Dynamic Risk Management: Investment, Capital Structure, and Hedging in the Presence of Financial Frictions

• Date: 01 June 2015
• Author: Thomas‐Olivier Léautier,Diego Amaya,Geneviève Gauthier
• DOI: http://doi.org/10.1111/jori.12025
• Published date: 01 June 2015

©2014 The Journal of Risk and Insurance. Vol.82, No. 2, 359–399 (2015).

DOI: 10.1111/jori.12025

Dynamic Risk Management: Investment, Capital

Structure, and Hedging in the Presence of

Financial Frictions

Diego Amaya

Genevi`

eve Gauthier

Thomas-Olivier L´

eautier

Abstract

This article develops a dynamic risk management model to determine a firm’s

optimal risk management strategy.This strategy has two elements. First, for

low-leverage values, the firm fully hedges its operating cash flow exposure,

due to the convexity of its cost of capital. When leverage exceeds a very high

threshold, the firm gambles for resurrection and stops hedging. Second, the

firm manages its capital structure through dividend distributions and in-

vestment. When leverage is low, the firm replaces depreciated assets, fully

invests in opportunities if they arise, and distribute dividends, all of these to-

gether to achieve its optimal capital structure. As leverage increases, the firm

stops paying dividends, while fully investing. After a certain leverage, the

firm also reduces investment until it stops investing completely. The model

predictions are consistent with empirical observations.

Introduction

Risk management is a critical issue for all firms. Over the last 15 years, many

financial and nonfinancial firms have adopted an integrated approach to measure

and manage all their risks, called enterprise risk management (ERM). The definition

of risk management is now broader; it includes not only derivatives usage, but also

the choice of capital structure, the constitution of cash reserves and lines of credit,

the structuring of the insurance portfolio, and sometimes operational policies (see,

Diego Amaya is in the Finance Department, Universit´

eduQu´

ebec `

a Montr´

eal (UQAM), Qu´

ebec,

Canada. Genevi`

eve Gauthier is in the Department of Management Sciences, HEC Montr´

eal,

and GERAD Qu´

ebec, Canada. Thomas-Olivier L´

eautier is at the ToulouseSchool of Economics

(IDEI-IAE-CRM), France. Diego Amaya can be contacted via e-mail: amaya.diego@uqam.ca.

Diego Amaya would like to thank FQRNT and IFM2for financial support. Genevi`

eve Gau-

thier would like to thank NSERC and IFM2for financial support. An earlier version of this

article was circulated under the title, “Coordinating Capital Structure With Risk Management

Policies.” We thank seminar participants at the Annual Conference on Risk Management and

Corporate Governance, the Annual Australasian Finance and Banking Conference, and the

Midwest Financial Association meetings for their comments on earlier versions of this article.

Any remaining inadequacies are ours alone.

359

360 The Journal of Risk and Insurance

e.g., Léautier, Rochet, and Villeneuve, 2007; Pettit, 2007; Hyot and Liebenberg, 2011;

Paape and Spekte, 2012 and the references they contain).

A rich academic literature (reviewed later in this section) has accompanied this cor-

porate interest in risk management. Numerous articles have identified fundamental

financial frictions that justify risk management (e.g., tax shield from debt, bankruptcy

and business disruption costs, costly external financing, asymmetry of information

between managers/insiders and investors/outsiders), and have derived the optimal

risk management strategy, given these frictions.

This article attempts to better relate corporate practice and finance theory of risk man-

agement. It proposes a reduced form model that represents what managers of large

publicly traded firms actually do. As reported by Graham and Harvey’s (2001) survey,

chief financial officers ( CFOs) are agnostic as to the origin of financial frictions. They

simply observe that the weighted average cost of capital (WACC)is a U-shaped func-

tion of the firm’s leverage ratio (Graham and Harvey, 2001; Cohen, 2004; Pettit, 2007,

pp. 110–111, 141–159). Takingthis observation as given, they make capital budgeting,

dividend distribution, and hedging decisions to maximize the expected net present

value (NPV) of the free cash flows, facing uncertainty about both future cash flows

and future investment opportunities, and the possibility of bankruptcy. This repre-

sentation of managerial decision-making cannot be derived from micro-foundations.

Yet, it provides valuable insights for it captures most of the real features of corpo-

rate decision-making; hence, the analysis’ predictions can be compared against actual

firms’ behavior, as captured by previous empirical studies.

This article first determines analytically the optimal risk management strategy, that

is, the mix of hedging, dividend distribution, refinancing, and investment policies.

Second, it illustrates the optimal strategy for a “representative” industrial firm, using

estimates of the main model parameters. Finally,it shows that the model’s predictions

are consistent with empirical observations.

The main result of this article is the optimal risk management strategy, which is

surprisingly simple. First, dividend distribution and investment jointly follow four

regimes (Proposition 1). For low leverage, the firm enjoys full financial flexibility: it fully

finances its investment needs and distributes dividends to reach its optimal leverage

ratio. For intermediate leverage, the firm faces financial tightness: it still fully finances

its investment needs but no longer distributes dividends, as leverage increases from

one period to the next. For higher leverage, the firm faces a financial constraint:itisno

longer able to fully finance its investment needs. The portion it finances is determined

to reach a target leverage, after which the marginal value of investing becomes nega-

tive. Finally, for high leverage, the firm faces financial hardship: it is no longer able to

finance any of its investment needs, not even depreciation.

Second, full hedging is optimal unless leverage gets higher than some threshold, in

which case gambling for resurrection becomes optimal (Proposition 2). These results

differ from previouswork (e.g., Bolton, Chen, and Wang, 2011; Rochet and Villeneuve,

2011), who find that when the firm’s cash reserve (or cash-to-capital ratio in Bolton et

al., 2011) is high enough, the firm becomes risk neutral and, since hedging is costly,

Dynamic Risk Management 361

stops hedging. In our model, the tax shield drives the concavity of the value function;

hence, the optimality of full hedging. By choosing leverage as the state variable, we

are able to capture the tax shield from debt, a real effect absent from Rochet and

Villeneuve (2011) and Bolton et al. (2011).

An essential finding of the analysis is that if the firm’s expected profitability is lower

than a threshold (function of the magnitude of its investment opportunity), the firm

does not exhaust the benefits of the tax shield; rather, it keeps an equity cushion

(Proposition 3): the optimal leverage target is lower than the static optimum that

minimizes the cost of capital.

The analysis enables us to estimate the value of hedging: a firm that fully hedges its

risk can increase its optimal leverage, which results in lower cost of capital, hence,

higher value.

The implications of the model are consistent with previously reported empirical find-

ings. First, Proposition 1 predicts that, ceteris paribus, dividend distribution decreases

when firms are less profitable on average or face higher investment opportunities,

which is confirmed by Fama and French (2002). Second, the importance of corporate

taxes in the decision to hedge (Proposition 2) is confirmed empirically by Graham

and Rogers (2002). Third, Graham (2000) reports that even profitable firms with low

expected cost of financial distress hold an equity cushion, consistent with our model

(Proposition 3). Finally, the numerical example developed in the article suggests the

value of hedging is around 5 percenton average, consistent with Allayanis and Weston

(2001).

As mentioned earlier, this article builds on a rich theoretical and empirical literature.

Most of the results hinge on the fact that the firm’s value is a concave function of

leverage with a unique maximum. In this model, the concavity of this function is

caused by the convexity of the expected return required by investors, itself motivated

by empirical considerations. Three families of theoretical models also produce value

functions of similar shape.

The first family of models develops the trade-off theory of capital structure (Leland,

1994, 1996; Leland and Toft, 1996): optimal capital structure trades-off the tax advan-

tage of debt against the direct and indirect bankruptcy costs. Since interest are tax

deductible, debt creates a tax shield. While there is no consensus on the appropriate

discount rate for the tax shield (Welch, 2008, pp. 504–507), all agree that the value of

the tax shield; hence, the value of the firm, increases with the leverage. On the other

hand, as leverage increases, so do the probability of bankruptcy and business disrup-

tion costs. In addition, firms may engage in risk-shifting behavior, choosing riskier

strategies that benefit shareholders at the expense of bondholders. Incorporating all

these effects, Leland (1996) derives the value of risky debt, the value of equity, and

the optimal capital structure and risk management strategy.

The second family of models relies on costly external financing. The interaction be-

tween costly external financing, underinvestment, and risk management was first

modeled in a two-period environment by Froot, Sharfstein, and Stein (1993) and Froot