Does VaR measure risk?

If you think this is a rhetorical question then consider another: What is the purpose
of risk management? Perhaps the most important answer to this question is to
prevent an institution suffering unacceptable loss. ‘Unacceptable’ needs to be defined
and quantified, the quantification must wait until later in this chapter. A simple
definition, however, can be introduced straight away:
An unacceptable loss is one which either causes an institution to fail or materially
damages its competitive position.
Armed with a key objective and definition we can now return to the question of
whether VaR measures risk. The answer is, at best, inconclusive. Clearly if we limit
the VaR of a trading operation then we will be constraining the size of positions that
can be run. Unfortunately this is not enough. Limiting VaR does not mean that we
have prevented an unacceptable loss. We have not even identified the scenarios,
which might cause such a loss, nor have we quantified the exceptional loss.
VaR normally represents potential losses that may occur fairly regularly – on
average, one day in twenty for VaR with a 95% confidence level. The major benefit of
VaR is the ability to apply it consistently across almost any trading activity. It is
enormously useful to have a comparative measure of risk that can be applied
consistently across different trading units. It allows the board to manage the risk
and return of different businesses across the bank and to allocate capital accordingly.
VaR, however, does not help a bank prevent unacceptable losses.
Using the Titanic as an analogy, the captain does not care about the flotsam and
jetsam that the ship will bump into on a fairly regular basis, but does care about
avoiding icebergs. If VaR tells you about the size of the flotsam and jetsam, then it
falls to stress testing to warn the chief executive of the damage that would be caused
by hitting an iceberg.
As all markets are vulnerable to extreme price moves (the fat tails in financial asset
return distributions) stress testing is required in all markets. However, it is perhaps
in the emerging markets where stress testing really comes into its own. Consideration
of an old and then a more recent crisis will illustrate the importance of stress testing.
Figure 8.1 shows the Mexican peso versus US dollar exchange rate during the
crisis of 1995. The figure shows the classic characteristics of a sudden crisis, i.e. no
prior warning from the behavior of the exchange rate. In addition there is very low
volatility prior to the crisis, as a result VaR would indicate that positions in this
currency represented very low risk.1 Emerging markets often show very low volatility
during normal market conditions, the lack of volatility results, in part, from the low
trading volumes in these markets – rather than the lack of risk. It is not uncommon
to see the exchange rate unchanged from one trading day to the next.

Figure 8.2 shows the VaR ‘envelope’ superimposed on daily exchange rate changes
(percent). To give VaR the best chance of coping with the radical shift in behavior the
exponentially weighted moving average (EWMA) volatility model has been used (with
a decay factor of 0.94 – giving an effective observation period of approximately 30
days). As can be seen, a cluster of VaR exceptions that make a mockery of the VaR
measured before the crisis heralds the start of crisis. The VaR envelope widens
rapidly in response to the extreme exchange rate changes. But it is too late – being
after the event! If management had been relying on VaR as a measure of the riskiness
of positions in the Mexican peso they would have been sadly misled. The start of the
crisis sees nine exchange rate changes of greater than 20 standard deviations,2
including one change of 122 standard deviations!