Advances in Risk Management

224 EVALUATING VALUE-AT-RISK ESTIMATES: A CROSS-SECTION APPROACH

Then compute the derivative∂D

j

t,t+H/∂w

s

t, that, for assetkis given by:

rkt,t+H−

∂VaRt,t+H

∂wst(k)

(11.15)

It is easy to notice that (24.15) is simply the difference between the actual
return on assetkand its marginal VaR, that is the change in portfolio VAR
resulting from a marginal change in a given position. Ranking all the securi-
ties on the basis of (11.15) can be of help to understand where a model fails,
and can suggest improvements to the model itself.
There are other applications. In order to chose the appropriate VaR model,
several models can be put in competition and in a reasonable time one can
collect a large amount of information about their behavior. As no financial
model is strictly true, this kind of testing procedure should provide support
as to choosing the most appropriate model.

11.6 Conclusion

We have presented an approach to backtesting VaR models that introduces
a new perspective on models’ behavior, as it is performed as a kind of
cross-section analysis of randomly generated portfolios. With this approach,
regulators and financial institutions can use basically all the existing tech-
niques, augmented by extra information coming from the cross-sectional
analysis.
Asidefromformaltesting, thiskindofapproachtobacktestingcanhelpto:

understand quickly if a model does work;

learn how and under what conditions models fail;

track their performance over time using detailed information coming
from many portfolios;

test global risk models simultaneously on more markets and asset classes;
and

discriminate among competing VaR models (as no financial model is ever
factually true), helping in the choice of the best model.

REFERENCES

Berkowitz, J. (2001) “Testing Density Forecasts with Application to Risk Management”,
Journal of Business and Economic Statistics, 19(4): 465–74.
Campbell, S.D. (2005) “A Review of Backtesting Procedures”,Finance and Economic
Discussion Series(Washington, DC: Federal Reserve Board).