Defining the risk factors

The risk factors should contain all market factors for which one wishes to assess risk.
This will depend upon the nature of one’s portfolio and what data is available. Important
variables are typically foreign-exchange (FX) and interest rates, commodity and
equity prices, and implied volatilities for the above. In many cases, the market factors
will consist of derived quantities, e.g. fixed maturity points on the yield curve and
implied volatilities, rather than directly observed market prices. Implied volatilities
for interest rates are somewhat problematic since a number of different mathematical
models are used and these models can be inconsistent with one another. It should
be noted that the risk factors for risk management might differ from those used for
pricing. For example, an off-the-run Treasury bond might be marked to market based
on a market-quoted price, but be valued for risk-management purposes from a curve
built from on-the-run bonds in order to reduce the number of risk factors that need
to be modeled.
A key requirement is that it should be possible to value one’s portfolio in terms of
the risk factors, at least approximately. More precisely, it should be possible to
assess the change in value of the portfolio that corresponds to a given change in the
risk factors. For example, one may capture the general interest-rate sensitivity of a
corporate bond, but not model the changes in value due to changes in the creditworthiness
of the issuer.
Another consideration is analytical and computational convenience. For example,
suppose one has a portfolio of interest-rate derivatives. Then the risk factors must
include variables that describe the term structure of interest rates. However, the
term structure of interest rates can be described in numerous equivalent ways, e.g.
par rates, zero-coupon discount rates, zero-coupon discount factors, etc. The choice
will be dictated by the ease with which the variables can be realistically modeled and
further computations can be supported.