Chapter 2: FAQs 41
normal distributions, standard deviations, etc. can all be
done analytically. This is also the case if the time hori-
zon is short so that derivatives can be approximated by
a position of delta in the underlying.
The simulations can be quite straightforward, albeit
rather time consuming. Simulate many realizations of
all of the underlyings up to the time horizon using
traditional Monte Carlo methods. For each realization
calculate the portfolio’s value. This will give you a dis-
tribution of portfolio values at the time horizon. Now
look at where the tail of the distribution begins, the left-
hand 5% tail if you want 95% confidence, or the 1% tail
if you are working to 99% etc.
If you are working entirely with normal distributions
then going from one confidence level to another is just
a matter of looking at a table of numbers for the stan-
dardized normal distribution, see the table below. As
long as your time horizon is sufficiently short for the
growth to be unimportant you can use the square-root
rule to go from one time horizon to another. (The VaR
will scale with the square root of the time horizon,
this assumes that the portfolio return is also normally
distributed.)
An alternative to using a parameterized model for the
underlyings is to simulate straight from historical data,
bypassing the normal-distribution assumption alto-
gether.
VaR is a very useful concept in practice for the following
reasons.
- VaR is easily calculated for individual instruments,
entire portfolios, or at any level right up to an entire
bank or fund