Ciencias

American Finance Association

Optimal Risk Management Using Options
Author(s): Dong-Hyun Ahn, Jacob Boudoukh, Matthew Richardson, Robert F. Whitelaw
Reviewed work(s):
Source: The Journal of Finance, Vol. 54, No. 1 (Feb., 1999), pp. 359-375
Published by: Blackwell Publishing for the American Finance Association
Stable URL: http://www.jstor.org/stable/222420 .
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THE JOURNALOF FINANCE * VOL. LIV,NO. 1 * FEBRUARY1999

Optimal Risk Management

Using Options

DONG-HYUN AHN,JACOB BOUDOUKH, MATTHEW RICHARDSON,
and ROBERT F. WHITELAW*
ABSTRACT
This article provides an analytical solution to the problem of an institution optimally managing the market risk of a given exposure by minimizing its Value-atRisk using options. The optimal hedge consists of a position in a single option
whose strike price is independent of the level of expense the institution is willing
toincur for its hedging program. This optimal strike price depends on the distribution of the asset exposure, the horizon of the hedge, and the level of protection
desired by the institution. Moreover,the costs associated with a suboptimal choice
of exercise price are economically significant.

H
ONLY ECENTLY AVE CADEMICSegun to study the risk management practices
R
A
b
of financialinstitutions and other corporations.1 This is surprising given
that for some time now, according to recent surveys (Smithson (1996a, 1996b)),
the majority of firms have been applying modern financial techniques to
managing some of their exposure to interest rates, equities, or exchange
rates. One of the difficulties in analyzing these institutions' risk management programs is that their concept ofrisk is quite different from the standard measures implied by multifactor pricing models. Ceteris paribus,
according to modern finance theory, it is cheaper for shareholders to diversify project risks on their own. Thus, a company's need to hedge either the
systematic or unsystematic risk of its cash flows is limited.
However, there are several reasons why this standard argument may not
holdtrue.2 First, to avoid costly external financing, firms may need risk
is,
management programs to maintain their access to cheap capital-that
internal funds (Froot et al. (1993) and Stulz (1990)). Second, in order to
reduce the value of the government's implicit call option on the firm's assets
* Ahn is from the University of North Carolina, Chapel Hill; Boudoukh is from New York
University andthe NBER; Richardson is from New York University and the NBER; and Whitelaw is from New York University. We thank Bruce Grundy, Eli Ofek, Oded Sarig, Tony Saunders, the editor, Ren6 Stulz, the referee, seminar participants at the Finance and Accounting
Conference at Tel Aviv University, and the discussant Ma'ayana Weisman for helpful comments
and suggestions.
1 See Allayannis and Ofek (1996),DeMarzo and Duffie (1995), Froot, Scharfstein, and Stein
(1993), May (1995), Mian (1996), Smith and Stulz (1985), Stulz (1990), and Tufano (1996),
among others, for a discussion of the underlying theory and empirics for why firms may have
incentives to hedge, and, given these incentives, how firms implement the hedges.
2 See Stulz (1997) for a general overview of institutions'
risk...