A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Medhat, Mamdouh Doctoral Thesis Measuring and Pricing the Risk of Corporate Failures PhD Series, No. 12.2015 Provided in Cooperation with: Copenhagen Business School (CBS) Suggested Citation: Medhat, Mamdouh (2015) : Measuring and Pricing the Risk of Corporate Failures, PhD Series, No. 12.2015, ISBN 9788793339071, Copenhagen Business School (CBS), Frederiksberg, http://hdl.handle.net/10398/9137 This Version is available at: http://hdl.handle.net/10419/208930 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. 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Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/ www.econstor.eu COPENHAGEN BUSINESS SCHOOL FAILURES MEASURING AND PRICING THE RISK OF CORPORATE SOLBJERG PLADS 3 DK-2000 FREDERIKSBERG DANMARK WWW.CBS.DK ISSN 0906-6934 Print ISBN: 978-87-93339-06-4 Online ISBN: 978-87-93339-07-1 Mamdouh Medhat MEASURING AND PRICING THE RISK OF CORPORATE FAILURES The PhD School of Economics and Management PhD Series 12.2015 PhD Series 12-2015 Measuring and Pricing the Risk of Corporate Failures Mamdouh Medhat1 PhD Dissertation November 3, 2014 1Financial support from the FRIC Center for Financial Frictions (grant no. DNRF102) is gratefully acknowledged. Correspondence: Mamdouh Medhat, Department of Finance, Copenhagen Business School, Solbjerg Plads 3A, DK-2000 Frederiksberg, Denmark. Phone: +45 3162 4294. Email: mme.fi@cbs.dk. Website: http://sf.cbs.dk/mmedhat. Mamdouh Medhat MEASURING AND PRICING THE RISK OF CORPORATE FAILURES 1st edition 2015 PhD Series 12.2015 © The Author ISSN 0906-6934 Print ISBN: 978-87-93339-06-4 Online ISBN: 978-87-93339-07-1 “The Doctoral School of Economics and Management is an active national and international research environment at CBS for research degree students who deal with economics and management at business, industry and country level in a theoretical and empirical manner”. All rights reserved. No parts of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval system, without permission in writing from the publisher. Contents Preface 5 Literature review 9 1 Additive Intensity Regression Models in Corporate Default Analysis 25 1.1 Introduction ........................................... 25 1.2 General model setup ...................................... 26 1.2.1 Relative and excess survival regression: The Cox and Aalen models ......... 27 1.2.2 Contrasting the Cox and the Aalen models ....................... 28 1.2.3 Frailty and dynamic effects ............................... 29 1.3 Additive regression models ................................... 29 1.3.1 The nonparametric additive regression model ..................... 30 1.3.2 The semiparametric additive regression model ..................... 35 1.4 Data and model specification .................................. 38 1.4.1 Data ........................................... 39 1.4.2 Nonparametric Aalen analysis ............................. 44 1.4.3 Semiparametric Aalen analysis ............................. 48 1.5 Model check ........................................... 50 1.5.1 Covariate misspecifications: Grouped martingale residual processes ......... 51 1.5.2 The model fit as a whole: Model-based covariance of residual processes ....... 51 1.5.3 Outliers and over-influence: Diagonal cumulative hat processes ........... 52 1.6 Revising the model ....................................... 52 1.6.1 Martingale residual processes ............................. 52 1.6.2 Model-based covariance of residual processes ..................... 54 1.6.3 Diagonal cumulative hat processes ........................... 55 1.6.4 Analysis based on clean data .............................. 55 1.7 Conclusion ........................................... 57 2 Cyclicality and Firm-size in Private Firm Defaults 61 2.1 Data and methodology ..................................... 63 2.1.1 Firm-specific explanatory variables .......................... 65 2.1.2 Macroeconomic explanatory variables ......................... 66 2.1.3 Estimation of firm-specific default intensities ..................... 66 2.2 Default prediction for private firms ............................... 69 2.2.1 Using accounting ratios alone ............................. 69 3 2.2.2 Including macroeconomic variables .......................... 70 2.2.3 Ranking firms with respect to default likelihood .................... 74 2.3 The macroeconomy’s impact on small and large firms’ default risk .............. 75 2.3.1 Macro-sensitivity analysis based on the Cox model .................. 77 2.3.2 Macro-sensitivity analysis based on the additive Aalen model ............ 80 2.4 Robustness and model check .................................. 82 2.4.1 Alternative criteria for defining small and large firms ................. 82 2.4.2 Independent censoring and entry-pattern ........................ 85 2.4.3 Lag length ....................................... 85 2.4.4 Grouped martingale residual processes ........................ 86 2.5 Concluding remarks ....................................... 86 3 Liquidity Risk and Distressed Equity 91 3.1 Model .............................................. 95 3.2 Theoretical results ........................................ 98 3.2.1 Optimal policies .................................... 98 3.2.2 Expected returns under the optimal policies ......................101 3.3 Data and variables ........................................107 3.3.1 Data ...........................................107 3.3.2 Measuring solvency and liquidity ...........................108 3.4 Empirical results ........................................111 3.4.1 Conditional betas ....................................112 3.4.2 Fama-MacBeth regressions ...............................112 3.4.3 Portfolio returns and alphas ..............................117 3.4.4 Long-short portfolios ..................................121 3.5 Concluding remarks .......................................125 Appendices 127 A Additional details and proofs ..................................129 A.1 Change of measure ...................................129 A.2 Proof of Proposition 1 .................................129 A.3 Proof of Proposition 2 .................................131 A.4 Proof of Proposition 3 .................................134 A.5 Proof of Proposition 4 .................................135 4 Preface These writings constitute my PhD dissertation in financial economics. The dissertation consists of three chapters. Each chapter can be read independently of the others, but all three chapters share the dissertation’s overall topic: Measuring and pricing the risk of corporate failures. The ability to adequately measure and price the risk of corporate failures is vital for creditors, sharehold- ers, and regulators of financial institutions. Whenever a firm uses debt instruments such as loans or bonds to finance its operations, the firm may fail to meet the debt’s contractual obligations. Typically, a failure is in the form of a default on a payment of interest or principle, but can also be a violation of a covenant attached to the debt or a bankruptcy filing by the firm or by the creditors on behalf of the firm. If a firm fails, it may be forced to temporarily or permanently halt its operations, which can entail losses: Creditors may realize a loss on their promised payments, while shareholders may see their entire equity stake wiped out. Therefore, creditors and shareholders need to adequately measure the risk of a failure, so that this risk can be reflected in the prices they are willing to pay—and the returns they require—for holding a firm’s financial securities. At the same time, regulators must be able to verify that a financial institution is adequately cushioned against this risk, so that losses do not destabilize an important institution or even the financial system itself. The overall questions addressed in this dissertation are, then, how should we adequately measure the risk of corporate failures, and, is the risk of corporate failures adequately reflected in the market prices of financial securities? As a testimony to the importance of these questions, they have been at the center of much academic and regulation-oriented research since the late 1960s. The chapters of this dissertation thus constitute three contributions to this still highly active field of research within financial economics: Chapters 1 and 2 contribute