23-RiskManagement Page 744 Wednesday, February 4, 2004 1:13 PM
744 The Mathematics of Financial Modeling and Investment Managementrisk can be eliminated by market mechanisms, while in an incomplete
market this is not possible.
It should be clear that the economic rationale for risk management
is different in different cases. There are essentially three possibilities.
First, risk can be transferred to firms that engineer a diversification ser-
vice. Insurance companies are the typical example. This means that
diversification is possible; that is, in the aggregate the residual risk is
very low simply because there are many uncorrelated events. For
instance, the residual risk of significant short-term fluctuations of the
average age of a population is very low except in exceptional cases (e.g.,
war or natural catastrophes). Thus life insurance is a statistically sound
business.
Second, risk can be transferred to “speculators” (e.g., persons or
entities who have a different risk-return profile or an information
advantage). Essentially, risks exist in aggregate but there are entities
willing to make bets on some portions of it. Note that if markets were
not correlated, there would be no risk in aggregate.
Third, risk can be transferred because there are positions that offset
each other in a true economic sense. In other words, there are “natural
hedges.” This means that the fluctuations of some basic variables create
simultaneous gains and losses approximately of the same size. This is
the case of interest rates. There are other cases, with more or less com-
plete natural hedges.WHY MANAGE RISK?
The basic motivation for risk management is financial optimization. In
this sense, the motivation for risk management has to be found in the
basic tenet of investment management: optimization of the risk-return
trade-off.
Financial optimization implies that a risk return trade-off indeed
exists. If some risk can be eliminated in aggregate, the market cannot
remunerate it. Therefore the assumption of that risk is always subopti-
mal and it should be eliminated. This is the case when risk can be diver-
sified away and when there are natural hedges, as in the case of interest
rates.
As risk management means the transfer of risk from one entity to
another, clearly if there is risk in aggregate there are limits to the size of
the risk management business. This is the case of the stock option busi-
ness. There is no natural hedge to stock market movements, at least
none has been discovered thus far. No financial agent profits from mar-