 0.035*** (0.011) (0.025) 0.006 -0.038* (0.022) ES -0.400 (0.345) (0.344) -0.331 (0.563) -0.127 -0.843*** (0.297) -0.867*** (0.302) (0.421) 0.067 -0.435** (0.205) -0.452* (0.232) (0.232) 0.046 -0.595*** (0.186) -0.614*** (0.208) (0.195) 0.166 Inv_grade low (0.022) 0.021 (0.026) 0.003 (0.049) -0.028 (0.017) 0.015 (0.020) -0.006 (0.042) 0.017 (0.012) -0.001 (0.015) -0.002 (0.040) 0.009 (0.010) -0.001 (0.013) 0.002 (0.030) 0.032 Inv_grade medium (0.014) 0.015 (0.017) 0.005 (0.017) 0.005 (0.011) 0.014 (0.014) 0.002 (0.014) 0.000 (0.006) -0.000 (0.007) -0.001 (0.007) -0.002 (0.005) -0.002 (0.006) -0.002 (0.006) -0.003 Non-fin_industry 0.023* (0.013) 0.046** (0.020) 0.045** (0.019) (0.011) 0.015 (0.017) 0.028* 0.032** (0.016) (0.006) -0.007 (0.010) -0.008 (0.010) -0.006 -0.010* (0.005) (0.010) -0.014 (0.011) -0.011 Uncertainty Index (0.008) 0.001 (0.009) -0.011 (0.006) -0.000 (0.007) 0.005 (0.004) -0.001 (0.004) -0.003 (0.003) 0.001 (0.003) -0.003 ln(Size) -0.004 (0.004) (0.004) -0.004 -0.007** (0.003) -0.006** (0.003) (0.002) 0.002 (0.002) 0.002 0.004* (0.002) 0.004** (0.002) Leverage 0.004* (0.022) (0.022) 0.004* (0.002) 0.002 (0.002) 0.002 (0.001) -0.000 (0.001) -0.000 (0.001) -0.001 (0.001) -0.001 Fin_crisis -0.049** (0.020) -0.049** (0.019) (0.017) -0.019 (0.016) -0.022 (0.009) 0.008 (0.008) 0.006 (0.008) 0.009 (0.008) 0.006 Downgrade 0.020* (0.012) (0.033) 0.006 0.020** (0.010) (0.026) 0.026 (0.006) 0.006 (0.016) 0.005 (0.006) 0.009 (0.013) 0.019 Watchup 0.005 (0.014) (0.014) 0.003 (0.011) 0.021* 0.020* (0.010) (0.007) -0.003 (0.007) -0.004 (0.006) -0.001 (0.006) -0.003 Watchdown -0.016 (0.012) (0.041) 0.041 (0.009) -0.014 0.075** (0.034) -0.013** (0.006) (0.026) 0.039 -0.009* (0.005) 0.052** (0.024) Low*ES 0.402 (0.672) (0.611) -0.382 (0.630) -0.191 (0.503) -0.467 Down*ES 0.088 (0.665) (0.513) -0.410 (0.294) -0.166 -0.404* (0.239) Watdown *ES (0.835) -0.960 -1.629** (0.680) -0.950* (0.485) -1.146** (0.446) Down*Unc 0.016 (0.015) (0.012) -0.011 (0.007) -0.002 (0.005) 0.000 Watdown *Unc (0.016) 0.015 (0.012) -0.005 (0.008) 0.004 (0.006) 0.007 Observations 1233 1233 1233 1233 1233 1233 1233 1233 1233 1233 1233 1233 R-squared 0.012 0.031 0.040 0.044 0.058 0.078 0.029 0.039 0.061 0.067 0.081 0.115 F-statistics 2.646 1.791 1.392 4.466 2.641 2.122 1.224 1.470 1.234 2.983 2.397 1.942
25
Further hypotheses will be explained by interpreting the OLS regression outcomes. The OLS regressions are run with different window lengths which are the same as for the event study window lengths. Table 8 illustrates the coefficient results and degrees of significance for different windows. A result of [-1, +5] window is excluded since it does not contain much informational value that none of the variables are significant, and its explanatory power is weaker than the other window models. (the result can be found in appendix II). Adding more explanatory power, including control variables and interaction terms, leads to the improvement of R-squared value. F-statistics values report the degree of best fits of the population from which the data were sampled by testing whether the coefficients are jointly different from 0.
Consistent with the studies of Steiner & Heinke (2001) and Finnerty et al. (2013), the results confirm the theory that non-financial firms are more sensitive to credit rating change announcements than financial firms. In regression (2) (3), (5), and (6) the CARs in [-20, +20] and [-10, +10] for non-financial firms are significant at a significance level of 5%, excluding regression (5) which has a significance level of 10%. The CAR obtained as non-financial firms during the window [-20, +20] is around 0.045% points or 0.046% points more than for financial firms. During the shorter window of [-10,+10], the increase of CAR is 0.028% points or 0.032% points more than for financial firms. Hypothesis 2 is partly explained by these models.
It is interesting to mention the regression (2) and (3) that during the financial crisis, the CAR earned during the window [-20, +20] is 0.049% points less than during the non-financial crisis period at a 95% confidence interval. The relationship between credit qualities and the abnormal return performances was not apparent in that none of the coefficients are significant, and the direction of the marginal effects are also not consistent.
The coefficients of expected shortfall were mostly negative as expected, which means that the increase of expected short (higher market risk) leads to significant decreases in the CAR. The ES coefficients in the windows of [-10, +10], [-2, +2], [-1, +1] are more significant than [-20, +20] window. This might be because the [-20, +20] window contains more contaminated data that can distort the relationship between CARs and the ES variable due to its longer window length. At a 1% significance level, a one percentage point increase in the expected shortfall results in decreases of CAR by 0.843% points and 0.867% points for the regression (4) and (5), respectively. The regressions (10) and (11) also show the same significance level with a decrease of 0.435% points and 0.452% points per one percentage point increase of the expected shortfall for each regression. Similarly, the regression (7) and (8) report the same results but with smaller marginal effects and weaker significance levels.
The interpretation of variables that have additional interaction terms should be more careful. The marginal effects can be calculated by differentiating the whole regression equation in terms of an independent variable that needs to be investigated. The result of regression (6) shows that a marginal effect of a one
26
percentage point increase of ES with various interaction terms is 0.067 – 0.382*Low – 0.410*Down – 1.629*Watdown. All the variables in this marginal effect equation contribute to negative CARs, but
particularly watch down events without having a low quality rating leads to a significant decrease of CAR by 1.562% points. Negative credit rating change with low quality rating decreases CARs even further with a one percentage point increase of ES. In regression (9) and (12), marginal effect equations of a one percentage point increase of ES are the same as the regression (6) but with different coefficient estimations. Sharpe decreases of 0.904% points, and 0.980% points in CARs are predicted when there is a one percentage point increase of ES without having a low quality rating. Recall that the studies of Hirk et al., (2019) and Abad & Robles (2014) reported the relationship between higher both idiosyncratic and systematic risk and credit rating. The results support the hypothesis 3 that the higher market risk exposed firms tend to react more negatively toward credit rating change.
Marginal effects on CAR of the downgrade variable and the watch downgrade variable are expected to be negative and for watch upgrade, vice versa. Concerning the downgrade variable, regressions without interaction terms (model number (2), (5), (8), and (11)) show that the coefficients are positive. However, this unexpected result is improved by adding interaction terms. In regression (6), marginal effect of downgrade events with various interaction terms is 0.026 – 0.410*ES – 0.011*Unc. Predicted CAR during the [-10, +10] window after a downgrade event is 0.395% points less than CAR after an upgrade event by an additional one percentage point increase of expected shortfall and uncertainty index return. Marginal effect equations for regression (9), (12) are the same as the regression (6) except for different coefficient predictions. The estimated marginal effects for downgrade events in regression (9) and (12) are 0.163% points, and 0.314% points decrease in CAR compared to the upgrade events, which are less than the marginal effect of regression (6). Regression (3) does not show a consistent result with the regressions of (6), (9), and (12).
Concerning the watch downgrade variable in regression (6), a marginal effect equation with interaction terms is 0.075 – 1.629*ES – 0.005*Unc. The largest marginal effect is observed in regression (6). After a watch downgrade event holding a one percentage point increase in expected shortfall and uncertainty index return, a CAR saw 1.559% points decrease whereas CARs in the regression (3), (9), and (12) saw decreases of 0.904% points, 0.907% points, and 1.087% points respectively. Additionally, an estimated CAR obtained by firms that have low credit quality bonds does not show a significant difference compared to an estimated CAR obtained by firms that have high credit quality bonds.
The results support a reciprocal effect between credit rating risk and market risk. It is interesting to remark that interaction terms boost up explanatory power. Especially, it is revealed that regression (6) using a window length of [-10, +10] shows the strongest marginal effects compared to the other windows.
27
5.3 Ordered Logistic regression results
Table 9 Ordered logistic regression results on market risk level
The dependent variable has three ordinal categories. The expected shortfall being over 10% falls into the “high” value category, being in between 5% to 10% falls into the “medium” value category, and being less than 5% falls into the “low” value category. The z-statistic is based on the robust standard error to prevent heteroskedasticity. *,** and *** indicate the significance level of 10%, 5%, 1% respectively.
Marginal Effects
Variable Coefficients z-statistic High Medium Low
Uncertainty Index 0.000** 2.16 0.000** 0.000** -0.000** ln(Size) -0.179*** -3.26 -0.016*** -0.020*** 0.037*** Leverage 0.033 1.38 0.003 0.004 -0.007 Liq_ratio 0.002 0.82 0.000 0.000 -0.000 Inv_grade low 1.229*** 4.23 0.113*** 0.139*** -0.252*** Inv_grade medium 0.253 1.40 0.023 0.029 -0.052 Fin_crisis 0.924*** 5.21 0.085*** 0.104*** -0.189*** Non-fin_industry 0.679*** 3.98 0.062*** 0.077*** -0.139*** Downgrade 1.725*** 11.00 0.159*** 0.195*** -0.353*** Watchup 0.959*** 3.64 0.088*** 0.108*** -0.197*** Watchdown 1.406*** 8.52 0.129*** 0.159*** -0.288*** Cut 1 -0.456 (0.630) Cut 2 2.174 (0.624) Observations 1233 Wald chi2 272.65 Prob > chi2 0.0000 Pseudo R2 0.111
Since the coefficients itself do not represent its marginal effect for the ordered logistic model, marginal effects are separately estimated. The threshold values are written in table 9 as cut 1 and 2 which is presented in figure 3 as κ1 and κ2. Cut 1 divides category into low market risk and medium market risk and cut 2 divides into
medium market risk and high market risk. Wald test works by rejecting or not rejecting the null hypothesis that joint coefficients are different from 0. It tests whether removing the variables from the model will significantly harm the fit of that model or not.
The primary purpose of using this model is to explain hypothesis 4, whether firms that experience a change to low investment-grade rating have a higher probability of high value at risk loss. Table 9
28
demonstrates that most of the variables are statistically significant at a 1% or 5% level. The low market risk category is used as the reference category for the marginal effects. If the investment-grade evaluated to “low” after the credit rating change, it is predicted to be 11.3 % points more likely to have a “high” level of the expected shortfall and 13.9% more to have a “medium” level of the expected shortfall with a 99% confidence interval. These results give compelling evidence that low credit quality represented by the increase in credit risk contributes to higher market risk. The outcome validates the theory that was tested in the papers of Hirk et al., (2019) and Abad & Robles, (2014). Recall that the Basel Committee (2009) found that a low liquidity ratio heightens credit risk and market risk as well. A liquidity ratio variable is added to study whether it affects the market risk after the credit rating change. The marginal effects of liquidity ratio are expected to be negative since a unit increase of liquidity ratio leads to a lower probability of having high market risk. However, based on outputs from table 9, a unit increase of liquidity ratio results in a higher probability of having a high expected shortfall, and the marginal effect is insignificant.
Consistent with researches of Creighton et al. (2007) and Vassalou & Xing (2003), where it explained that the stock price reaction is notably volatile in the small firms after the credit rating change due to the higher default risk in comparison with bigger-size firms. It is interesting to check the size variable in that a unit decrease of a firm’s size results in 1.6% points higher market risk.
Additionally, it is predicted to increase the probability of having high market risk with 8.5% points during the financial crisis period. Firms that experience credit rating downgrade and watch downgrade tend to have higher chances to have a high market risk with an increase of 15.9% points and 12.9% points compared to the low market risk based on table 9. The firms that experience watch upgrade have 8.8% points higher probability to have high market risk, which is less than the negative credit rating experienced firms.
However, it is important to note that a direction of causation between the independent variable of the degree of market risk and the dependent variable of credit rating event is not clear. The result also can be interpreted that there is a possibility that credit rating agencies (CRAs) announce downgrades or watch downgrades after observing a heightened market risk. Therefore, it is questionable whether the CRAs provide informational value or simply reporting the current bad situation by announcing downgrades of credit rating. Despite that the CRAs reduce information asymmetry in the market, the CRAs were criticized that they provide wrongly estimated (too optimistic on debt payments) credit rating during the financial crisis (Jollineau et al., 2014). Moreover, Bodenstedt et al. (2013) revealed that Moody’s prediction ability to estimate
impairment risk was significantly low during the financial crisis. Therefore, the CRAs have been doubted by some researchers since the financial crisis. By this, it is difficult to say whether the Moody’s “predicted” downgrades or “announced” downgrades.
29
6. Conclusion
This paper aims to empirically identify the interconnection between credit and market risk. Based on an event study, the informational value of credit rating on the European stock market was investigated. The statistical results strongly support that the European stock market tends to react more to negative credit rating news than to positive credit rating news.
This study used the OLS regression model to test the significance of the determinants of CAR by credit rating changes on the European market reaction, including expected shortfall value as market risk. According to the result of the OLS regression analysis, non-financial firms reacted more significantly to the credit rating change than financial firms. As one of the crucial findings of this paper, the estimation results suggest that investors reacted negatively toward companies that have higher market risk at a significant level after credit rating announcements. In addition, the interaction effects play an essential role in enhancing the explanatory powers of the expected shortfall variable and negative credit rating change variables.
Subsequently, the ordered logistic model is used to examine a direct connection between credit rating and market risk. By this analysis, the model predicts the probability of whether selected determinants of market risk, for instance, low quality credit rating or liquidity ratio, contribute to the categorized market risk level. Based on estimation outputs, it can be concluded that firms that owned low credit quality debts are significantly more likely to have high market risk. Moreover, a firm that experiences negative credit rating change has a considerably higher chance of being categorized as having a high market risk. From a probabilistic perspective, this result sheds light on the direct relationship between credit rating risk and market risk that being exposed to low credit quality risk contributes to a higher probability of high market risk.
This paper has shown that credit risk on bond credit rating affects the European stock market.
Furthermore, this study further expands the understanding of the mutual interaction between credit risk and market risk using the quantitative models. The empirical analysis provides evidence that the market risk estimation using expected shortfall plays an essential role as one of the determinants of the informational value of credit rating risk. Furthermore, this paper also suggests that credit rating risk also contributes to the degree of market risk.
This research elucidates the hypotheses based on previous literature, but it raises some questions of whether the gathered data of abnormal returns are accurate enough to see clear effects by an event study. To understand the implications of the results clearly, future studies should consider data contamination caused by multiple events occurring in the same event windowwhere it supposed to contain only a credit rating change event. It is also essential to consider that the credit rating announcements are unanticipated, then
