One
of the few VaR methodologies to satisfy all four of the criteria for a
coherent risk measure
(As defined by Artzner,
Delbaen, Eber and Heath, Risk Magazine November 1997) |
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Sub-additivity |
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Homogeneity |
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Monotonicity |
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Risk-free
condition |
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CrashMetrics is the only
real-time VaR methodology to focus on the events that wipe out major institutions.
We provide on-site training in implementing this methodology and full data
sets across major markets. Email CrashM@paulwilmott.com
for details. |
A few examples
of recent dramatic
falls in the
S&P500
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STOP PRESS
"When we examine banks, we expect them
to have systems in place that take account of outsize market moves." Alan
Greenspan in response to the Long-Term Capital Management fiasco.
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What
is CrashMetrics?
The
normal relationship between market variables is different under stress
or ‘crash’ conditions. As such, any statistical measures used to determine
how a portfolio value will respond to a crash should be derived solely
from the extreme values of the historical data in parameters measurement
and crash protection. Yet it is precisely these ‘outliers’ that are often
treated with little respect. Furthermore, it is common experience that
it is far easier to predict the results of an extreme event, a market crash
or a hurricane, than it is to predict the probability of such an event.
It would be nice not to rely too heavily on a poor estimate of a probability
when we are talking about the scenarios that could result in the collapse
of a bank.
The
CrashMetrics concept can be applied to both trading and hedging of crash
events but the simplest and most obvious application of CrashMetrics
is the estimation of the value at risk of a portfolio. In creating
CrashMetrics, we are aware of the need for an intuitive tool that
is easily communicated and accepted in the real world. There will be points
of discussion in the model, as there should be in any useful mathematical
model approximating the real world, but the framework is such that the
model can be readily adapted and extended to the needs of the individual
institution. Loosely
speaking, Value at Risk, or VaR, is ‘an estimate, with a given
degree of confidence, of how much one can lose from one’s portfolio over
a given time horizon.’ There have been many suggestions for how to
estimate VaR, every bank and academic has their own preferred version.
Whatever the precise details of the implementation, the data required for
the calculations are typically parameters for the ‘underlyings’ and measures
of a portfolio’s current exposure to these underlyings. The parameters
include volatilities and correlations of the assets, and, for longer time
horizons, drift rates. The exposure of the portfolio is measured by the
deltas, and, if necessary, the gammas (including cross derivatives) and
the theta of the portfolio.
The acknowledged problems
with most VaR measures concern the estimation of parameters and of distribution
of returns. Rarely are the parameters such as volatility and correlation
stable, it is even questionable whether they exist. Moreover the common
assumption of Normality of returns is easily shown to be incorrect. Almost
all financial time series data shows fatter tails and higher peaks. Even
if returns were Normal, the existence of nonlinear products, such as options,
in a portfolio distorts the distribution to such an extent that Normality
is irrelevant.
There have been numerous
attempts to modify the simple VaR assumptions to correct for these problems.
Unfortunately, none of them are consistently successful. In the technical
report which can be downloaded from this site, we outline the new CrashMetrics
methodology. We ask what are we trying to achieve when we estimate VaR
and can we reduce or even eliminate dependence on any quantities which
we cannot accurately measure? If Value at Risk is about normal market
conditions then Crashmetrics is the opposite side of the coin, it is about
‘fire sale’ conditions and the far-from-orderly liquidation of assets in
far-from-normal conditions. CrashMetrics is a dataset and methodology for
estimating the exposure of a portfolio to extreme market movements or crashes.
Practitioners enjoying the
sun in South Africa while learning about CrashMetrics
Key points in the CrashMetrics
methodology are the following.
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We assume that the crash is
unhedgeable
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We determine the worst outcome
for the value of the portfolio, either in paper-value or margin-call terms
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Parameters such as volatility
and correlation play no part
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There are few assumptions made
about the distribution of returns
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The method shows how to mitigate
the effects of the crash by the purchase or sale of derivatives in an optimal
fashion, so-called Platinum Hedging
Derivatives have sometimes been
thought of as being a dangerous component in a portfolio, in the CrashMetrics
methodology they are put to a benign use.
Download
CrashMetrics dataset (29k)
Download
Technical Report (154k)
Download
Demonstration spreadsheet (73k)
CrashMetrics
is a registered trademark.
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