Peter Remiáš

Robert Verner

Investment Management and Financial Innovations

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“Size of issue leader as determinant of debt offerings yields”AUTHORSRobert VernerPeter Remiáš https://orcid.org/0000-0003-3323-579XARTICLE INFORobert Verner and Peter Remiáš (2015). Size of issue leader as determinant ofdebt offerings yields. Investment Management and Financial Innovations, 12(4-si), 187-191RELEASED ON Thursday, 24 December 2015JOURNAL "Investment Management and Financial Innovations"FOUNDER LLC “Consulting Publishing Company “Business Perspectives”NUMBER OF REFERENCES0NUMBER OF FIGURES0NUMBER OF TABLES0© The author(s) 2021. This publication is an open access article.businessperspectives.orgInvestment Management and Financial Innovations, Volume 12, Issue 4, 2015 187 Robert Verner (Slovakia), Peter Remiáš (Slovakia) Size of issue leader as determinant of debt offerings yields Abstract This papers focuses on analysis of impact of size of leading underwriter and bookrunners on primary bond yields using ordinary and generalized least squares. The results indicate that yields spreads increase with the size of the leader and bookrunners. It suggests that cooperation with global leaders increases the yields of offering. However, it might also indicate, that issuers with worse credit rating and credit quality intentionally select larger issue leaders in order to cover the intended volume of issue. Based on obtained results it might be concluded that generalized least squares performed better than OLS primarily due to the increase of determination coefficients and decline of information criteria.  Keywords: corporate bond offering, generalized least squares, ordinary least squares, underwriting. JEL Classification: C22, C24, G12. Introduction Regarding underwriter selection, several studies showed advantages of hiring a high reputation issue leader (Carter and Manaster, 1990; Wang and Yung, 2011) with strong connection to institutional investors (Chen and Wilhelm, 2008; Neupane and Thapa, 2013). Underwriter reputation had been also examined by Beckman et al. (2001), Hajduova (2014), Roten and Mullineaux (2002), Loureiro (2010), Andres et al. (2014), and Chua (2014) stating that the selection of top-tier underwriters had significant impact on security valuation and long-term performance. McKenzie and Takaoka (2008) explored the role of the leading underwriter’s reputation in defining the probability of switching of underwriters between the particular issues. They argued that the probability of a switch significantly increased if the rating of the leading underwriter of the initial issue declined. There was also an evidence that leaders who raised the degree of overpricing of the initial issue were more likely to be selected to act as the leading underwriter of the consequent offering. Krigman et al. (2001) stated that offerings of switching companies had been significantly less underpriced than those of non-switching companies and firms usually switched leaders mostly to graduate to higher reputation underwriter. 1. Methodology 1.1. Ordinary least squares. In a multiple linear regression we focus on estimation of linear relationship between dependent (endogenous, explained, controlled, regressands) variable Yi and independent (exogenous, explanatory, control, regressors) variables: 1 1 2 2 ,ki i i i K Ki iX Y X X ... X u  where i = 1, 2,…,n denotes the number of observation, k = 1, 2,…,K represents the k-th  independent variable,  is the intercept,  1,…, K define the slopes of linear relationships between Yi and Xki and ui represents the random error (disturbance). ui might be for instance a result of wrong specification of the linear relationship (when in fact is nonlinear), omission of crucial factors that might influence the relationship, or measurement error.  and 1,…, K are not known and have to be properly estimated (hat symbol denotes estimates): 1 1 2 2i i i K Kiiˆ ˆ ˆˆ ˆY X X ... X . Every observation i has a corresponding error attached which is defined as i i îe Y Y  (Tká , 2001). The difference between the disturbance ui and residual ei is in fact that while ei  is directly observable, ui is unknown. The idea behind ordinary least squares method is in the minimization of the residual sum of squares given as: 2121 1 2 21niini i i K KiiRRS eˆ ˆ ˆˆY X X ... X  by minimizing first-order conditions: 021niieRSS and  12 0ni kiiRSSe X . for 1, 2, ,k ... K .  Solving these equations we get the ordinary least squares estimators. This can be more easily done in matrix form. If we consider the regression y = X  + u, where:                                                        Robert Verner, Peter Remiáš, 2015. Ing. Robert Verner, Ph.D., MBA, Department of Economics, Faculty of Business Economy with seat in Košice, University of Economics in Bratislava, Slovakia. Ing. Peter Remiáš, Ph.D. Student, Department of Quantitative Methods, Faculty of Business Economy with seat in Košice, University of Economics in Bratislava, Slovakia. Investment Management and Financial Innovations, Volume 12, Issue 4, 2015 188 12nYYyY,  11 12 121 22 21 2kkn n nkX X XX X XXX X X, 12k,  12nuuuu. n defines the number of observation samples and k is the number of independent variables with n > k. If we denote the vector of residuals as ˆe y X , the residual sum of squares might be introduced as: 21nTTiiT T T T T TRSS e e e y X y Xy y y X X y X X . By differentiating the residual sum of squares with respect to  we obtain 2 2T TRSSX y XX , which should be equal to zero. The solution to this equation results into ordinary least squares estimates of regression coefficients:  1T TOLSˆ X X X y.  Although the ordinary least squares is presumably the most popular method for estimating parameters in linear regression, their correct application requires several assumptions:  disturbances iu have zero mean, i.e. 0iuE ; disturbances iu have constant variance, i.e. 2var iiu ; disturbances iu are not correlated, i.e. 0jiuuE  for ,ji nji ,...,2,1, ; independent variables are nonstochastic; linear specification is correct. Given above mentioned assumptions, OLSˆ  is the best linear unbiased estimate (BLUE) of . In addition to above mentioned assumptions it holds that: If ui are independent and identically distributed 20, ,N  OLS is also maximum likelihood estimator and it can be showed that it is minimum variance unbiased estimator. If explanatory variables are not perfectly correlated (no perfect multicollinearity), there exists unique solution to normal equations. The crucial efficiency assumptions of ordinary least squares regarding disturbances may therefore be summarized into variance-covariance matrix, i.e. u ~ 20, nI . 1.2. Generalized least squares. Violations of first group of above mentioned assumptions means that OLSˆ  is no longer the best linear unbiased estimate (BLUE) of . If disturbances do not have constant variance (heteroskedasticity) or are correlated, ordinary least square might be misleading and inefficient. Generalized least squares method relaxes the assumptions that 20, nu I  so that u ~ 20,u  where  is positive definite matrix of dimension (n  n), i.e. the variance-covariance matrix of residuals has changed. This model applies the fact that for every positive definite matrix  there exists a nonsingular matrix  such that  = . Therefore we can transform the original model y = X  + u by premultiplying it by -1: -1y = -1X  + -1u i.e. ,y X u  where 1 ,y y  1X  and 1u u  with u  having zero mean and 2 nvar u I . Consequently, the ordinary least squares applied on transformed model is the best linear unbiased estimate of : 111 1 1 111 1 1T TGLST T T TT Tˆ X X X yX X X yX X X y .. 2. Data  We focused on 23 844 EUR and USD denominated straight bond offerings with fixed coupon issued between January 2003 and April 2015 from the BondRadar information service. Regarding analyzed sample, we examined following independent variables: prestige of issue leader (in total size of led issues); prestige of bookrunner 1 to 4 (in total size of led issues). Independent variable was the spread over middle value of interest rate swaps (in case of EUR issues) or over US Treasury yields (in case of USD issues) with corresponding maturity in basis points. Yields of US Treasuries are approximately equal to USD interest rate swaps.  3. Results Ordinary least squares are the most popular econometric method and under several assumptions they might be the best linear unbiased estimator. They are simple, easy to solve and available in almost every statistical and econometrical software. Investment Management and Financial Innovations, Volume 12, Issue 4, 2015 189 Table 1 presents the results of ordinary least squares regression coefficient estimation on our sample of 23 844 initial bond offerings. Table 1. Estimation results of ordinary least squares Variable Coefficient Std. error t-ratio p-value const 111.464 3.7538 29.69 2.70E-190*** LEADER 5.71E-05 2.64E-06 21.61 1.31E-102*** BOOK1 8.38E-06 2.16E-06 3.884 0.0001*** BOOK2 -1.81E-05 2.18E-06 -8.316 9.57E-17*** BOOK3 1.15E-05 2.60E-06 4.443 8.91E-06*** BOOK4 4.98E-05 3.41E-06 14.62 3.47E-48*** Source: Processed by authors. Obtained results indicate that all independent variables have significant impact on offering yields. If we look at the sign of the coefficient estimate (except second bookrunner in order), the larger the leading institution, the larger yield spreads. This outcome is remarkable since it suggests that cooperation with global leaders increases the yields of offering. However, it might also indicate, that issuers with worse credit rating (credit quality) select larger leaders in order to cover the intended volume of issue. Figure 1 introduces the plot of actual and fitted values by observations, while Figure 2 shows the residuals by observations.  Source: Processed by authors. Fig. 1. Actual vs. OLS fitted values by observation  Source: Processed by authors. Fig. 2. OLS residuals by observation Investment Management and Financial Innovations, Volume 12, Issue 4, 2015 190 Table 2 presents the performance measures of ordinary least squares. The determination (R-squared) and adjusted determination coefficient are around 23.4% which is low value for financial data. Adjusted determination coefficient is always lower or equal to standard determination coefficient, since it penalizes the model for quantity of parameters. Akaike (Akaike, 1974), Hannan-Quinn (Hannan and Quinn, 1979) and Schwarz (Schwarz, 1978) are criteria for the model selection. The goal is to find the model with the lowest information criterion.Table 2. Performance of ordinary least squares Mean dependent variable 183.7421 S.D. dependent var 204.1883 Sum squared residuals 9.60E+08 S.E. of regression 200.6518 R-squared 0.234542 Adjusted R-square 0.23434 F (5,23838) 170.5757 P-valued (F) 6.80E-179 Log-likelihood -160240.8 Akaike criterion 320493.7 Schwarz criterion 320542.1 Hannan-Quinn 320509.4 Source: Processed by authors. Constant variance of residuals was tested by Breusch-Pagan test (Breusch and Pagan, 1979). Test statistic of 595.372 and zero p-value rejected the null hypothesis of homoskedasticity, i.e. ordinary least squares estimates of regression coefficient are significant, but possibly inefficient. Generalized least squares may therefore constitute better linear alternative. In order to check the correct specification of linear model we performed RESET test (Ramsey, 1969) with linear specification as null hypothesis. RESET test rejected the null hypothesis with F-statistic of 6.546 and p-value of 0.00144. Thus as we assumed, a nonlinear choice might be more suitable.  Table 3 introduces the results of coefficients estimation produced by generalized least squares. Comparing to OLS, coefficient estimates have little changed, however, all of them are significant.  Table 3. Estimation results of generalized least squares Variable Coefficient Std. error t-ratio p-value const 109.046 3.36066 32.45 4.78E-226*** LEADER 5.54E-05 2.44E-06 22.71 5.17E-113*** BOOK1 1.15E-05 2.07E-06 5.556 2.79E-08*** BOOK2 -1.55E-05 2.03E-06 -7.606 2.94E-14*** BOOK3 1.09E-05 2.53E-06 4.319 1.58E-05*** BOOK4 4.85E-05 3.77E-06 12.84 1.24E-37*** Source: Processed by authors. Figures 3 and 4 show the actual and fitted values produced by generalized least squares as well as GLS residuals by observations. If we look on the performance of generalized least squares estimates (Table 4), we might argue that in comparison with OLS they had slightly higher determination coefficient (26.46% vs. 23.45%), which in simplicity means that they better fitted the data. All three information criteria were more than three time lower as well.  Table 4. Performance of generalized least squares Sum squared residuals 96878 S.E. of regression 2.01594 R-squared 0.2646 Adjusted R-square 0.264398 F (5.23838) 170.8712 P-valued (F) 3.40E-179 Log-likelihood -50546.86 Akaike criterion 101105.7 Schwarz criterion 101154.2 Hannan-Quinn 101121.4 Source: Processed by author. It might be concluded that generalized least squares performed better than OLS primarily due to the increase of determination coefficients and decline of information criteria.   Source: Processed by authors. Fig. 3. Actual vs. GLS fitted values by observation Investment Management and Financial Innovations, Volume 12, Issue 4, 2015 191  Source: Processed by authors. Fig. 4. GLS residuals by observation Conclusion Despite the ongoing uncertainty, corporations continue to massively offer their debt (Koblen, Szabo & Krná ová, 2013). In this work we aimed at analysis of impact of leading underwriter and bookrunners on primary bond yields using ordinary and generalized least squares. Obtained outcomes suggest that yield spreads are growing with size if the leader and  bookrunners. This fact might indicate, that issuers with worse credit rating and credit quality intentionally select larger issue leaders in order to cover the intended volume of issue. Based on obtained results it might be concluded that generalized least squares performed better than OLS primarily due to the increase of determination coefficients and decline of information criteria.  References 1. Andres, C. et al. (2014). Underwriter reputation and the quality of certification: Evidence from high-yield bonds, Journal of Banking & Finance, Vol. 40, pp. 97-115. 2. Beckman, J. et al. (2001). The influence of underwriter reputation, keiretsu affiliation, and financial health on the underpricing of Japanese IPOs, Pacific-Basin Finance Journal, 9 (5), pp. 513-534. 3. Carter, R., Manaster, S. (1990). Initial public offerings and underwriter reputation, The Journal of Finance, 45 (4), pp. 1045-1067. 4. Chen, Z., Wilhelm Jr, W.J. (2008). A theory of the transition to secondary market trading of IPOs, Journal of Financial Economics, 90 (3), pp. 219-236. 5. Chua, A. (2014). Market conditions, underwriter reputation and first day return of IPOs, Journal of Financial Markets, 19, pp. 131-153. 6. Hajduova, Z. (2014). Integrated cost model for improving the production in companies, Quality Innovation Prosperity, 18 (2), pp. 90-99. 7. Koblen, I., Szabo, S., & Krná ová, K. (2013). Selected information on European Union research and development programmes and projects focused on reducing emissions from air transport. Naše more, Znanstveno-stru ni asopis za more i pomorstvo, 60 (5-6), pp. 113-122. 8. Krigman, L. et al. (2001). Why do firms switch underwriters? Journal of Financial Economics, 60 (2), pp. 245-284. 9. Loureiro, G. (2010). The reputation of underwriters: A test of the bonding hypothesis, Journal of Corporate Finance, 16 (4), pp. 516-532. 10. McKenzie, C.R., Takaoka, S. (2008). Underwriter reputation and switching, Mathematics and Computers in Simulation, 78 (2), pp. 215-222. 11. Neupane, S., Thapa, C. (2013). Underwriter reputation and the underwriter-investor relationship in IPO markets, Journal of International Financial Markets, Institutions and Money, Vol. 24, pp. 105-126. 12. Roten, I.C., Mullineaux, D.J. (2002). Debt underwriting by commercial bank-affiliated firms and investment banks: More evidence, Journal of banking & finance, 26 (4), pp. 689-718. 13. Tká , M. (2001). Štatistické riadenie kvality. Ekonóm. 14. Wang, W., Yung, C. (2009). IPO Information Aggregation and Underwriter Quality, Review of Finance, 15 (2), pp. 301-325.  

Size of issue leader as determinant of debt offerings yields

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Size of issue leader as determinant of debt offerings yields

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