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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 firm’s 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.
1
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. Haussman’s 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
2
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
Cost of local-currency-denominated debt
=
Risk-free rate
+
Total risk premium
1) Currency (risk) premium
2) Default (risk) premium
Country (risk) premium
3) Jurisdiction premium
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.
3
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 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 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
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.
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).
4
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 domesticcurrency debt obligations is what Standard and Poor’s calls “economic or country risk”5,
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 Moody’s – 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.
“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).
6
5
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.”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 Moody’s or Standard
and 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 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 = 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
8
See Moody's Investors Service (2001a), p.1.
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.
9
6
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 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 (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).
7
(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 firm’s 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 “intermediaterisk” 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.
8
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 firm’s 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 firm’s 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 = PD·LGD.
9
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 optiontheoretic 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).
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), Saá-Requejo and Santa Clara (1997), Briys and De Varenne (1997), and Hsu, Saá-Requejo, and
Santa Clara (2002).
16
10
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, Merton’s assumption of a constant risk-free interest rate is relaxed and
stochastic (risk-free) interest rates à 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 bidask 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
Pt (T ) = exp[−rT ] 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.
11
(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.
Vt = Et + Dt
(1)
Together with (A.1), this implies that the value of the firm and the value of its
assets are identical.
(A.5) Itô dynamics of firm value: The value of the firm (i.e. the value of its assets), Vt,
follows a geometric Brownian motion process:
dVt
= µ dt + σ V dZ1, t
Vt
(2)
where µ is the instantaneous expected rate of return on the firm value, σ V2 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
dZ1, t = ε1 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
ET = max(0, VT − B) .
(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.
12
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 σ V , the face value of the debt, B, is
the strike price, τ ≡ T − t is remaining time to maturity, and r is the risk-free interest rate:
Et = Vt Φ(h1 ) − Be − rτ Φ(h2 )
(4)
where Φ (⋅) is the standard normal cumulative density function and
 Be − rτ
V   1 
ln  t  + r + σ V2 τ − ln
B
2 

 Vt
h1 =  
=
σV τ
h2 = h1 − σ V
 1 2
 + σ V τ
 2
σV τ
 Be − rτ
− ln
 Vt
τ =
 1 2
 − σ V τ
 2
σV τ
(5)
.
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
Dt = Vt − Et
Dt = Vt Φ (− h1 ) + Be − rτ Φ (h2 )
(6)
The yield to maturity, yt, of the (risky) discount bond in a continuous time
framework is the solution to the equation
Dt = Be − yτ ,
(7)
1 D 
y t = − ln  t  .
τ B
(8)
that is,
The corporate default premium (also called “yield spread” or “credit spread”), s t , is then
defined as the difference between the yield to maturity of the risky zero coupon bond and
the risk-free rate, i.e.
st ≡ yt − r .
(9)
Substituting equations (6) and (8) into equation (9), the corporate default premium
becomes:
1 D 
s t = − ln  t  − r
τ B
1 Vt Φ (−h1 ) + Be − rτ Φ (h2 ) 
 Dt  1
− rτ
= − ln   + ln e = − ln 

τ B τ
τ 
Be − rτ

1
13

1 
1
= − ln Φ (h2 ) + Φ(− h1 )
dt
τ 

  12 σ V2τ + ln(d t )  1  12 σ V2τ − ln(d t ) 
 ,
 + Φ −
s t = − ln Φ −

 d 
τ  
σV τ
σ
τ
t
V



1
(10)
where d t ≡ Be − rτ Vt , 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 Merton’s very simple
model: The corporate default premium is a function of only three variables. These are (1)
firm value volatility, σ V , (2) the quasi-debt ratio, d (a form of leverage ratio), and (3) the
time to maturity of the debt contract, τ . As usual in option pricing, the rate of return on
the underlying security (here the growth rate in the value of the firm, µ) has no impact on
the default premium.
Further, Merton shows that ∂s ∂σ V2 > 0 , ∂s ∂d > 0 , and ∂s ∂τ <> 0 . 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<<1). In other words, for firms with a leverage ratio d
>1, an increasing time to maturity τ will lead to a declining default premium (∂s/∂τ <0); for leverage ratios
below 1, the credit spread first rises and then falls as maturity increases; for very low leverage ratios
(d<<1), the default premium increases with longer time to maturity. The Merton model produces the
classical hump shaped term structure of credit spreads – a non-intuitive result but a fact often found in
actual data.
14
Shimko et al. (1993) suggest to integrate the Vasicek (1977) term-structure-ofinterest-rates model into the Merton (1974) framework, i.e. they assume that the shortterm risk-free interest rates follows a (stationary) Ornstein-Uhlenbeck process of the form
dr = α (γ − r )dt + σ r dZ 2, t
(11)
where γ is the long-run mean which the short-term interest rate r is reverting to, α > 0 is
the speed at which this convergence occurs, σ r is the instantaneous variance (volatility)
of the interest rate, and dZ 2, t = ε 2 dt is a (second) standard Gauss-Wiener process
whose correlation with the stochastic firm value factor, dZ1, t , is equal to ρ , i.e.
dZ 1, t ⋅ dZ 2, t = ρ dt .
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 τ is no longer Pt (τ ) = exp[−rτ ] but becomes
2
1 − e −ατ
(R(∞) − r ) − τ R(∞) − σ r 3 1 − e −ατ
Pt (τ ) = exp
4α
 α
(
)  ,
2

(12)
and the yield to maturity of this risk-free discount bond – what Vasicek (1977) calls the
“term structure of interest rates” – is
1
Rt (τ ) = − ln Pt (τ ) ,
(13)
τ
where R(∞) = Rt (∞) = lim Rt (τ ) = γ + σ r λ α − 12 σ r2 α 2 is the yield to maturity of a zero
τ →∞
coupon bond whose remaining maturity approaches infinity, and λ 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
Dt∗ = Vt Φ (−h1∗ ) + BPt Φ (h2∗ ) ,
(14)
where
 BP (τ )  1 ∗
 Vt  1 ∗
+ T
− ln t
ln 
+ T
BPt (τ )  2
Vt  2


∗
h1 =
=
T∗
T∗
(15)
22
See p. 185.
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. rt = Rt (0) = lim Rt (τ ) .
23
τ →0
15
 BP (τ )  1 ∗
− T
− ln t
Vt  2

∗
∗
∗
h2 = h1 − T =
T∗
,
where T ∗ , in turn, is
τ
T ∗ = ∫ σ D2 ∗ ( s ) ds
0
 2 σ r2 2 ρσ V σ r
= τ  σ V + 2 +
α
α


 2σ 2 2 ρσ r σ V
 + e −ατ − 1  3r +
α2

 α
(
)
 σ r2 −2ατ
 −
e
− 1 , (16)
3
 2α
(
)
where σ D2 ∗ ( s ) , in turn, is
σ D2 ( s ) = σ V2 + σ P2 ( s ) − 2 ρσ V σ P ( s ) ,
∗
and where σ P2 ( s ) , finally, is
 1 − e −αs
σ ( s ) = 
 α
2
P
2
 2
 σ r .

σ P2 ( s ) is the instantaneous variance (volatility) of the return on the risk-free zero coupon
bond P with maturity s;24 σ D2 ( s ) 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) s t under stochastic interest rates (i.e. the equivalent of equation 10 under
interest rate risk): s t is now the difference between the yield to maturity on the risky zero
coupon bond, yt (τ ) = −1 τ ⋅ ln ( Dt∗ B) , and the yield to maturity on the risk-free zero
coupon bond of the same maturity Rt (τ ) = − 1 τ ⋅ ln Pt (τ ) , i.e.
s t = yt (τ ) − Rt (τ )
1  D∗  1
= − ln  t  + ln Pt
τ B τ
1 V Φ (−h1∗ ) + BPt Φ (h2∗ ) 
= − ln  t

τ 
BPt


1 
1
= − ln Φ (h2∗ ) + ∗ Φ (−h1∗ )
τ 
dt

24
See also Vasicek (1977), pp. 180 and 186.
16
∗
∗
∗
∗
1   1 T + ln(d t )  1  12 T − ln(d t ) 
 + ∗ Φ −
 .
s t = − ln Φ − 2
 d


τ  
T∗
T∗
t



(17)
where d t∗ ≡ BPt Vt 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 s t is a
function of a fourth important determinant: interest rate volatility σ r . A comparison of
equations (17) and (10) reveals only two differences. First, the quasi-debt ratio in (10),
d t ≡ Be − rτ Vt , is replaced by d t∗ ≡ BPt Vt 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,
σ V2τ , is replaced by the variance of the return on the risky bond over its remaining life,

 2σ 2 2 ρσ r σ V  σ r2 −2ατ
σ 2 2 ρσ V σ r 
 + e −ατ − 1  3r +
−
T ∗ = τ  σ V2 + r2 +
(e − 1).
This
α
α 2  2α 3
α


 α
difference accounts for the fact that the value of risky debt, Dt∗ , and, hence, the value of
(
)
the firm, Vt , are now functions of two stochastic variables, V and r. As a consequence, s t
is now also function of interest rate volatility σ r .25
The impacts on the default premium of changes in the three already identified
determinants (leverage d , firm value volatility σ V , and remaining time to maturity τ )
remain essentially the same under stochastic interest rates.26 What is the impact on
spreads of changes in interest rate volatility σ r ? Generally, increases in σ 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 ∂s ∂σ r is ambiguous. It
depends in a complex fashion on α , ρ , τ , σ 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 ρ between the two stochastic
factors dZ1 and dZ2, and of α, the speed of convergence of the risk-free rate r to its long run mean γ. 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 σV. See Shimko et al. (1993), pp. 61-63.
27
See Cossin and Pirotte (2001), p. 51, and Shimko et al. (1993), p. 62.
17
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 lossgiven-default rate (LGD), that is EL = PD·LGD. Assuming for simplicity that (1) LGD is
equal to one (i.e. if the firm defaults, the whole investment is lost), (2) investors are riskneutral, 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 company’s probability of
default, i.e. s = f(PD).
18
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:
P( F ) = P( F ∩ S c ) + P( F ∩ S )
= P( S c ) ⋅ P ( F / S c ) + P( S ) ⋅ P ( F / S )
= [1 − P ( S )] ⋅ P( F / S c ) + P( S ) ⋅ P ( F / S )
(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 S c (= 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) P( S ) is the default probability of the sovereign (“sovereign risk”);
(2) 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 “crisis” period. We call this
probability the “stand-alone” default probability of the firm.
(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.
In terms of credit ratings (which are nothing else than estimates of default
probabilities), the four probabilities P( F ), P( S ), P ( F / S c ), and P( F / S ) have direct
correspondents. In Moody’s terminology, 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 (18) makes intuitive
sense. When the sovereign default probability is zero, the firm’s default probability
reduces to its stand-alone default probability, i.e. P( F ) = P( F / S c ) . As the sovereign
default probability rises and approaches 100% ( P( S ) = 1 ), the importance of stand-alone
19
default risk ( P( F / S c ) ) vanishes compared to direct ( P(S ) ) and indirect sovereign risk
( P( F / S ) ); at the limit (i.e. 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 ) . When the firm’s stand-alone default probability is zero ( P( F / S c ) = 0 )
but there is sovereign risk ( P( S ) > 0 ), the firm’s default probability is 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) is also equal to zero, the firm’s (overall) default
probability is also equal to zero ( P( F ) = 0 ). Finally, when there is direct sovereign risk
( P( S ) > 0 ) and indirect sovereign risk (or transfer risk in foreign currency terms) is
100%
( P( F / S ) = 1 ),
the
firm’s
default
probability
equals P( F ) = [1 − P( S )] ⋅ P( F / S c ) + P( S ) . This boundary case is the key to understand
the concept of the “sovereign ceiling”:
Definition: In the context of a firm’s 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
P( F / S ) = 1 .
Whenever indirect sovereign risk (or transfer risk) equals 100%, equation (18)
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 standalone default probabiliy P( F / S c ) 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 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 in low ratings), this floor translates into a ceiling, hence the concept
“sovereign ceiling”. When indirect sovereign (or transfer) risk is smaller than 100%
( 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 (2001). In a simple
theoretical model similar to the framwork used in this section, Durbin and Ng (2001)
show that 100% transfer risk (i.e. indirect sovereign risk in domestic currency
obligations) 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, 100% 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
20
market’s 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 ( ∂s / ∂sG ) 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 ∂s / ∂sG will be a test
of whether the sovereign ceiling applies or not: if ∂s / ∂s G ≥ 1 , the sovereign ceiling in
spreads applies; ∂s / ∂s G < 1 , the sovereign ceiling does not apply.
3.4. Other Potential Determinants
Once assumption A.1 (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. As surveyed in section 2, 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 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.
Among all these factors, only potential differences in liquidity are controlled for
explicitly in the present investigation. One might expect the risk-free bond issues to be
larger and more liquid than the corporate issues, such that the liquidity premium on
corporate bonds will be larger than that on risk-free bonds. As a result, we would expect
that the higher the liquidity, l, of a given bond issue, the lower its spread. That is, 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:
21
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-tomaturity) 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.
+
+
+
+− +− −
s = f (s G , d * , σV , σ r , τ , l ) .
(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.
At the end of our sample period (May 2003), the Republic of South Africa’s local currency debt was
rated A by Standard & Poor’s and A2 by Moody’s (i.e. the same rating), see Table -1 in appendix A3 for
the history of South Africa’s ratings by the two rating agencies.
29
22
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 riskfree 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 onshore (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).
23
(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: y a = 100 (1 + y s 200) 2 − 1 where ys stands for "annualised yield compounded
[
]
semi-annually" and ya stands for "annualised yields compounded annually".
24
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).
25
4.2.2. Quasi-Debt to Firm Value (Leverage) Ratio
Here, we have to calculate d t∗ ≡ BPt Vt , 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 τ . 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.
26
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 riskfree bond.
(3)
E, the market value of equity, is required in order to calculate the firm’s 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 firm’s
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
D = P T ( B T + B NT ) .
B T + B NT is equal to B1 (or B2, respectively) obtained above. Thus the crucial
variable to obtain is P T , 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
D = P T B1 .
P T 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 semiannually (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.
27
[
]
y s = 200 (1 + y a 100) 0.5 − 1 .
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 P T .
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
V = E + D = MV + PT B1 .
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
( σ V ) on the basis of V1 and V2 prior to the life of the bond. However, an estimate
of σ 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 firm’s assets).
Now, we have got the necessary elements to calculate the quasi-debt-to-firm or
leverage ratio, d t∗ ≡ BPt Vt . 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
28
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 τ 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).
29
4.2.4. Firm Value Volatility
This is the instantaneous standard deviation of the return on the firm value, σ 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, σ 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 σ 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 Et = Vt Φ(h1 ) − Be − rτ Φ(h2 )
V Φ(h1 )
simultaneously for the two unknowns, V and σ V .32 This is,
and σ E = σ V
E
however, beyond the scope of this paper. We use an approximation instead. We solve the
nonlinear equation
− ln ( Be − rτ Vt ) + 12 σ V2τ
V Φ(h1 )
with h1 =
σ E = σV
E
σV τ
numerically for σ V using estimates of all the other variables ( σ E , E=MV, V,
d ≡ Be − rτ V ,τ) as inputs.
However, before we can proceed to the calculation of σ V , we need to obtain an
estimate of the daily equity return volatility σ E . Such an estimate is obtained as follows.
 E 
First, we compute daily stock returns according to ut = ln  t  , where E is the daily
 Et −1 
stock closing prices. Then, we calculate the variance of ut according to the formula
1 T
∑ (ut − u ) 2 , where T is the number of trading days over which the rolling
T − 1 t =1
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
s2 =
32
See appendix A1.2 for an explanation of the second equation.
30
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, σ E , by applying the standard formula σ E = s τ , where τ =
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 σ V .
V Φ (h1 )
The equation σ E = σ V
is solved by an iterative procedure.33 We use the first
E
estimate, sv12m?, obtained above as starting value for σ 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, σ 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 σ 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 1233
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. α, ρ ) and on some complex non-linearities which are difficult to dealt with.
31
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 σ 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.
∆r = a (b − r ) ∆t + σ r ∆Z t .
With Zt being a standard Wiener process, ∆r is normally distributed with instantaneous
mean equal to a (b − r ) ∆t and instantaneous variance equal to σ r2 ∆t , i.e.,
∆r ∼ N[ a (b − r ) ∆t , σ r2 ∆t ]
Taking monthly observations of the 3-months BA rate, we calculate the variance of the
monthly (absolute) changes, Vˆar ( ∆r ) , by the usual method. Recalling that time t is
expressed in years, so that ∆t = 1 month = 1/12 years = τ , the variance Vˆar ( ∆r ) 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 BA’s 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.
32
Vˆar ( ∆r ) = σ r2τ
Hence, σ r is estimated as
σr =
Vˆar (∆r )
τ
= Vˆar (∆r ) ⋅ 12
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 BESA database contains two
measures of trading volume: (1) monthly data for all bonds on "Total Spot Nominal
traded for [month] (excluded repos)"; (2) the corresponding figures on "Total Spot Clean
consideration for [month] (excluded repos)". Both are nominal figures. Of the two
available measures, though, we believe that "Total Spot Clean consideration for [month]
(excludes repos)" is more appropriate. The reason is the following: suppose between two
coupon payment dates, a given coupon bond is traded every month by the same notional
33
amount outstanding (e.g., every month, ZAR 1bn of notional amount is traded in that
bond) and the clean price stays roughly constant throughout this period. For this bond,
measure (1) will indicate a continuous, linear increase in turnover (=liquidity) solely
because of accruing interest (recall that total spot nominal traded is the notional amount
outstanding multiplied by the gross price). Measure (2) will indicate no change in
turnover (=liquidity) for this bond, because clean price and amount traded are constant. It
seems to us that the simple fact that a coupon bond comes closer to the coupon payment
date does not increase its liquidity. Hence, we think measure (2) is better. Next, we create
the variable TOVC?, representing the "Total Spot Clean consideration for [month]
(excludes repos)" for each corporate bond.
Now, we have to decide between AOS? and TOVC?. As to the question of what
appropriate proxies for liquidity are, the discussion in Sarig and Warga (1989a), and the
study by Elton and Green (1998) imply that trading volume would represent the best
measure.35 However, Sarig and Warga (1989a) note that this information is not available
"because bond trading is not centralized in any particular location, this information is not
available even to the banks collecting price data." In our case, this means that only if the
bonds are solely traded at BESA (or, at least, if BESA represents a significant part of
total trading), this trading volume data is an appropriate proxy for the liquidity of the
bonds. According to BESA officials, the trading volumes of bonds traded offshore is
negligible. As a result, for the months we have this BESA trading volume data available,
i.e. TOVC?, we can use it to proxy for liquidity. It is a fully appropriate measure.36
4.3. Sample and Data
Considering the data constraints explained in section 4.2, we will use monthly or
daily data provided by the Bond Exchange of South Africa (henceforth BESA) and
Thomson Financial Datastream (DS) over the period July 2000 to May 2003. As later in
the econometric exercise we will only use monthly figures, those variables available at
daily frequency will be converted into monthly ones by computing a simple average.
Our sample has N=12 corporate bonds and T (number of months) dependent on
each series (max = 33, min = 9). The symbol “?” stands for the cross-section identifier of
each corporate bond, which in turn will be used in EVIEWS 4.1 for estimation purposes.
35
The three other proxies suggested by these authors are: (1) the bond's age, (2) bid-ask spreads of price
quotations, and (3) the amount of bonds outstanding, due to the potential correlation between the existing
stock of a particular bond and the flow of trade in this bond.
36
Normally, offshore transfers involve 2 counterparts trading with one another directly. The transactions
would typically be cleared through an institution such as Euroclear or Cedel. We thank Bernard Claassens
of BESA for his invaluable help in answering our questions regarding the measurement of liquidity.
34
These are: _AB01 _ABL1 _HAR1 _IPL1 _IPL2 _IS59 _IS57 _IV01 _NED1 _SFL1
_SBK1 _SBK4.
5. Empirical Methodology and Results
5.1. Sources of Variability and Statistical Properties of Corporate Default Spreads
A first important step in panel econometrics is to disentangle the source of
variability in our dependent variable. That is, we aim to understand the nature of the
dependent or endogenous variable of our econometric model.37 Put differently: are
variations in corporate spreads mostly accounted for by the time dimension (“within
variance”) or are they due to cross-section differences, i.e. firm specific effects (“between
variance”) unaccounted for by those variables derived in section 3?
We study both the levels and the first differences of corporate spreads (scor? and
d(scor?), respectively). Then, we proceed to decompose the total variation in the
corporate spreads as explained in appendix A2.1. Table 4 (appendix A3) displays the
results of this decomposition.
As we can see from table 4, while the variance between different scor? explains
almost near 73% of the total variation in corporate spreads levels, it is the other way
around in the case of d(scor?). Here, the within variation accounts for 98.8% of the total
variability in the first differences of the spreads. A first, preliminary implication of these
results is that we may expect to see significant individual effects (whether fixed or
random) in the model estimated on the basis of spreads levels, and certainly no role for
them in the regression where the first difference d(scor?) is the dependent variable.
5.2. Set-Up of Model: A General Error Components Specification
5.2.1. Corporate Spreads in Levels
As said, we are interested in both the levels and the first differences of corporate
default spreads, labeled scor? and d(scor?), respectively. The level equation is specified
as follows:
k
scorit = β 0 + β1ssovit + ∑ β k X k ,it + vit ,
(20)
j =2
37
Another implication relates to the estimation properties, in particular to the efficiency involved by
different estimators. We will come back to this in sections 5-2) and 5-3).
35
where ssov it is the sovereign spread which best matches scorit in terms of maturity and
other bond characteristics; X k ,it is a set of firm-specific control variables defined in
section 3 and operationalized in section 4, namely:
•
•
•
•
•
•
•
Quasi-debt to firm value (or leverage ratios, di?)
Volatility of returns on the firm’s value (sv1000d or sv12m, sv24m)
Life to maturity (m?)
Volatility of risk-free interest rates (sigspotm?)
A proxy for liquidity (tovc?)
An interaction term (m?*di)
Another interaction term (sigspotm?*di?),
and v it = u i + eit is the error component term (an individual random disturbance u i –
which adds to β 0 when this effect is considered as fixed- plus an i.i.d., white noise term,
namely eit ).
For the moment, we assume that β 1i = β 1 and β ji = β j with j=2…k, that is equal
slopes across different units (corporate bond spreads). We will test whether this
assumption holds or not in a few moments. The traditional Gauss-Markov assumptions
are, in principle, valid. They are the following:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
E (eit) = E (ui)= 0
E (eit2) = σ2e
E (ui2) = σ2u
E (eit uj) = 0 for all i, t and j.
E (eit ejs) = 0 if t ≠ s or i ≠ j
E (ui uj) = 0 if i ≠ j
5.2.2. Corporate Spreads in First Differences
In order to write down the econometric model, it suffices to take the first
difference to both sides of equation (20) above. Thus, we obtain the following expression:
k
d ( scorit ) = β1 d ( ssovit ) + ∑ β k d ( X k ,it ) + v ' it ,
(21)
j =2
where v ' it = v it − v it −1 = e it − e it −1 .
A caveat is in order. Any measurement error in the spreads level equation (20)
will be fully translated to (21), so care should be taken in this regard. Also note the
possibility that the error term, namely v'it is serially correlated (e.g. a moving average
36
term of the component eit ). By construction, the individual effects and the common
intercept term β 0 are eliminated. As a natural consequence, the variability of the sample
should now be overwhelmingly within. This is precisely what comes out from our
variance breakdown in section 5.1.
5.3. Panel Regression Results of Level Equation
We proceed to the econometric estimation in four steps: (1) we perform tests of
pooling; (2) we briefly discuss the convenience of a fixed effects model versus a random
effect specification; (3) we present the regression output corresponding to the spread
level equations (as shown in equation 20) as well as a battery of tests intended to help
discern which is the best regression; these results refer to one particular kind of estimator
(i.e. Pooled-OLS, fixed effects (LSDV) and random effects (RE-FGLS); (4) we show the
econometric results of the first difference model (as shown in equation 19) and compare
them to those obtained in the best level equation.
5.3.1. Tests of Pooling
Following traditional panel econometric modelling (e.g. Hsiao (1986)), we
proceed to test the existence of specific corporate bond spread effects in the model, not
accounted by our explanatory variable set. We perform two standard Wald F–tests to
check the null of: a) homogeneous slopes and intercepts in equation (20) – Pooled OLS is
the right model – (against an alternative of homogeneous slopes and different intercepts –
fixed effects is the proper model); and b) homogeneous slopes and different intercepts
(against an alternative of different slopes in ssov? and different intercepts). The procedure
of these tests as well as the full description of their results are shown in tables A2.1 and
A2.2 in appendix A2.2.
The results of the first test indicate we reject the null that the model has
homogeneous intercepts and slopes, at a 5% level of significance (and even at a 1%
level). A robustness check, implying a change in asset returns volatility (sv24m or sv12m
instead of sv1000d) yields the same conclusion.
Provided the conclusion of the first Wald-test, the results of the second test
suggest we have to reject the null that the model has different intercepts but
homogeneous slopes associated to SSOV? at a 5% level of significance (and even at a 1%
level). A robustness check, implying a change in asset returns volatility (sv24m or sv12m
instead of sv1000d) yields the same conclusion.
37
In conclusion, we would expect to observe different responses from SCOR? to
SSOV? across different corporate bonds or issuers. This is very relevant in terms of a
policy-oriented analysis. However, we wonder whether the different slopes are not the
product of typical small-sample biasedness, very likely to occur in our case.
Notwithstanding this result, in what follows we will assume away the heterogeneity in the
slope of SSOV? in order to be able to compare RE-FGLS to other estimators.38
5.3.2. Fixed or Random Effects?
The result of the foregoing tests, notwithstanding our finding on the heterogeneity
of the slopes associated to SSOV? (subject to potential biasedness), leads us to ask
whether one may really consider these corporate bond-specific effects as fixed or random.
Some authors (e.g. Mundlak (1978)) have considered that this distinction is an
erroneous interpretation and we should always treat these effects as random. According to
him, the fixed effects model is simply analysed conditionally on the effects present in the
observed sample (Greene, 2000). Moreover, this model might be viewed as applying only
to the cross-sectional units in the study, not to the ones left out of the sample. The only
exception would be the case when the cross-sectional units exhaust the sample. Indeed,
this is our case given that all “true” corporate and banking bonds are included in our
sample. Our T, on the other hand, is not long enough to assume away both effects are
indistinguishable (i.e. we would know all observations). This is so because the shortness
of the sample for some explanatory variables (for instance liquidity, i.e. tovc?) constrains
the full utilisation of corporate spreads in the time dimension. Should we exclude these
variables, we would be nearly exhausting the maximum number of available periods that
correspond to BESA history.
Therefore, if no substantial differences between both estimators are found, that is,
if their properties are as good and their specification errors behave similarly, we will
suppose that no real differences regarding the treatment of the nature of the group effects
exist in our model.
5.3.3. Model Selection
5.3.3.1. Regression Output
In any case, RE-FGLS would not be estimable because we could not assign weights when the β ' s are
heterogeneous across units. This is another reason why we keep on working with the assumption of equal
slopes.
38
38
Based on the specification suggested by equation (20) we run different
regressions, each one regarding one particular kind of estimator (i.e. Pooled-OLS, fixed
effects (LSDV) and random effects (RE-FGLS)). Then, we evaluate the quality and
properties of these estimators in comparative perspective so as to finally be able to
choose the best regression.
The first three regressions are correspondingly: Pooled-OLS (a single intercept in
(20), i.e. β 0 ), LSDV (fixed effects or within estimator, i.e. considering u i as a parametric
shift in (20), additive to β 0 ) and RE-FGLS (error components model, as it stands in
equation 20). The results are reported in table 5 (appendix A3)39. All three estimators are
obtained using the White heteroskedasticity-consistent standard errors & covariance.
Please note that RE-FGLS estimators are both robust to heteroskedasticity ( E (e it ) 2 = σ 2 i
and/or E (u t ) 2 = σ 2 ui and serial correlation over time ( E (e it e js ) = 0∀t ≠ s . However, as
it is not necessarily the case of the LSDV estimation, we also corrected for both sources
of inefficiency by using a proper weighing matrix.
The RE-FGLS estimates show how inefficient are the weights assigned by
Pooled-OLS to the between-units variation in relation to the LSDV estimator. Indeed, an
overwhelmingly majority of the point estimates (βs) yielded by the RE-FGLS regression
are much closer to the LSDV than to the pooled-OLS ones (the exception being the signs
and values of sigspotm? , sv1000d? and d1? in the regression where autocorrelation and
heteroskedascity are remedied –though sigspotm? is not statistically significant). The
closeness of RE-FGLS to LSDV estimators results from the fact that RE-FGLS attaches
less weight to the between variations than Pooled-OLS.
RE-FGLS may converge to Pooled-OLS or to LSDV estimators as a special case,
as we said before. The degree of convergence hinges on the variances σ u , σ e and T, the
time dimension. Moreover, these three parameters determine the magnitude of the
weights used by RE-FGLS. This is explained in appendix A2.3.
Once Pooled-OLS estimates are discarded as a result of their relative inefficiency,
we have to decide which estimator between RE-FGLS and LSDV yields the most reliable
and robust results. In order to do this we perform several tests. A first step is to test the
null that σ u =0 or see what the value of the estimate for σ e is. This comes next.
39
In all regressions, d1 and sigspotm? (i.e. leverage and interest rate volatility) yielded the more robust
results.
39
5.3.3.2. Test for Existence of Random Effects
This is typically a Breusch-Pagan test to check whether the null that σ u = 0 ((iii)
from the Gauss-Markov assumptions laid out above) can be rejected or not. The results
reported in appendix A2.4 confirm the rejection of the null that no random effects on the
cross-sectional units are present. This is evidence in favour of the RE-FGLS estimator.
While the result of this test tells us we should not discard the RE-FGLS model, it
does not conclude, on the other hand, that we should rule out the (corrected) LSDV
model. For instance, it may happen that given the specificities of the sample, LSDV
turned out to be close to RE-FGLS, as it seems to be the case in our exercise. Put
differently, were all cross sections and almost the entire T dimension known, there would
not be a “real” random distribution because the population would then be known.
Therefore, the distinction made between both kinds of effects should ultimately result
irrelevant, as Mundlak (1978) pointed out.
Suppose, notwithstanding, we concluded the other way around (accepting the null
of no random effects, or "the variance of the u's is equal to zero"). This conclusion would
favour the adoption of the LSDV model in any case. Again, we should take into account
Mundlak’s argument: irrespective of what this test concludes, we might end up with both
effects being undistinguishable.
Recapitulating, the value and statistical significance of σ u can have a bearing on
determining whether the RE-FGLS model is close to Pooled-OLS or LSDV; or, in other
words, on determining the weights implied by the RE-FGLS estimator –as appendix A2.3
demonstrates. However, as it is also shown in appendix A2.3, these weights also depend
on the size of T and the magnitude of the variance of regression σ 2 e : for small T, when
σ 2 e tends to zero, irrespective of the value of σ 2 u , the RE-FGLS estimator will converge
to the LSDV model. This seems to be our case: indeed, σ 2 e ≈ 0 . Put differently, when
σ 2 e ≈ 0 all variation across units is due to the different u i s , which, because they are
constant across time, would be equivalent to the LSDV estimator used in the fixed effects
model.
5.3.3.3. Haussman’s Test of Endogeneity
A further way to test whether the RE-FGLS estimators are superior to those
obtained through LSDV is to perform a Haussman’s test. Briefly, under the null
of E ( X k ,it u i ) = 0 , which implies exogenous regressors, both LSDV and RE-FGLS
estimators are consistent but only the latter is efficient. By contrast, under the alternative,
the random effects estimators are inconsistent while the within hold consistent. We do the
40
test by using both LSDV and LSDV corrected for serial correlation and
heteroskedasticity. The results of Haussman’s test suggest the null can be convincingly
accepted in both cases40
In conclusion, despite the RE-FGLS estimates tend to converge to the within or
LSDV ones, we could still prefer the first in virtue of its higher relative efficiency (under
the null of exogenous regressors). However, when we correct the LSDV estimators for
the loss of efficiency implied by heteroskedastic variances and serially correlated
residuals, we get the best fit, for equivalent properties. A final test accepts the null of no
cross residual-correlation in the corrected LSDV model (see appendix A2.4). Thus, we
select the corrected LSDV model as our representative regression output for corporate
spreads in levels.41
5.4. Regression Results of First-Difference Equation
Recall in this case we want to estimate (21)
k
d ( scorit ) = β1 d ( ssovit ) + ∑ β k d ( X k ,it ) + v ' it ,
j =2
where v ' it = v it − v it −1 = e it − e it −1 .
This means that all individual variability disappears. We would therefore expect
Pooled-OLS to be at least efficiently estimated in the model with d(scor?) as the
dependent variable because all the between variability is gone. However, as we also
control for heteroskedasticity (and serial correlation), a FGLS version of the model is
estimated. Table 6 (appendix A3) reports the econometric output.
These results confirm the robustness of the point estimates yielded by our
corrected LSDV model in levels. All coefficients display similar values and significance
levels.
6. Discussion of Results
40
It is obvious when we look at the coefficient vectors and their covariance matrices, which are very
similar. This near equality hinders the inversion of the matrix resulting from the subtraction of the two
covariance matrices. Some columns or rows are not linearly independent.
41
Both RE-FGLS and (corrected) LSDV are performed using a weighting matrix, so their R2 are fully
comparable (and so they are with respect to the model in first differences shown below)
41
Table 7 (appendix A3) summarizes our findings. It considers both the corrected
LSDV model in levels and Pooled-FGLS in first differences as our best models. Overall,
we observe that all major theoretical determinants (sovereign risk premia, leverage, firm
value volatility, time to maturity) turn out to be highly statistically significant. Also, with
the exception of our proxy for liquidity (TOVC?), all variables for which we expect a
certain sign conform to our expectation.
More specifically, we find, first, that a 1% increase in sovereign default risk
(ssov?) increases corporate spreads by near 0.83%, which is less than on a one on one
basis. This effect is found statistically very significant. Following Durbin and Ng (2001),
this finding would be taken as evidence of corporates piercing the sovereign ceiling on
local currency denominated debt. In our case, it means that markets assess the default
likelihood of ZAR denominated debt issued by South African corporates as not strictly
bounded by the sovereign default probability. In other words, it can be concluded along
the lines of section 3.3 that given direct sovereign risk is positive ( P( S ) > 0 ), indirect
sovereign risk (or transfer risk in foreign currency terms) is less than 100%
( P( F / S ) < 1 ). That is, the firm’s default probability P(F ) increases less than
proportionally when the likelihood that a sovereign default occurs rises. Therefore,
although corporate bond yields are generally higher than sovereign bond yields over our
sample period (see figure 1, appendix A3), this fact could owe to relatively higher firm
stand-alone risk (i.e. higher P( F / S c ) ) rather than to the application of the sovereign
ceiling in terms of spreads. Higher firm stand-alone risk is, in turn, accounted for by firm
specific variables.
Accordingly, the quasi-debt to firm value ratios or simply leverage ratios (d1?) are
also statistically very significant. On average, we find e.g. that a 0.50 increase in d1? –
debt is 50% higher in relation to the firm’s value- raises corporate spreads by
approximately 0.013 or 130 basis points Regardless of the time to maturity of firm’s
debt, this means that higher leverage, i.e. higher debt in relation to the firm own
resources, drives default risk up. A higher leverage ratio implies the resources owned by
the firm are closer to a net worth threshold, where the firm finds default unavoidable.
Third, the volatility of returns on the firm’s assets is statistically highly
significant, too. This confirms that the stochasticity of corporate assets is an issue to be
dealt with here, more importantly when it comes to banks.
Fourth, even though the bond time to maturity appears as negatively and
significantly related to corporate default risk (contrary to intuition), the effect of an
average increase of about one year in the maturity length would only reduce corporate
spreads by 30 bps (a drop in scor? of 0.003). The negative sign could be attributed to the
fact that the term structure of corporate spreads has been mostly negatively sloped (i.e.
42
longer maturities, lower spreads) and that most of the corporates analysed here hold
investment grade status (though near lower notch). This status makes the link between
maturity and risk weaker.
Fifth, the volatility of risk-free interest rates does not add to corporate default
spreads by itself, but by means of its interaction term with leverage (d1?). As this riskfree rate is more volatile, higher risk follows and subsequently higher expected returns
are requested, namely wider corporate spreads. As noted by Shimko et al. (1993), the
impact of risk-free interest rate volatility on corporate spreads depends on many factors:
(1) leverage (this is basically our finding) (2) the term structure of risk-free interest rates
(which we do not have) and (3) the correlation between the risk-free rate stochastic
process and asset returns stochastic process (assumed constant in this paper, but
presumably higher in the case of banking firms, which account for roughly half of our
sample). We conclude that the volatility of risk-free interest rates pushes up corporate
default risk as the firm is highly leveraged. In other words, if the firm is not leveraged
(d1=0), interest rate volatility has no impact.
Finally, there is no significant effect of our proxy for liquidity. Perhaps this is not
a good measure of how easily these bonds are traded and converted into cash.
Nevertheless, no other data is thus far available.
7. Conclusions
The purpose of this paper is two-fold. First, it investigates to what extent the
practice by rating agencies and international banks to impose a rating ceiling on subsovereign bond issues is reflected in market prices of local currency denominated South
African debt. Second, it aims at quantifying the importance of sovereign risk in
determining corporate yield spreads, after controlling for firm-specific determinants,
which are derived from a structural model following the literature by Merton (1974) and
Shimko et al (1993). The aim of this literature is to price corporate defaultable bonds
assuming the value of equity of the firm, E, is equivalent to a call option on the assets of
the firm, V, i.e. the well-known Black-Scholes theorem. In sum, the idiosyncratic
determinants of corporate default risk premia are (1) the volatility of returns on the firm’s
assets, (2) the remaining time to maturity of debt, (3) leverage and (4) risk-free interest
rate volatility. To these four, the liquidity of traded debt is added. As we are in the case of
an emerging country, where the sovereign is not a risk-free issuer, we also add sovereign
risk to those four determinants.
43
Applying panel econometric techniques, we estimate the impact of sovereign risk
and firm-specific variables on corporate default risk. Our findings can be summarized as
follows.
First, we find that the elasticity of corporate spreads with respect to sovereign
spreads ( ∂s / ∂sG ) is statistically significantly lower than 1 (approximately 0.83). Recall
that if the sovereign spread turns out to be a significant explanatory factor of corporate
spreads, the size of the coefficient ∂s / ∂sG will be a test of whether the sovereign ceiling
applies or not: if ∂s / ∂s G ≥ 1 , the sovereign ceiling in spreads applies; on the other hand,
if ∂s / ∂s G < 1 , the sovereign ceiling does not apply. Thus, our finding is an indication that
the “country ceiling” for local currency denominated debt does not strictly hold for all 9
companies analyzed in the sense that the yields of their ZAR-denominated bonds
outstanding increase less than 1% when government bonds yields rise by the same
amount. In other words, markets view indirect sovereign risk as being less than 100%.
Therefore, despite corporate bond yields are generally higher than sovereign bond yields
over our sample period (see figure 1, appendix A3), this fact could owe to relatively
higher firm stand-alone risk rather than to the application of the sovereign ceiling in
terms of spreads.
Second, higher firm stand-alone risk can, in turn, be accounted for by firm
specific variables. These variables are generally very robust. They are the firm’s leverage
(quasi-debt to firm value ratio), the volatility of returns on the firm’s assets, remaining
time to maturity of debt and risk-free interest rate volatility when the corporate is highly
leveraged. However, liquidity is found to be insignificant.
In comparison with Durbin and Ng (2001), our own estimates of ∂s / ∂sG for
domestic-currency-denominated (i.e. the South African rand) corporate bonds are similar
to their results 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).
Finally, even when the sovereign ceiling in terms of spreads does not strictly
apply, what our finding (an elasticity of 0.83) brings to debate is actually the fact that
sovereign risk is yet very relevant in determining the corporate cost of debt for those
borrowers able to issue bonds at BESA. This relates fundamentally to macroeconomic
risk, driven by the perceptions on the probability of sovereign default on local currency
denominated debt.
44
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46
Lando, David, 1998, "On Cox Processes and Credit Risky Bonds," Review of Derivatives
Research, Vol. 2 (2/3), pp. 99-120.
Litterman, Robert, and Thomas Iben, 1991, "Corporate bond valuation and the term
structure of credit spreads," Journal of Portfolio Management, Vol. 17, pp. 52-64.
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Risky Fixed and Floating Rate Debt," Journal of Finance, Vol. 50 (3), pp. 789819.
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Debt When Interest Rats are Stochastic," Journal of Fixed Income, Vol.
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47
Appendix
A1. Mathematical Appendix
A1.1. Calculation of the Impact of Interest Rate Volatility on Corporate Default
Premium
The partial derivative of equation (17) with respect to σ r is

1
1
∂s
∂h2∗ ∂ d1∗
∂ (− h1∗ ) 1 
∗
∗
∗
'(
)
(
)
'(
)
h
h
h
=− ⋅
⋅
Φ
⋅
+
⋅
Φ
−
+
Φ
−
⋅
⋅  (A1)

2
1
1
∂σ r
∂σ r ∂σ r
∂σ r d ∗ 
τ [Φ (h2∗ ) + d1∗ Φ (−h1∗ )] 
where
∂h2∗
∂T ∗  1 ln(d ∗ )  
1 
ω+
=−

 −
  ≤≥ 0 ,
∂σ r
∂σ r  4 2T ∗  
T ∗ 
∂ d1∗
1
= − ∗ ⋅ ω ≤≥ 0 ,
d
∂σ r
∂ (−h1∗ )
∂T ∗  1 ln(d ∗ )  
1 
ω
=−
−
+

 +
  ≤≥ 0 ,
∂σ r
∂σ r  4
2T ∗  
T ∗ 
and where
∂T ∗
2 ρσ V 
 2σ
 4σ r 2 ρσ V  σ r −2ατ
−ατ
= τ  2r +
− (e
− 1) ≤≥ 0 and
 + (e − 1)  3 +
∂σ r
α 
α 2  α 3
α
α
−ατ
−ατ 2
−ατ
1
1 ∂P σ r ατ − (1 − e ) − 2 (1 − e )  − αλ ατ − (1 − e ) 
=
≤≥ 0 .
ω=
P ∂σ r
α3
The sign of ∂s ∂σ r is ambiguous. It depends in a complex fashion on α , ρ , τ , σ r , and
d∗.
A1.2. Derivation of Volatility of Firm Value as a Function of Equity Volatility and
Interest Rate Volatility
Given the assumptions of section 3.1 (i.e. the Merton (1974) model) – in
particular assumption A.5, which states that there is only one source of risk, namely the
volatility of asset returns V – Ito’s lemma implies that the volatility of equity, σ E , is
∂E V 42
(A2)
.
σ E = σV
∂V E
42
For a short overview of Ito’s lemma, see for instance Hull (1997), pp. 220-227.
48
Starting from equation (4) and considering that Φ '(h1 ) Φ '(h1 ) = Be − rτ V , the partial
derivative of the value of equity with respect to the value of the firm is ∂E ∂V = Φ(h1 ) .
Hence, equation (A2) becomes
V Φ(h1 )
.
(A3)
σ E = σV
E
In the model of section 3.2 (i.e. the model by Shimko et al. (1993)), however,
there are two sources of risk: firm value risk, represented by σ V , and interest rate risk,
represented by σ r . In this case, the value of equity Et∗ = Vt Φ (h1∗ ) − BPt Φ(h2∗ ) follows a
more complicated Ito process, namely
∂E ∗
∂E ∗
∂E ∗
1 ∂2 E∗
1 ∂2 E∗
∂2 E∗
2
2
+
+
dE ∗ =
dV +
dr +
dt +
(
dV
)
(
dr
)
(drdV ) . (A4)
2 ∂V 2
2 ∂r 2
∂V
∂r
∂t
∂r ∂V
Substituting equations (2) and (11) into equation (A4) and considering that (i) terms of
higher order in dt can be ignored, (ii) dZ12 = dZ 22 = dt , and (iii) dZ1dZ 2 = ρ dt , we obtain
 ∂E ∗

∂E ∗
∂E ∗ 1 ∂ 2 E ∗ 2 2 1 ∂ 2 E ∗ 2 ∂ 2 E ∗
+
dE = 
µV +
α (γ − r ) +
σ VV +
σr +
ρσ V σ rV  dt
2
2
∂r
∂t 2 ∂V
∂r ∂V
2 ∂r
 ∂V

 ∂E ∗

 ∂E ∗ 
+
σ V V  dZ1 + 
σ r  dZ 2 .
(A5)
 ∂V

 ∂r

∗
Dividing both sides of (A5) by the value of equity E ∗ and calculating the variance of the
resulting equity returns, we obtain
∗
  ∂∂EV∗ σ V V 

 ∂∂Er σ r 
 dE ∗ 
Var  ∗  = Var  
dZ
+
dZ



1
2
∗
∗


 E 

 E 
 E

2
2
 ∂E σ V 
 ∂E σ 
2 ∂E σ V ∂E σ
=  ∂V ∗V  dt ⋅ Var (ε1 ) +  ∂V ∗ r  dt ⋅ Var (ε 2 ) + ∂V V ∗ 2∂V r Cov(dz1 , dz2 )
(E )
 E

 E 
∗
2
∗
2
∗
∗
 ∂E σ V 
 ∂E σ 
2 ∂E σ V ∂E σ ρ
=  ∂V ∗V  dt +  ∂V ∗ r  dt + ∂V V ∗ ∂2V r dt
(E )
 E

 E 
∗
∗
∗
∗
 ( ∂E )2 σ V2V 2 + ( ∂∂EV ) 2 σ r2 + 2 ∂∂EV σ V V ∂∂EV σ r ρ 
=  ∂V
 dt
( E ∗ )2


2
= σ E∗ dt
∗
∗
∗
∗
Hence, the instantaneous standard deviation of equity returns (“equity volatility”), σ E∗ , is
given by
 ( ∂∂EV ) 2σ V2V 2 + ( ∂∂Er ) 2σ r2 + 2 ∂∂EV
=
( E ∗ )2

∗
σE
∗
∗
∗
∂E ∗
∂r
σ VVσ r ρ 
1
2
 .

(A6)
49
Considering that ∂E ∗ ∂V = Φ(h1∗ ) and ∂E ∗ ∂r =
1 − e −ατ
α
BPt Φ (h2∗ ) , equation (A6) results
in
1
2
−ατ

2
 1 − e −ατ
2
∗ 
∗  1− e
∗ 
 Φ (h1∗ ) 2σ V2V 2 + 
BPt Φ (h2 )  σ r + 2Φ (h1 ) 
BPt Φ (h2 )  σ V V σ r ρ 
α
α






σ E∗ = 
∗ 2
 .
(E )






(A7)
Equation (A7) is the equivalent of (A3) in the model with stochastic interest rates.
A1.3. Numerical Procedure to Calculate Volatility of Firm Value
The first step is to calculate σ V for all firms over all months assuming σ V = sv12m?; we
call this estimate SVold. Then, we use SVold as an input in the first iteration, i.e. we
V Φ(h1 )
, substituting SVold on the RHS (i.e. inside h1) in place of the
calculate σ E = σ V
E
(still unknown) σ V . We call the resulting σ V of this first iteration SVsolution. For the
V Φ(h1 )
, getting a
second iteration, we use SVsolution as input into the equation σ E = σ V
E
new SVsolution. We repeat this procedure (i.e. we iterate) until the difference between two
subsequent values for SVsolution becomes smaller than or equal to 0.000001. Convergence
is achieved after 7 iterations.
A2. Econometric Issues
A2.1. Variability Decomposition of Corporate Default Spreads
First, we decompose the deviation of each individual observation from the overall
mean into two components: (1) the deviation of each observation from its group mean,
and (2) the deviation of the group means from the overall mean; formally:
[
]
 scor − scor  = scor − scor +  scor − scor 
it
it
i
i




Second, we square both sides of this equation in order to obtain the squared deviations of
each observation from the (overall) mean
50
(
2
)
 scor − scor  =  scor − scor +  scor − scor 
it
it
i
i





2
Third, as the double product of both terms on the RHS is usually very small, we can
neglect it so that the squared deviation can be written as approximately:
2
(
 scor − scor  ≈ scor − scor
it
it
i


)
2
+  scori − scor 


2
Then, summing across N cross-sectional and Ti time-series observations (as we have got
an unbalanced panel, T is potentially different for each of the N cross-sections, hence Ti),
we obtain:
N
Ti
2
N
Ti
[
∑ ∑ scorit − scor  ≈ ∑ ∑ scorit − scori
i =1 t =1
i =1 t =1
]
2
N
+ ∑ Ti  scori − scor 


i =1
2
whereby the term on the LHS represents the "Total Variation" (TV) in the sample, the
first term on the RHS represents the "Within Variation" (WV), and the second term
represents the "Between Variation" (BV), i.e. we have
Total variation (TV) = Within Variation (WV) + Between Variation (BV).
A2.2. Tests of Pooling
We perform two Wald-tests, the purpose of which is to compare the sum of
squared residuals of an unrestricted model (SSRU) to the sum of squared residuals of a
restricted model, adjusted by the respective degrees of freedom (dfr and dfu)43:
 SSRR − SSRU
 dfr − dfu
F [dfn, dfd , α ] = 
SSRU


dfu

Where α is the significance level of the test.


.



Note that these tests are valid if the residuals are jointly normally distributed (see Baltagi
1995), i.e. homoskedasticity is assumed.
43
See Greene (2000), pp 617.
51
We first test the null of homogeneous slopes and intercepts (i.e. Pooled OLS is the
right model) against an alternative of homogeneous slopes and different intercepts (Fixed
effects is the proper model). This requires testing the goodness of fit of the Pooled-OLS
regression against the LSDV model, assuming the corporate bond spread effects as
parametric shifts in the regression function. Table B-1 shows the full results of this test.
Table A2.1
Wald F-Test: Pooled OLS vs Fixed Effects
explanatory variables: ssov? sv1000d? m? tovc? d1? m?*d1?
sigspotm? D1?*sigspotm?
H0: the model has homogeneous slopes and intercepts
Sum of Squared residuals version
ssru FE (different intercepts but homogeneous slopes)
ssrr Pooled-OLS (homogeneous slopes and intercepts)
N=12, T= 35 (adjusted endpoints)
F-stat
Critical F at 5%
0,001
0,009
287,916
1,812
All estimators are cross-section unweighed; All display White
Heteroskedasticity-Consistent Standard Errors & Covariance
As the null of the former test is rejected, we proceed to check the null of
homogeneous slopes and different intercepts against the alternative of different slopes
associated to lnssov? and different intercepts in equation (18)44. Table B-2 shows the full
results of this test.
Table A2.2
44
We obtain the SSR for the unrestricted model by estimating a fixed effect equation letting the coefficients
of SSOV? to be cross-section specific. Hence, we have 12 additional parameters to be estimated, which add
up to the 12 different intercepts and the remaining c=7 common explanatory variables. Moreover, 10 out of
12 cross-section specific SSOV? turn out highly significant at a 1% level (_IPL1 and_NED1 being the non
significant variables).
52
Wald F-Test: Fixed Effects vs Fixed Effects w/different slopes
explanatory variables:SSOV? Sv1000d? M? TOVC? D1? M?*D1? sigspotm?
sigspotm?*D1? cross-section specific explanatory variable: SSOV?
H0: the model has homogeneous slopes but different intercepts
Sum of Squared residuals version
ssru FE-SSOV (different intercepts and slopes)
ssrr FE (different intercepts but homogeneous slopes)
N=12, T= 35 (adjusted endpoints)
F-stat
Critical F at 5%
Critical F at 1%
0,001
0,001
7,113
1,813
2,293
OBS:
All estimators are cross-section unweighed; All display White
Heteroskedasticity-Consistent Standard Errors & Covariance
A2.3. RE-FGLS Weighting as a Special Case of OLS or LSDV Estimators
These weighs used by RE-FGLS can be represented by θ, where this last can be
written as follows:
(1 − θ )2 =
σ 2e
σ 2 e + Tσ 2 u
=λ
As each variable now is y it − θ y i
For instance, when θ = 0 RE-FGLS converges to OLS (forcefully because
σ u = 0 ), while θ = 1 implies RE-FGLS equals LSDV (either because σ 2 e = 0 or
T → ∞ ). In order to verify the latter case, we should be able to reject the null that σ u = 0
2
and show that most of the regression variability is accounted for by individual variability
(i.e. σ 2 e near zero). This is precisely the purpose of the Breusch Pagan test shown next.
A2.4. Statistical Tests
Existence of random effects
Table A2.3
53
Breusch-Pagan Test: existence of random effects
explanatory variables: ssov? sv1000d? m? tovc? d1?
m?*d1? sigspotm?
H0: variance of ui's=0
Breusch-Pagan
Critical Chi-square at 5%
7066,390
3,841
Cross-correlated residuals
Another important issue is the potential presence of cross-correlated residuals,
provided some omitted variables can equally affect each corporate spread. In other words,
a violation to the assumption E (eit e js ) = 0∀i ≠ j is likely to happen. We also test for this
through a Breusch-Pagan Lagrange multiplier test. The rejection of the null of no crosscorrelation in the RE-FGLS model would indicate to us the convenience of estimating a
Seemingly Unrelated Regressors (SUR) model by Feasible Generalised Least Squares45.
The Lagrange multiplier (LM) test is built upon the following statistic:
M M −1
Breusch-Pagan LM= λ LM = N ∑ ∑ r 2 ij → χ 2 M ( M −1)
i =1 j =1
2
Where r 2 ij is the cross-squared
linear correlations between different units (different corporate bond spreads), M=N=12.
The pairwise correlations r 2 ij are computed since the LSDV corrected (for serial
correlation and heteroskedasticity) model. The results point to the acceptance of the null
hypothesis. Therefore, SUR-FGLS is not necessary.
Breusch-Pagan
Chi-square 95%
Chi-square 99%
61,693
85,965
95,626
45
SUR-FGLS, by jointly estimating the cross covariance matrix, allows correcting for the latter source of
bias. The SUR-FGLS specification also corrects for cross-section heteroskedasticity. This specification is
sometimes referred to as the Parks estimator. Even in small samples the unbiasedness property of the SUR
estimator holds. Consistency and asymptotic efficiency are also guaranteed (see Baltagi, 1995 and Zellner,
1962).
54
A3. Tables and Figures
Table 1: History of Credit Ratings by the Republic of South Africa and Firms Analyzed
(until May 31, 2003)
Issuer
Republic of
South Africa
Date
May 7, 2003
Nov. 12, 2002
Standard & Poor’s
Local Currency
Foreign
Credit
Currency Credit
Rating (Issuer)
Rating (Issuer)
Long
Long
Term/Outlook
Term/Outlook
A/stable
BBB/stable
A-/positive
BBB-/positive
Feb. 25, 2000
A-/stable
BBB-/stable
March 6, 1998
BBB+/stable
BB+/stable
Nov. 20, 1995
Oct. 3, 1994
BBB+/positive
--
Nov. 16, 1998
BBBpi 2/
--------------
BB+/positive
BB/positive
------------------------
ABSA Bank
African Bank
Harmony Gold
Imperial Group
Iscor
Investec Bank
Nedcor
Sasol
Standard Bank
Nov. 16, 1998
BBBpi 2/
Feb. 19, 2003
--
Nov. 16, 1998
BBBpi 2/
---
BBB/stable
--------
Date
Feb. 26, 2003
Nov. 29, 2001
Oct. 12, 2001
Feb. 7, 2000
Oct. 2, 1998
Jul. 17, 1998
Mar. 7, 1997
Nov. 20, 1995
Oct. 3, 1994
Feb. 27, 2003
Dec. 6, 2001
Oct. 17, 2001
Feb. 8, 2000
Oct. 2, 1998
Jul. 17, 1998
Jan. 22, 1996
----
Moody’s
Domestic Currency
Foreign Currency
Bond Rating
Bond Rating
(Senior Unsecured)
(Senior Unsecured)
Long
Long
Term/Outlook
Term/Outlook
A2/stable
Baa2/positive
A2/stable
Baa2/stable
Baa1/rev. for up
Baa3/rev. for up
Baa1/positive
Baa3/positive
Baa1/stable
Baa3/stable
Baa1/rev. for down
Baa3/rev. for down
Baa1/negative
Baa3/negative
Baa1
--Baa3
-Baa2/positive 1/
-Baa2/stable 1/
-Ba1/rev. for up 1/
-Ba1/positive 1/
-Ba1/stable 1/
-Ba1/rev. for down 1/
-Ba1 1/
-------
-Feb. 27, 2003
Dec. 6, 2001
Oct. 17, 2001
Feb. 8, 2000
Oct. 2, 1998
Jul. 17, 1998
Dec. 11, 1996
Feb. 27, 2003
Dec. 6, 2001
Oct. 17, 2001
Feb. 8, 2000
Oct. 2, 1998
Jul. 17, 1998
Jan. 22, 1996
-Feb. 27, 2003
Dec. 6, 2001
Oct. 17, 2001
Feb. 8, 2000
Oct. 2, 1998
Jul. 17, 1998
Jan. 22, 1996
------------------------
-Baa2/positive 1/
Baa2/stable 1/
Ba1/rev. for up 1/
Ba1/positive 1/
Ba1/stable 1/
Ba1/rev. for down 1/
Ba1 1/
Baa2/positive 1/
Baa2/stable 1/
Ba1/rev. for up 1/
Ba1/positive 1/
Ba1/stable 1/
Ba1/rev. for down 1/
Ba1 1/
-Baa2/positive 1/
Baa2/stable 1/
Ba1/rev. for up 1/
Ba1/positive 1/
Ba1/stable 1/
Ba1/rev. for down 1/
Ba1 1/
Notes:
1/ Long Term Bank Deposit Ratings. These ratings are all equal to the Country Ceiling for Foreign
Currency Bank Deposits.
2/ “pi” = Public information Rating. Ratings with a 'pi' subscript are based on an analysis of an issuer's
published financial information, as well as additional information in the public domain. They do not,
however, reflect in-depth meetings with an issuer's management and are therefore based on lesscomprehensive information than ratings without a 'pi' subscript.
55
Table 2: The Determinants of Corporate Default Risk
Type of risk
Systematic
Firm-specific
Name of determinant and symbol in theoretical framework
Sovereign default risk (sG)
Expected impact
on corporate
default premium
+
Leverage (quasi-debt to firm value ratio) (d*)
+
Firm value volatility (σV)
+
Time to maturity (τ)
+/-
Risk-free interest rate volatility (σr)
+/-
Liquidity (l)
Interaction
terms
*
Leverage*time to maturity (d τ)
+/-
Leverage*risk-free interest rate volatility (d*σr)
+/-
56
57
Table 3: South African Corporate Bonds: Main Features and Corresponding
Benchmark Instruments
Firm
Activity
Firm Bond
Principal
Amount
Outstanding
(ZAR
million)46
1250
Percent of
Debt Traded47
Issue Date
Risk-free
Benchmark
Corresponding
RSA
Government
Bond
Data
Range
01/03/00
EIB 1999
13%
03/06/05
RSA 1984 13%
15/07/05 R124
01/03/00
to
04/06/03
12/10/01
EIB 1999
13%
03/06/05
RSA 1984 13%
15/07/05 R124
12/10/01
to
04/06/03
EIB 2001
11%
28/12/06
EIB 2001
11%
28/12/06
RSA 1996
12.50%
21/12/06 R184
RSA 1996
12.50%
21/12/06 R184
11/06/01
to
04/06/03
14/09/01
to
04/06/03
INTL.BK.RE
CON.&DEV.
2002 10
3/4%
12/12/07
EIB 1998 12
1/4%
20/05/03
(pen. coupon:
15/05/02)
RSA 2001 10%
28/02/07-09
R194 (RY=
RYAV)48
06/02/02
to
04/06/03
07/05/98
to
15/05/02
ABSA
Bank
Banking
ABSABANK
LTD. 2000 15%
01/03/05 AB01
African
Bank
Specialty
& Other
Financial
Activities
Mining
AFRICAN BANK
2001 12 1/2%
28/02/05 ABL1
1000
29%
(Rest: AB02
ZARm 3100
since 22/3/02)
100%
HARMONY
GOLD 2001 13%
14/06/06 HAR1
IMPERIAL
GP.(PTY.) 2001
11% 14/03/06
IPL1
IMPERIAL
GP.(PTY.) 2002
12.75% 28/02/08
IPL2
1200
100%
11/06/01
800
50%
(Rest: IPL2
ZARm 800)
14/09/01
800
50%
(Rest: IPL1
ZARm 800)
06/02/02
ISCOR 1983
12.50% 01/03/03
IS59 (penultimate
coupon: 27/08/02)
0.2
3%
(Rest: IS57
ZARm 7.5)
01/02/83
ISCOR 1982
14.50% 31/10/02
IS57 (penultimate
coupon: 26/04/02)
7.5
97%
(Rest: IS59
ZARm 0.2)
01/08/82
EIB 1997 13
1/2%
11/11/02
(pen. coupon:
06/11/01)
INVESTEC
BANK LTD. 2000
16% 31/03/12
IV01
NEDCOR BANK
LTD.2001 11.3%
20/09/0649 NED1
2016
EIB 1999
13%
31/08/10
20/09/01
EIB 2001
11%
28/12/06
RSA 1996
12.50%
21/12/06 R184
25/09/01
to
04/06/03
SASOL
Oil & Gas
SASOL
FINANCING
2000 14%
30/06/03 SFL1
(penultimate
coupon: 23/12/02)
900
67%
(Rest: IV02
ZARm 1000
since 31/3/03)
33%
(Rest: NED2
ZARm 4000
since 01/07/02)
100%
17/06/00
Nedcor
Specialty
& Other
Financial
Activities
Banking
RSA 1981
12.5% 01/09/03
R106
(penultimate
coupon:
25/02/03)
RSA 1981
13.00%
15/09/02 R111
(penultimate
coupon:
11/03/02)
RSA 1989 13%
31/08/09-11
R153
24/06/00
EIB 1998 12
1/4%
20/05/03
(pen. coupon:
15/05/02)
RSA 1981
12.5% 01/09/03
R106
(penultimate
coupon:
25/02/03)
23/06/00
to
15/05/02
Standard
Bank
Banking
STANDARD
BANK SA. 2000
1200
31/05/00
EIB 1999
13%
RSA 1984 13%
15/07/05 R124
03/07/00
to
Harmony
Gold
Imperial
Group
(PTY)
ISCOR
Investec
Bank
Diversified
Industry
Steel &
Other
Metals
2000
21%
(Rest: SBK2
28/10/97
to
06/11/01
13/07/00
to
04/06/03
46
End May 2003, except for IS57, IS59 and SFL1: end December 2000. Principal amount outstanding at
that time was equal to amount issued for all bonds.
47
End May 2003, except for IS57, IS59 and SFL1: end December 2000.
48
RY = redemption yield (yield to maturity); RYAV = redemption yield to average life, i.e. this is the yield
to maturity calculated as if the bond were entirely redeemed on 28/02/2008. R194 is a so-called "threelegged" bond – a South African peculiarity. All benchmark bonds of the Republic of South Africa are threelegged bonds (the others are R150, R153, R157, and R186). All three-legged instruments are priced on the
mid (second) leg (see Asset and Liability Management Division (2001)), whence redemption yield =
redemption yield to average life.
49
20/09/06 is the exercise data of the first call option, not the maturity date.
58
Firm
Activity
Firm Bond
Principal
Amount
Outstanding
(ZAR
million)46
15.50% 01/06/05
SBK150
STANDARD
BANK SA. 2002
12.50% 15/02/05
SBK451
1000
Percent of
Debt Traded47
ZARm 1500,
SBK3 ZARm
2000, SBK4
ZARm 1000)
18%
(Rest: SBK1
ZARm 1200,
SBK2 ZARm
1500, SBK3
ZARm 2000)
Issue Date
Risk-free
Benchmark
Corresponding
RSA
Government
Bond
03/06/05
27/06/02
EIB 1999
13%
03/06/05
Data
Range
04/06/03
RSA 1984 13%
15/07/05 R124
27/06/02
to
04/06/03
50
01/06/05 is the exercise date of the first call option, not the maturity date (as wrongly indicated in
Datastream, see BESA website: list of corporate bond issues and "Static Data" files; see also Standard Bank
Group (2002), p. 137, for the exact details of this bond).
51
This bond qualifies as tertiary capital in terms of applicable banking legislation. Interest payments and
redemption may be deferred if requested by the Registrar of Banks. See Standard Bank Group (2002), p.
137.
59
Table 4: Sources of Variability in Corporate Default Spreads
Variable
Total Variance
Within Variance
Between Variance
scor? as %
100
27.4
72.6
d(scor?) as %
100
98.8
1.2
60
Table 5: The determinants of corporate default premia: panel regression in levels
Sample:
2000:07 2003:05
Pooled OLS
Coefficients
C
SSOV?
SV1000d?
M?
TOVC?
D1?
M?*D1?
SIGSPOTM?
SIGSPOTM?*D1?
-0,019
1,061
0,055
0,001
0,000
0,031
0,000
0,320
-0,659
prob
FE (LSDV or
FE (LSDV or
within)
within) Corrected
Coefficients
0,000
0,000
0,344
0,151
0,000
0,746
0,112
0,068
0,839
-0,018
-0,002
0,000
-0,010
0,004
-0,206
0,367
AR (1)
AR (2)
Adjusted R-squared
Log likelihood
prob
Coefficients
prob
0,000
0,000
0,147
0,001
0,061
0,241
0,002
0,043
0,047
0,824
0,058
-0,003
0,000
0,027
0,000
-0,085
0,247
0,632
0,173
0,325
0,921
0,991
1048,799
1356,197
1424,645
0,000
0,000
0,000
0,599
0,000
0,970
0,211
0,017
RE (FGLS)
Coefficients
prob
0,018
0,859
-0,008
-0,002
0,000
-0,004
0,002
-0,210
0,380
0,001
0,000
0,384
0,002
0,077
0,545
0,007
0,029
0,042
0,000
0,000
0,917
White Heteroskedasticity-Consistent Standard Errors & Covariance in all cases
“prob” indicates the level of significance of each estimate.
61
Table 6: The determinants of corporate default premia: panel regression in first
differences
Sample:
2000:07 2003:05
Pooled-GLS
Coefficients
D(SSOV?)
D(SV1000d?)
D(M?)
D(TOVC?)
D(D1?)
D(M?*D1?)
D(SIGSPOTM?)
D(SIGSPOTM?*D1?))
AR(1)
Adjusted R-squared
Log likelihood
prob
0,830
0,046
-0,002
0,000
0,020
0,001
-0,061
0,236
-0,144
0,000
0,000
0,001
0,245
0,002
0,403
0,398
0,028
0,004
0,890
1398,719
White Heteroskedasticity-Consistent Standard Errors & Covariance in all cases
“prob” indicates the level of significance of each estimate.
62
Table 7: The Determinants of Corporate Default Risk: Summary of Empirical Results
Type of Risk
Systematic
Firm-specific
Variable
Impact on Corporate Default Spreads
Expected
Estimated
Sovereign default risk**
+
+
Leverage (quasi-debt to firm value ratio)**
+
+
Firm value volatility **
+
+
Time to maturity**
+/-
-
Risk-free interest rate volatility
+/-
+
-
+
+/-
+
+/-
+
Liquidity
Leverage y Time to
Interaction
Maturity
Terms
Leverage y Risk-free
interest rate volatility*
Note: ** and * means the variable is statistically significant at the 1% and 5% level, respectively.
63
AFRICAN BANK 2001 12 1/2% 28/02/05 ABL1
REP.OF SOUTH AFRICA 1984 13% 15/07/05 R124
12.05.2003
12.04.2003
12.03.2003
12.02.2003
12.01.2003
12.12.2002
12.11.2002
12.10.2002
12.09.2002
ABSA 2000 15% 01/03/05 AB01
REP.OF SOUTH AFRICA 1984 13% 15/07/05 R124
12.08.2002
12.07.2002
12.06.2002
12.05.2002
12.04.2002
12.03.2002
12.02.2002
12.01.2002
12.12.2001
12.11.2001
12.10.2001
01.05.2003
01.03.2003
01.01.2003
01.11.2002
01.09.2002
01.07.2002
01.05.2002
01.03.2002
01.01.2002
01.11.2001
01.09.2001
01.07.2001
01.05.2001
01.03.2001
01.01.2001
01.11.2000
01.09.2000
01.07.2000
01.05.2000
01.03.2000
Figure 1: Firm Bond Yields and Corresponding Sovereign and Risk-Free Yields
Panel 1: ABSA Bank AB01
17
16
15
14
13
12
11
10
9
EUROPEAN INV.BK. 1999 13% 03/06/05
Panel 2: African Bank ABL1
17
16
15
14
13
12
11
10
9
EUROPEAN INV.BK. 1999 13% 03/06/05
64
IMPERIAL GP.(PTY.) 2001 11% 14/03/06 IPL1
REP.OF SOUTH AFRICA 1996 12.50% 21/12/06 R184
14.05.03
14.04.03
14.03.03
14.02.03
14.01.03
14.12.02
14.11.02
14.10.02
14.09.02
HARMONY GOLD 2001 13% 14/06/06 HAR1
REP.OF SOUTH AFRICA 1996 12.50% 21/12/06 R184
14.08.02
14.07.02
14.06.02
14.05.02
14.04.02
14.03.02
14.02.02
14.01.02
14.12.01
14.11.01
14.10.01
14.09.01
11.05.2003
11.04.2003
11.03.2003
11.02.2003
11.01.2003
11.12.2002
11.11.2002
11.10.2002
11.09.2002
11.08.2002
11.07.2002
11.06.2002
11.05.2002
11.04.2002
11.03.2002
11.02.2002
11.01.2002
11.12.2001
11.11.2001
11.10.2001
11.09.2001
11.08.2001
11.07.2001
11.06.2001
Panel 3: Harmony Gold HAR1
16
15
14
13
12
11
10
9
EUROPEAN INV.BK. 2001 11% 28/12/06
Panel 4: Imperial Group IPL1
15
14
13
12
11
10
9
EUROPEAN INV.BK. 2001 11% 28/12/06
65
ISCOR 1982 14.50% 31/10/02 IS57
REP.OF SOUTH AFRICA 1981 13.00% 15/09/02 R111
01.04.2002
01.01.2002
01.10.2001
01.07.2001
01.04.2001
01.01.2001
01.10.2000
01.07.2000
01.04.2000
01.01.2000
01.10.1999
IMPERIAL GP.(PTY.) 2002 12.75% 28/02/08 IPL2
REP.OF SOUTH AFRICA 2001 10% 28/02/07-09 R194
01.07.1999
01.04.1999
01.01.1999
01.10.1998
01.07.1998
01.04.1998
01.01.1998
01.10.1997
01.07.1997
01.04.1997
01.01.1997
01.10.1996
01.07.1996
01.04.1996
01.01.1996
06.05.03
06.04.03
06.03.03
06.02.03
06.01.03
06.12.02
06.11.02
06.10.02
06.09.02
06.08.02
06.07.02
06.06.02
06.05.02
06.04.02
06.03.02
06.02.02
Panel 5: Imperial Group IPL2
15
14
13
12
11
10
9
INTL.BK.RECON.&DEV. 2002 10 3/4% 12/12/07
Panel 6: Iscor IS57
23
21
19
17
15
13
11
9
EUROPEAN INV.BK. 1997 13 1/2% 11/11/02
66
INVESTEC BANK LTD. 2000 16% 31/03/12 IV01
REP.OF SOUTH AFRICA 1989 13% 31/08/09-11 R153
13.05.03
13.03.03
13.01.03
13.11.02
13.09.02
13.07.02
13.05.02
ISCOR 12.50% 01/03/03 IS59
REP.OF SOUTH AFRICA 12.5% 01/09/03 R106
13.03.02
13.01.02
13.11.01
13.09.01
13.07.01
13.05.01
13.03.01
13.01.01
13.11.00
13.09.00
13.07.00
01.01.03
01.10.02
01.07.02
01.04.02
01.01.02
01.10.01
01.07.01
01.04.01
01.01.01
01.10.00
01.07.00
01.04.00
01.01.00
01.10.99
01.07.99
01.04.99
01.01.99
01.10.98
01.07.98
01.04.98
01.01.98
01.10.97
01.07.97
01.04.97
01.01.97
01.10.96
01.07.96
01.04.96
01.01.96
Panel 7: Iscor IS59
24
22
20
18
16
14
12
10
8
EUROPEAN INV.BK. 1998 12 1/4% 20/05/03
Panel 8: Investec Bank IV01
17
16
15
14
13
12
11
10
9
EUROPEAN INV.BK. 1999 13% 31/08/10
67
SASOL FINANCING 2000 14% 30/06/03 SFL1 final
RSA 12.5% 01/09/03 R106 final
20.02.2003
20.01.2003
20.12.2002
20.11.2002
20.10.2002
20.09.2002
20.08.2002
20.07.2002
20.06.2002
20.05.2002
20.04.2002
20.03.2002
20.02.2002
20.01.2002
20.12.2001
NEDCOR 11.3% 20/09/06 NED1 (next call, annual comp.)
REP.OF SOUTH AFRICA 1996 12.50% 21/12/06 R184
20.11.2001
20.10.2001
20.09.2001
20.08.2001
20.07.2001
20.06.2001
20.05.2001
20.04.2001
20.03.2001
20.02.2001
20.01.2001
20.12.2000
20.11.2000
20.10.2000
20.09.2000
20.08.2000
20.07.2000
20.06.2000
20.05.2003
20.04.2003
20.03.2003
20.02.2003
20.01.2003
20.12.2002
20.11.2002
20.10.2002
20.09.2002
20.08.2002
20.07.2002
20.06.2002
20.05.2002
20.04.2002
20.03.2002
20.02.2002
20.01.2002
20.12.2001
20.11.2001
20.10.2001
20.09.2001
Panel 9: Nedcor NED1
15
14
13
12
11
10
9
EUROPEAN INV.BK. 2001 11% 28/12/06
Panel 10: Sasol SFL1
15
14
13
12
11
10
9
8
EUROPEAN INV.BK. 1998 12 1/4% 20/05/03 - RED. YIELD
68
STANDARD BANK SA. 2002 12.50% 15/02/05 SBK4
REP.OF SOUTH AFRICA 1984 13% 15/07/05 R124
27.05.03
13.05.03
29.04.03
15.04.03
01.04.03
18.03.03
04.03.03
18.02.03
04.02.03
21.01.03
07.01.03
STANDARD BANK SA. 2000 15.50% 01/06/05 SBK1
REP.OF SOUTH AFRICA 1984 13% 15/07/05 R124
24.12.02
10.12.02
26.11.02
12.11.02
29.10.02
15.10.02
01.10.02
17.09.02
03.09.02
20.08.02
06.08.02
23.07.02
09.07.02
25.06.02
03.05.2003
03.03.2003
03.01.2003
03.11.2002
03.09.2002
03.07.2002
03.05.2002
03.03.2002
03.01.2002
03.11.2001
03.09.2001
03.07.2001
03.05.2001
03.03.2001
03.01.2001
03.11.2000
03.09.2000
03.07.2000
Panel 11: Standard Bank SBK1
16
15
14
13
12
11
10
9
EUROPEAN INV.BK. 1999 13% 03/06/05
Panel 12: Standard Bank SBK4
14
13.5
13
12.5
12
11.5
11
10.5
10
EUROPEAN INV.BK. 1999 13% 03/06/05
69
Figure 2: South African Corporate Default Premia, Oct. 1997—May 2003
.030
.05
.025
.04
.020
.03
.015
.010
.02
.005
.01
.000
-.005
.00
1998
1999
2000
SCOR_AB01
SCOR_ABL1
SCOR_HAR1
2001
2002
SCOR_IPL1
SCOR_IPL2
SCOR_IS57
1998
1999
2000
SCOR_IS59
SCOR_IV01
SCOR_NED1
2001
2002
SCOR_SBK1
SCOR_SBK4
SCOR_SFL1
70
Figure 3: South African Sovereign Default Premia, Oct. 1997—May 2003
.020
.025
.016
.020
.015
.012
.010
.008
.005
.004
.000
.000
-.005
-.004
-.010
-.015
-.008
1998
1999
2000
SSOV_AB01
SSOV_ABL1
SSOV_HAR1
2001
2002
SSOV_IPL1
SSOV_IPL2
SSOV_IS57
1998
1999
2000
SSOV_IS59
SSOV_IV01
SSOV_NED1
2001
2002
SSOV_SBK1
SSOV_SBK4
SSOV_SFL1
71