Risk Management
One of the important tasks in risk measurement is the estimation of VAR, an
acronym for value at risk.
VAR Measurement
Let us now detail what we mean by VAR measurement starting with the out-
come of the measurement process. The outcome is a statement as follows:
“Under usual market conditions, there is a 2.5-percent chance of losing X
dollars in one day given the current list of positions.” The value Xis the value
at risk and is based on the current (day’s close) mark to market. The value of
Xis typically based on the statistics of the daily market movement in the past
two to three years—that is, the distribution of price movements—and, more
importantly, on the correlation between the price movements of various as-
sets. The exercise is therefore to determine what the likely value of Xis.
Also note that there is nothing magical about use of the 2.5-percent
value in the VAR statement. It is an artifact left from the cultural condi-
tioning of dealing with Gaussian distributions and represents two standard
deviations in the Gaussian case. That value could therefore be 1 percent or
any number that one fancies.
Another key aspect of the preceding statement is the use of the phrase,
“usual market conditions.” This is because the measurement approach that
works under usual market conditions is not sound under extreme market
conditions. This is because the correlations that may be considered as rela-
tively stable under usual market conditions become erratic under extreme
market conditions causing the VAR approach to break down.
Applying the same reasoning based on the correlation between asset
prices, it is easy to deduce that commonly applicable methods to measure the
VAR on a portfolio may not be used in the case of risk arbitrage. The an-
nouncement of the deal causes a qualitative shift in the way the two compa-
nies are viewed in the marketplace. The historical correlation between them
is no longer relevant. The market dynamic now also reflects the possibility
of merger between the two companies and there is an increased level of cor-
relation between the returns of the bidder and target stocks. Therefore, any
VAR methodology that relies on long-term historical correlation is rendered
inappropriate.
Furthermore, use of the historical correlation could potentially inflate
the VAR numbers, increasing risk capital requirements, resulting in an un-
realistic increased cost of doing business. This leads us to look for reason-
able ways to evaluate the value at risk involved in risk arbitrage trades.
The risk arbitrage trade at hand can be viewed in two ways. On event
of deal failure, it is equivalent to holding two separate securities, and tradi-
184 RISK ARBITRAGE PAIRS