The Mathematics of Financial Modelingand Investment Management

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23-RiskManagement Page 753 Wednesday, February 4, 2004 1:13 PM


Risk Management 753

the probability distribution, the more measures required. Over a period
of several months—a typical time horizon for asset management—distri-
butions are assumed to be Gaussian and that one risk measure suffices.
But phenomena such as volatility clustering, trend reversals, large move-
ments, and structural breaks produce distributions that are not Gaussian.
There is a need to measure what might happen at the extremes. It is not
infrequent that single risk measures such as variance or VaR are being
complemented by scenario analysis to evaluate the risk of extreme move-
ments.
In addition, a single measure might not be equally appropriate for
all investment styles. For example, firms focused on emerging markets
might use information ratios, which reflect returns on assets, to comple-
ment tracking error. Multiple measures might be required by (institu-
tional) clients. Tracking error and information ratios or volatility are
considered standard in some markets and an increasing number of cli-
ents are asking for VaR. VaR is required in managing funds for endow-
ments and foundations with a statutory requirement to generate positive
returns; in Germany, VaR measures are now regulatory for funds man-
aging the investments of depository institutions. Multiple measures
might be requested by fund managers themselves, in an attempt to
improve their performance.
In some instances, it’s important to understand in absolute terms
how much money might be lost. This is the case with guaranteed-return
funds or funds being managed for the parent company, for example, an
insurance firm or investment bank. A few firms are using EVT; the
objective is to ensure the ability to survive a market crash. One might
want to be able to take into account different aspects or different views.
VaR allows a uniform measure of risk across asset classes. Though with
time horizons of 2–3 months volatility clustering phenomena disappear,
ARCH-GARCH models are being used at some firms to gain an under-
standing of the clustering of risk.

Getting Down to the Lowest Level
Risk and performance are increasingly being measured at lower levels.
Instead of looking at sector levels (e.g., geographical areas, currency or
industry sector), firms are beginning to look at the single-asset level.
While most firms are not there yet, this is the declared goal.
There is also a tendency at producing risk numbers daily, with daily
reporting to fund managers, monthly to management, and (typically)
quarterly to clients. Investment consultants and regulators consider it
fundamental that asset managers be aware of the risk at all times, but
not everyone agrees that crunching out the numbers daily is appropriate
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