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The Determinants of Corporate Bond Yield Spreads in South Africa: Firm-Specific or Driven by Sovereign Risk?

Martin Grandes (DELTA, ENS/EHESS, Paris) Marcel Peter (International Monetary Fund)1

First version: November 21, 2003 This version: February 24, 2004

Only for comments. Please do not circulate. Abstract: This paper investigates to what extent the practice by rating agencies and international banks of not rating companies higher than the sovereign (country ceiling rule) is reflected in market prices of South African local currency denominated debt. Moreover, it seeks to quantify the importance of sovereign risk in determining corporate yield spreads, after controlling for firm-specific determinants. The main findings are, first, that the country ceiling (in local-currency terms) does not hold for all 9 companies analyzed, in the sense that the yields of their rand-denominated bonds outstanding increase less than 1% when government bonds yields rise by the same amount. Accordingly, the elasticity of corporate spreads with respect to sovereign spreads results significantly lower than 1 (approximately 0.83). And second, other firm specific features (leverage, volatility of returns on the firms value, maturity and risk-free interest rate volatility), are also found statistically significant determinants of corporate spreads. Keywords: sovereign (default) risk, corporate (default) risk, sovereign ceiling, risk premium, yield spreads, South Africa JEL Classifications: F21, F34, G12, G13, G15

1 The authors wish to thank Bernard Claassens and Mark Raffaelli (Bond Exchange of South Africa) for their invaluable help on questions about the South African bond market, and Candy Perque from the World Bank for answering questions on the rand-denominated IBRD/IFC bonds outstanding. They also acknowledge generous financial support provided by the Swiss Agency for Development and Co-operation to the project which gave rise to this study.

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Table of Contents Table of Contents ............................................................................................................................................2 1. Introduction ...........................................................................................................................................3

1.1. Why South Africa? ..............................................................................................................................4 1.2. Sovereign Risk and the Sovereign Ceiling Rule ..............................................................................5

2. Review of Related Literature.................................................................................................................7 3. Theoretical Framework: Determinants of the Corporate Default Premium.........................................10

3.1. Starting Point: The Merton (1974) Model .........................................................................................11 3.2. Adding Stochastic Interest Rates: The Shimko et al. (1993) Model..................................................14 3.3. Adding Sovereign Risk......................................................................................................................17 3.4. Other Potential Determinants ............................................................................................................21 3.4. Synthesis............................................................................................................................................22

4. Operationalization of Variables and Data............................................................................................22 4.1. Dependent Variable: How Are Corporate Default Spreads Measured?.............................................22 4.2. Explanatory Variables .......................................................................................................................25

4.2.1. Sovereign Default Premium.......................................................................................................25 4.2.2. Quasi-Debt to Firm Value (Leverage) Ratio..............................................................................26 4.2.3. Time to Maturity........................................................................................................................29 4.2.4. Firm Value Volatility.................................................................................................................30 4.2.5. Interest Rate Volatility...............................................................................................................31 4.2.6. Liquidity ....................................................................................................................................33

4.3. Sample and Data................................................................................................................................34 5. Empirical Methodology and Results....................................................................................................35

5.1. Sources of Variability and Statistical Properties of Corporate Default Spreads................................35 5.2. Set-Up of Model: A General Error Components Specification .........................................................35

5.2.1. Corporate Spreads in Levels ......................................................................................................35 5.2.2. Corporate Spreads in First Differences......................................................................................36

5.3. Panel Regression Results of Level Equation .....................................................................................37 5.3.1. Tests of Pooling .........................................................................................................................37 5.3.2. Fixed or Random Effects? .........................................................................................................38 5.3.3. Model Selection .........................................................................................................................38 5.3.3.1. Regression Output...................................................................................................................38 5.3.3.2. Test for Existence of Random Effects ....................................................................................40 5.3.3.3. Haussmans Test of Endogeneity............................................................................................40

5.4. Regression Results of First-Difference Equation ..............................................................................41 6. Discussion of Results...........................................................................................................................41 7. Conclusions .........................................................................................................................................43 8. References ...........................................................................................................................................45 Appendix .......................................................................................................................................................48

A1. Mathematical Appendix.....................................................................................................................48 A1.1. Calculation of the Impact of Interest Rate Volatility on Corporate Default Premium...............48 A1.2. Derivation of Volatility of Firm Value as a Function of Equity Volatility and Interest Rate Volatility..............................................................................................................................................48 A1.3. Numerical Procedure to Calculate Volatility of Firm Value......................................................50

A2. Econometric Issues ............................................................................................................................50 A2.1. Variability Decomposition of Corporate Default Spreads .........................................................50 A2.2. Tests of Pooling .........................................................................................................................51 A2.3. RE-FGLS Weighting as a Special Case of OLS or LSDV Estimators.......................................53 A2.4. Statistical Tests ..........................................................................................................................53

A3. Tables and Figures.............................................................................................................................55

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1. Introduction

The cost of capital - in particular the cost of debt - is an important determinant of economic growth in emerging economies. Borrowers in emerging countries be it the government itself or the country's firms that are able to tap international capital markets generally pay a considerable risk premium (country premium, see diagram below) over comparable risk-free assets (such as US-Treasury securities) when issuing bonds or contracting loans in hard currency. When these debt instruments are denominated in domestic currency, one of the main components of this "total risk premium" is the "currency (risk) premium" (sometimes also referred to simply as currency risk2), which reflects the risk of a depreciation or devaluation of the domestic currency.3

Diagram: The Cost of Debt for an Emerging Market Borrower

A second important component is the "default (risk) premium". The default

premium reflects the financial health (solvency) of the borrower under consideration and compensates for the risk that he/she "defaults", i.e. is unable (or unwilling, in the case of a government) to service his/her debt. The third component of the total risk premium is a "jurisdiction (or "onshore-offshore") premium" that is caused by differences between domestic ("onshore") financial regulations and international ("offshore") legal standards. In the literature, the sum of the default premium and the jurisdiction premium is often called "country (risk) premium" or simply "country risk" (see diagram). Moreover, if the borrower in question is the government itself, the default risk premium, or the country risk premium, is called the "sovereign risk premium" or simply "sovereign risk".

The purpose of this paper is to assess the importance of sovereign default risk in determining local-currency-denominated corporate financing costs, choosing South Africa as case study. In particular, we will try to answer the following questions: Can we 2 This currency risk premium is not to be confused with the exchange risk that can arise as a result of an investor's risk aversion and/or because of covariance of consumption with exchange rates. 3 In a companion paper, Grandes, Peter, and Pinaud (2003), we analyze the determinants of the currency premium in South Africa.

Cost of local-currency-denominated debt

=

Risk-free rate

+ 1) Currency (risk) premium

Total risk premium 2) Default (risk) premium

3) Jurisdiction premium Country (risk) premium

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observe something like a sovereign ceiling in local-currency-denominated corporate yield spreads? Is a given increase in sovereign risk, as measured by the sovereign bond spread (sovereign risk premium), associated with a more or less than proportionate increase in South African corporate bond spreads (corporate default premia)? Do idiosyncratic (i.e. company-specific) factors help explain corporate default risk premia? The crucial policy issue in this context is to what extent corporate debt costs can be lowered when public sector solvency improves.

Before we proceed with our investigation into these questions, let us briefly

motivate the choice of South Africa as a case study, and introduce the concept of sovereign ceiling.

1.1. Why South Africa?

We selected South Africa as a case study for the following reasons. First, South Africa is one among few emerging markets to have a corporate bond market in local currency (i.e. the rand).4 Admittedly, this market is still very small: during our sample period (July 2000 May 2003), there were only nine private sector South African firms with a total of 12 bonds outstanding (see table 2 in appendix A3). However, even though small, the South African corporate bond market has a considerable growth potential, according to a recent report by the Rand Merchant Bank (2001). Among the reasons, the report mentions that (i) South African corporates are under-leveraged and will need more debt in the future to create a more optimal financing structure; (ii) local banks and institutional investors have a great appetite for this asset class because they are significantly underweight in fixed-income instruments compared to their peers in similarly developed capital markets; (iii) as the government has stabilized its fiscal deficits and increasingly resorted to foreign currency borrowing to bolster its international reserves needed to cope with currency instability, the governments dominant role in the domestic debt market may gradually decrease, which in turn could crowd in demand for corporate bonds.

Second, our empirical study uses a so far unexploited dataset provided by the

Bond Exchange of South Africa (BESA). Third, the current nine corporate issuers are important South African companies. Looking at the prospective development of South Africas corporate bond market, we think the experience of these borrowers could help inform the decisions made by other potential issuers to resort to the local bond market as an alternative source of finance.

4 In the terminology of Eichengreen and Hausmann (1999), South Africa is one of few emerging markets not to suffer from the Original Sin problem. A country suffers from Original Sin, if it cannot borrow abroad in its own currency (the international component) and/or if it cannot borrow in local currency at long maturities and fixed rates even at home (the domestic component).

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1.2. Sovereign Risk and the Sovereign Ceiling Rule

Empirically, a high correlation between sovereign defaults and company defaults

has been observed in the past, that is, it has been very hard for companies to avoid default once the sovereign of their incorporation had defaulted. This historical regularity was used by all major rating agencies to justify their country (or sovereign) ceiling policy, which usually meant that the debt of a company in a given country could not be rated higher than the debt of its government. The economic rationale behind the sovereign rating ceiling for foreign-currency debt obligations is direct sovereign intervention risk, also called transfer risk; the rationale behind the sovereign rating ceiling for domestic-currency debt obligations is what Standard and Poors calls economic or country risk5, but what we prefer to call indirect sovereign risk.

The term transfer risk (or direct sovereign intervention risk) is usually only used

in a foreign currency context. It refers to the probability that a government with (foreign) debt servicing difficulties imposes foreign exchange payment restrictions (e.g. debt payment moratoria) on otherwise solvent companies and/or individuals in its jurisdiction, forcing them to default on their own foreign currency obligations. Indirect sovereign risk is the equivalent of transfer risk in domestic currency obligations. It refers to the probability that a firm defaults on its domestic-currency debt as a result of distress or default of its sovereign. As a matter of fact, economic and business conditions are likely to be hostile for most firms when a government is in a debt crisis. It is indirect sovereign risk that we are primarily concerned about in this paper. Section 3.3 elaborates on it. Both, direct sovereign intervention risk (transfer risk) and indirect sovereign risk, are closely related to pure sovereign risk.6

Until 2001, the three main rating agencies, Moody's Investors Service, Standard and Poor's, and Fitch Ratings, followed their country or sovereign ceiling policy more or less strictly. They amended it, however, under increasing pressure from capital markets after the ex-post zero-transfer-risk experience in Russia (1998), Pakistan (1998), Ecuador (1999), and Ukraine (2000).7 Moodys the last among the big three rating agencies to abandon the strict sovereign ceiling rule justified the policy shift as follows: This shift in our analytic approach is a response to recent experience with respect to transfer risk [in Ecuador, Pakistan, Russia, and Ukraine] Over the past few years, the behaviour of governments in default suggested that they may now have good reasons to allow foreign

5 See Standard & Poor's (2001), p.1. 6 Sovereign risk refers in principle to the probability that a government defaults on its debt. The terms sovereign risk, direct/indirect sovereign risk and transfer risk are, however, often used interchangeably, as for instance in Obstfeld and Rogoff (1996), p. 349. 7 See Moody's Investors Service (2001b), Standard & Poor's (2001), Fitch Ratings (2001).

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currency payments on some favored classes of obligors or obligations, especially if an entitys default would inflict substantial damage on the countrys economy.8

Under specific and very strict conditions, rating agencies now allow firms to

obtain a higher rating than the sovereign of their incorporation (or location). These conditions are stricter for piercing the sovereign foreign currency rating than the sovereign local currency rating. Bank ratings are almost never allowed to exceed the sovereign ceiling (in both foreign and domestic currency terms) because their fate is supposedly very closely tied to that of the government. Table 1 (see appendix A3) shows that, among those of the nine firms analyzed which had a rating by Moodys or Standard and Poors, eight were rated at or below the government. The only temporary exception was Sasol, a globally operating oil and gas company. It was assigned a BBB foreign currency credit rating by Standard & Poors on February 19, 2003, about three months before the governments foreign currency rating was itself upgraded to BBB (May 7) from BBB minus. All other rated firms in our sample were rated at or below the sovereign ceiling, for both foreign and local-currency ratings. Moreover, as the table indicates, four of the five banks or financial firms (ABSA Bank, Investec Bank, Nedcor, and Standard Bank) have always been rated at the sovereign ceiling.

One of our objectives in this study is to analyze to what extent a sovereign

ceiling can be observed in rand-denominated corporate yield spreads.9 This will entail, in a first step, to verify whether the bond yields of the firms analyzed are always higher than comparable yields of government bonds. As panels 1 through 12 of figure 1 (see appendix A3) show, all South African corporate bonds analyzed bear indeed higher yields than sovereign bonds of similar maturity and coupon do.

However, corporate spreads that exceed comparable government spreads are only

a necessary but not sufficient condition for the existence of a sovereign ceiling in corporate spread data: the spread of a given firm may be higher than a comparable government spread because the firm, on a stand-alone basis (i.e. independent of the creditworthiness of the government in whose jurisdiction it is located), has a higher default probability than that government. Recall that the spread is essentially a compensation that an investor requires for the expected loss rate he faces on an investment, the expected loss rate (EL) being the product of the probability of default (PD) times the loss-given-default rate (LGD), i.e. EL = PDLGD. Thus, whenever we observe rand-denominated corporate spreads that exceed comparable government spreads, we will have to find out whether these observations are due to a high stand-alone

8 See Moody's Investors Service (2001a), p.1. 9 In terms of spreads, the sovereign ceiling actually translates into a sovereign floor. However, we stick to the ceiling terminology in order to be consistent with the literature in this field.

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default probability of the firm or to high indirect sovereign risk. Section 3.3 provides a framework to disentangle the different risks.

Confronted with this identification problem, we will resort to a result obtained by

Durbin and Ng (2001). They show in a simple theoretical model that the rating agencies main justification of the sovereign ceiling rule namely, that whenever a government defaults, firms in the country will default as well, i.e. that transfer risk is 100% implies that a 1% increase in the government spread should be associated with an increase in the firm spread of at least 1%. We will use this finding to more systematically study the overall impact of sovereign risk on corporate spreads in South Africa. In particular, we will apply Durbin and Ngs finding and estimate the elasticity of corporate bond yield spreads with respect to sovereign yield spreads in order to test whether the sovereign ceiling applies for the firms analyzed. Apart from Durbin and Ng (2001), there are no empirical investigations available on that subject to our knowledge. Unlike Durbin and Ng (2001), we will also control for firm-specific variables derived from the literature on corporate debt pricing. The rest of the paper is organized as follows. Section 2 reviews the related literature. Section 3 introduces the theoretical framework from which the determinants of the corporate default premium are derived. The description and operationalization of these determinants follows in section 4. Section 5 sets forth the empirical methodology to estimate their relative importance and presents the econometric results. The results are discussed in section 6 and section 7 concludes.

2. Review of Related Literature

The present study is closest in spirit to the one by Durbin and Ng (2001). Both are interested in (i) assessing whether a sovereign ceiling can be observed in corporate yield spreads (i.e. whether corporate yields are always higher than comparable sovereign yields), and (ii) quantifying the impact of sovereign risk on corporate financing costs. The main differences are threefold. First, while Durbin and Ng (2001) analyze the relationship between corporate and sovereign yield spreads on foreign currency bonds in emerging markets, we study this relationship between corporate and sovereign yield spreads on domestic currency bonds. Second, Durbin and Ng (2001) work with a broad cross-section of over 100 firm bonds from various emerging markets, while we work with all domestic currency denominated and publicly traded firm bonds available in one particular emerging economy, South Africa.10 Third, we also control for firm specific determinants

10 We actually take all publicly traded bonds of South African firms whose shares are quoted on the Johannesburg Stock Exchange (JSE).

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(e.g. leverage and asset volatility) in our assessment of the impact of sovereign risk on corporate default premia, while this is not the case in Durbin and Ng (2001).

Durbin and Ng (2001) argue that the existence of a sovereign ceiling in yield

data would imply two things. First, if firms are always riskier than their governments (the rating agencies first justification of the sovereign ceiling), then there should be no instance where a given corporate bond has a lower yield spread than an equivalent sovereign bond issued by the firms home government. Second, Durbin and Ng (2001) show in a simple theoretical model that the rating agencies main justification for the sovereign ceiling rule namely, that whenever a government defaults, firms in the country will default as well, i.e. that transfer risk is 100% implies that a 1% increase in the government spread should be associated with an increase in the firm spread of at least 1%. In other words, in a regression of corporate spread changes on corresponding sovereign spread changes, the beta-coefficient should be greater than or equal to one.

With respect to the first argument, they find that the corporate and sovereign bond

yield spreads in their sample are not fully consistent with the application of the sovereign ceiling rule: several firms have foreign currency bonds that trade at significantly lower spreads than comparable bonds of their government. With respect to the second argument, they find that when the riskiness of the country of origin is not controlled for, the beta-coefficient is indeed slightly larger than one. However, when the riskiness of the country of origin is taken into account, it turns out that the beta-coefficient is significantly smaller than one for corporate bonds issued in low-risk and intermediate-risk countries but significantly higher than one in high-risk countries.11 They conclude that in relatively low-risk countries, market participants judge transfer risk to be less than 100%, that is, they do not believe the statement that firms will always default when the government defaults.12 As a consequence, the second justification for the sovereign ceiling rule would be invalidated in these cases.

Apart from Durbin and Ng (2001), there seems to be very little research on the

determinants of corporate default risk in emerging markets. We know of no other theoretical or empirical study that investigates the relationship between sovereign risk and corporate debt pricing in an emerging market environment. This could be due to the fact that most of these corporate bond markets are not yet well developed.

11 The 13 countries for which US dollar denominated corporate bond yields were available have been ranked by average government spreads; the low-risk group is composed of the 5 countries with the lowest spreads, the intermediate-risk group of the next 5 countries, and the high-risk group of the three with the highest spreads. See Durbin and Ng (2001), p. 30. 12 Durbin and Ng (2001), p. 19.

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There are, however, two related literature strands. First, there exists a wealth of theoretical and empirical studies on the determinants of corporate default risk premia in industrial countries or, more specifically, in the United States. One of the first such investigations, Fisher (1959), finds that the yield spread on a firms bonds depends on (i) the probability that the firm will default (which Fisher measures by the three variables earnings variability, period of solvency, and debt/equity ratio) and (ii) on the marketability (or liquidity) of the firms bonds. In his famous theoretical paper, Merton (1974) uses the option pricing theory developed by Black and Scholes (1973) to the pricing of corporate debt (the so-called contingent claims analysis). In his highly simplified model, the corporate default risk premium is a function of only three variables: (i) the volatility of the returns on the firm value, (ii) the debt-to-firm value ratio (both measuring the probability of default), and (iii) the time to maturity of the bond. Later on, Shimko, Tejima, and Van Deventer (1993) are the first to introduce stochastic (risk-free) interest rates into the Merton model. As a result, corporate default premia become also function of interest rate volatility.

Several empirical studies also document the importance of bond indenture

characteristics. Ho and Singer (1984) show that the existence of a sinking fund is associated with lower bond yield spreads. Cook and Hendershott (1978) demonstrate, among other things, that the existence of a call option embedded in a corporate bond increases the yield spread. In their large panel study of US industrial firm bonds, Athanassakos and Carayannopoulos (2001) find that, beside all these factors (i.e. default probability, time to maturity, presence of call options, presence of a sinking fund), tax effects13, business cycle conditions, and temporary demand and supply of bonds imbalances also affect corporate yield spreads. Analyzing US corporate bond spreads, Elton, Gruber, Agrawal, and Mann (2001) finally find that expected loss14 accounts for only about 18% of the spread on 10-year A-rated industrial bonds. More important determinants of corporate spreads are, first, differential taxes (i.e. that state and local taxes must be paid on corporate bonds but not on government bonds), which account for 36% of the spread and, second, a risk premium that accounts for up to 39% of the spread. According to Elton et al. (2001), p. 273, this risk premium is a compensation for systematic risk that cannot be diversified away and is affected by the same influences that affect systematic risk in the stock market.

The distinguishing feature of industrial countries and the US in particular is

that government bonds are risk-free (i.e. sovereign risk is zero). This implies that, once controlled for all determinants mentioned above except default risk, the US corporate yield spread above an equivalent US Treasury bond yield reflects only corporate default

13 Such tax effects occur in the U.S. because interest payments on corporate bonds are subject to state and local taxes, whereas government bonds are not subject to these taxes. 14 Expected loss equals the probability of default times the loss-given-default rate, i.e. EL = PDLGD.

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risk. This is in sharp contrast to emerging markets where almost by definition government bonds are not risk-free. In an emerging market, the corporate yield spread above an equivalent government bond yield does not reflect corporate default risk, even after controlling for all other factors. It merely reflects corporate default risk in excess of sovereign default risk. Hence, it appears that in emerging economies there is a crucial additional determinant of corporate default risk: the default risk of the government, i.e. sovereign risk. Sovereign risk is precisely what the rating agencies sovereign ceiling rule is all about. Section 3.3 elaborates on this idea.

The second strand of related literature concerns the empirical studies that assess

the determinants of government yield spreads (i.e. sovereign default risk premia) in emerging markets. Examples are Edwards (1984), Edwards (1986), Boehmer and Megginson (1990), Eichengreen and Mody (1998), and Westphalen (2001). Most of these studies identify the classical sovereign default risk determinants, like total indebtedness (debt/GDP ratio), debt service burden (debt/exports ratio), level of hard currency reserves (Reserves/import or GDP ratio) and others. However, they completely ignore the relationship between sovereign and corporate default risk.

3. Theoretical Framework: Determinants of the Corporate Default Premium

The theoretical literature on the pricing of defaultable fixed-income assets also

called credit risk pricing literature can be classified into three broad approaches:15 (1) the classical or actuarial approach, (2) the structural approach, or firm value or option-theoretic approach, sometimes also referred to as contingent claims analysis, and (3) the reduced-form or statistical or intensity-based approach. The basic principle of the classical approach is to assign (and regularly update) credit ratings as measures of the probability of default of a given counterparty, to produce rating migration matrices, and to estimate (often independently) the value of the contract at possible future default dates. Typical users of this approach include the rating agencies (at least the traditional part of their operations) and the credit risk departments of banks.16 The structural approach is based on Black and Scholes (1973) and Merton (1974).17 It relies on the balance sheet of the borrower as well as the bankruptcy code to endogenously derive the probability of default and the credit spread, based on no-arbitrage arguments and making some additional assumptions on the recovery rate and the process of the risk-free interest rates.

15 This paragraph draws heavily on Cossin and Pirotte (2001). 16 For a survey of these methods, see for instance Caouette, Altman, and Narayanan (1998). 17 Other important contributions to this approach include Shimko et al. (1993), Longstaff and Schwartz (1995), Sa-Requejo and Santa Clara (1997), Briys and De Varenne (1997), and Hsu, Sa-Requejo, and Santa Clara (2002).

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The reduced-form approach models the probability of default as an exogenous variable calibrated to some data. The calibration of this default probability is made with respect to the data of the rating agencies or to financial market series acting as state variables.18

As the classical approach is both too subjective and too backward looking and the

reduced-form approach is atheoretical with respect to the determinants of default risk, we adopt the simplest version of the structural approach as the theoretical framework for our investigation. In four steps, the determinants of corporate default risk are derived. In the first step, we recapitulate briefly the Merton (1974) model of risky debt valuation. In the second step, Mertons assumption of a constant risk-free interest rate is relaxed and stochastic (risk-free) interest rates la Shimko et al. (1993) are introduced. In the third step, we relax the assumption that government bonds are risk-free, i.e. we allow for sovereign (credit) risk; we introduce (in a more or less ad-hoc fashion) the sovereign default premium as an emerging-market specific, additional determinant of corporate default risk. In the fourth step, we briefly consider some potential further determinants that result once the frictionless market assumption is relaxed or specific bond indenture provisions are taken into account. A final subsection synthesizes and summarizes the determinants identified.

3.1. Starting Point: The Merton (1974) Model

The model starts with the following simplifying assumptions:19

(A.1) Markets are frictionless: There are no transaction costs, no taxes, no short-selling restrictions, no information asymmetries; assets are perfectly divisible and continuously traded; borrowing and lending rates are equal (i.e. absence of bid-ask spreads).

(A.2) Market participants are price takers: There are sufficiently many investors with comparable wealth levels such that they can buy or sell as much of an asset as they want at the market price.

(A.3) Constant risk-free interest rates: There is a riskless asset whose rate of return per unit of time is known and constant, i.e. the term structure of interest rates is flat. Thus, the price of a riskless discount bond paying $1 at maturity T is

]exp[)( rTTPt = where r is the instantaneous risk-free interest rate.

18 For readers interested in reduced-form models, we refer to the works of Pye (1974), Litterman and Iben (1991), Fons (1994), Das and Tufano (1996), Jarrow and Turnbull (1995), Jarrow, Lando, and Turnbull (1997), Lando (1998), Madan and Unal (1998), Duffie and Singleton (1999), Collin-Dufresne and Solnik (2001) and Duffie and Lando (2001), most of which are surveyed and nicely put into a broader context by Cossin and Pirotte (2001) and Bielecki and Rutkowski (2002). 19 This section is based on Merton (1974); Jones, Mason, and Rosenfeld (1984), p. 612; Shimko et al. (1993), pp. 59-60; and Cossin and Pirotte (2001), pp. 17-22.

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(A.4) Modigliani-Miller environment: The value of the firm, Vt, is invariant to its capital structure; it is equal to the (market) value of equity, Et, plus the (market) value of a representative zero-coupon noncallable debt contract, Dt, maturing at time T with face value B, i.e.

ttt DEV += (1)

Together with (A.1), this implies that the value of the firm and the value of its assets are identical.

(A.5) It dynamics of firm value: The value of the firm (i.e. the value of its assets), Vt, follows a geometric Brownian motion process:

tVt

t dZdtV

dV,1 += (2)

where is the instantaneous expected rate of return on the firm value, 2V is the instantaneous variance of the return on the firm value per unit of time (henceforth called asset return volatility or simply firm value volatility) , and

1, 1tdZ dt= is a (first)20 standard Gauss-Wiener process.

(A.6) Shareholder wealth maximization: Management acts to maximize shareholder wealth.

(A.7) Perfect antidilution protection: There are neither cash flow payouts, nor issues of any new type of security during the life of the contract, nor bankruptcy costs. This implies that default can only occur at maturity if the firm cannot meet the repayment of the face value of the debt, B.

(A.8) Perfect bankruptcy protection: Firms cannot file for bankruptcy except when they are unable to make the required cash payments. In this case, the absolute priority rule cannot be violated: shareholders obtain a positive payoff only if the debt holders are perfectly reimbursed.

Given these assumptions, the value of the equity of the firm, E, at time T (i.e.

maturity) is ),0max( BVE TT = . (3)

That is, from the point of view of the payoff structure, the equity of the firm, E, is equivalent to a call option on the assets of the firm, V.

Assuming V can be traded or perfectly replicated, the well-known Black-

20 A second Wiener process will be introduced in the next sub-section.

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Scholes call option pricing formula can be applied, where the value of the firm, V, is the price of the underlying, the volatility of its return is V , the face value of the debt, B, is the strike price, tT is remaining time to maturity, and r is the risk-free interest rate:

)()( 21 hBehVEr

tt = (4)

where )( is the standard normal cumulative density function and

V

Vt

r

V

Vt

V

Ber

B

V

h

22

1

2

1ln

2

1ln +

=

++

=

(5)

V

Vt

r

V

V

Be

hh

2

12

2

1ln

==

.

Given that the value of the firm is the sum of its equity and its debt, equations (1) and (4) imply that the value of the risky zero coupon bond is

ttt EVD =

)()( 21 hBehVDr

tt += (6)

The yield to maturity, yt, of the (risky) discount bond in a continuous time framework is the solution to the equation

yt BeD

= , (7)

that is,

=

B

Dy tt ln

1

. (8)

The corporate default premium (also called yield spread or credit spread), ts , is then

defined as the difference between the yield to maturity of the risky zero coupon bond and the risk-free rate, i.e.

rys tt . (9)

Substituting equations (6) and (8) into equation (9), the corporate default premium becomes:

rB

Ds tt

= ln1

+=+

=

rr

trt

Be

hBehVe

B

D )()(ln

1ln

1ln

1 21

14

+= )(1)(ln1 12 hd

ht

+

+=

V

tV

tV

tVt

d

d

ds

)ln(1)ln(ln

1 2212

21

, (10)

where tr

t VBed , i.e. the ratio of the present value (at the risk-free rate) of the

promised payment to the current value of the firm, is what Merton calls the quasi debt firm value ratio or simply the quasi-debt ratio.

For our purpose, equation (10) is the central result from Mertons very simple model: The corporate default premium is a function of only three variables. These are (1) firm value volatility, V , (2) the quasi-debt ratio, d (a form of leverage ratio), and (3) the time to maturity of the debt contract, . As usual in option pricing, the rate of return on the underlying security (here the growth rate in the value of the firm, ) has no impact on the default premium.

Further, Merton shows that 02 > Vs , 0> ds , and 0 s . That is, the

corporate default spread is an increasing function of firm value volatility and of leverage, as one would intuitively expect, and can be an increasing or decreasing function of remaining time to maturity, depending on leverage.21

3.2. Adding Stochastic Interest Rates: The Shimko et al. (1993) Model

In this section, assumption A.3 (constant risk-free interest rates) is relaxed, that is the risk-free interest rate is allowed to be stochastic. This implies that interest rate risk is integrated into the pricing of credit risk. Shimko et al. (1993) were among the first to propose this extension. We use their model because it is the simplest that still manages to convey the basic intuition: interest rate volatility is a further determinant of the corporate default premium.

21 Merton (1974), p. 456, and Sarig and Warga (1989b), p. 1356, show that the term structure of credit risk premia is downward sloping for highly leveraged firms (i.e. d >1), humped shaped for medium leveraged firms, and upward sloping for low leveraged firms (d

15

Shimko et al. (1993) suggest to integrate the Vasicek (1977) term-structure-of-interest-rates model into the Merton (1974) framework, i.e. they assume that the short-term risk-free interest rates follows a (stationary) Ornstein-Uhlenbeck process of the form

tr dZdtrdr ,2)( += (11) where is the long-run mean which the short-term interest rate r is reverting to, > 0 is the speed at which this convergence occurs, r is the instantaneous variance (volatility) of the interest rate, and 2, 2tdZ dt= is a (second) standard Gauss-Wiener process whose correlation with the stochastic firm value factor, tdZ ,1 , is equal to , i.e.

dtdZdZ tt = ,2,1 .

When short-term risk-free interest rates are characterized by the dynamics of equation (11), Vasicek (1977)22 shows that the price of a risk-free zero coupon bond with remaining maturity is no longer ]exp[)( rPt = but becomes

( ) ( )

=

2

3

2

14

)()(1

exp)(

eRrReP rt , (12)

and the yield to maturity of this risk-free discount bond what Vasicek (1977) calls the term structure of interest rates is

)(ln1

)(

tt PR = , (13)

where 2221)(lim)()(

rrttRRR +===

is the yield to maturity of a zero

coupon bond whose remaining maturity approaches infinity, and is the (constant) market price of risk as defined in Vasicek (1977), p. 181.23

Following Shimko et al. (1993), the value of the risky zero coupon bond the equivalent of equation (6) under stochastic interest rates can be written as

)()( 21 += hBPhVD ttt , (14)

where

+

=+

=T

TV

BP

T

TBP

V

h t

t

t

t

2

1)(ln

2

1

)(ln

1

(15)

22 See p. 185. 23 Note that now that the yield to maturity has been defined, the short-term risk-free interest rate r (called spot rate by Vasicek (1977)) of equation (11) can be defined as the yield to maturity of a risk-free zero coupon bond whose remaining maturity approaches zero, i.e. )(lim)0(

0

tttRRr

== .

16

==T

TV

BP

Thh t

t

2

1)(ln

12

,

where T , in turn, is

=

0

2 )( dssTD

( ) ( )12

221

2 23

2

23

2

2

22

++

++=

ee rVrrrVrV , (16)

where )(2 sD

, in turn, is

)(2)()( 222 sss PVPVD += ,

and where )(2 sP , finally, is

2

2

2 1)( rs

P

es

=

.

)(2 sP is the instantaneous variance (volatility) of the return on the risk-free zero coupon bond P with maturity s;24 )(2 s

D is the instantaneous volatility of the return on the risky

zero coupon bond D with maturity s; and T is the integrated instantaneous variance of the risky discount bond D over the remaining life of this debt contract.

Now, we have got all the elements to calculate the corporate default premium (or credit spread) ts under stochastic interest rates (i.e. the equivalent of equation 10 under

interest rate risk): ts is now the difference between the yield to maturity on the risky zero

coupon bond, )(ln1)( BDy tt= , and the yield to maturity on the risk-free zero

coupon bond of the same maturity )(ln1)( tt PR = , i.e.

)()( ttt Rys =

tt P

B

Dln

1ln

1

+

=

+=

t

tt

BP

hBPhV )()(ln

1 21

+=

)(1

)(ln1

12 hd

ht

24 See also Vasicek (1977), pp. 180 and 186.

17

+

+=

T

dT

dT

dTs t

t

tt

)ln(1)ln(ln

1 21

21

. (17)

where ttt VBPd is as before the quasi-debt ratio, i.e. the ratio of the present value

(at the risk-free rate) of the promised payment to the current value of the firm, but this time with a variable (stochastic) risk-free rate.

The central result from equation (17) is that the corporate default premium ts is a

function of a fourth important determinant: interest rate volatility r . A comparison of equations (17) and (10) reveals only two differences. First, the quasi-debt ratio in (10),

tr

t VBed , is replaced by ttt VBPd

in (17), accounting for the fact that the face

value of the risky debt, B, is now discounted at a variable (and stochastic) risk-free rate r. Second, the variance of the return on the firm value over the remaining life of the bond,

2V , is replaced by the variance of the return on the risky bond over its remaining life,

( )

++

++=

23

2

2

22 221

2

VrrrVrV eT ( )12

23

2

er . This

difference accounts for the fact that the value of risky debt, tD , and, hence, the value of

the firm, ,tV are now functions of two stochastic variables, V and r. As a consequence, ts

is now also function of interest rate volatility r .25

The impacts on the default premium of changes in the three already identified

determinants (leverage ,d firm value volatility V , and remaining time to maturity ) remain essentially the same under stochastic interest rates.26 What is the impact on spreads of changes in interest rate volatility r ? Generally, increases in r tend to increase the corporate credit spread, especially if leverage is high.27 However, this result is not universally true. As appendix A1.1 shows, the sign of rs is ambiguous. It depends in a complex fashion on , , , ,r and d

.

3.3. Adding Sovereign Risk

The central argument in this paper is that in an emerging market context, sovereign (default or credit) risk has to be factored into the corporate default premium equation as an additional determinant. All structural models of corporate credit risk

25 In principle, the corporate yield spread st is also function of the correlation between the two stochastic factors dZ1 and dZ2, and of , the speed of convergence of the risk-free rate r to its long run mean . For the present exercise, however, these two parameters are assumed to be constant over the sample period. 26 In particular, the impact of maturity continues to be ambiguous not only because of its dependence on leverage but also V. See Shimko et al. (1993), pp. 61-63. 27 See Cossin and Pirotte (2001), p. 51, and Shimko et al. (1993), p. 62.

18

pricing implicitly assume that government bonds are risk-free, i.e. that sovereign risk is absent. As these models are implicitly placed in a context of a AAA-rated country (typically the US), this assumption seems justified. In analyzing emerging bond markets, however, the zero-sovereign-risk assumption has to be relaxed. In the international rating business, the importance of sovereign default risk for the pricing of all corporate obligations has given rise to the concept of the sovereign ceiling, the rule that the rating of a corporate debt obligation (in domestic and foreign currency) can usually be at most as high as the rating of government obligations.

What is the economic rationale for sovereign risk to be a determinant of corporate

default risk in domestic currency terms? Unlike in foreign currency obligations where the influence of sovereign risk is essentially due to direct sovereign intervention (or transfer) risk, the impact of sovereign risk in domestic currency obligations is more indirect. When a sovereign is in distress or default, economic and business conditions are likely to be hostile for most firms: the economy will likely be contracting, the currency depreciating, taxes increasing, public services deteriorating, inflation escalating, interest rates soaring, and bank deposits may be frozen. In particular, the banking sector is more likely than any other industry to be directly or indirectly affected by a sovereign in payment problems. This vulnerability is due to their high leverage (compared to other corporates), their volatile valuation of assets and liabilities in a crisis, their dependence on depositor confidence, and their typically large direct exposure to the sovereign. As a result, default risk of any firm is likely to be a positive function of sovereign risk. We will call this type of risk indirect sovereign risk. An interesting observation in this context is that Elton et al. (2001) find that even in the US corporate default premia incorporate a significant risk premium because a large part of the risk in corporate bonds is systematic rather than diversifiable. One could argue that in emerging markets, a major source of systematic risk is (indirect) sovereign risk, as measured by the yield spread of government bonds over comparable risk-free rates (i.e. the sovereign default premium).

Let us formalize these considerations in a simple framework. Recall that the

corporate default premium (or spread) on a firm bond is essentially a compensation that an investor requires for the expected loss rate he/she faces on that investment. The expected loss rate (EL) is the product of the probability of default (PD) times the loss-given-default rate (LGD), that is EL = PDLGD. Assuming for simplicity that (1) LGD is equal to one (i.e. if the firm defaults, the whole investment is lost), (2) investors are risk-neutral, and (3) we consider only one-period bonds (i.e. there is no term-structure of default risk), the expected loss rate becomes equal to the probability of default (EL = PD). In this case, the corporate spread is only function of the companys probability of default, i.e. s = f(PD).

19

Now, let us have a closer look at the firms probability of default, PD, in the presence of sovereign risk. Using simple probability theory and acknowledging that a firms default probability is dependent on the sovereigns probability of default, one can show that the following probabilistic statement holds:

)()()( SFPSFPFP c +=

)/()()/()( SFPSPSFPSP cc +=

)/()()/()](1[ SFPSPSFPSP c += (18)

where the different events are defined as follows:

(1) event F : firm i defaults,

(2) event S : the sovereign where firm i is located defaults,

(3) event cS (= complement of event S): the sovereign does not default.

Inspecting equation (18), we see that the probability of default of the firm, P(F) = PD, is the result of a combination of three other probabilities:

(1) )(SP is the default probability of the sovereign (sovereign risk);

(2) )/( cSFP is the probability that the firm defaults given that the sovereign

does not default. We can interpret this probability as the firms default probability in normal times, as opposed to a crisis period. We call this probability the stand-alone default probability of the firm.

(3) )/( SFP is the probability that the firm defaults given that the sovereign has

defaulted. We can interpret this as the probability that the sovereign forces the firm which would not otherwise default into default. In other words,

)/( SFP can be interpreted as direct sovereign intervention (or transfer)

risk in foreign currency obligations, or what we have called indirect sovereign risk in domestic currency obligations.

In terms of credit ratings (which are nothing else than estimates of default

probabilities), the four probabilities ),/(),(),( cSFPSPFP and )/( SFP have direct

correspondents. In Moodys terminology, for instance, a banks domestic currency issuer rating would correspond to )(FP , which itself can be interpreted as the result of the

combination of its Bank Financial Strength rating, )/( cSFP , of the domestic currency issuer rating of its sovereign of incorporation (or location), )(SP , and of the indirect sovereign risk applicable in its case, )/( SFP .

Examining a few boundary cases, we realize that equation (18) makes intuitive sense. When the sovereign default probability is zero, the firms default probability reduces to its stand-alone default probability, i.e. )/()( cSFPFP = . As the sovereign default probability rises and approaches 100% ( 1)( =SP ), the importance of stand-alone

20

default risk ( )/( cSFP ) vanishes compared to direct ( )(SP ) and indirect sovereign risk ( )/( SFP ); at the limit (i.e. when 1)( =SP ), the firms default probability reduces to indirect sovereign risk (or transfer risk in foreign currency obligations), i.e.

)/()( SFPFP = . When the firms stand-alone default probability is zero ( 0)/( =cSFP ) but there is sovereign risk ( 0)( >SP ), the firms default probability is equal to the product of direct and indirect sovereign risk ( )/()( SFPSP ); in this case, only if indirect sovereign risk (or transfer risk) is also equal to zero, the firms (overall) default probability is also equal to zero ( 0)( =FP ). Finally, when there is direct sovereign risk ( 0)( >SP ) and indirect sovereign risk (or transfer risk in foreign currency terms) is 100% ( 1)/( =SFP ), the firms default probability equals )()/()](1[)( SPSFPSPFP c += . This boundary case is the key to understand the concept of the sovereign ceiling: Definition: In the context of a firms default probability, its credit rating, or its credit spread, the phrase the sovereign ceiling applies refers to the case when indirect sovereign risk (or transfer risk in foreign currency obligations) is 100%, that is, when

1)/( =SFP .

Whenever indirect sovereign risk (or transfer risk) equals 100%, equation (18) implies that the firms (overall) default probability )(FP will always be at least as high as the default probability of its sovereign, )(SP , independently of how low its stand-

alone default probabiliy )/( cSFP is. In other words, when indirect sovereign risk

(transfer risk) is 100%, the sovereign default probability (and, hence, the sovereign spread) acts as a floor to the firms default probability (and its spread). In terms of credit ratings (where low default probabilities are mapped into high ratings, and high default probabilities in low ratings), this floor translates into a ceiling, hence the concept sovereign ceiling. When indirect sovereign (or transfer) risk is smaller than 100% ( 1)/(

21

markets appreciation of indirect sovereign risk: a coefficient that is larger than one would imply that the market prices in an indirect sovereign risk of 100% (i.e. whenever the government defaults, the prevailing economic conditions force the firms into default as well); a coefficient smaller than one would imply that the market judges indirect sovereign risk to be less than 100%. It will be interesting to compare our own estimates for domestic-currency-denominated (i.e. rand) corporate bonds with the results obtained by Durbin and Ng (2001) for foreign-currency-denominated corporate bonds. They found, among other things, that the coefficient was significantly smaller than one for the low-risk country group of which South Africa was a part (together with Czech Republic, Korea, Mexico, and Thailand).

In light of these considerations, we will add the sovereign default premium, or sovereign spread sG, (in an admittedly more or less ad-hoc fashion) to our estimating equation. We will, first, test whether the sovereign spread can be considered as an additional determinant of corporate credit spreads. We would expect the associated coefficient ( / Gs s ) to be positive, as increasing sovereign risk should be associated with higher corporate risk as well. Second, if the sovereign spread turns out to be a significant explanatory factor for corporate spreads, the size of the coefficient / Gs s will be a test of whether the sovereign ceiling applies or not: if 1/ Gss , the sovereign ceiling in spreads applies; 1/

22

taxation of bond returns (i.e. interest payments and capital gains) is the same for all types of bonds in South Africa (unlike in the U.S.); macroeconomic conditions will be controlled for insofar as they are reflected in the sovereign spreads; embedded call options are controlled for by working with yields-to-next-call (instead of yield-to-maturity) for the two bonds28 that contain such call options, the 10 other corporate bonds do not contain any such features; and sinking fund provisions are absent in all 12 corporate bonds we analyze. 3.4. Synthesis

According to the theoretical framework laid out in this section, the corporate default premium is essentially a function of (i) sovereign risk, (ii) leverage, (iii) firm value volatility, (iv) interest rate volatility, (v) remaining time to maturity, and (vi) liquidity, i.e.

),,,,,( *+++++

= ldsfs rVG . (19)

In section 5, we estimate a linearized version of equation (19). Motivated by the results of the Merton and Shimko et al. models, we are also considering two interaction terms: one between leverage and maturity, the other between leverage and interest rate volatility. Table 2 (see appendix A3) summarizes the determinants as well as their interactions and lists their expected impact on the corporate default spreads.

4. Operationalization of Variables and Data

This section first discusses how the corporate default premium as well as each of the determinants identified in section 3 (see Table 2, appendix A3) are measured. Then, the data sources are briefly introduced.

4.1. Dependent Variable: How Are Corporate Default Spreads Measured? In order to compute corporate default premia (or spreads), we collect yield to maturity (or redemption yield) data of South African firm bonds and comparable risk-free bonds issued in ZAR (i.e. South African rand). As the bonds issued by the South African government cannot be considered risk-free29, we select ZAR-denominated bonds

28 NED1 and SBK1, see section 4.1. 29 At the end of our sample period (May 2003), the Republic of South Africas local currency debt was rated A by Standard & Poors and A2 by Moodys (i.e. the same rating), see Table -1 in appendix A3 for the history of South Africas ratings by the two rating agencies.

23

issued by AAA-rated supranational organizations as our risk-free benchmarks. A respectable number of such bonds has been issued by the International Bank for Reconstruction and Development (IBRD, usually known as World Bank), the European Investment Bank (EIB), and the European Bank for Reconstruction and Development (EBRD). Elton et al. (2001) argue that one should use spreads calculated as the difference between yield to maturity on a zero coupon corporate bond (called corporate spot rate) and the yield to maturity on a zero-coupon government bond of the same maturity (government spot rate) rather than as the difference between the yield to maturity on a coupon-paying corporate bond and the yield to maturity on a coupon-paying government bond.30 Indeed, spreads calculated as the difference between spot rates is also what our theoretical framework prescribes. However, we find that there are no zero-coupon bonds available for South African firms. We attempt to circumvent the inexistence of firm discount bonds as follows:

a) By estimating spot rates. A clear disadvantage of estimating these rates though, is that all estimation methods suggested in the literature (see Elton, 2001 #35, Athanassakos, 2001 #34), turn out to be inapplicable to our case because of the lack of observations. b) By finding the yield-to-maturity of the risk-free bond with the same coupon and the same maturity as the corporate borrower. The problem is that such corresponding risk-free bonds do not exist, except by chance. However, it is evident that, for a given maturity, it will generally be impossible to find a risk-free bond with the same coupon amount as a risky corporate bond because the default premium is also reflected in the size of the coupon. Therefore, we choose those liquid bonds the maturity dates of which are closest to the maturity dates of the firm bonds. As we are looking at the pure default premium, the underlying bonds must be denominated in the same currency and should be issued in the same jurisdiction. This poses a problem because neither do South African companies borrow abroad in US dollars, nor do riskless borrowers issue local-currency (i.e. rand) denominated bonds on-shore (i.e. in Johannesburg). However, AAA-rated supranational organizations like the EIB, the IBRD, and the EBRD are issuing ZAR-denominated bonds in offshore markets. Thus, the corporate spreads we will calculate based on these instruments will include a jurisdiction premium. However, the latter should remain constant over our sample period

30 They give three reasons for this argument: (1) Arbitrage arguments hold with spot rates, not with yield to maturity on coupon bonds; (2) Yield to maturity depends on coupon; so if yield to maturity is used to define the spread, the spread will depend on the amount of the coupon; (3) Calculating the spread as the difference in yield to maturity on coupon paying bonds with the same maturity means that one is comparing bonds with different duration and convexity (See Elton et al. (2001), pp. 251-252).

24

(July 2000-May 2003) as there were no significant changes in the legal environment or the capital control regimes. Before moving on to compute corporate default premia, we proceed to clear out our database from potential anomalies or data that might bias the results of our econometric estimation. First, we drop out of the sample all public companies (known as parastatals), because they are regarded as holding the same risk-class as the sovereign borrower, the Republic of South Africa (RSA). Second, for some corporates we eliminate outlier data due to inconsistent price quotes or yield to maturity at given points in time. Third, we exclude those corporate bonds for which no benchmark risk-free bond is available. After cleaning the database, we have got 12 bonds issued by 9 firms, 5 of which are banking and the remaining 4 industrial corporates. These bonds are viewed as highly liquid and may be considered as the most representatives among the traded private debt. The firms bonds, their main features, the corresponding risk-free benchmark bonds (i.e. supranationals), and the RSA bonds that we will use to calculate the comparable sovereign default premia, are summarized in table 3 (appendix A3). For instance, HARMONY GOLD 2001 13% 14/06/06 HAR1 means that Harmony Gold issued a bond in 2001 (code: HAR1) that pays a 13% coupon and matures on June 14, 2006.

10 of the 12 bonds have a fixed coupon rate and a fixed maturity date. The remaining two NED1 and SBK1 have a fixed coupon rate until the date of exercise of the (first) call option. For these two bonds, the BESA database reports yields to next call instead of yields to maturity, which we use for our analysis. We assign an identifier code to each corporate bond with the purpose of clearly naming not only the dependent variable but also the explanatory variables associated with firm specific effects. Furthermore, it will help pin down the cross section identifiers in the forthcoming panel econometric model (setting? =_AB01 _ABL1 _HAR1 and so on and so forth). These codes conform to the last four bolded letters inside the third column in table 3 (see appendix A3), namely:_AB01 _ABL1 _HAR1 _IPL1 _IPL2 _IS59 _IS57 _IV01 _NED1 _SFL1 _SBK1 _SBK4.

We work with daily yield data from Thomson Financial Datastream for the period starting on August 28, 2000. Yield data for the period preceding this date is from BESA. The way BESA determines the daily bond yields is described in Bond Exchange of South Africa (2003b). The yield calculation is based on the closing gross (i.e. including accrued interest) price of the bond. We convert BESA yield data to an annual-compounding basis so as to make them homogenous with respect to DS observations. We apply the following formula: [ ]1)2001(100 2 += sa yy where ys stands for "annualised yield compounded semi-annually" and ya stands for "annualised yields compounded annually".

25

To these yields, we make the following adjustment: We size the data range for all yields according to the longest series available. For the starting date, the constraining series is the risk-free benchmark corresponding to IS57 (EIB 13.5% 11.11.02), which starts on 28.10.97. For the ending date, it is the availability of BESA data: 04.06.03. Thus, the range of our data runs from 28.10.1997 to 04.06.2003. The corporate spreads scor?, as the framework set out at the beginning would imply, are computed as follows:

scor?=(y?/100)-(rf?/100)

Where y? is the simple yield to maturity (or redemption yield) of each of the corporate bonds listed above and rf? is the simple yield to maturity (or redemption yield) of each of the associated risk-free benchmark bonds. These corporate spreads are plotted in figure 2 (see appendix A3). 4.2. Explanatory Variables 4.2.1. Sovereign Default Premium We also work with sovereign daily yield (sov) data from Thomson Financial Datastream for the period starting on August 28, 2000. Identically, yield data for the period preceding this date is from BESA. Again, the sovereign yield calculation is based on the closing gross price of the bond. We proceed as in the case of the corporate default spreads. Thus, sovereign default premia can be calculated in the same manner: ssov?=(sov?/100)-(rf?/100) Please note that for sovereign countries holding a AAA or AA status, ssov=0 precisely because the sovereign is the risk-free benchmark asset, as implicitly assumed by Merton (1974) and later structural models. There are some caveats in order. As it is shown in figure 3 (see appendix A3), sovereign spreads are sometimes negative or zero, i.e. risk-free bond redemption yields are higher than or equal to RSA bond yields, for a comparable maturity. At least two important reasons would account for the relatively high yields of the supranational bonds: (1) for the latter liquidity dries up over time; (2) domestic investors are unable to buy Eurobonds (lack of full financial integration of South African bond markets).

26

4.2.2. Quasi-Debt to Firm Value (Leverage) Ratio Here, we have to calculate ttt VBPd

, as seen in section 3.2. This in turn requires the calculation of the following components: (1) B, the face value of total debt. We follow Finger et al. (2002), defining: B =

Financial debt - Minority debt = Short-term_borrowing + Long term_borrowing + 0.5*(Other_short-term_liabilities + Other_long-term_liabilities) + 0*(Acct_Payable) - k*Minority_Interest

For the four industrials (ISCOR, Harmony, Imperial and SASOL), we label the face value of debt B1. For banks, we form two estimates of B: (1) B1 as for the industrials, and (2) B2 = B1 + Tot_Deposits/Sec_Deposits (i.e. B1 plus total deposits received from customers).

We assume that at any time between the publication of two annual reports, market participants behave as if the actual debt level were the one reported in the most recent annual report. Hence, we can now create the series B1? and B2? (expressed in millions of ZAR).

(2) Pt, the price of a risk-less discount bond that pays one unit of currency (rand in

our case) at maturity . Our problem is that we do not work with discount (i.e. zero coupon) bonds because there are none available, neither for the risk-free rate nor the corporate bonds. We are working with coupon bonds instead. Despite this problem, we gather the prices of the corresponding risk-free bonds (from EIB and IBRD) in Datastream. The question here is which price is the appropriate one to be used, the gross price (GP, i.e. including accrued interest) or the clean price (CP, excluding accrued interest).

The gross prices (GP) serve also as basis for the calculation of the yield to maturity on these coupon paying bonds. However, for our purpose, the GP series seems not quite adequate as it always rises over time after a coupon has been paid until the next coupon payment. Then, at the coupon payment date, the GP series makes a discrete drop and then starts to rise anew. For discount (i.e. zero coupon) bonds instead, GP and CP are the same. Over time, the actual price of a discount bond fluctuates around an upward trend so that, at maturity, the price is equal to 100.

The clean price (CP), on the other hand, represents a smoother time series, i.e. it is not characterised by this regular increases and drops. Its level and time path is determined by the relation of the coupon rate with respect to the yield to maturity.

27

If the former is larger than the yield, the price is above 100; if the coupon rate is smaller than the current market yield, the price is below 100; and at maturity, the price is equal to 100. A look at the data of CP (and GP) confirms that the prices often exceed 100, depending on the coupon amount compared to the market interest rates. Note that prices of zero coupon bonds cannot exceed 100! Notwithstanding the latter finding, and assuming coupon and zero coupon bonds may behave similar in this case (strong assumption), we gather CP for the "equivalent" risk-free (i.e. EIB and IBRD) bonds and divide them by 100 (to obtain the prices per 1 ZAR face value). Then, we create the series PRF?, which stands for prices of corresponding risk-free bond.

(3) E, the market value of equity, is required in order to calculate the firms market value V. We can work with either the price per share (which implies that B and D, the market value of debt, should also be transformed to a per-share basis, i.e. by dividing them by the number of shares (NOSH)) or the total market capitalisation (MV = share price times number of shares outstanding, i.e. P*NOSH'), which is readily available in Datastream. We collect market capitalization data (in millions of ZAR) for the 9 firms, creating the series MV? for each of the 12 bonds.

(4) D, the market value of debt, is also required in order to calculate the firms

market value V. We estimate D following Jones et al. (1984), and Cossin and Pirotte (2001), i.e. market value of debt (D) = market value of traded debt (PTBT) + estimated market value of nontraded debt (PNTBNT). The market value of nontraded debt (PNTBNT) is estimated by assuming that the ratio of book to market was the same for traded and nontraded debt, i.e. we assume that PT = PNT. Hence, we have

)( NTTT BBPD += . NTT BB + is equal to B1 (or B2, respectively) obtained above. Thus the crucial

variable to obtain is TP , the price of traded debt. To simplify the calculation, we assume that each bond analysed is the only debt instrument traded of the firm in question.31 As a result, our estimate of the market value of debt will be

1BPDT= .

TP is obtained as follows. First, we recover the corporate yield series y? (not the gross yield gy?). Given that these are annualised yields (ya) compounded annually, we transform them back into the original annualised yields compounded semi-annually (ya) by using the formula (see above)

31 This is true for ABL1, HAR1, and SFL1 over the sample period. IS57 represents 97%, IV01 67%, IPL1 and IPL2 50%, NED1 33%, AB01 29%, SBK1 21%, SBK4 18% and IS59 3% of traded debt, respectively.

28

[ ]1)1001(200 5.0 += as yy . With these semi-annually compounded yields, we can obtain the corresponding (clean) bond prices using the Excel function PRICE and specifying the necessary parameters (settlement date, maturity date, coupon rate, yield, redemption amount per $100 face value, frequency of coupon payments per year, type of day count basis). A quick comparison with the CP series from Datastream (for the period after August 28, 2000) confirms that the bond prices obtained in this way are indeed the clean prices. Dividing the clean prices obtained by 100, we obtain TP . We generate the series PT? i.e. the daily prices of traded (and nontraded) debt.

(5) V, the value of the firm. We estimate V following Jones et al. (1984) and

{Cossin, 2001 #162), that is: value of the firm (V) = market value of equity (E=MV) + market value of debt (D) or

1TV E D MV P B= + = + .

We generate two estimates for V V1 and V2 corresponding to B1 and B2, namely:

(1) V1?=PT?*B1?+MV? (2) V2?= PT?*B2?+MV?

As most prices are close to one (the average prices PT range between 0.96 and 1.16 with standard deviations ranging between 0.011 and 0.060), we also calculate a third estimate for the value of the firm, V3, assuming PT =1.

(3) V3?=B1?+MV? V3 has the advantage of being a much longer time series than V1 and V2. The series of V1 and V2 are rather short due to the very limited availability of PT. Recall that PT has been calculated on the basis of the yields of the corresponding bonds. As a result, the PT series obviously start with the issuance of the corresponding bonds. Hence, we cannot calculate historical standard deviations ( V ) on the basis of V1 and V2 prior to the life of the bond. However, an estimate of V can be obtained on the basis of V3. Therefore, we will only use V3 for this specific purpose (i.e. to calculate the volatility of returns on the firms assets). Now, we have got the necessary elements to calculate the quasi-debt-to-firm or

leverage ratio, ttt VBPd . Again, we are calculating the three different estimates of d:

(1) uses the estimate B1 of the face value of debt and the corresponding estimate for the value of the firm V1; (2) uses the estimate B2 (i.e. including customer deposits for the financial institutions) and the corresponding estimate for the firm value, V2; and (3) uses

29

the estimate B1 for the face value of debt but the simplified estimate V3 for the value of the firm. Thus, we create the following variables:

(1) D1?=B1?*PRF?/V1? (2) D2?=B2?*PRF?/V2? (3) D3?=B1?*PRF?/V3?

4.2.3. Time to Maturity Time to maturity, labelled or T-t, is the number of days usually expressed in years until debt matures. As Cossin Cossin and Pirotte (2001), note, we would in principle have to estimate the maturity of the debt of a firm. Merton (1974) assumes that the sole debt the firm has incurred consists of a zero coupon bond. To the extent that a firm has a complex capital structure with several different fixed income products (e.g. callable convertibles, callable non-convertibles, bonds with sinking fund requirements, etc.), one would have to calculate some weighted average maturity (or duration) of all liabilities. However, we restrict ourselves to control for the maturity of the corporate bonds in our sample, assuming that the two reference bonds (i.e. the corresponding South African sovereign bond and the associated "risk-free" bond) have identical maturity. We calculate our time to maturity variable, m, on the basis of the Datastream series called Life to final date (LFFL). The definition of LFFL in DS says that this is the period from the settlement date to the final maturity of the issue. Graphical inspection of the series reveals some unexpected patterns. First, the LFFL series are not linearly decreasing as one would expect but in waves. The reason is that we are working with daily data based on working days (approximately 261 a year). The waves are caused by the fact that interest also accumulates over the weekends when bond markets are closed. As a result, the LFFL series shows "drops" on Mondays. Second, the two bonds that mature within the sample period (IS57 and IS59) show a LFFL equal to 0 three working days before the actual maturity date. The reason is that settlement in South Africa takes place three working days after the actual trade occurred. This means that the bond price indicated at day t is really the price that has to be paid at day t+3. As LFFL indicates the number of days from the settlement date to the final maturity and the settlement date is on day t+3, the LFFL series shows this lead of three working days. This implies that we obtain our variable time to maturity (m) by lagging LFFL three times, i.e. m?=LFFL?(t-3).

30

4.2.4. Firm Value Volatility This is the instantaneous standard deviation of the return on the firm value, V . We calculate two estimates of this variable. For the first estimate, we follow Cossin and Pirotte (2001), and calculate the standard deviation of the logarithmic total return on the value of the firm V, V . We use the third estimate of the firm value, V3, obtained above when we computed the leverage ratios. However, as the debt component B1 of the value of the firm estimate V3 is an annual series that we have extended to a monthly series (see above), we do not calculate this standard deviation on the basis of daily but monthly data. That is, we first calculate monthly log-returns of V3, then we calculate trailing standard deviations of these log-returns, which we subsequently annualize (by multiplying them by the square root of 12). We calculate two alternatives for this first estimate of V : (1) using a 12-month trailing standard deviation of monthly log-returns, labeled sv12m?, and (2) using a 24-month trailing standard deviation, labeled sv24m? For the second estimate, we adapt the procedure proposed by Ronn and Verma (1986), in the following way. They solved the two equations )()( 21 hBehVE

rtt =

and 1( )

E V

V h

E = simultaneously for the two unknowns, V and V .

32 This is,

however, beyond the scope of this paper. We use an approximation instead. We solve the nonlinear equation

1( )

E V

V h

E = with

( ) 2121

ln r t V

V

Be Vh

+=

numerically for V using estimates of all the other variables ( E , E=MV, V, rd Be V ,) as inputs.

However, before we can proceed to the calculation of V , we need to obtain an estimate of the daily equity return volatility E . Such an estimate is obtained as follows.

First, we compute daily stock returns according to

=

1

lnt

tt E

Eu , where E is the daily

stock closing prices. Then, we calculate the variance of tu according to the formula

=

=T

tt uuT

s1

22 )(1

1, where T is the number of trading days over which the rolling

standard deviations are calculated. The appropriate size of T with daily data brings out another issue. While Hull (1997), suggests T between 90 and 180 trading days (in order to take account of the fact that this volatility is time varying), Finger (2002), finds that a 1000-day window performs best. We also believe that by using a measure of volatility

32 See appendix A1.2 for an explanation of the second equation.

31

over a longer period, we are able to better capture the effect of this variable on corporate default risk. Thus, we calculate rolling standard deviations over a horizon of T = 1000 trading days before day t. We call them s1000?. Then, we get an estimate of the stock

price volatility per annum, E)

, by applying the standard formula E s =)

, where = 1/261 in our case because the number of trading days per year over our sample period (1997-2003) is 261 on average. Now, we have got the necessary elements to calculate our second estimate of V .

The equation 1( )

E V

V h

E = is solved by an iterative procedure.33 We use the first

estimate, sv12m?, obtained above as starting value for V . Convergence is achieved after 7 iterations. This second estimate is labeled sv1000d? 4.2.5. Interest Rate Volatility This is the instantaneous standard deviation of the risk-free rate, r , as discussed in section 3-2. We derive it assuming the risk-free rate is governed by the dynamics proposed in Vasicek (1977). To estimate r we face several problems. The first important problem is that we do not have such an instantaneous (i.e. very short term, e.g. overnight rate) interest rate because our risk-free benchmark bonds are from supranational organizations like the IBRD, the EIB, or the EBRD, not from a country with a capital market and a (more or less) complete yield curve. Two options seem to be available to overcome this problem. First, we could simply use the yields of our risk-free benchmark bonds as proxies for the non-existing short-term interest rates. The disadvantages of this approach are that (1) these yields are really yields to maturity, not interest rates, i.e. their time to maturity is not fixed (e.g. overnight, 1-month, 3-months, etc.) but their remaining life approaches zero; and (2) we have a data availability problem. These risk-free benchmark yields (see table 3, appendix A3) usually start around the issue date of our corporate bonds. This implies that we do not have enough (daily or monthly) observations to calculate historical volatilities at the beginning of the sample. Only for AB01, ABL1, SFL1, SBK1 and SBK4 do the yield series of the risk-free benchmarks start sufficiently before the issue date of these corporate bonds so that we are able to calculate, for instance, a full 12- 33 See Appendix A1.3 for details of this procedure. For the sake of simplicity, we keep assuming that r, the risk-free interest rate, is constant over time (as in Merton, 1974). Although we provide a theoretical derivation of the variance of equity when risk-free rates are variable (equation A7), the resulting formula appears extremely complicated to apply because it depends on a wide range of potential values for some parameters (e.g. , ) and on some complex non-linearities which are difficult to dealt with.

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month historical volatility series. For the other 7 bonds, the lacking monthly observations in the case of a 12-month trailing standard deviation range up to 12 months. However, this latter problem can be overcome by choosing other supranational bonds that have longer yield series available and whose volatilities are highly correlated with the original yield series. The second option to overcome the problem of absence of a short-term risk-free interest rate (i.e. with fixed maturity) is to work with a short-term ZAR interest rate from the South African money market, assuming it is "risk-free". According to Bond Exchange of South Africa (2003a), it is the 3-month JIBAR (=Johannesburg Interbank Agreed Rate) that performs the function of anchor point at the very short end of the ZAR yield curve. Time series data for the 3-month JIBAR is available in Bloomberg (code: JIBA3M), but the series starts only on 01/02/1999. Looking for an appropriate proxy, we found another 3-month interest rate that could perform that function: the 3-month "Bankers' Acceptances" (BA) rate (also available in Datastream). Over the period 1999-present, the 3-months JIBAR is at a spread of about 32 basis points over the BA rate on average (with a standard deviation of 9 bps) and the correlation between the two is 1. Let us now try to estimate r using (1) monthly data on the ZAR 3-months Bankers' Acceptance (BA) rate; and (2) using the monthly yield data from our benchmark supranational bonds (or their proxies).34 We directly work with a discrete time version of equation (11), i.e.

tr Ztrbar += )( .

With Zt being a standard Wiener process, r is normally distributed with instantaneous mean equal to trba )( and instantaneous variance equal to tr

2 , i.e.,

r N[ ttrba r 2,)( ]

Taking monthly observations of the 3-months BA rate, we calculate the variance of the

monthly (absolute) changes, )( rarV , by the usual method. Recalling that time t is expressed in years, so that t = 1 month = 1/12 years = , the variance )( rarV of the stochastic process just described can be written as:

34 In case (1) we use the same interest rate volatility for all 12 corporate bonds, while in (2) we use - for each corporate bond - the volatility of the corresponding benchmark bond. Also note that we could have computed daily historical volatilities using BAs rate. Even though this is practically feasible, we did not because we will finally estimate an econometric model based on monthly observations, due to other explanatory variables for which daily data do not exist or are not available. These figures are available upon request to the authors.

33

2)( rrarV = Hence, r is estimated as

12)()( == rarVrarVr

We label them sigspotm?. Then, we do exactly the same with monthly data of our risk-free benchmark yields (or their proxies). We label them sigrfm. 4.2.6. Liquidity Possible proxies for liquidity of our corporate bonds are (1) trading volume or value turnover, (2) amounts of bonds outstanding, (3) bid-ask spreads:

(1) Value-turnover (VA) = the value of the bonds traded on an exchange on a particular day: not available for our corporate bonds in DS. However, it is available in BESA from January 2000 on.

(2) Amount outstanding (AOS in thousands of ZAR): available in both, DS and BESA.

(3) Bid yield (RB) and ask (or offered) yield (RO): not available in DS, nor in BESA database.

However, a look at AOS data raises questions. First, the individual series do not change over time, that is Amount issued (AIS) = AOS (at least for our 12 corporate bonds). The DS series gives the nominal amount outstanding over the whole period. Second, data is available over the whole period of analysis, i.e. from 28.10.1997 until 04.06.2004. This is suspicious because many of the bonds have been issued only recently, i.e. about since 2000. The only explanation we have for this phenomenon is that DS gives the amount initially issued simply for any date. However, this inconsistency might not be that grave because the constraint with respect to the availability of data is, at any rate, the dependent variable (i.e. the corporate bond yield spreads). Then, we transform them into millions (from thousands) and create: aos?=aos?/1000.

With respect to VA, as mentioned above, the BES