Market Risk
Chapter 1 defi ned value at risk (VaR) as the maximum potential loss that a business unit
or a position can generate in a given time horizon within a defi ned percentage of potential
scenarios (the so-called confi dence level), where extremely adverse scenarios are excluded.
In formal terms, if V is the value of a given portfolio, V
is its initial value, and 1 a is
the desired con dence level (e.g., 99%), then VaR
(i.e., the amount of loss that can be
exceeded only in a percentage of potential cases equal to a) is the amount such that
Pr(V V
< VaR
) = a
or alternatively, since V
V represents a loss whenever V < V
V > VaR
) = a
How can the risk manager estimate VaR in practice? Let us consider VaR for a trader
dealing in UK stocks and calculated on a daily horizon at a 99% con dence level. If the
trader has invested in a basket of stocks that closely resembles the FTSE100, a simple
way would be to consider FTSE100 daily returns in the last 200 business days, sort them
in ascending order, and then identify the percentage VaR with the third-lowest return in
the sample. If, for instance, the three worst losses were 4.1%, 4.7% and 6.95%, the
maximum loss that can be excedeed only in 1% of cases is 4.1%. In fact, according to
historical experience, the index (and therefore the trader) may lose more than VaR only
in 1% of cases (i.e., two days out of a 200-day sample). This method is known as histori-
cal simulation, and the risk manager would implicitly be assuming that the distribution
of tomorrows returns could be reasonably approximated by the return distribution of the
last 200 days. Of course, it is crucial to decide how many days should be included in the

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