Three essays on bankruptcy risk

Abstract Market prices of corporate bond spreads and of credit default swap (CDS) rates do not match each other. In this paper, we argue that the liquidity premium, the cheapest-to-deliver (CTD) option and actual market segmentation explain the pricing differences. Using the European transaction data from Reuters and Bloomberg, we estimate the liquidity premium that is time- varying and firm-specific. We show that when time-dependent liquidity premiums are considered, corporate bond spreads and CDS rates behave in a much closer way than previous studies have shown. We find that high equity volatility drives pricing differences that can be explained by the CTD option.

An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

A way to play bankruptcy problems.

The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

A Proportional Approach to Bankruptcy Problems with a guaranteed minimum

In a distribution problem, and specfii cally in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. The Constrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that no agent receives more than her claim, a problem that can arise when using the egalitarian division. We propose an alternative modi cation, by using a convex combination of P and EA. The recursive application of this new rule finishes at the CEA rule. Our solution concept ensures a minimum amount to each agent, and distributes the remaining estate in a proportional way. Keywords: Bankruptcy problems, Proportional rule, Equal Awards, Convex combination of rules, Lorenz dominance. JEL classi fication: C71, D63, D71.

Solidarity and uniform rules in bankruptcy problems

The idea of ensuring a guarantee (a minimum amount of the resources) to each agent has recently acquired great relevance, in both social and politi- cal terms. Furthermore, the notion of Solidarity has been treated frequently in redistribution problems to establish that any increment of the resources should be equally distributed taking into account some relevant characteris- tics. In this paper, we combine these two general concepts, guarantee and solidarity, to characterize the uniform rules in bankruptcy problems (Con- strained Equal Awards and Constrained Equal Losses rules). Keywords: Constrained Equal Awards, Constrained Equal Losses, Lower bounds, Bankruptcy problems, Solidarity. JEL classification: C71, D63, D71.

A New Approach for Bounding Awards in Bankruptcy Problems

The solution for the ‘Contested Garment Problem’, proposed in the Babylonic Talmud, suggests that each agent should receive at least some part of the resources whenever the demand overcomes the available amount. In this context, we propose a new method to define lower bounds on awards, an idea that has underlied the theoretical analysis of bankruptcy problems from its beginning (O’Neill, 1982) to present day (Dominguez and Thomson, 2006). Specifically, starting from the fact that a society establishes its own set of ‘Commonly Accepted Equity Principles’, our proposal ensures to each agent the smallest amount she gets according to all the admissible rules. As in general this new bound will not exhaust the estate, we analyze its recursive application for different sets of equity principles. Keywords: Bankruptcy problems, Bankruptcy rules, Lower bounds, Recursive process

Discrimination in Bankruptcy Situations

In a bankruptcy situation, not all claimants are affected in the same way. In particular, some depositors may enter into a situation of personal bankruptcy if they lose part of their investments. Events of this kind may lead to a social catastrophe. We propose discrimination among the claimants as a possible solution. A fact considered in the American bankruptcy law (among others) that establishes some discrimination on the claimants, or the Santander Bank that in the Madoff’s case reimbursed only the deposits to its particular customers. Moreover, the necessity of discriminating has already been mentioned in different contexts by Young (1988), Bossert (1995), Thomson (2003) and Pulido et al. (2002, 2007), for instance. In this paper, we take a bankruptcy solution as the reference point. Given this initial allocation, we make transfers from richer to poorer with the purpose of distributing not only the personal incurred losses as evenly as possible but also the transfers in a progressive way. The agents are divided into two groups depending on their personal monetary value (wealth, net-income, GDP or any other characteristic). Then, we impose a set of Axioms that bound the maximal transfer that each net-contributor can make and each net-receiver can obtain. Finally, we define a value discriminant solution, and we characterize it by means of the Lorenz criterion. Endogenous convex combinations between solutions are also considered. Keywords: Bankruptcy, Discrimination, Compensation, Rules JEL classification: C71, D63, D71.

The Simple Economics of Conglomeration with Bankruptcy Costs: Separate or Joint Financing?

Which projects should be financed through separate non-recourse loans (or limited- liability companies) and which should be bundled into a single loan? In the pres- ence of bankruptcy costs, this conglomeration decision trades off the benefit of co- insurance with the cost of risk contamination. This paper characterize this tradeoff for projects with binary returns, depending on the mean, variability, and skewness of returns, the bankruptcy recovery rate, the correlation across projects, the number of projects, and their heterogeneous characteristics. In some cases, separate financing dominates joint financing, even though it increases the interest rate or the probability of bankruptcy.

Conglomeration with bankruptcy costs: Separate or joint financing?

The paper analyzes the determinants of the optimal scope of incorporation in the presenceof bankruptcy costs. Bankruptcy costs alone generate a non-trivial tradeoff between thebenefit of coinsurance and the cost of risk contamination associated to joint financing corporate projects through debt. This tradeoff is characterized for projects with binary returns,depending on the distributional characteristics of returns (mean, variability, skewness, heterogeneity, correlation, and number of projects), the bankruptcy recovery rate, and the taxrate advantage of debt relative to equity. Our testable predictions are broadly consistentwith existing empirical evidence on conglomerate mergers, spin-offs, project finance, andsecuritization.

Five essays on bankruptcy

Chapter 2 Bankruptcy Initiation In The New Era of Chapter 11 2.1 Abstract The bankruptcy act of 1978 placed corporate managers (as debtor in possession) in control of the bankruptcy process. Between 2000 and 2001 managers apparently lost this control to secured creditors. This study examines financial ratios of firms filing for bankruptcy between 1993 and 2004 and tests the hypothesis that the change from manager to creditor control created or exacerbated the managerial (and dominant creditor) incentive to delay bankruptcy filing. We find a clear deterioration in the financial conditions of firms filing after 2001. This is consistent with managers (or creditors who control them) delaying filing for bankruptcy. We also observe patterns of operating losses and liquidations that suggest adverse economic consequences from such delay. Chapter 3 Bankruptcy Resolution: Priority of Claims with the Secured Creditor in Control 3.1 Abstract We present new evidence on the violation of priority of claims in bankruptcy using a sample of 222 firms that tiled for Chapter 11 bankruptcy over the 1993-2004 period. Our study reveals a dramatic reduction in the violations of priority of claims compared to research on prior periods. These results are consistent with changes in both court practices and laws transferring power to the secured creditors over our sample period. We also find an increase in the time from the date of a bankruptcy filing to reaching plan confirmation where priority is not violated. Chapter 4 Bankruptcy Resolution: Speed, APR Violations and Delaware 4.1 Abstract We analyze speed of bankruptcy resolution on a sample of 294 US firms filing for bankruptcy in the 1993-2004 period. We find strong association between type of Chapter II filing and speed of bankruptcy resolution. We also find that violations to the absolute priority rule reduce the time from bankruptcy filing to plan confirmation. This is consistent with the hypothesis that creditors are willing to grant concessions in exchange for faster bankruptcy resolution. Furthermore, after controlling for the type of filing and violations to the absolute priority rule, we do not find any difference in the duration of the bankruptcy process for firms filing in Delaware, New York, or other bankruptcy districts. Chapter 5 Financial Distress and Corporate Control 5.1 Abstract We examine the replacement rates of directors and executives in 63 firms filing for bank ruptcy during the 1995-2002 period. We find that over 76% of directors and executives are replaced in the four year period from the year prior to the bankruptcy filing through three years after. These rates are higher than those found in prior research and is consistent with changes in bankruptcy procedures and practice (i.e. the increased secured creditors control over the process due to both DIP financing and changes in the Uniform Commercial Code) having a significant impact on the corporate governance of firms in financial distress. Chapter 6 Financial Statement Restatements: Decision to File for Bankruptcy 6.1 Abstract On a sample of 201 firms that restated their financial statements we analyze the process of regaining investor trust in a two year period after the restatement. We find that 20% of firms that restate their financial statements tile for bankruptcy or restructure out of court. Our results also indicate that the decisions to change auditor or management is correlated with a higher probability of failure. Increased media attention appears to partly explain the decision of firms to restructure their debt or tile for bankruptcy.

Compromise solutions for bankruptcy situations: a note

Although classic bankruptcy problems take into account a single claims vector, Pulido et al. (2008) show that there are real bankruptcy situations where agents face more than one reference vector. In particular, they consider the claims and an additional reference vector. To analyze these situations, they propose the extreme and the diagonal approaches. Nonetheless, the former approach depends on the order of the vectors: if we interchange the claims and the reference vectors, the result changes. Moreover their study is limited to the case in which the reference vector is lower than the claims vector. In the present note, we propose an extension that solves these short- comings by introducing the idea of impartiality. Keywords: bankruptcy problems; reference point; compromise solution; impartiality.

The Omega model: from bankruptcy to occupation times in the red

Ruin occurs the first time when the surplus of a company or an institution is negative. In the Omega model, it is assumed that even with a negative surplus, the company can do business as usual until bankruptcy occurs. The probability of bankruptcy at a point of time only depends on the value of the negative surplus at that time. Under the assumption of Brownian motion for the surplus, the expected discounted value of a penalty at bankruptcy is determined, and hence the probability of bankruptcy. There is an intrinsic relation between the probability of no bankruptcy and an exposure random variable. In special cases, the distribution of the total time the Brownian motion spends below zero is found, and the Laplace transform of the integral of the negative part of the Brownian motion is expressed in terms of the Airy function of the first kind.

Bankruptcy prediction using fuzzy methods

In this thesis, a classi cation problem in predicting credit worthiness of a customer is tackled. This is done by proposing a reliable classi cation procedure on a given data set. The aim of this thesis is to design a model that gives the best classi cation accuracy to e ectively predict bankruptcy. FRPCA techniques proposed by Yang and Wang have been preferred since they are tolerant to certain type of noise in the data. These include FRPCA1, FRPCA2 and FRPCA3 from which the best method is chosen. Two di erent approaches are used at the classi cation stage: Similarity classi er and FKNN classi er. Algorithms are tested with Australian credit card screening data set. Results obtained indicate a mean classi cation accuracy of 83.22% using FRPCA1 with similarity classi- er. The FKNN approach yields a mean classi cation accuracy of 85.93% when used with FRPCA2, making it a better method for the suitable choices of the number of nearest neighbors and fuzziness parameters. Details on the calibration of the fuzziness parameter and other parameters associated with the similarity classi er are discussed.