Optimal Resolutions of Financial Distress by Contract

We study theoretically the possibility for the parties to efficiently resolve financial distress by contract as opposed to exclusively rely on state intervention. We characterize which financial contracts are optimal depending on investor protection against fraud, and how efficient is the resulting resolution of financial distress. We find that when investor protection is strong, issuing a convertible debt security to a large, secured creditor who has the exclusive right to reorganize or liquidate the firm yields the first best. Conversion of debt into equity upon default allows contracts to collateralize the whole firm to that creditor, not just certain physical assets, thereby inducing him to internalize the upside from efficient reorganization. Concentration of liquidation rights on such creditor avoids costly inter-creditor conflicts. When instead investor protection is weak, the only feasible debt structure has standard foreclosure rights, even if it induces over-liquidation. The normative implications are that lifting legal restrictions on floating charge financing, convertibles and concentration of liquidation rights, and increasing investor protection against fraud should improve the efficiency of resolutions of financial distress.Corporate Bankruptcy, Creditor Protection, Financial Contracting

Optimal Portfolio Liquidation for CARA Investors

We consider the finite-time optimal portfolio liquidation problem for a von Neumann-Morgenstern investor with constant absolute risk aversion (CARA). As underlying market impact model, we use the continuous-time liquidity model of Almgren and Chriss (2000). We show that the expected utility of sales revenues, taken over a large class of adapted strategies, is maximized by a deterministic strategy, which is explicitly given in terms of an analytic formula. The proof relies on the observation that the corresponding value function solves a degenerate Hamilton-Jacobi-Bellman equation with singular initial condition.Liquidity; illiquid markets; optimal liquidation strategies; dynamic trading strategies; algorithmic trading; utility maximization

Topics in optimal liquidation and contract theory

The thesis consists of three parts. The first one presents an exhaustive study of three new models arising in the context of the so-called optimal liquidation problem. This is the problem faced by an investor who aims at selling a large number of stock shares within a given time horizon and wants to maximise his expected utility of the cash resulting from the sale. Such an investor has to take into account the impact that his selling strategy has on the underlying stock price. The models studied in the thesis assume that market risk follows a fairly general L´evy process and that the investor has an exponential utility. In each of the three different model formulations, an explicit or semi-explicit expression for the optimal liquidation strategy is derived. The second part of the thesis presents a study of an optimal liquidation problem embedded in a contractual problem. In particular, a contractual relationship between an investor and a broker is modelled on the basis of a suitable liquidation strategy and the corresponding affected mark-to-market assert price. The analysis of the model determines the broker’s compensation and the liquidation strategy that maximise the broker’s as well as the investor’s expected utilities. The third part of the thesis studies a continuous time principal-agent problem in which the agent’s outside options depend on his past performance. In this new model, even if the agent does not expect any compensation from the principal at all, the agent may still apply work effort with a view to improving his outside options. Formulated as an optimal control and stopping problem for both the agent and the principal, the optimal contract is identified

When is FDI a Capital Flow?

In this paper we analyze the conditions under which a foreign direct investment (FDI) involves a net capital flow across countries. Frequently, foreign direct investment is financed in the host country without an international capital movement. We develop a model in which the optimal choice of financing an international investment trades off the relative costs and benefits associated with the allocation and effectiveness of control rights resulting from the financing decision. We find that the financing choice is driven by managerial incentive problems and that FDI involves an international capital flow when these problems are not too large. Our results are consistent with data from a survey on German and Austrian investments in Eastern Europe

Numerical methods for an optimal order execution problem

This paper deals with numerical solutions to an impulse control problem arising from optimal portfolio liquidation with bid-ask spread and market price impact penalizing speedy execution trades. The corresponding dynamic programming (DP) equation is a quasi-variational inequality (QVI) with solvency constraint satisfied by the value function in the sense of constrained viscosity solutions. By taking advantage of the lag variable tracking the time interval between trades, we can provide an explicit backward numerical scheme for the time discretization of the DPQVI. The convergence of this discrete-time scheme is shown by viscosity solutions arguments. An optimal quantization method is used for computing the (conditional) expectations arising in this scheme. Numerical results are presented by examining the behaviour of optimal liquidation strategies, and comparative performance analysis with respect to some benchmark execution strategies. We also illustrate our optimal liquidation algorithm on real data, and observe various interesting patterns of order execution strategies. Finally, we provide some numerical tests of sensitivity with respect to the bid/ask spread and market impact parameters

Portfolio optimization in the case of an asset with a given liquidation time distribution

Management of the portfolios containing low liquidity assets is a tedious problem. The buyer proposes the price that can differ greatly from the paper value estimated by the seller, the seller, on the other hand, can not liquidate his portfolio instantly and waits for a more favorable offer. To minimize losses in this case we need to develop new methods. One of the steps moving the theory towards practical needs is to take into account the time lag of the liquidation of an illiquid asset. This task became especially significant for the practitioners in the time of the global financial crises. Working in the Merton's optimal consumption framework with continuous time we consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. While a standard Black-Scholes market describes the liquid part of the investment the illiquid asset is sold at a random moment with prescribed liquidation time distribution. In the moment of liquidation it generates additional liquid wealth dependent on illiquid assets paper value. The investor has the logarithmic utility function as a limit case of a HARA-type utility. Different distributions of the liquidation time of the illiquid asset are under consideration - a classical exponential distribution and Weibull distribution that is more practically relevant. Under certain conditions we show the existence of the viscosity solution in both cases. Applying numerical methods we compare classical Merton's strategies and the optimal consumption-allocation strategies for portfolios with different liquidation-time distributions of an illiquid asset.Comment: 30 pages, 1 figur

Optimal financial contracts for large investors: the role of lender liability

This paper explores the optimal financial contract for a large investor with potential control over a firm's investment decisions. The authors show that an optimally designed menu of claims for a large investor will include features resembling a U.S. version of lender liability doctrine, equitable subordination. This doctrine permits a firm's claimants to seek to subordinate a controlling investor's financial claim in bankruptcy court, but only under well-specified conditions. Specifically, the authors show that this doctrine allows a firm to strike an efficient balance between two concerns: (i) inducing the large investor to monitor, and (ii) limiting the influence costs that arise when claimants can challenge existing contracts in bankruptcy court. ; The paper also provides a partial rationale for a financial system in which powerful creditors do not generally hold blended debt and equity claims.Bank loans ; Bank investments ; Venture capital