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down into a single number that expresses the probability and size of loss in the future.
There are six steps to forecasting risk:● Decompose each instrument into its fundamental categories of risk.
● Aggregate the exposures of all instruments in the portfolio into these categories.
● Combine exposures to risk factors and the joint characteristics of these risk factors.
● Understand what is normal or common variation within the system.
● Determine causes of special variation in a system.
● Forecast the movements in risk factors and special variation.The Value at Risk of a portfolio is a sum of the risks of the constituent instruments, where
the sum takes into account not only the risks of the individual instruments, but also the
cross-instrument interactions.● Delta normal Value at Risk, where risk is a linear combination of exposures.
● Historical simulation, which better allows for nonlinearities and nonnormality.
● Monte Carlo simulation and stress testing, which incorporates a range of risk types
and extreme scenarios.Most trading/investment systems, especially those that make use of leverage, are
subject to some form of VaR for trading limits. The real value of VaR is not in its cal-
culation of current risk, but in its calculation of what-if scenario risks, and therefore we
recommend Monte Carlo simulation, because (among other reasons) scenarios can be
used to perform kaizen improvement of the system. A new security or ETF or option
can be added to a VaR representation of a portfolio to generate a theoretical result.
Of course, over the long term the logic behind a systematic hedging strategy must be
backtested.26.4. Summary
Portfolios of securities and derivatives require constant monitoring. No system, no mat-
ter how well planned or well built should be left unattended. Calculations to monitor a
trading/investment system will be unique to the system itself, although systems of differ-
ent types—trigger, filter, signal strength—will have metrics in common. In any case, we
prefer graphical representation of complex calculations; interpreting graphs is easier than
interpreting data, especially time series data.● Is this system in conformance with the backtest?
● What performance calculations do I want to monitor?
● Is my system placing bets that I do not understand?
● If any of these three are out of control, how do I control and adjust my system?All the way back in K|V 1.2 the product team should have determined the monitoring
metrics and measurement components needed to provide evidence of conformity of prod-
uct to requirements. Risk managers will use performance and risk metrics to identify and
control nonconforming trading/investment systems to prevent losses.26.4. SUMMARY