Value at Risk

Value at Risk

Value at Risk The highest lost that a company could get in a period

(Usually in a daily period)

VaR calculation Methods:

* Correlation

* Historical simulation

* Monte Carlo simulation

The Historical method involves simply taking the empirical P/L history and ordering it. Suppose we have 100 observations of the returns of our portfolio. Using a spreadsheet we would simply order the returns from largest to smallest. The Value at Risk for the 95th percentile would then be the 6th largest loss. The advantage of the Historical method is that it requires no assumption to be made about the nature or shape of the distribution of returns. The disadvantage is that we are thus implicitly assuming that the shape of future returns will be the same as those of the past.

For this to be statistically likely we need to ensure that we have a sufficient number of observations and that they are representative of all possible states of the portfolio (i.e. incorporate data from both bull and bear markets). Using monthly data statistical certainty would typically require 34 years of data before we could be comfortable with this assumption. Since we seldom if ever have this much history the empirical method is not considered as accurate as either the parametric or simulation method.

The parametric or analytic method requires an assumption to be made about the statistical distribution (normal, log-normal etc.) from which the data is drawn. We can think of parametric approaches as fitting curves through the data and then reading off the VaR from the fitted curve. The attraction of parametric VaR is that relatively little information is needed to compute it.. The main weakness is that the distribution chosen may not accurately reflect all possible states of the market and may under or overestimate the risk. This problem is particularly acute when using value at risk to assess the risk of asymmetric distributions such as portfolios containing options and hedge...