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100 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS
costly) it is for a bank 248 to raise external funds (on short notice), the more
risk averse it will be with respect to fluctuations in its internal wealth. They
assume that a bank can enter into new lucrative transactions with an initial
cash investment I and a return f(I) that is a concave function. 249 I can be
funded by internal sources w stemming from the bank’s existing assets or by
raising external funds e that have convex costs c (Froot et al. [1993] specify
that function in the light of agency and information problems 250 ).
The bank’s problem is then:
g(w) = max[f(I)- I - c], subject to I = w + e (3.2)
It can be shown that g is a concave function 251 and that this shape creates
the rationale for risk management. Since c is convex, that is, the more costly
it is for the bank to raise external funds, the more the bank will want to
make sure that the fluctuations in its internal wealth w are limited in order
to have the funds available it needs for investment. The bank therefore cares
about the distribution of its end of investment horizon wealth and is not risk
neutral anymore.
The increasing costs to raising new external funds (both for debt and
equity) make the firm’s concern with risk management endogenous, 252 that
is, an integral part of the internal decision-making process. In order to avoid
these costs, a firm will behave in a risk-averse fashion 253 at the company
level (independent of the risk preferences of its stakeholders), even though
the firm’s objective function itself is not concave. 254
The necessity to generate sufficient internal funds from the existing assets
to finance planned investments is complicated by the fact that (financial)
risks cause volatility in the firm’s cash flows, which in turn causes difficul-
248 Froot et al. (1993) show the same line of reasoning for industrial corporation.
249 Here, Froot and Stein assume that the production technology of banks is concave
as it typically is for industrial companies.
250 They assume that cash flows are costlessly observable to company insiders, but
are observable to external creditors only at some cost. Cash flows from the existing
assets can be observed at a cost, but it is infinitely costly to observe the cash flows
from the new investment project. The difference between internal and external funding
costs will be greater for firms that are more leveraged and whose types of investment
are difficult for outsiders to evaluate and that offer relatively little tangible
collateral. See Froot et al. (1993), p. 1636.
251 See Froot and Stein (1998a), p. 61.
252 See Froot et al. (1993), p. 1632.
253 See Froot and Stein (1998a), p. 58. As Miller (1995), p. 484, points out correctly,
these costs (especially the underwriting costs) are relatively higher for smaller banks,
which should make them even more risk-averse than larger banks.
254 See Allen and Santomero (1996), p. 14.