Liquidity Risk and Corporate Demand for Hedging and Insurance Essay

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Liquidity Risk and Corporate Demand for Hedging and Insurance∗

Jean-Charles Rochet† and St´phane Villeneuve‡ e

First Version: January 8, 2004 This Version: May 17, 2004

∗ Acknowledgments: We thank Bruno Biais, Charles Goodhart and Jean Tirole for their comments, as well as seminar participants at the LSE (FMG) and Toulouse University. † Toulouse University, (IDEI, GREMAQ) and Toulouse Business School. ‡ Toulouse University (GREMAQ).

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Liquidity Risk and Corporate Demand for Hedging and Insurance Abstract: We analyze the demand for hedging and insurance by a corporation that faces liquidity risk. Namely, we consider a firm that is solvent (i.e. exploits a technology with positive expected net present value) but potentially illiquid (i.e. that may face a borrowing constraint). As a result, the firm’s optimal liquidity management policy consists in accumulating reserves up to some threshold and distribute dividends to its shareholders whenever its reserves exceed this threshold. We study how this liquidity management policy interacts with two types of risk: a Brownian risk that can be hedged through a financial derivative, and a Poisson risk that can be insured by an insurance contract. We derive individual demand functions for hedging and insurance by corporations. We show that there is a finite price above which both demand functions are zero. Surprisingly we find that the patterns of insurance and hedging decisions as a function of liquidity are pole apart: cash poor firms should hedge but not insure, whereas the opposite is true for cash rich firms. We also find non monotonic effects of profitability and leverage. This may explain the mixed findings of empirical studies on corporate demand for hedging and insurance: linear specifications are bound to miss the impact of profitability and leverage on risk management decisions.

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Introduction

Corporate risk management has been the subject of a large academic literature in the last twenty years. This literature aims at filling the gap between the irrelevance results derived from the benchmark of perfect capital markets (Modigliani and Miller, 1958) and the practical importance of risk management decisions in modern corporations. Several directions have been explored for explaining how and why firms should hedge their risks:1 • managerial risk aversion (Stulz, 1984), • tax optimization (Smith and Stulz, 1985), • cost of financial distress (Smith and Stulz, 1985), • cost of external financing (Stulz, 1990; Froot, Scharfstein and Stein, 1993).2 A few papers have applied these ideas to model corporate demand for insurance.3 The testable implications derived from these models are different, but there is now a consensus among financial economists that profitability and leverage should be important determinants of firms’ hedging and insurance policies. All of the above theories predict indeed that more profitable firms should hedge less and that more leveraged firms should hedge more. However this is not confirmed by the data. Indeed, although the empirical literature (see for example Tufano 1996 and Geczy et al. 1997) typically finds that liquidity is an important determinant of hedging (more liquid firms hedge less), leverage does not seem to have a clear and robust impact on hedging decisions. The main objective of this paper is to show that when liquidity management and risk management decisions are endogenized simultaneously, the theoretical impact of profitability and leverage is non monotonic: the firms that gain the most from actively managing their risks are not the less profitable nor the most indebted. Moreover when insurance decisions are explicitly modeled, we find that the optimal patterns of hedging and insurance decisions by firms are exactly opposite: cash poor firms should hedge but not insure, whereas the opposite is true for cash rich firms. Thus the relation between liquidity, leverage and optimal risk management decisions of firms may be more complex than
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