24-08-2012, 04:04 PM
Dynamic Risk Management
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Abstract
Both financing and risk management involve promises to pay which need to be
collateralized resulting in a financing vs. risk management trade-off. We study this
trade-off in a dynamic model of commodity price risk management and show that
risk management is limited and that more financially constrained firms hedge less
or not at all. We document that these predictions are consistent with the evidence
using panel data for fuel price risk management by airlines. More constrained
airlines hedge less both in the cross section and within airlines over time. Risk
management drops substantially as airlines approach distress and recovers only
slowly after airlines enter distress.
Introduction
What determines the extent to which firms engage in risk management? A central insight
from the theoretical literature is that firms engage in risk management because financing
constraints render them effectively risk averse (see Froot, Scharfstein, and Stein (1993)).
This insight has motivated a large number of empirical papers; however, the empirical
findings do not support the prediction that firms more likely to face financial constraints,
such as small firms, are more likely to manage risk. Indeed, the main robust pattern that
emerges from this literature is that small firms engage in less risk management, leading
Stulz (1996) to conclude that “[t]he actual corporate use of derivatives, however, does
not seem to correspond closely to the theory.”
In this study, we theoretically and empirically challenge the notion that financial
constraints and risk management should be positively correlated. We provide a model
that predicts that risk management should be lower and even absent for firms that are
more financially constrained. The basic theoretical insight is that collateral constraints
link the availability of financing and risk management. More specifically, if firms must
have sufficient collateral to cover both future payments to financiers and future payments
to hedging counterparties, there is a trade-off between financing and risk management.
When net worth is low and the marginal value of internal resources is high, firms optimally
choose to use their limited net worth to finance investment at the expense of hedging.
Risk management: State of the literature
Much of the extant empirical literature on risk management has been guided by the
theoretical insights of Froot, Scharfstein, and Stein (1993). One of their central findings
is that “if external funds are more costly to corporations than internally generated funds,
there will typically be a benefit to hedging.” They and the empirical literature following
their work interpret this finding to imply a positive relation between measures of financial
constraints and risk management activity. In other words, if a firm is more financially
constrained, it should typically have more of a need for hedging. For example, in his
noted empirical study of risk management.
Dynamic risk management
We provide a dynamic model of firm financing and risk management in which firms
need to collateralize all promises. Firms’ financial constraints are the motive for risk
management. In the model, firms are subject to commodity price risk for an input used
in production as well as productivity risk,5 and choose their investment, financing, and
risk management policies given collateral constraints. Firms are effectively risk averse
in net worth and thus may hedge, despite the fact that in our model, consistent with
standard neoclassical production theory, profit functions are convex in input prices. The
model predicts a fundamental trade-off between financing and risk management: more
constrained firms should engage in less risk management, both in the cross section and
the time series.
Environment
Time is discrete and the horizon is infinite. The firm is risk neutral, subject to limited
liability, and discounts payoffs at rate 2 (0, 1). We write the firm’s problem recursively
and denote variables measurable with respect to next period with a prime. The firm has
access to a standard neoclassical production function with decreasing returns to scale.
Production requires capital k as well as an input good x0. An amount of capital k and
inputs x0 produce output b A0kbx0 where b > 0, > 0, and b+ < 1. Capital depreciates
at rate 2 (0, 1) and inputs are used up in production. The input has an exogenous price
p0 which is stochastic. The price of capital is normalized to 1. The price of the output
good is subsumed in the total factor productivity b A0 > 0 which is stochastic. We denote
the exogenous state by s (Aˆ, p) and assume that the state s 2 S follows a joint Markov
process where the transition probability from the current state s to state s0 next period
is denoted (s, s0).
The financing risk management trade-off
Our theory has two important implications. First, firms engage only in limited risk
management; indeed, the most striking observation about risk management is its absence.
Second, firms which are more financially constrained engage in less risk management,
that is, there is an important link between firm financing and risk management. These
implications are consistent with the basic size pattern reported in the literature and with
the detailed evidence on risk management by airlines that we provide.
Airline industry as an empirical laboratory
We test the predictions of our theory by examining fuel price risk management in the
airline industry. The airline industry offers an excellent laboratory for the following
reasons. First, as in our model, the cost of jet fuel is a major cost for airlines, comprising
on average 20% of costs and as much as 30% or more when oil prices are high. As a result,
jet fuel price volatility represents a major source of cash flow risk for airlines. Second,
more detailed data on the extent of risk management are available from airlines’ 10-K
SEC filings than for other firms. The data set is based on a hand-collected data set of U.S.
airlines’ Form 10-K, Item 7(A), which provides “Quantitative and Qualitative Disclosures
about Market Risk.” In particular, the time-series dimension of our panel data on the
extent of risk management, as opposed to only data on whether or not firms hedge, allows
us to study the within-firm relation between net worth and hedging. Third, focusing on
one industry holds constant characteristics of the economic environment, such as the
fraction of tangible capital and inputs used in production, that vary across industries.