40 Frequently Asked Questions In Quantitative Finance
What is Value at Risk and How is it
Used?
Short Answer
Value at Risk, or VaR for short, is a measure of the
amount that could be lost from a position, portfolio,
desk, bank, etc. VaR is generally understood to mean
the maximum loss an investment could incur at a given
confidence level over a specified time horizon. There
are other risk measures used in practice but this is the
simplest and most common.
Example
An equity derivatives hedge fund estimates that its
Value at Risk over one day at the 95% confidence level
is $500,000. This is interpreted as one day out of 20 the
fund expects to lose more than half a million dollars.
Long Answer
VaR calculations often assume that returns are normally
distributed over the time horizon of interest. Inputs for
a VaR calculation will include details of the portfolio
composition, the time horizon, and parameters govern-
ing the distribution of the underlyings. The latter set of
parameters includes average growth rate, standard devi-
ations (volatilities) and correlations. (If the time horizon
is short you can ignore the growth rate, as it will only
have a small effect on the final calculation.)
With the assumption of normality, VaR is calculated by
a simple formula if you have a simple portfolio, or by
simulations if you have a more complicated portfolio.
The difference between simple and complicated is
essentially the difference between portfolios without
derivatives and those with. If your portfolio only con-
tains linear instruments then calculations involving
