A. Why South Africa?

We selected South Africa as a case study essentially for three reasons. First, South Africa is one of the few emerging markets to have a corporate bond market in local currency (i.e., the rand).⁵ Admittedly, this market is still very small: during our sample period (July 2000–May 2003), there were only nine South African private sector firms that had a total of 12 bonds outstanding (Table 1 in Appendix III).⁶ However, despite its limited size, the South African corporate bond market has considerable growth potential, according to a recent report by the Rand Merchant Bank (2001). Among the reasons the report mentions are that (i) South African corporates are under-leveraged and will need more debt in the future to optimize their financing structures; (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 government’s 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 an as-yet unexploited dataset provided by BESA. Third, the nine corporate issuers mentioned above are important South African companies. Looking at the prospective development of South Africa’s 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.

B. Sovereign Risk and the Country or Sovereign Ceiling Rule

Empirically, there has been a high correlation between sovereign defaults and company defaults. That is, it has been very difficult for companies to avoid default once the sovereign of their jurisdiction has defaulted. This historical regularity has been used by all major rating agencies to justify their country or sovereign ceiling policy, which usually means that the debt of a company in a given country cannot 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 & Poor’s calls “economic or country risk,”⁷ which 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 III.C elaborates on it. Both direct sovereign intervention risk (transfer risk) and indirect sovereign risk are closely related to (pure) sovereign risk.⁸

Until 2001, the “big three” main rating agencies, Moody’s Investors Service, Standard & 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).⁹ Moody’s—the last among the big three 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 behavior of governments in default suggested that they may now have good reasons to allow foreign currency payments on some favored classes of obligors or obligations, especially if an entity’s default would inflict substantial damage on the country’s economy.”¹⁰

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 tends to be closely tied to that of the government. Table 2 (Appendix III) shows that among the nine firms analyzed, which had a rating by Moody’s or Standard & Poor’s, 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 & Poor’s on February 19, 2003—about three months before the government’s 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 the two objectives of this study is to analyze the extent to which a sovereign ceiling can be observed in rand-denominated corporate yield spreads.¹¹ This entails, in a first step, verifying whether the bond yields (spreads) of the firms analyzed are always higher than comparable yields (spreads) of government bonds. As panels 1 through 12 of Figure 1 (Appendix III) show, all South African corporate bonds analyzed indeed bear higher yields than sovereign bonds of similar maturity and coupon.

However, corporate spreads exceeding comparable government spreads are only a necessary but not a 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., independently 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), that is, EL = PD·LGD. 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 default probability of the firm or to high indirect sovereign risk. Section III.C provides a framework to disentangle the different risks.

Confronted with this identification problem, we will resort to a result obtained by Durbin and Ng (2005). They 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., transfer risk is 100 percent)— implies that a 1 percent increase in the government spread should be associated with an increase in the firm spread of at least 1 percent. 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 Ng’s 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 (2005), there are no empirical investigations available on that subject to our knowledge. Unlike Durbin and Ng (2005), we will also control for firm-specific variables derived from the literature on corporate debt pricing.

A. Starting Point: The Merton (1974) Model

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). Merton’s model hinges on a number of critical assumptions. They are: (i) competitive and frictionless markets; (ii) constant risk-free interest rates (i.e., flat-term structure of interest rates); (iii) the firm holds a single type of liability: a non-callable zero-coupon bond; (iv) the value of the firm follows a geometric Brownian motion process;²¹ (v) firm management acts to maximize shareholder wealth; (vi) there is perfect antidilution²² and bankruptcy protection;²³ and (vii) the Modigliani-Miller theorem holds (i.e., the firm’s value is independent of its capital structure).

In this highly simplified model, the corporate default risk premium s (also called yield spread or credit spread) is a function of only three variables: (i) the volatility of the returns on the firm value σ_V (or simply firm-value volatility), (ii) the quasi-debt ratio d (a form of leverage ratio),²⁴ and (iii) the remaining time to maturity of the bond τ,

where s_t ≡ y_t – r with y_t being the yield to maturity of the risky zero-coupon bond and r the (constant) risk-free interest rate.

Merton (1974) shows that $\partial s/\partial {\sigma }_V^2>0$, $\partial s/\partial d>0$, and ∂s/∂τ <>0, that is, the corporate default spread is an increasing function of firm-value volatility and leverage, which seems intuitive; however, it can be an increasing or decreasing function of remaining time to maturity, depending on leverage. The Merton model thus produces the classical hump-shaped “term structure of credit spreads”—a non-intuitive result but a fact often found in actual data.²⁵ This term structure of credit risk spread is downward sloping for high-leveraged firms (i.e., d >1),²⁶ hump-shaped for medium-leveraged firms, and upward sloping for low-leveraged firms (d<1). In other words, for firms with a leverage ratio d >1, an increase in time to maturity τ will lead to a declining default premium (∂s/∂τ < 0); for intermediate leverage ratios (d between around 0.7 and 1), the credit spread first rises and then falls as maturity increases; for low leverage ratios (d below about 0.7), the default premium increases with longer time to maturity. Before discussing the economic intuition of $\partial s/\partial {\sigma }_V^2>0$ and ∂s/∂d > 0, we extend the Merton model by introducing interest rate risk.

B. Adding Stochastic Interest Rates: The Shimko, Tejima, and Van Deventer (1993) Model

Shimko, Tejima, and Van Deventer (1993) proposed to extend the Merton model by relaxing the assumption of constant risk-free interest rates, letting interest rates be stochastic instead. They achieve this extension by integrating the Vasicek (1977) term-structure-of-interest-rates model into the Merton (1974): framework, thereby integrating interest rate risk into the pricing of credit risk.

The fundamental result of the model by Shimko, Tejima, and Van Deventer (1993) is that once (risk-free) interest rates are allowed to be stochastic, interest rate volatility σ_r becomes an additional determinant of the corporate default premium s. They also confirm the importance of the three determinants found by Merton (1974): firm leverage d, firm-value volatility σ_V, and remaining time to maturity of the bond τ. Strictly speaking, the corporate yield spread s is also a function of the correlation ρ between the stochastic factor of the firm-value process V and the stochastic factor of the interest rate process r, and of α, the speed of convergence of the risk-free rate r to its long-run mean γ.²⁷ For the present empirical investigation, however, these two parameters are assumed to be constant over the sample period.

In summary, Shimko, Tejima, and Van Deventer (1993) find that the corporate default premium s is essentially a function of four important determinants: (i) firm leverage (measured by the quasi-debt ratio d); (ii) firm-value volatility σ_V; (iii) remaining time to maturity of the bond τ; and (iv) interest rate volatility σ_r,

What is the impact on the corporate credit spread s of changes in these four determinants? Apart from identifying an additional determinant (σ_r), the major difference of the model by Shimko, Tejima, and Van Deventer. compared to that by Merton is that the nonlinear impacts of these determinants on the spread are more complex. One can show that the spread s is a positive function of firm leverage d and firm-value volatility σ_V, but can be either an increasing or decreasing function of interest rate volatility σ_r and remaining time to maturity τ, depending on the size of α (the speed of convergence of the risk-free rate r to its long-run mean γ), ρ, (the correlation between shocks to the firm-value returns and interest rate shocks), τ, σ_r, σ_V, and d.²⁹ The economic intuition of these effects is as follows:

• Firm leverage: The higher a firm’s debt in relation to the value of its assets (d), other things equal, the lower its net worth and, hence, the closer it is to default (i.e., bankruptcy) at any given moment in time. To be compensated against the higher probability of default (and, hence, expected loss), investors will ask a higher default premium (i.e., spread).

• Firm-value volatility: The higher the day-to-day fluctuations in the value of the firm’s assets (σ_V), other things equal, the higher the probability that—purely by chance—the asset value is smaller than the value of the debt on the day the debt is due, that is, that the firm defaults. To be compensated against the resulting higher default probability and expected loss, investors will ask a higher spread.

• Interest rate volatility: The corporate spread can be an increasing or decreasing function of interest rate volatility σ_r, depending on the firm’s leverage d, its asset volatility σ_V, the correlation between asset return shocks and interest rate shocks ρ, and the term structure of interest rates (represented by the parameters α, τ, and σ_r). However, Shimko, Tejima, and Van Deventer note that “the credit spread is an increasing function of [interest rate volatility] for reasonable parameter values.”³⁰ To find out whether this is the case in our data sample, we proceed as follows. First, we estimate the parameter values of α and ρ implied by our data.³¹ Then, we simulate the impact of changes in σ_r on s for various combinations of sample values for d, σ_V, and τ (Table 5). The simulations show that for all combinations of sample values for d, σ_V, and τ, the corporate spread either stays constant (for small d, σ_V, or τ) or increases as interest rate volatility rises (i.e., ∂s/∂σ_r ≥ 0). Moreover, the stronger the impact of σ_r on s, the higher leverage d. To control for this dependence, we will also include the interaction term σ_rd in the (linearized) estimating equation;³² we expect its coefficient to be positive.

• Time to maturity: The corporate default spread can also be an increasing or decreasing function of remaining time to maturity τ, depending on the same parameters as the impact of changes in interest rate volatility. More precisely, the Shimko, Tejima, and Van Deventer model produces a term structure of credit spreads that is similar to the one obtained in the Merton model, except that now it is not only the result of the dependence on leverage d but also σ_V: for small values of d or σ_V, the spread increases when time to maturity τ lengthens; for intermediate values of d or σ_V, the spread first increases sharply, then reaches a maximum, and finally declines gradually as τ increases; for high d or σ_V, the spread declines as maturity increases. The economic intuition behind this theoretical result is as follows: if there is only a short time to go before maturity and leverage or, if firm-value volatility is high, the risk of default (and, hence, the spread) is high; the more time there is to go before maturity, the more opportunities the firm with the same leverage (or asset return volatility) will have to increase earnings and reduce leverage and, hence, the lower its default risk and spread. As before with σ_r, we run simulations to check whether the spectrum of values for d, σ_V, and τ in our sample produces such a complex term structure of credit spread or whether it is simpler. The simulations show again a strong dependence of ∂s/∂τ on leverage d: at the mean values of σ_V (= 23.4 percent) and σ_r (= 1.0 percent), the spread increases with maturity for values of d between 0.1 and about 0.7; it first increases and then decreases with maturity for d between about 0.7 and 0.85; and it decreases with maturity for d above 0.85.³³ To control for this dependence in the simplest possible way, we also include the interaction term τd in the linearized estimating equation, along with maturity τ. We expect the coefficient of maturity alone to be positive and the one of the interaction term to be negative.

C. 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 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 United States), 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 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 foreign- but also domestic-currency terms) 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,³⁴ 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, and 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. The banks’ 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 and others (2001) find that—even in the United States—corporate default premia incorporate a significant risk premium because a large part of the risk in corporate bonds is systemic rather than diversifiable. One could argue that in emerging markets, a major source of systemic 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 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 = PD·LGD. Assuming for simplicity that (i) LGD is equal to one (i.e., when the firm defaults, the entire investment is lost), (ii) investors are risk-neutral, and (iii) 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) and the corporate spread is only function of the company’s probability of default, s = f(PD).

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

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 S^c (= complement of event S): the sovereign does not default.

Inspecting equation (3), we see that the probability of default of the firm, P(F) = PD, is the result of a combination of three other probabilities:

1. P(F/S^c) is the probability that the firm defaults given that the sovereign does not default. We can interpret this probability as the firm’s default probability in “normal” times, as opposed to a “(debt) crisis” period. We call this probability the stand-alone default probability of the firm;

2. P(S) is the default probability of the sovereign (sovereign risk);

3. P(F/S) 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, P(F/S) 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.³⁵

In terms of credit ratings (which are nothing other than estimates of default probabilities), the four probabilities P(F), P(F/S^c), P(S), and P(F/S) have direct correspondents. In Moody’s case, for instance, a bank’s “domestic currency issuer rating” would correspond to P(F), which itself can be interpreted as the result of the combination of its “bank financial strength rating,” P(F/S^c), of the “domestic currency issuer rating” of its sovereign of incorporation (or location), P(S), and of the indirect sovereign risk applicable in its case, P(F/S).

Examining a few boundary cases, we realize that equation (3) makes intuitive sense. When the sovereign default probability is zero, the firm’s default probability reduces to its stand-alone default probability: P(F) = P(F/S^c). As the sovereign default probability rises and approaches 100 percent (P(S) = 1), the importance of stand-alone default risk (P(F/S^c)) vanishes compared to direct (P(S)) and indirect sovereign risk (P(F/S)); at the limit (when P(S) = 1), the firm’s default probability reduces to indirect sovereign risk (or transfer risk in foreign-currency obligations), i.e., P(F) = P(F/S). If the firm’s stand-alone default probability were zero (P(F/S^c) = 0) but there is sovereign risk (P(S) > 0), the firm’s default probability would be equal to the product of direct and indirect sovereign risk (P(S) ⋅ P(F/S)); in this case, only if indirect sovereign risk (or transfer risk) were also equal to zero would the firm’s (overall) default probability also be equal to zero (P(F) = 0). Finally, when there is direct sovereign risk (P(S) > 0) and when indirect sovereign risk (or transfer risk) is 100 percent (P(F/S) = 1), the firm’s default probability equals

This boundary case is the key to understand the concept of the sovereign ceiling:

Whenever indirect sovereign risk (or transfer risk) equals 100 percent, equation (4) implies that the firm’s (overall) default probability P(F) will always be at least as high as the default probability of its sovereign, P(S), independently of how low its stand-alone default probability P(F/S^c). In other words, when indirect sovereign risk (transfer risk) is 100 percent, the sovereign default probability (and, hence, the sovereign spread) acts as a floor to the firm’s default probability (and its spread). In terms of credit ratings (where low default probabilities are mapped into high ratings, and high default probabilities into low ratings), this floor translates into a ceiling, hence the concept of sovereign ceiling. When indirect sovereign (or transfer) risk is smaller than 100 percent (P(F/S) < 1), the firm’s overall default probability (spread) can be lower than the sovereign’s default probability (spread) if its stand-alone default probability is sufficiently small.

To test whether the sovereign ceiling applies in our rand-denominated corporate spreads data, we resort to a result obtained by Durbin and Ng (2005). In a simple theoretical model similar to the framework used in this section, Durbin and Ng (2005) show that 100 percent transfer risk (i.e., indirect sovereign risk in domestic-currency obligations) implies that a one-percent increase in the government spread should be associated with an increase in the firm spread of at least one percent. In other words, in a regression of corporate spread changes on corresponding sovereign spread changes, 100 percent indirect sovereign risk implies that the beta-coefficient should be greater than or equal to one. In the logic of their model, the size of this estimated coefficient can be interpreted as the market’s appreciation of indirect sovereign risk: a coefficient that is larger than one would imply that the market factors in an indirect sovereign risk of 100 percent (i.e., whenever the government defaults, the prevailing economic conditions force the firms into default as well); a coefficient statistically smaller than one would imply that the market judges indirect sovereign risk to be less than 100 percent. 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 (2005) 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 add the sovereign default premium, or sovereign spread, $S_t^{\mathit{\text{sov}}}$ (in an admittedly ad-hoc fashion) to our estimating equation. $S_t^{\mathit{\text{sov}}}$ is defined as

with $y_t^{\mathit{\text{sov}}}$ the yield to maturity on the (risky) government discount bond and R_t the yield to maturity on the risk-free discount bond with the same maturity. In section V, we first test whether the sovereign spread can be considered as an additional determinant of corporate credit spreads. We expect the associated coefficient (∂s/∂s^sov) to be positive, as increasing sovereign risk should be associated with higher corporate risk as well. Then, if the sovereign spread turns out to be a significant explanatory factor for corporate spreads, the size of the coefficient ∂s/∂s^sov will be a test of whether the sovereign ceiling applies or not: If ∂s/∂s^sov ≥ 1, the sovereign ceiling in spreads applies; ∂s/∂s^sov < 1, the sovereign ceiling does not apply.

D. Other Potential Determinants

Once the assumption of frictionless markets is relaxed and/or particular bond indenture provisions are allowed, other determinants of the corporate default premium have to be taken into account. These include differential taxation of corporate and risk-free bonds, differences in liquidity of corporate and risk-free bonds, business cycle (macroeconomic) conditions, temporary demand for and supply of bonds imbalances, and specific bond indenture provisions, such as call options embedded in corporate bonds or the presence of a sinking fund provision.³⁶

Among all these factors, only potential differences in liquidity are controlled for explicitly in the present investigation. Liquidity refers to the ease with which a bond (issue) can be sold without a significant price discount. One might expect the risk-free bond issues to be larger and thus more liquid than the corporate issues, such that the liquidity premium on corporate bonds will be larger than the one on comparable risk-free bonds. As a result, we would expect that the higher the liquidity, l, of a given corporate bond relative to that of a comparable risk-free bond, the lower the corporate spread. Thus, we expect ∂s/∂l to be negative.

With the exception of short-run demand and supply imbalance, which have to be omitted for lack of appropriate data, all other factors are implicitly controlled for: 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 United States); macroeconomic conditions will be controlled for insofar as they are reflected in sovereign spreads; embedded call options are controlled for by working with yields-to-next-call (instead of yield-to-maturity) for the one bond³⁷ that contains such a call option, the eight other corporate bonds do not contain any such features; and sinking fund provisions are absent in all nine corporate bonds we analyze.

E. Synthesis

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

The plus or minus signs on top of each of the right-hand-side variables indicate how each of these determinants is expected to influence the corporate default premium (or spread) according to the theory.

In section V, we estimate a linearized version of equation (5). Motivated by the results of the Merton and Shimko, Tejima, and Van Deventer models, we will also consider two interaction terms: one between interest rate volatility and leverage (σ_r d), and the other between maturity and leverage (τd). These will help us to unambiguously determine the expected signs of the coefficients involving σ_r and τ: we expect the coefficient of σ_rd to be positive, as the impact of interest rate volatility on spreads appears to be increasing with leverage; the coefficient of σ_r alone could be positive or insignificant because the spread (and hence the influence of any determinant) vanishes as leverage tends toward zero. The coefficient of τd, on the other hand, is expected to be negative, along with a positive coefficient for maturity τ alone because the spread increases with maturity when leverage is small, whereas it declines with maturity when leverage is high. Table 3 (Appendix III) summarizes the determinants (together with their interactions) and lists their expected impact on the corporate default spread.

A. Dependent Variable: How Is the Corporate Default Premium Measured?

Before the corporate default premium (or spread) can be calculated, appropriate corporate and risk-free securities need to be identified. This task is complicated by the absence of corporate zero-coupon bonds and the fact that bonds issued by the South African government cannot be considered risk-free.

We circumvent the absence of corporate zero-coupon bonds by using coupon-paying bonds to calculate spreads. According to the Merton-Shimko framework, we should calculate the spread as the difference between the yield to maturity on a zero-coupon corporate bond (called corporate spot rate) and the yield to maturity on a zero-coupon risk-free bond of the same maturity (risk-free spot rate).³⁸ However, we find that there are no zero-coupon bonds available for South African firms. An attempt to circumvent the nonexistence of firm discount bonds by estimating the spot rates—for instance, by the procedure suggested by Nelson and Siegel (1987)—fails owing to the lack of a sufficient number of outstanding bonds per firm.³⁹ Given the impossibility of estimating spot rates, the next best alternative would be to work with spreads calculated as the difference between the yield to maturity of the coupon-paying firm bond and the yield to maturity of the risk-free bond with the same coupon and the same maturity. The problem is that such corresponding risk-free bonds generally do not exist because the corporate default premium is also reflected in the size of the coupon so that the risk-free coupon bond with a similar maturity tends to have a lower coupon. Again, estimating yields to maturity of equivalent risk-free coupon bonds is rendered impossible by the absence of appropriate risk-free zero-coupon bonds.⁴⁰ Therefore, our second best (or third best, actually) strategy to compute the corporate yield spreads is to take the yield to maturity of a given corporate bond and to subtract the yield to maturity of a risk-free bond that has a maturity and coupon amount as close as possible to that of the corporate bond. As a result, the spreads we calculate will fail to completely isolate the pure default premium. That is, due to slightly different maturities and coupon sizes, they will also include some term structure effects, as is the case in many other empirical investigations of credit spreads (see Durbin and Ng, 2005; Kamin and Von Kleist, 1999; Eichengreen and Mody, 1998; Larrain, Reisen, and von Maltzan, 1997; or Edwards, 1986).

The second issue— that South African government bonds cannot be considered risk-free⁴¹—is dealt with by taking rand-denominated bonds issued by supranational organizations as our risk-free benchmark instruments. As we are interested in isolating the pure default premium, the risk-free bonds should be denominated in the same currency and should be issued in the same jurisdiction as the corporate bonds. This poses a problem because no South African companies issue bonds abroad in U.S. dollars, nor do riskless borrowers issue ZAR- (i.e., rand-) denominated bonds onshore (i.e., in Johannesburg). However, triple-A-rated supranational organizations like the European Investment Bank (EIB), the International Bank for Reconstruction and Development (IBRD, usually known as the World Bank), and the European Bank for Reconstruction and Development (EBRD) are issuing ZAR-denominated bonds in offshore markets. In the absence of more appropriate alternatives, we will calculate the corporate spreads using the ZAR-denominated corporate bonds traded on the Bond Exchange of South Africa and these ZAR-denominated “supranational” bonds traded in offshore markets as our risk-free benchmarks. As a result, the calculated spreads will include a jurisdiction premium (Box 1). However, the presence of this jurisdiction premium in our measure of spreads should not bias the results because the jurisdiction premium very likely remained constant over the sample period (July 2000–May 2003) as there were no significant changes in the legal environment or the capital control regime.

Once these two issues are clarified, we start collecting end-month yield to maturity data for corporate and supranational bonds from Thomson Financial Datastream (DS) and BESA. We have to resort to both sources because DS contains no data for ZAR-denominated South African corporate bonds prior to August 28, 2000, while BESA contains no data on the supranational bonds that we have selected as risk-free benchmarks. Thus, for the period starting on August 28, 2000, we gather the yields for all South African firm bonds from DS. For the period preceding this date, we take the yields for these bonds from the BESA database.⁴² For the risk-free supranational bonds, all yield data is from DS.⁴³

Next, we clear from our database potential anomalies or data that might bias the results of our econometric estimation. First, we drop all public companies (known as parastatals) from the sample because they are regarded as belonging to the same risk class as the sovereign, the Republic of South Africa (RSA). Second, for some corporates we eliminate outlier data due to inconsistent price or yield to maturity quotes at certain points in time. Third, we only take the bonds of those firms whose shares are listed on the Johannesburg Stock Exchange (JSE) because our empirical investigation requires stock price data. Fourth, we eliminate all floating rate bonds as they are priced differently. And fifth, we work with only one bond per firm to facilitate the empirical analysis and interpretation of the results.⁴⁴ If a firm has more than one bond outstanding, we select the more liquid one;⁴⁵ if several bonds display similar liquidity, we chose the one with the longer time series available.

After this elimination procedure, we end up with nine corporate bonds issued by five banking and four industrial firms. The nine firms, their bonds, the bonds’ main features, the corresponding risk-free benchmark bonds (i.e., supranational bonds), and the RSA bonds that will be used to calculate the comparable sovereign default premia (see section IV.B) are summarized in Table 1 (Appendix III). For instance, “HARMONY GOLD 2001 13 percent 14/06/06 HAR1” means that Harmony Gold issued a bond in 2001 (code: HAR1) that pays a 13 percent coupon and matures on June 14, 2006. Seven of the nine 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. Because of anomalous price behavior of some bonds after the penultimate coupon payment, we only use yield data series up to the date of the penultimate coupon payment for both corporate and risk-free bonds. Hence, the maximum data range of corporate and corresponding risk-free yield series extends from May 20, 1998 (starting date of the risk-free benchmark corresponding to IS59, i.e., EIB 1998 12 ¼ percent May 20, 2003) to June 4, 2003 (availability of BESA data). Panels 1 to 9 of Figure 1 (Appendix III) plot, for each bond, the daily yields to maturity of the corporate, the corresponding RSA (“sovereign”), and the corresponding risk-free (supranational) bond.

Finally, using EViews programming notation, the corporate credit spread, SCOR, is calculated as

where y is the yield to maturity (or redemption yield) of the corporate bond; rf is the yield to maturity of the risk-free benchmark bond that corresponds as closely as possible to the corporate bond in terms of maturity and coupon (“the corresponding risk-free benchmark”); and “?” stands for each of the nine corporate bonds. We assign an identifier code to each of these bonds with the purpose of naming not only the dependent variable but also the explanatory variables associated with firm characteristics (see next section). These codes correspond to the BESA acronyms and are marked in bold in the third column in Table 1 (Appendix III). They are: AB01, ABL1, HAR1, IPL1, IS59, IV01, NED1, SFL1, and SBK1. Figure 2 (Appendix III) shows the resulting corporate spreads (or default premia) at the frequency (monthly) and over the sample period (July 2000–May 2003) actually used in this study.

B. Explanatory Variables

C. Sample and Data

Our “sample” consists of an unbalanced panel of monthly data for nine corporate bonds (N = 9) listed and traded on the BESA during the period July 2000 to May 2003.⁴⁷ “Sample” because the four industrial and five financial corporate issuers of these bonds essentially constitute the population of South African firms with bonds outstanding. The beginning of the sample (July 2000) is constrained by the availability of BESA data on our liquidity proxy (trading volume, TOVC). Observations are always as of end-month. The time-series dimension, T, of the panel varies between 21 and 35 months, i.e., 21 ≤ T ≤ 35. Data are from BESA, DS, and Bloomberg. Table 5 (Appendix III) reports the descriptive statistics of the major variables discussed in section IV.

A. The Econometric Model: Fixed Effects with Different Slopes for Sovereign Risk

The linearized version of equation (5) that we estimate takes the form of a fixed effects (FE) model:⁴⁸

where SCOR_it is the corporate spread of firm bond i at end-month t, as defined in section IV.A; SSOV_it is the sovereign spread which best matches SCOR_it in terms of maturity and coupon amount (see section IV.B); X_1,it, …, X_{k, it} is the set of k = 7 firm-specific control variables (including their interaction terms) defined in section III and operationalized in Table 4 (Appendix III), namely:

1. Quasi-debt-to-firm-value (or leverage) ratio (d_t = D1?, D2?, or D3?);

2. Volatility of returns on the firm’s value (σ_V = SV1000D?, SV12M? or SV24M?);

3. Volatility of risk-free interest rate (σ_r = SIGSPOTM? or SIGRFM?);

4. Time to maturity (τ = M?);

5. Liquidity, proxied by the trading volume (l = TOVC?);

6. Interaction between maturity and leverage (τ · d_t); and

7. Interaction between interest rate volatility and leverage (σ_r · d_t);

α_i denotes the (unobservable) firm-specific effect, assumed time-invariant in the present context (“fixed effect”); β_i and γ₁, γ₂,…, γ₇ are the coefficients to be estimated; and ε_it is a normally distributed error term with zero mean, E(ε_it) = 0.

Ideally, we would want to estimate the coefficients α_i and β_i as well as separate γ_j-coefficients (i.e., γ_1,i, γ_2,i,…, γ_7,i for i = 1,…, N) in individual time-series regression for each of the N = 9 firms. However, with 21 ≤ T ≤ 35 observations per firm, it would be difficult to obtain efficient and unbiased estimates for the nine firm-specific coefficients. To reduce collinearity problems and increase the degrees of freedom and the efficiency of estimation, we pool the time series of our nine firm bonds together. However, pooling data amounts to imposing restrictions on the parameters. In a fully pooled model, for instance, we assume that the parameters α_i, β_i, and γ_1,i, γ_2,i,…, γ_7,i are the same across all nine firms, i.e., that α_i = α, β_i = β, and γ_{j, i}=γ_j for all i = 1,…, N firms and j = 1,…, k control variables. However, we can also have less restrictive pool specifications, like the one proposed in equation (6), where the intercepts α_i and the slope coefficients β_i of our main variable of interest, SSOV, are allowed to vary across the nine firms. The specification of equation (6) is the outcome of the following tests.

B. Choosing the Appropriate Estimator and First Results

Once the specification is chosen— equation (6): FE with different slopes for sovereign risk—we have to analyze the OLS regression residuals in order to make the necessary adjustments to the estimator. When we deal with combined cross-section and time-series data, we should suspect both cross-sectional heteroskedasticity and residual autocorrelation within a given cross-sectional unit to be present. In addition, we should test whether there is contemporaneous correlation between the error terms of the different cross-sections (firms). Contemporaneous cross-section correlation is likely because the nine firms are potentially exposed to the same shocks (e.g., changes in investors’ risk appetite for, or sentiment towards, South African securities as an asset class). Even though heteroskedasticity, autocorrelation, and (contemporaneous) cross-section correlation do not destroy the consistency of the OLS estimator, OLS is no longer efficient (i.e., minimum-variance) and, hence, standard errors will be biased.⁵² Thus, hypothesis testing on the basis of inefficient estimators may be misleading. Fortunately, some form of feasible generalized least squares (FGLS) estimators can correct for the lack of efficiency in these cases.

Before we proceed to test and correct for heteroskedasticity, autocorrelation, and cross-section correlation in our data sample, let us give—for the sake of completeness— the estimation results for (i) separate OLS regressions for all nine firms (slope-coefficients for SSOV only); (ii) pooled OLS; (iii) fixed effects (FE); and (iv) FE with different slopes for sovereign risk (equation 6) before correction. The first four columns of Table 6 (Appendix III) show the corresponding estimation results. In column 1, showing selected estimates from the nine individual firm regressions, most of the firm-specific SSOV-coefficients are significant and all of them are smaller than one. Most of the other determinants (not reported) however are not significant while the R² are all very high—a typical indication of multicollinearity. In the pooled OLS regression (column 2), on the other hand, the (unique) SSOV-parameter is significantly larger than one, while it is significantly smaller than one in the FE regression (column 3); in the FE model with different slopes for SSOV (column 4), finally, the firm-specific coefficients are larger than one for four firms (ABSA Bank, African Bank, SASOL, and Standard Bank) and smaller for the five others (Harmony Gold, Imperial Group, ISCOR, Investec Bank, and Nedcor Bank). In all three pooled regressions, however, the very low Durbin-Watson statistic indicates serious misspecification (autocorrelation).

C. A Robustness Check: Corporate Spreads in First Differences

In their study of the impact of sovereign risk on foreign-currency-denominated corporate bond spreads, Durbin and Ng (2005) work with first differences of bond spreads instead of levels.⁵⁷ To make our results comparable to theirs and to check the robustness of our level estimates, we also estimate a first difference equation. Taking first differences of equation (6), we obtain

where Δ is the first-difference operator, u_it = ε_it – ε_it–1, and all other components are as defined in equation (6). Note that the individual (or fixed) effects α_it in equation (6) are eliminated by taking first-differences. As a result, estimation of equation (7) will be a regression through the origin (i.e., without intercept). Also note that we will have to expect (negative) autocorrelation in the error term.

Going through the same testing procedure as for the level equation, we accept the model of equation (7) as the appropriate pooled specification and we find that an FGLS estimator correcting for heteroskedasticity and first-order autocorrelation should be used.⁵⁸ Column 7 in Table 6 reports the estimates. An essential first observation is that size and significance of the estimated coefficients are very similar to the estimates of the level equation (6).

D. Discussion of Results

Table 6 (Appendix III) summarizes the estimation results from the different specifications and estimators discussed in the previous three sections. Column 6 contains the final estimates of the level-equation (6), after correction for heteroskedasticity and serial correlation. To give an idea of the robustness of these estimates, column 7 also reports the estimated coefficients from the first-difference-equation (7).

Overall, we observe that the coefficients of most of the theoretical determinants (sovereign risk, firm-value volatility, leverage,⁵⁹ and interest rate volatility⁶⁰) have the expected sign and are statistically significant at conventional levels (Table 7). This result is in contrast with the mostly insignificant coefficients in the study by Durbin and Ng (2005). Only one control variable is clearly not significant: the monthly bond trading volume (TOVC), our proxy for a bond’s liquidity. The fit of the model is surprisingly good: in the level equation, the adjusted R-squared is 96 percent, that is, 96 percent of the variation in corporate spreads is accounted for by the variation in the explanatory variables (and fixed effects), while the standard error of the model is 0.001, that is, 10 basis points. In the first-difference equation, the adjusted R-squared is 75 percent with a similar standard error of 10 basis points.

Sovereign risk (SSOV) turns out to be a highly significant determinant of corporate spreads in most cases. In the level regression, the sovereign risk coefficient of only one firm—Harmony Gold (HAR1)— is marginally not significant at the five-percent level (although it is significant at the 10 percent level). In the first-difference equation, it is only the SSOV-coefficient of African Bank (ABL1) that is marginally not significant at the 5 percent level (but also significant at the 10 percent level). The size of these coefficients varies between 0.42 for Nedcor Bank (NED1) and 0.96 for ABSA Bank (AB01), implying that a 100 basis-point increase in the sovereign default premium is associated with an increase in corporate spreads of between 42 and 96 basis points.

Does the sovereign ceiling in spreads apply? According to the analytical framework of section III.C, the finding that there is a less than one-to-one correspondence between sovereign and corporate spreads for all firms (i.e., $\partial s_t/\partial s_t^{\mathit{\text{sov}}}<1$) would be taken as evidence that the sovereign ceiling does not apply for these firms.⁶¹ But are the estimated SSOV-coefficients statistically different from one? We address this question formally by means of Wald tests (Appendix II.E).⁶²

According to these Wald tests, there is evidence that the sovereign ceiling does not apply for the three large industrial companies. For Imperial Group (IPL1, a large, diversified, multinational firm) and ISCOR (IS59, the largest steel producer on the African continent), the null hypothesis that β_i = 1 is rejected at the one-percent level in both the level and first-difference regressions. With SSOV-coefficients of 0.61 and 0.42, respectively, there is clear evidence that the sovereign ceiling in spreads does not apply. For SASOL (SFL1), a large chemicals and fuels multinational, there is also some evidence, with a SSOV-coefficient (0.83) significantly smaller than one at the nine-percent level in the level equation and at the five-percent level in the first-difference equation. In terms of equations (3) and (4), the fact that the bond spreads of these companies are generally higher than comparable sovereign spreads (Figure 1, Appendix III) can therefore not be due to 100 percent indirect sovereign risk P(F/S) (i.e., the application of the sovereign ceiling) but must be due to relatively high stand-alone default risk P(F/S^c). Higher firm stand-alone risk, in turn, is accounted for by firm-specific variables.

This is good news for these three companies: some day in the future when financial markets judge them to be sufficiently strong (i.e., when their stand-alone default probability P(F/S^c) is sufficiently low), their overall default probability P(F) could fall below sovereign default risk P(S). As a result, they might obtain (local currency) credit ratings that are lower than those of the South African government (i.e., they might “pierce the sovereign ceiling”) and thus raise debt finance at lower cost than their government.

For the banks in the sample, the sovereign ceiling in spreads seems to apply in general. The sovereign risk coefficients of ABSA Bank (AB01; 0.96 and 0.98 in the level and first-difference equations, respectively) and African Bank (ABL1; 0.92 and 0.93, respectively) are statistically not different from one. The SSOV-coefficients of Standard Bank (SBK1; 0.89 and 0.92) and Investec Bank (IV01; 0.78 and 0.88) are also not significantly different from one in the first-difference equation. In the level equation, however, SBK1’s coefficient is marginally smaller than one (at the 8 percent level) and IV01’s significantly so (at the two-percent level). The sovereign risk coefficient of Nedcor Bank (NED1) is a surprising anomaly that would merit further investigation: at about 0.40 in both equations, it is the smallest SSOV-coefficient in the sample.⁶³ In terms of the model in section III.C, SSOV-coefficients equal to one mean that bond markets judge indirect sovereign risk for these banks to be 100 percent (i.e., P(F/S) = 1), which implies that the default probabilities P(F) of these firms and, hence, spreads will be at least as high as those of the government (equation 4). Thus, the fact that these banks’ spreads are generally higher than the comparable sovereign spreads (Figure 1, Appendix III), is due to the application of the sovereign ceiling rather than to higher stand-alone default risk P(F/S^c). In other words, even if the stand-alone default probabilities P(F/S^c) of these banks were much lower than the government’s default probability P(S), their overall default probabilities P(F) and spreads would still be higher than those of their government because of the application of the sovereign ceiling. The finding that bond markets seem to price into spreads of banks a kind of sovereign ceiling is consistent with rating agency practice of generally not rating financial institutions higher than their sovereign.

The following firm- or bond-specific factors are also found to significantly affect corporate default premia:⁶⁴

• Firm-value volatility (SV1000D). An increase in the volatility (standard deviation) of returns on the firm’s assets by 10 percentage points will increase corporate spreads by 48 basis points.

• Firm leverage, as measured by the quasi-debt-to-firm-value ratio (D1). The effect of a change in leverage on corporate spreads is reinforced by interest rate volatility, as expected; but it does not seem to depend on remaining time to maturity. This means that the higher interest rate risk is, the stronger the impact of a change in leverage on spreads. Quantitatively, if interest volatility were zero, an increase in a firm’s leverage ratio by 0.5—for instance, from 0.3 to 0.8—would increase its spread by approximately 95 basis points; if interest rate risk is at its sample mean instead (1.01 percent per annum, see Table 5), the same 0.5 increase in the quasi-debt ratio would raise spreads by about 114 basis points.

• Interest rate volatility (SIGSPOTM). The volatility of the risk-free interest rate is a highly significant determinant of spreads in interaction with leverage, as expected; on its own, however, it is only marginally significant (at the seven percent level) and has the wrong sign. Considering the influence of interest rate volatility on its own as insignificant, we obtain the result implied by theory, namely that the impact of a change in this volatility on spreads depends positively on leverage and vanishes if leverage tends towards zero. Quantitatively, an increase in interest rate volatility by one-percentage point will increase the credit spread of our firms by about 19 basis points if their leverage stands at the sample mean (0.51); if leverage stood at the sample minimum (0.08), a one percentage point increase in interest volatility would increase corporate spreads by only three basis points. If we considered the estimated parameter of interest rate volatility in isolation as significant instead, the overall effect on spreads would still be positive for all leverage levels above 0.41. Under this assumption, a change in volatility by one percentage point would increase spreads still by about four basis points if leverage were at the sample mean.

• Time to maturity (M). Remaining time to maturity is also a statistically significant determinant of corporate credit spreads, but seems to have the wrong (negative) sign. In addition, the interaction term with leverage is not significant. Quantitatively, an increase in remaining time to maturity by one year decreases corporate credit spreads by about 30 basis points. This result is less counterintuitive than it might appear at first: It suggests that during our sample period (July 2000–May 2003), the term structure of credit spreads of our nine firms has been downward sloping on average, independently of their leverage. According to the theoretical model, the credit spread term structure of a firm is downward sloping if the firm’s leverage and/or its asset return volatility are relatively high. On the one hand, it is very well possible that the average term structure of credit risk of our nine firms has been downward sloping during July 2000–May 2003. On the other hand, this outcome might be spurious and due to pooling the data of the nine firms. In other words, if we had had sufficient data to run separate regressions for the nine firms, it is possible that the firms with relatively low leverage and asset volatility would have shown an upward-sloping term structure, whereas only those with relatively high leverage and asset volatility would have displayed a downward-sloping credit risk term structure.

Our proxy for a corporate bond’s liquidity (TOVC), the ZAR amount traded during the month, is not significant.⁶⁵ This result suggests that TOVC is not a good proxy for liquidity. One potential reason is that TOVC does not measure the liquidity relative to the risk-free bonds. We would ideally want to use the ratio of corporate bond turnover over risk-free bond turnover; but turnover data for the risk-free benchmark bonds were unfortunately not available. Another reason could be that we are faced with a timing problem: the dependent variable—the corporate spread—is observed on the last day of the month, whereas TOVC is the total amount traded during the month; that is, the latter might not be a good proxy for liquidity on the last day of the month.

Finally, a variance decomposition of the corporate default spreads confirms earlier findings that aggregate (systemic) factors appear to be much more important than firm-specific factors in determining these spreads (Table 8). Using the estimated parameters of the level and first-difference equations (Columns 6 and 7 in Table 6), we decompose the levels and changes of the corporate default premia into the four components (i) firm-specific factors, (ii) sovereign risk (the systemic factor), (iii) fixed effects (only for corporate spread levels), and (iv) the residuals.⁶⁶ The data show that in both the level and the first-difference equations, the variation in sovereign risk (a systemic factor) explains about 12 to 13 times more of the total variation than the variation in the combined firm-specific factors derived from the contingent claims approach à la Merton and Shimko. In the level equation, 13 percent of the variation in corporate spreads is explained by the variation in sovereign risk, while only one percent of total variation is explained by the combined firm-specific factors.⁶⁷ In the first-difference equation, sovereign risk explains 61 percent of total variation, while firm-specific factors explain only 5 percent, with 34 percent of total variation remaining unexplained.