## Box 1. The Cost of Debt for an Emerging Market Borrower ## Source details **Canonical URL:** [Box 1. The Cost of Debt for an Emerging Market Borrower](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05217.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05217.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05217.pdf.json) --- ### Cost decomposition and definitions - Cost of local-currency-denominated debt = Risk-free rate + 1) Currency (risk) premium + Total risk premium 2) Default (risk) premium 3) Jurisdiction premium = Country (risk) premium. - Terms used interchangeably in the paper: default premium, credit spread, yield spread, spread. ### Main empirical findings (South Africa case study) - Sovereign risk is the single most important determinant of corporate default premia in South Africa: for almost all firms analyzed, sovereign risk is statistically and economically the most important determinant of their credit spread. - Sovereign ceiling does not apply to industrial multinational companies in the sample: elasticity of their spreads with respect to sovereign spreads is between 0.42 and 0.83. - Sovereign ceiling appears to apply to most financial companies: elasticities statistically not different from one, between 0.78 and 0.98. - Firm-specific factors derived from the contingent claims approach (leverage, firm-value volatility, remaining time to maturity, and risk-free interest rate volatility) are statistically significant determinants of corporate spreads, but economically their importance is minor relative to sovereign risk. - Policy implication: macroeconomic policies that reduce sovereign default risk and improve the government’s credit rating can significantly reduce the cost of debt capital for corporate borrowers, stimulating investment and economic growth. ### Why South Africa was selected (sample) - South Africa: one of the few emerging markets with a corporate bond market in local currency (the rand). - Sample period: July 2000–May 2003. - Number of South African private sector firms in sample: nine firms with a total of 12 bonds outstanding. - Rationale: sample firms are important South African companies; local-currency market has growth potential due to under-leveraged corporates, appetite from local banks and institutional investors, and potential decrease in government dominance of domestic debt. ### Sovereign ceiling — concept and empirical test - Sovereign ceiling (rating agencies’ policy): debt of a company in a given country cannot be rated higher than the debt of its government. - Distinction: - Direct sovereign intervention risk (transfer risk) — typically foreign-currency context. - Indirect sovereign risk — domestic-currency context: probability a firm defaults on domestic-currency debt as a result of sovereign distress/default. - Durbin and Ng (2005) result used as test: 100 percent transfer/indirect sovereign risk implies a 1 percent increase in government spread should be associated with at least a 1 percent increase in firm spread; in regressions of corporate spread changes on sovereign spread changes, the beta should be ≥ 1 if the sovereign ceiling applies. - Empirical observation: all corporate bonds analyzed bore higher yields than sovereign bonds of similar maturity (necessary but not sufficient for a sovereign ceiling). ### Theoretical framework — determinants of corporate default premium - Methodological approach: structural (contingent claims) approach extended to include stochastic interest rates and sovereign default premium. - Key determinants identified: sovereign risk (sovereign spread), leverage (quasi-debt ratio d), firm-value volatility (Vσ), interest rate volatility (rσ), remaining time to maturity (τ), liquidity (l). - Merton (1974) baseline: corporate default spread s = s(Vσ, d, τ) with ∂s/∂Vσ > 0; ∂s/∂d > 0; ∂s/∂τ ambiguous. - Shimko, Tejima, and Van Deventer (1993) extension: s = s(Vσ, d, τ, rσ); interest rate volatility rσ typically increases s, especially for higher d. Interaction terms expected: positive coefficient on d·rσ; include d·τ with τ coefficient expected positive and d·τ negative. - Adding sovereign risk: formal decomposition of firm default probability P(F) = P(S)·P(F|S) + P(S^c)·P(F|S^c). Sovereign ceiling applies when P(F|S) = 1. Durbin and Ng (2005) implication: ∂s/∂sov ≥ 1 under sovereign ceiling. ### Operational synthesis and estimating equation - Theoretical synthesis: s = s(sov, d, Vσ, rσ, τ, l) with expected signs indicated. - Linearized estimating equation includes interaction terms: d·rσ and d·τ. - Representative sample statistics mentioned: - Mean firm-value volatility Vσ = 23.4 percent. - Interest rate volatility rσ = 1.0 percent (sample value used in simulations). - Estimated α = 0.70. - Estimated ρ = 0. - Example firm-specific correlations: IPL1 had ρ = -0.42, HAR1 had ρ = 0.33. - Sample: nine firms, 12 rand-denominated corporate bonds (July 2000–May 2003). - Final theoretical-operational equation (as presented): Equation (5): s = s(sov, d, Vσ, rσ, τ, l). ### Data, measurement, and sample construction - Dependent variable operationalization: - Spread st ≡ SCOR? = y? – rf?, where y is corporate bond yield to maturity and rf is yield to maturity of a risk-free bond with maturity and coupon close to the corporate bond. - Acknowledged limitations: spreads include term structure effects and likely include jurisdiction premium because risk-free benchmarks are ZAR-denominated supranational bonds traded offshore. - Jurisdiction premium presumed constant over sample period (July 2000–May 2003). - Data sources and processing: - End-month yields to maturity from Thomson Financial Datastream (DS) and Bond Exchange of South Africa (BESA). - BESA yields compounded semi-annually converted to annual-compounding via ya = 100[(1+ys/200)^2 -1]. - Data cleaning and selection rules: - Drop parastatals; eliminate inconsistent price or yield outliers; include only firms with shares listed on the Johannesburg Stock Exchange (JSE); exclude floating rate bonds. - Use only one bond per firm (more liquid bond selected); for callable bonds use “yields to next call”. - Truncate yield series at the penultimate coupon payment date. - Final sample after elimination: - Nine corporate bonds issued by five banking and four industrial firms. - Bond identifiers: AB01, ABL1, HAR1, IPL1, IS59, IV01, NED1, SFL1, SBK1. - Maximum data range: May 20, 1998 to June 4, 2003; actual analysis monthly over July 2000–May 2003. - Explanatory variables (operational proxies): - Sovereign spread: sovts ≡ SSOV? = sov? – rf?. - Firm-specific determinants: leverage (D1?, D2?, or D3?), firm-value volatility (SV1000D?, SV12M?, SV24M?), interest rate volatility (SIGSPOTM? or SIGRFM?), time to maturity (M?), liquidity proxied by trading volume (TOVC?). - Interaction terms: M·D1 and SIGSPOTM·D1. ### Empirical methodology and specification tests - Estimation model (equation (6)): - SCORit = αi + βi SSOVit + Σ_{j=1..k} γj Xjit + εit, with firm-specific intercepts αi and firm-specific slopes βi on SSOV; control slopes γj constrained equal across firms. - Pooling tests (analysis-of-covariance F-tests): - Test 1: reject fully pooled model in favor of FE (F statistic = 3.16; critical F(8;202) at 1 percent = 2.60). - Test 2: reject FE with homogeneous slopes in favor of FE with different slopes for SSOV (F statistic = 2.87; critical F(8;194) at 1 percent = 2.60). - Heteroskedasticity tests: - LM test statistic = 73.99; critical chi-squared with 8 df at 1 percent = 20.09; reject homoskedasticity. - LR test statistic (reported) = 55.48; critical chi-squared with 8 df at 1 percent = 20.09; reject homoskedasticity. - Correction: adopt FGLS estimator correcting for heteroskedasticity. - Autocorrelation tests and corrections: - LM test for AR(1): LM = 74.68; critical chi-squared with 1 df at 1 percent = 6.63; reject no-autocorrelation. - Breusch-Godfrey test for AR(2): BG = 109.82; critical chi-squared with 2 df at 1 percent = 9.21; evidence of second-order correlation. - Adopt FGLS allowing for AR(2) plus heteroskedasticity correction; AR(1) and AR(2) parameters highly significant; observations fall from 237 to 219 after AR(2). - Contemporaneous cross-section correlation: - Breusch-Pagan LM statistic = 48.08; degrees of freedom = 36; LM smaller than critical chi-squared with 36 df at 5 percent; cannot reject no contemporaneous correlation; SUR-weighted FGLS not necessary. - Preferred estimator: - FGLS corrected for heteroskedasticity and second-order autocorrelation (AR(2)); choice robust to alternate variable measures. ### Robustness: first-differences specification - First-difference equation (equation (7)) estimated to compare with Durbin and Ng (2005). - First-differences eliminate fixed effects; regression through the origin expected. - Testing leads to pooled specification and FGLS correcting for heteroskedasticity and first-order autocorrelation. - Column 7 in Table 6 reports first-difference estimates; size and significance of coefficients similar to level equation. ### Main estimation results and key statistics - Overall fit and precision: - Level equation adjusted R-squared: 96 percent. - Level equation standard error of the model: 0.001 (10 basis points). - First-difference equation adjusted R-squared: 75 percent. - First-difference equation standard error: 10 basis points. - Significance of determinants: - Sovereign risk (SSOV), firm-value volatility (SV1000D), leverage (D1), and interest rate volatility (SIGSPOTM in interaction) have expected signs and are statistically significant. - Monthly bond trading volume (TOVC) is not significant. - Sovereign risk (SSOV) firm-specific coefficient range and interpretation: - Range of SSOV-coefficients: between 0.42 for Nedcor Bank (NED1) and 0.96 for ABSA Bank (AB01). - Interpretation: a 100 basis-point increase in the sovereign default premium is associated with an increase in corporate spreads between 42 and 96 basis points. - Firm-specific SSOV coefficient estimates (selected): - AB01: 0.96 (level); 0.98 (first-difference). - ABL1: 0.92 (level); 0.93 (first-difference). - SBK1: 0.89 (level); 0.92 (first-difference). - IV01: 0.78 (level); 0.88 (first-difference). - NED1: about 0.40 in both equations (smallest coefficient). - IPL1: 0.61. - IS59: 0.42. - SFL1: 0.83. - HAR1: SSOV marginally not significant at the 5 percent level in level regression. - Wald tests of sovereign ceiling (βi = 1): - Evidence that sovereign ceiling does not apply for IPL1 (SSOV = 0.61) and IS59 (SSOV = 0.42): null βi = 1 rejected at the one-percent level in both level and first-difference regressions. - SASOL (SFL1) SSOV = 0.83: significantly smaller than one at the nine-percent level in level equation and at the five-percent level in first-difference equation. - For banks: AB01 and ABL1 SSOV coefficients not statistically different from one (consistent with sovereign ceiling applying); SBK1 and IV01 mixed results across specifications; NED1 anomalously low (~0.40). - Economic interpretation: - For Imperial Group, ISCOR, and SASOL, higher corporate spreads relative to sovereigns are due to relatively high stand-alone default risk, not 100 percent indirect sovereign risk. - These firms could, in principle, “pierce the sovereign ceiling” if stand-alone default probability falls sufficiently. ### Sovereign risk dominance and variance decomposition - Sovereign risk is the dominant driver: - In level equation, sovereign risk explains 13 percent of total variation in corporate spread levels. - In first-difference equation, sovereign risk explains 61 percent of total variation in corporate spread changes. - Sovereign risk explains 12 to 13 times more of total variation than combined firm-specific factors from contingent claims. - Level equation: combined firm-specific factors explain 1 percent; fixed effects explain 93 percent. - First-difference equation: firm-specific factors explain 5 percent; residuals account for 34 percent. - Quantitative elasticities: a 100-basis-point increase in sovereign yield spreads is associated with an increase in firms’ yield spreads of between about 40 and 100 basis points. ### Firm-specific determinants — quantitative effects - Firm-value volatility (SV1000D): - An increase in volatility by 10 percentage points increases corporate spreads by 48 basis points. - Leverage (D1): - If interest volatility were zero, an increase in leverage by 0.5 increases spreads by approximately 95 basis points. - If interest rate risk is at sample mean (1.01 percent per annum), same 0.5 increase raises spreads by about 114 basis points. - Leverage effect reinforced by interest rate volatility. - Interest rate volatility (SIGSPOTM) and interaction with leverage: - Increase in interest rate volatility by one-percentage point increases credit spread by about 19 basis points if leverage at sample mean (0.51). - If leverage at sample minimum (0.08), one-percentage-point increase raises spreads by only three basis points. - If SIGSPOTM considered in isolation, effect on spreads positive for leverage levels above 0.41; at sample mean would increase by about four basis points. - Time to maturity (M): - Remaining time to maturity statistically significant with negative sign: one-year increase decreases corporate credit spreads by about 30 basis points (sample-average downward-sloping term structure). - Liquidity proxy (TOVC): - TOVC not significant in main specification. - Using ln(1+TOVC) (range ZAR 0 to ZAR 4.08 billion) makes liquidity significant but with wrong (positive) sign; other coefficients unchanged. ### Theoretical operational definition and application of sovereign ceiling - Contingent-claims view: risky corporate bond = long risk-free bond + short put on firm assets; Black-Scholes formula applicable. - Sovereign ceiling defined when indirect sovereign risk equals 100 percent: whenever sovereign defaults, firm defaults. - Durbin and Ng (2005) test: elasticity of corporate spreads w.r.t. sovereign spreads ≥ 1 implies sovereign ceiling applies. - Methodology applicable to rating agencies, banks (IRB of Basel II), and supervisors for estimating counterpart PDs for foreign-currency debt exposures given: - (i) counterpart’s stand-alone FX default probability ( ( /) c PF S ); - (ii) sovereign default probability ( ( ) PS ); - (iii) probability of direct sovereign intervention ( )/( SFP ). ### Policy implications - Macroeconomic policy: reducing sovereign default risk and improving sovereign credit rating can lower corporate borrowing costs and stimulate investment and growth. - Financial supervision: supervisors should account for sovereign risk dominance when assessing system-wide risk, especially for banking sector exposures. - Rating agencies and banks: methodology can strengthen rating processes in emerging markets and help compute PDs for counterparty exposures in IRB framework; applicable to local- and foreign-currency exposures where reasonably liquid firm and sovereign bonds exist. ### Methodological notes and appendices (selected) - Variance decomposition formula and derivation presented in Appendix I. - Numerical procedure to calculate firm-value volatility: iterative procedure starting with Vσ = SV12M; convergence tolerance 0.000001; convergence achieved after seven iterations. - Econometric tests (Appendix II): pooling tests follow Hsiao (1986) and Baltagi (1995); tests executed using FGLS correcting for heteroskedasticity and AR(2). - Specification test details: - Test 1: SSRU FE = 0.000304; SSRR Pooled OLS = 0.000342; N = 9; pooled observations = 219; df_u = 202; df_r = 210; F = 3.16. - Test 2: SSRU FE with different slopes for SSOV = 0.000273; SSRR FE = 0.000304; df_u = 194; df_r = 202; F = 2.87. - Selected regression diagnostics and coefficients (from Table 6 and Wald tests) reported in the source. *Source: _wp05217 - Box 1. The Cost of Debt for an Emerging Market Borrower* ### References.............................................................................................................. ### References ### Tables (listed) - 1. South African Corporate Bonds: Issuers, Main Features, and Corresponding Benchmark Instruments .....................................................................................................46 - 2. History of Credit Ratings by the Republic of South Africa and Firms Analyzed .............47 - 3. The Determinants of Corporate Default Premia: Expected Impact ...................................48 - 4. Data Sources and Measurement of Variables ....................................................................49 - 5. Descriptive Statistics of Variables .....................................................................................50 - 6. The Determinants of Corporate Default Premia: Regressions Results ..............................51 - 7. The Determinants of Corporate Default Premia: Summary of Empirical Results.............52 - 8. Variance Decompositions of Corporate Default Premia in Levels and First Differences .........................................................................................................................52 ### Figures (listed) - 1. Firm Bond Yields and Corresponding Sovereign and Risk-Free Yields ...........................53 - 2. South African Corporate Default Premia, July 2000–May 2003.......................................58 - 3. South African Sovereign Default Premia, Corresponding to the Corporate Default Premia, July 2000–May 2003 ............................................................................................58 ### Boxes - 1. The Cost of Debt for an Emerging Market Borrower..........................................................4 ### Appendices - I. Mathematical Appendix ....................................................................................................40 - II. Econometric Tests .............................................................................................................42 - III. Tables and Figures ............................................................................................................46 ### Introduction — key concepts and research focus - The cost of capital is identified as an important determinant of economic growth. - Emerging market borrowers able to tap international capital markets generally pay a considerable risk premium over comparable risk-free assets (such as U.S. Treasury securities). - When debt instruments are denominated in domestic currency, the total risk premium is decomposed into: - currency (risk) premium, which reflects the risk of a depreciation or devaluation of the domestic currency; - default (risk) premium, which reflects the financial health (solvency) of the borrower and compensates for the risk of default (inability or unwillingness to service the debt in full and on time); - jurisdiction (or onshore-offshore) premium, 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. - When the borrower is the government, the default premium (or country risk) is called the sovereign risk premium or sovereign risk. - Companion work: Grandes, Peter, and Pinaud (2003) analyze the determinants of the currency premium in South Africa. ### Research questions addressed in the paper - Does sovereign risk help explain corporate default premia? - If yes, is a given increase in sovereign risk (measured by the sovereign yield spread) associated with changes in corporate default premia? *Source: _wp05217 - References (extract) — pages and sections as listed in the supplied content.* ### Box 1. The Cost of Debt for an Emerging Market Borrower ### Box 1. The Cost of Debt for an Emerging Market Borrower ### Cost decomposition and definition - Cost of local-currency-denominated debt = Risk-free rate + 1) Currency (risk) premium + Total risk premium 2) Default (risk) premium 3) Jurisdiction premium = Country (risk) premium. - In the paper, the terms default premium, credit spread, yield spread, or simply spread are used as synonyms. ### Main empirical findings (South Africa case study) - Sovereign risk is the single most important determinant of corporate default premia in South Africa: for almost all firms analyzed, sovereign risk is statistically and economically the most important determinant of their credit spread. - Sovereign ceiling does not apply to industrial multinational companies in the sample: elasticity of their spreads with respect to sovereign spreads is between 0.42 and 0.83. - Sovereign ceiling appears to apply to most financial companies: elasticities statistically not different from one, between 0.78 and 0.98. - Firm-specific factors derived from the contingent claims approach (leverage, firm-value volatility, remaining time to maturity, and risk-free interest rate volatility) are statistically significant determinants of corporate spreads, but economically their importance is minor relative to sovereign risk. - Policy implication: macroeconomic policies that reduce sovereign default risk and improve the government’s credit rating can significantly reduce the cost of debt capital for corporate borrowers, stimulating investment and economic growth. ### Why South Africa was selected - South Africa is one of the few emerging markets to have a corporate bond market in local currency (the rand). - Sample period: July 2000–May 2003. - Number of South African private sector firms in sample: nine firms with a total of 12 bonds outstanding. - Rationale: sample firms are important South African companies; the local-currency market has growth potential due to under-leveraged corporates, appetite from local banks and institutional investors, and a potential decrease in government dominance of domestic debt. ### Sovereign ceiling (concept and empirical test) - Sovereign ceiling (rating agencies’ policy): debt of a company in a given country cannot be rated higher than the debt of its government (applies to both foreign- and local-currency ratings historically). - Distinction: - Direct sovereign intervention risk (transfer risk) — typically foreign-currency context: probability a government imposes foreign exchange payment restrictions causing otherwise solvent firms to default on foreign obligations. - Indirect sovereign risk — domestic-currency context: probability a firm defaults on domestic-currency debt as a result of sovereign distress/default. - Identification challenge: corporate spreads exceeding comparable government spreads may reflect high stand-alone firm default probability or high indirect sovereign risk. - Durbin and Ng (2005) result used as test: 100 percent transfer/indirect sovereign risk implies a 1 percent increase in government spread should be associated with at least a 1 percent increase in firm spread; in regressions of corporate spread changes on sovereign spread changes, the beta should be ≥ 1 if the sovereign ceiling applies. - Empirical observation in sample: all corporate bonds analyzed bore higher yields than sovereign bonds of similar maturity, but this is necessary, not sufficient, for a sovereign ceiling. ### Theoretical framework — determinants of corporate default premium - Methodological approach: simplest structural (contingent claims) approach, extended to include stochastic interest rates and sovereign default premium. - Key determinants identified: - Sovereign risk (sovereign default premium / sovereign spread). - Leverage (quasi-debt ratio d). - Firm-value volatility (Vσ). - Interest rate volatility (rσ). - Remaining time to maturity (τ). - Liquidity (l) — higher relative liquidity of corporate bond implies lower spread (∂s/∂l negative). - Merton (1974) baseline: - Corporate default spread s = s(Vσ, d, τ). - Sign results: ∂s/∂Vσ > 0; ∂s/∂d > 0; ∂s/∂τ ambiguous (term structure hump-shaped depending on d). - Shimko, Tejima, and Van Deventer (1993) extension: - Allow stochastic risk-free interest rates; corporate spread s = s(Vσ, d, τ, rσ) (also depends on correlation ρ and speed of mean reversion α, assumed constant in empirical work). - Interest rate volatility rσ typically increases s for reasonable parameter values, with impact stronger for higher d. - Interaction terms: expect positive coefficient on d·rσ; include d·τ to capture leverage dependence of term-structure effect (expect τ coefficient positive and d·τ negative). - Adding sovereign risk: - Formal decomposition of firm default probability P(F): - P(F) = P(F ∩ S) + P(F ∩ S^c) = P(S)·P(F|S) + P(S^c)·P(F|S^c). - Definitions: - P(F|S^c): stand-alone default probability of firm (normal times). - P(S): sovereign default probability (sovereign risk). - P(F|S): probability firm defaults given sovereign default (indirect sovereign risk / transfer risk). - Sovereign ceiling definition: sovereign ceiling applies when P(F|S) = 1 (indirect sovereign risk 100 percent). Under this case, firm default probability (and spread) will always be at least as high as sovereign’s. - Durbin and Ng (2005) implication used as empirical test: if ∂s/∂sov ≥ 1 then sovereign ceiling applies; if ∂s/∂sov < 1 it does not. ### Operational synthesis and estimating equation - Theoretical synthesis (equation form): - s = s(sov, d, Vσ, rσ, τ, l) with expected signs indicated by theory. - Linearized estimating equation to be estimated in section V includes interaction terms: - Interaction between interest rate volatility and leverage (d·rσ) — expected positive coefficient. - Interaction between maturity and leverage (d·τ) — expected negative coefficient, with τ alone expected positive. - Representative numeric parameter estimates and sample statistics mentioned: - Mean firm-value volatility Vσ = 23.4 percent. - Interest rate volatility rσ = 1.0 percent (sample value used in simulations). - Estimated α = 0.70. - Estimated ρ = 0 (correlation between short-term interest rate changes and firm-value returns assumed zero overall; example firm-specific correlations: IPL1 had ρ = -0.42, HAR1 had ρ = 0.33). - Sample: nine firms, 12 rand-denominated corporate bonds (July 2000–May 2003). - Final theoretical-operational equation (as presented): - Equation (5): s = s(sov, d, Vσ, rσ, τ, l) (signs of effects indicated in text). *Source: _wp05217 - Box 1. The Cost of Debt for an Emerging Market Borrower* ### section III) are operationalized. The data sources as well as the sample characteristics are ### _wp05217 - section III) are operationalized. The data sources as well as the sample characteristics are ### A. Dependent Variable: How Is the Corporate Default Premium Measured? - Objective: calculate corporate default premium (spread) as difference between corporate spot rate and risk-free spot rate per Merton-Shimko framework. - Practical constraints: - No corporate zero-coupon (spot) bonds available for South African firms. - South African government bonds cannot be considered risk-free. - Operational choice for spreads: - Use yield to maturity of coupon-paying corporate bond (y) minus yield to maturity of a risk-free bond (rf) with maturity and coupon as close as possible to those of the corporate bond: - st ≡ SCOR? = y? – rf? - Acknowledged limitations: - Spreads will include term structure effects and will not completely isolate the pure default premium. - Jurisdiction premium likely included because risk-free benchmarks are ZAR-denominated supranational bonds traded offshore (EIB, IBRD, EBRD). - Jurisdiction premium presumed constant over sample period (July 2000–May 2003) due to no significant legal or capital control regime changes. - Data sources and processing: - End-month yields to maturity collected from Thomson Financial Datastream (DS) and Bond Exchange of South Africa (BESA). - For South African firm bonds: DS from August 28, 2000 onward; BESA for period before August 28, 2000. - For risk-free supranational bonds: all yield data from DS. - Conversion: BESA yields compounded semi-annually converted to annual-compounding via ya = 100[(1+ys/200)^2 -1], where ys is annualized yield (in percent) compounded semi-annually and ya is annualized yield (in percent) compounded annually. - Data cleaning and sample selection rules: - Drop parastatals (public companies). - Eliminate inconsistent price or yield outlier data. - Include only firms whose shares are listed on the Johannesburg Stock Exchange (JSE). - Exclude floating rate bonds. - Use only one bond per firm: select the more liquid bond (liquidity measured by trading volume); if similar liquidity, choose bond with longer time series. - For callable bonds (NED1 and SBK1), use “yields to next call” as reported by BESA. - Truncate yield series at the penultimate coupon payment date to avoid anomalous price behavior after penultimate coupon. - Final sample after elimination: - Nine corporate bonds issued by five banking and four industrial firms. - Bond identifiers (BESA acronyms, used as variable identifiers): AB01, ABL1, HAR1, IPL1, IS59, IV01, NED1, SFL1, SBK1. - Maximum data range extends from May 20, 1998 to June 4, 2003 (availability of BESA data); actual analysis frequency monthly over July 2000–May 2003. ### B. Explanatory Variables - Sovereign default premium (sovereign spread) construction: - For each corporate bond, select an RSA coupon bond with maturity and coupon amount as close as possible to the corporate bond and to the risk-free bond. - Data sources: BESA up to July 2000; DS thereafter. - Sovereign spread defined as: - sovts ≡ SSOV? = sov? – rf? - sov is yield to maturity of corresponding sovereign bond; rf is yield to maturity of corresponding risk-free benchmark bond. - Note: for AAA sovereigns SSOV would be zero because sovereign bond is risk-free benchmark. - Caveat: sovereign spreads sometimes zero or negative (supranational yields higher or equal to RSA bond yields) due to (i) supranational bond liquidity drying up with age; (ii) domestic investors unable to buy eurobonds. - Firm-specific determinants (empirical counterparts of five theoretical determinants from section III): - (i) Quasi-debt-to-firm-value (leverage) ratio (td): D1?, D2?, or D3?; - (ii) Volatility of returns on firm’s value (Vσ): SV1000D?, SV12M?, or SV24M?; - (iii) Volatility of risk-free interest rate (rσ): SIGSPOTM? or SIGRFM?; - (iv) Time to maturity (τ): M?; - (v) Liquidity (l), proxied by trading volume: TOVC?; - Interactions included: maturity × leverage (tdτ⋅) and interest-rate volatility × leverage (rt dσ⋅). - Operationalization summary: Table 5 (Appendix III) summarizes measurement and subcomponents of the five firm- or bond-specific determinants. ### C. Sample and Data - Sample definition: - Unbalanced panel of monthly data for nine corporate bonds (9N=) listed and traded on BESA during July 2000 to May 2003. - The four industrial and five financial corporate issuers essentially constitute the population of South African firms with bonds outstanding. - Time dimension: - Observations are end-month. - Time-series dimension T varies between 21 and 35 months, i.e., 21 ≤ T ≤ 35. - Data sources: BESA, DS, and Bloomberg. - Descriptive statistics: reported in Table 5 (Appendix III). ### V. Empirical Methodology and Results - Research focus: test whether sovereign default premium is a significant determinant of corporate spreads and whether its coefficient is < 1 (sovereign ceiling does not apply) or ≥ 1 (sovereign ceiling applies). - A. The Econometric Model: Fixed Effects with Different Slopes for Sovereign Risk - Estimated linearized model (fixed effects with firm-specific intercepts and firm-specific slopes for SSOV): - SCORit = αi + βi SSOVit + Σ_{j=1..k} γj Xjit + εit (equation (6) in text) - SCORit: corporate spread of firm bond i at end-month t. - SSOVit: sovereign spread matching SCORit in maturity and coupon. - Xjit: set of k = 7 firm-specific control variables (see list in section III operationalized in Table 4 (Appendix III)). - αi: unobservable time-invariant firm-specific effect (fixed effect). - βi and γj: coefficients to be estimated; εit: normally distributed error term with zero mean. - Practical estimation strategy: - Ideally would estimate αi, βi, and firm-specific γj for each firm, but limited observations per firm (21 ≤ T ≤ 35) make that inefficient. - Pool time series from nine firms to increase degrees of freedom; pooling imposes parameter restrictions. - Allow intercepts αi and slopes βi on SSOV to vary across firms while constraining control-variable slopes γj to be the same across firms (resulting specification is equation (6)). - Tests for pooling (analysis-of-covariance F-tests per Hsiao (1986) and Baltagi (1995)): - Test 1: - H0: same intercepts (αi equal) and same slopes (βi equal, γji equal) across all firms (fully pooled model appropriate). - H1: different intercepts but same slopes across firms (fixed effects appropriate). - Test 2: - H0: different intercepts (αi) but same slopes (βi equal, γji equal) across firms (FE model). - H1: different intercepts (αi) and different slopes for sovereign risk (βi vary) but same slopes for control variables (γji equal) across firms (FE with different slopes for SSOV, equation (6)). *Source: _wp05217 - section III) are operationalized. The data sources as well as the sample characteristics are (PDF chapter/section).* ### Appendix II.A provides the details of these tests. ### _wp05217 - Appendix II.A provides the details of these tests. ### Specification tests and model selection - F-statistic for the test of same intercepts and slopes (fully pooled model): F= 3.16. - The F-statistic (F= 3.16) is larger than the critical value at the one-percent level of significance; reject the null of same intercepts and slopes in favor of the FE model. - Test 2: null of homogenous slopes but different intercepts (FE model) is rejected at the one-percent level in favor of FE with different slopes for SSOV (equation (6)). - Robustness: using alternative measures for leverage (D2 and D3 instead of D1), firm-value volatility (SV12M and SV24M instead of SV1000D), and interest rate volatility (SIGMARF instead of SIGSPOTM) does not alter the conclusions of the specification tests. - Choice between FE and RE: - FE appropriate because inference is restricted to the specific set of N firms analyzed. - N = 9 (the nine South African corporates analyzed) and these firms constitute essentially the entire population of South African firms with bonds listed and traded at the local bond market (BESA). - RE estimator infeasible because number of cross-sections N = 9 is lower than number of coefficients to be estimated k = 17 (including the constant). ### Choosing the appropriate estimator and diagnostic corrections - Primary concerns with OLS residuals in panel context: cross-sectional heteroskedasticity, residual autocorrelation within cross-sectional units, and contemporaneous cross-section correlation. - Heteroskedasticity testing: - Applied Lagrange multiplier (LM) test and approximate likelihood ratio (LR) test to OLS estimates of equation (6). - Both LM and LR tests reject null of homoskedasticity at the one-percent level. - Correction: adopt FGLS estimator correcting for heteroskedasticity (results reported in column 5 of Table 6). - Durbin-Watson statistic improved somewhat after heteroskedasticity correction but autocorrelation remained. - Autocorrelation testing and correction: - Used LM test for first-order serial correlation in a fixed effects model (Baltagi (1995)) and Breusch-Godfrey (BG) test for higher-order autocorrelation. - Evidence suggests at least first-order autocorrelation; BG experimentation indicates second-order correlation in residuals. - Adopted FGLS estimator allowing for second-order autoregression in the error term plus heteroskedastic-variance correction (results in column 6 of Table 6). - Durbin-Watson statistic after FGLS with AR(2): around two (indicating autocorrelation no longer a problem). - AR(1) and AR(2) parameters are (highly) significant, justifying AR(2) correction. - Note: number of observations falls from 237 to 219 after introducing AR(2). - Contemporaneous cross-section correlation testing: - Breusch-Pagan LM test applied to FGLS residuals (heteroskedasticity and AR(2) corrected). - Null hypothesis that all contemporaneous residual covariances are zero cannot be rejected at the five-percent level. - Conclusion: SUR-weighted FGLS not necessary. - Preferred estimator: - FGLS corrected for heteroskedasticity and second-order autocorrelation is chosen as the preferred estimator for equation (6). - Choice robust to alternative measures: leverage D2/D3, firm-value volatility SV12M/SV24M, interest rate volatility SIGMARF. - Working controls chosen for reporting: leverage D1, firm-value volatility SV1000D, interest rate risk SIGSPOTM (most significant results). ### Robustness check: first-differences specification - First-difference equation (equation (7)) estimated to check robustness and comparability to Durbin and Ng (2005). - First-differences eliminate individual fixed effects; regression through the origin expected. - Expect (negative) autocorrelation in error term. - Testing procedure for first-differences leads to pooled specification and use of FGLS correcting for heteroskedasticity and first-order autocorrelation. - Column 7 in Table 6 reports first-difference estimates. - Essential observation: size and significance of estimated coefficients in first-difference specification are very similar to estimates of the level equation (6). ### Main estimation results and key statistics - Overall significance and fit: - Coefficients of most theoretical determinants (sovereign risk, firm-value volatility, leverage, and interest rate volatility) have expected sign and are statistically significant at conventional levels (Table 7). - Exception: monthly bond trading volume (TOVC), proxy for bond liquidity, is clearly not significant. - Level equation adjusted R-squared: 96 percent. - Level equation standard error of the model: 0.001 (10 basis points). - First-difference equation adjusted R-squared: 75 percent. - First-difference equation standard error: 10 basis points. - Sovereign risk (SSOV) effects: - SSOV is a highly significant determinant of corporate spreads in most cases. - In the level regression, Harmony Gold (HAR1) SSOV coefficient is marginally not significant at the five-percent level (significant at the 10 percent level). - In the first-difference regression, African Bank (ABL1) SSOV coefficient is marginally not significant at the 5 percent level (significant at the 10 percent level). - Range of firm-specific SSOV-coefficients: between 0.42 for Nedcor Bank (NED1) and 0.96 for ABSA Bank (AB01). Interpretation: a 100 basis-point increase in the sovereign default premium is associated with an increase in corporate spreads between 42 and 96 basis points. - Firm-specific SSOV coefficient estimates (level and first-difference where reported): - ABSA Bank (AB01): 0.96 (level); 0.98 (first-difference). - African Bank (ABL1): 0.92 (level); 0.93 (first-difference). - Standard Bank (SBK1): 0.89 (level); 0.92 (first-difference). - Investec Bank (IV01): 0.78 (level); 0.88 (first-difference). - Nedcor Bank (NED1): about 0.40 in both equations (smallest SSOV-coefficient in sample). - Imperial Group (IPL1): SSOV = 0.61. - ISCOR (IS59): SSOV = 0.42. - SASOL (SFL1): SSOV = 0.83. - Harmony Gold (HAR1): SSOV marginally not significant at 5 percent in level regression. - Tests of sovereign ceiling (Wald tests): - For Imperial Group (IPL1) and ISCOR (IS59), null hypothesis βi = 1 rejected at the one-percent level in both level and first-difference regressions (SSOV = 0.61 and 0.42, respectively): evidence that sovereign ceiling does not apply. - For SASOL (SFL1), SSOV = 0.83: significantly smaller than one at the nine-percent level in the level equation and at the five-percent level in the first-difference equation: some evidence sovereign ceiling does not apply. - For banks: - ABSA Bank (AB01) and African Bank (ABL1): SSOV coefficients statistically not different from one (consistent with sovereign ceiling applying to these banks). - Standard Bank (SBK1) and Investec Bank (IV01): SSOV coefficients not significantly different from one in first-difference equation; SBK1 marginally smaller than one at the 8 percent level in level equation; IV01 significantly smaller than one at the two-percent level in level equation. - Nedcor Bank (NED1): anomalously low SSOV (~0.40) merits further investigation. - Interpretation: SSOV-coefficients equal to one imply markets judge indirect sovereign risk for these banks to be 100 percent ((/ )PF S = 1), i.e., default probabilities and spreads at least as high as government. - Economic interpretation: - For Imperial Group, ISCOR, and SASOL, corporate spreads higher than comparable sovereign spreads are due to relatively high stand-alone default risk ( )/( c SFP) rather than to 100 percent indirect sovereign risk (i.e., sovereign ceiling). - Implication for these firms: if their stand-alone default probability )/( c SFP falls sufficiently, their overall default probability ()PF could fall below sovereign default risk ()PS, potentially allowing them to “pierce the sovereign ceiling” and obtain lower-cost local currency finance than the government. ### Methodological notes and ancillary findings - Separate OLS regressions for the nine firms (column 1 of Table 6) show most firm-specific SSOV-coefficients significant and all smaller than one; other determinants mostly not significant; R-squared values very high (multicollinearity indication). - Pooled OLS (column 2): unique SSOV-parameter significantly larger than one. - FE regression (column 3): SSOV significantly smaller than one. - FE with different slopes for SSOV (column 4): firm-specific coefficients larger than one for ABSA Bank, African Bank, SASOL, and Standard Bank; smaller than one for Harmony Gold, Imperial Group, ISCOR, Investec Bank, and Nedcor Bank. - In pooled regressions prior to corrections, very low Durbin-Watson statistic indicates serious misspecification (autocorrelation). - After FGLS with heteroskedasticity and AR(2) correction (column 6): - Durbin-Watson ~ 2. - Goodness-of-fit measures improved substantially. - Firm-specific SSOV coefficients all smaller than one and, except for Harmony Gold bond HAR1, significant at least at the five-percent level. - Contemporaneous cross-section correlation: Breusch-Pagan LM test applied to FGLS residuals cannot reject null at five-percent level; SUR-weighted FGLS not necessary. *Source: _wp05217 - Appendix II.A provides the details of these tests.* ### Appendix III), is due to the application of the sovereign ceiling rather than to higher ### _wp05217 - Appendix III), is due to the application of the sovereign ceiling rather than to higher ### Sovereign risk as dominant determinant of corporate spreads - Sovereign risk is the single most important determinant of corporate default premia in South Africa for almost all firms analyzed. - Quantitative elasticities: a 100-basis-point increase in sovereign yield spreads is associated with an increase in firms’ yield spreads of between about 40 and 100 basis points. - Variance decomposition: - In the level equation, variation in sovereign risk explains 13 percent of total variation in corporate spread levels. - In the first-difference equation, sovereign risk explains 61 percent of total variation in corporate spread changes. - Sovereign risk explains 12 to 13 times more of the total variation than the combined firm-specific factors derived from the contingent claims approach. - In the level equation: combined firm-specific factors explain 1 percent of total variation; fixed effects explain 93 percent of variance (between-variation dominant). - In the first-difference equation: firm-specific factors explain 5 percent of total variation; residuals account for 34 percent of total variation. ### Sovereign ceiling findings by firm type - Industrial (multinational) firms (four large firms): - The sovereign ceiling (in local-currency terms) does not apply. - Estimated elasticities of their spreads with respect to sovereign spreads are between 0.42 and 0.83 (significantly lower than one). - Higher corporate spreads relative to sovereigns for these firms are attributed to relatively high stand-alone firm default risk captured by firm-specific variables. - Financial firms (five firms, four affected): - The sovereign ceiling appears to apply for four of the five financial companies. - Elasticities are statistically not different from one, between 0.78 and 0.98. - Implication: even if stand-alone default probabilities of these banks were much lower than the government’s default probability, their overall default probabilities—and hence spreads—would still be higher than those of the government because of the sovereign ceiling. - Result consistent with rating-agency practice of generally not rating financial institutions higher than their sovereign. ### Firm-specific determinants (contingent claims approach) and quantitative effects - Determinants derived from Merton/Shimko contingent-claims approach: (i) quasi-debt-to-firm-value leverage (D1), (ii) firm-value volatility (SV1000D), (iii) risk-free interest rate volatility (SIGSPOTM), (iv) remaining time to maturity (M), plus liquidity differences (TOVC). - Firm-value volatility (SV1000D): - An increase in volatility (standard deviation) of returns on the firm’s assets by 10 percentage points will increase corporate spreads by 48 basis points. - Firm leverage (quasi-debt-to-firm-value ratio D1): - If interest volatility were zero, an increase in a firm’s leverage ratio by 0.5 (for example, from 0.3 to 0.8) would increase its spread by approximately 95 basis points. - If interest rate risk is at its sample mean (1.01 percent per annum, see Table 5), the same 0.5 increase raises spreads by about 114 basis points. - Effect of leverage on spreads is reinforced by interest rate volatility; impact does not seem to depend on remaining time to maturity. - Interest rate volatility (SIGSPOTM): - On its own: only marginally significant (at the seven percent level) and has the wrong sign when considered in isolation. - Interaction with leverage: highly significant determinant of spreads; impact of a change in volatility on spreads depends positively on leverage and vanishes as leverage tends to zero. - Quantitatively: - An increase in interest rate volatility by one-percentage point will increase the credit spread of firms by about 19 basis points if leverage is at the sample mean (0.51). - If leverage is at the sample minimum (0.08), a one percentage point increase in interest volatility would increase corporate spreads by only three basis points. - If the estimated parameter of interest rate volatility were considered in isolation as significant, the overall effect on spreads would still be positive for all leverage levels above 0.41; under that assumption, a change in volatility by one percentage point would increase spreads by about four basis points if leverage were at the sample mean. - Time to maturity (M): - Remaining time to maturity is statistically significant but with a negative sign. - Quantitatively, an increase in remaining time to maturity by one year decreases corporate credit spreads by about 30 basis points. - Interpretation: over the sample period July 2000–May 2003, the term structure of credit spreads of the nine firms was on average downward sloping; result may reflect pooling of firms with heterogeneous term-structure profiles. - Liquidity proxy (TOVC): - The ZAR amount traded during the month (TOVC) is not significant in the main specification. - If using ln(1+TOVC) (range ZAR 0 to ZAR 4.08 billion), liquidity becomes significant but has the wrong (positive) sign; other coefficients remain essentially unchanged. - Suggested reasons: TOVC may not measure liquidity relative to risk-free bonds; timing mismatch between monthly turnover and spread observed on last day of month. ### Theoretical framework and operational definition of sovereign ceiling - Contingent-claims approach: risky corporate bond = long risk-free bond with similar characteristics + short put on firm assets; Black-Scholes formula applicable. - Corporate default premium defined as difference between yield to maturity of risky corporate bond and yield to maturity of a risk-free bond with identical characteristics. - Sovereign ceiling defined as instance where indirect sovereign risk equals 100 percent: whenever the sovereign defaults on its debt, the firm defaults on its debt as well. - Durbin and Ng (2005) result used: if sovereign ceiling applies, elasticity of corporate spreads with respect to sovereign spreads should be greater than or equal to one. - Empirical test: estimate elasticity of corporate spreads w.r.t. sovereign spreads controlling for firm-specific factors; if elasticity ≥ 1 then SFP = 1; if elasticity significant but < 1 it can be used as rough estimate of SFP. - Formula for counterpart overall PD on foreign-currency debt exposure (equation (2) in paper): ( /)( )[ ( / )( /)] cc P D P F SP S P F SP F S = + −. (notation preserved as in source) ### Policy implications and applications - Macroeconomic policy: - Policies oriented toward reducing sovereign default risk—and hence improving a government’s credit rating—can significantly reduce the cost of debt capital for corporate borrowers, potentially stimulating investment and economic growth. - Financial supervision: - The preponderance of sovereign risk over idiosyncratic risk in emerging economies should be taken into account by supervisory agencies when assessing financial-system risks, particularly for the banking sector. - Rating agencies and banks: - The methodology can strengthen rating processes in emerging markets and help internationally active banks estimate probabilities of default (PD) of corporate and bank exposures in the context of the IRB approach of Basel II. - Method applicable to local- and foreign-currency exposures provided reasonably liquid firm and sovereign bonds exist in the respective currencies. - Ingredients to calculate counterpart PD for a foreign-currency debt exposure per methodology: - (i) default probability associated with counterpart’s stand-alone FX rating labeled ( /) c PF S; - (ii) sovereign default probability associated with sovereign’s FX credit rating labeled ( ) PS; - (iii) probability of direct sovereign intervention (“transfer risk”) labeled )/( SFP. ### Methodology notes and appendices - Data and sample: monthly panel of four industrial and five financial South African firms during July 2000–May 2003. - Variance decomposition: - Level equation rewritten as CS = FE + SY + FS + RE (notation as in Appendix equations). - Decomposition formula: Var(CS) = Cov(CS,FE) + Cov(CS,SY) + Cov(CS,FS) + Cov(CS,RE) (proposition and derivation in Appendix I). - Numerical procedure to calculate volatility of firm value: - Iterative procedure transforming equation 1() EV Vh Eσσ Φ = to 1() E V E Vh σ σ = Φ, starting with assumption Vσ = SV12M to obtain sv_old; iterate substituting previous solution until difference < 0.000001; convergence achieved after seven iterations. - Econometric tests (Appendix II): - Tests for pooling follow Hsiao (1986) and Baltagi (1995), using two F-tests comparing SSRU and SSRR. - Tests executed using an FGLS estimator that corrects for (cross-section) heteroskedasticity and second-order autocorrelation. - Tables A2.1 to A2.3 summarize results (tables referenced in source). *Italicized source: content unit from the provided IMF PDF chapter/section.* ### section V.A. ### _wp05217 - section V.A. ### Specification and Model Comparison Tests - Test 1: Pooled OLS is the restricted model; fixed effects (FE) is the unrestricted model. - Explanatory variables: SSOV? SV1000D?M? TOVC? D1? M?*D1? SIGSPOTM? D1?*SIGSPOTM? (i.e., k = 8) - SSRU FE (different intercepts but same slopes) = 0.000304 - SSRR Pooled OLS (same slopes and intercepts) = 0.000342 - N = 9, T_max = 35; number of pooled observations: 219 - df_u = 219-N-k = 219-9-8 = 202 - df_r = 219-k-1 = 219-8-1 = 210 - F statistic = 3.16 - Critical F(8;202) at 1 percent = 2.60 - Note: SSRs are obtained using FGLS and correcting for AR(2) in error terms. - Test 2: FE is the restricted model; FE with different slopes for SSOV (equation 6) is the unrestricted model. - Explanatory variables: SSOV? SV1000D?M? TOVC? D1? M?*D1? SIGSPOTM? D1?*SIGSPOTM? (i.e., k = 8) - SSRU FE with different slopes for SSOV (slopes for all other explanatory variables are the same) = 0.000273 - SSSR FE (different intercepts but same slopes) = 0.000304 - N = 9, T_max = 35; number of pooled observations: 219 - df_u = 219-2*N-(k-1) = 219-18-7 = 194 - df_r = 219-N-k = 219-9-8 = 202 - F statistic = 2.87 - Critical F(8;194) at 1 percent = 2.60 - Note: SSRs are obtained using FGLS and correcting for AR(2) in error terms. ### Heteroskedasticity Tests - Null hypothesis H0: residual variances are homoskedastic (i.e., 22 i ss = for all i); H1: residual variances are heteroskedastic (i.e., 22 i ss ≠ for all i). - Lagrange Multiplier (LM) Test (adapted to an unbalanced panel): - LM statistic formula: LM = (N/2) * Σ_i ( (T_i * s_i^2 / s^2) - 1 )^2 (as described in text) - Degrees of freedom: chi-squared with N-1 df. - Based on equation (6), OLS results imply LM = 73.99. - Critical chi-squared with 8 df at 1 percent = 20.09. - Conclusion: H0 is rejected (evidence of heteroskedasticity). - Approximate Likelihood Ratio (LR) Test (adapted to an unbalanced panel): - LR statistic formula: LRT = -2 Σ_i ln( s_i^2 / s^2 ) (as described in text) - Degrees of freedom: chi-squared with N-1 df. - Based on equation (6), OLS results imply LM = 55.48 (reported for LR test context). - Critical chi-squared with 8 df at 1 percent = 20.09. - Conclusion: H0 is rejected (evidence of heteroskedasticity). ### Tests for Autocorrelation - LM test for First-Order Serial Correlation in a Fixed Effects Model: - H0: no autocorrelation (ρ = 0); H1: first-order autocorrelation (AR(1)). - LM statistic (formula shown) is asymptotically chi-squared with 1 df under H0. - OLS applied to equation (6) yields LM = 74.68. - Critical chi-squared with 1 df at 1 percent = 6.63. - Conclusion: reject H0 — at least first-order serial correlation is present. - Breusch-Godfrey (BG) Test of Higher-Order Autocorrelation: - H0: no autocorrelation (ρ = 0); H1: errors follow AR(p). - BG statistic = n·R^2 from auxiliary regression; asymptotically chi-squared with p df. - Testing for AR(2) in OLS residuals of equation (6) results in BG = 109.82. - Critical chi-squared with 2 df at 1 percent = 9.21. - Experimentation shows test statistic peaks at p = 2. - Conclusion: evidence of second-order correlation in the error terms. ### Contemporaneous Cross-Section Correlation - Breusch-Pagan LM test (adjusted for an unbalanced panel): - H0: off-diagonal elements of residual variance-covariance matrix are zero (no contemporaneous cross-section correlation); H1: cross-section correlation present. - LM statistic formula: LM = Σ_{i