WHERE IS THE NEXT ICEBERG?
Does Value at Risk (VAR) measure risk? If you think this is a rhetorical question then consider another: What is the purpose of risk management? The most important answer to this question is to prevent an institution from suffering unacceptable loss. 'Unacceptable' needs to be defined:
An unacceptable loss is one that either causes an institution to fail or materially damages its competitive position.
Armed with a key objective and definition of unacceptable loss we can now return to the question of whether VAR measures risk. The answer is at best inconclusive. 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 circumstances that might cause such a loss. Nor have we quantified it.
Using the Titanic as an analogy, the captain does not care about the flotsam and jetsam that the ship will encounter on a regular basis, but he does care about the icebergs. If VAR tells you about the flotsam and jetsam, then it falls to stress testing to warn you of the damage that would be caused by hitting an iceberg.
The Mexican peso crisis illustrates the importance of stress testing. Figure 1 shows the Mexican peso vs. U.S. dollar exchange rate during the crisis of 1995.
Figure 1 shows the classic characteristics of a sudden crisis, i.e. no prior warning from the behavior of the exchange rate. There is very low volatility prior to the crisis; VAR would therefore indicate that positions in this currency represented very low risk.
Figure 2 shows the VAR 'envelope' superimposed on daily exchange rate changes (percentage changes). The start of the crisis is heralded by a cluster of VAR exceptions that make a mockery of the VAR prior to the crisis. The VAR envelope widens rapidly in response to the crisis, but is too late being after the event! If management had been relying on VAR as a measure of the riskiness of positions in Mexican peso they would have been sadly misled. The start of the crisis sees nine exchange rate changes of greater than 20 standard deviations (20 times the return volatility prior to the crisis), including one change of 122 standard deviations!
STRESS TESTING FINDING THE ICEBERGS
By now it should be clear that VAR is inadequate as a measure of risk. Risk management must provide a way of identifying and quantifying the effects of extreme price changes on a bank's portfolio. This is better undertaken using stress testing. Further, it is important that the stress testing undertaken is systematic in nature, rather than occasional and incomplete. Systematic stress testing has the following characteristics:
* Regularity, stress tests should be undertaken daily;
* Gamma risk, or non-linearity;
* asymmetries;
* correlation breakdowns;
* stressing different combinations of asset classes together
and separately;
* use of appropriate size shocks.
Table 1 shows a matrix of different stress tests for an interest rate portfolio that includes options. It is an example of a matrix of systematic stress tests.
The columns represent different parallel shifts in the yield curve and the rows represent different multiples of volatility. This stress test matrix is dealing with Gamma risk by stressing the portfolio with a series of shifts of different magnitudes. If digital options are present in the portfolio the grid can be further sub-divided and the maximum value in each cell displayed in place of portfolio values at specified points. The matrix deals with the potential for an asymmetric loss profile by using upward and downward shifts of both interest rates and implied volatility. Graphing the stress test matrix can demonstrate this more clearly:
The first thing to note is that the worst-case loss is not coincident with the largest price move applied. In this example the worst case loss occurs with small moves in rates because the book is Gamma positive.
In a large portfolio it is clear that systematically stressing every combination of assets will create an unmanageable number of calculations--70,587 combinations for a portfolio of 10 assets. In practice only a tiny fraction of the theoretical number of combinations need to be tested. A little thought can pick out the key risk concentrations in the bank's portfolio and ensure these are tested thoroughly. Once a potentially unacceptable loss has been identified it can then be discussed by heads of trading and risk management to determine whether it is an acceptable risk. Alternatively, risk control limits can be set in terms of stress tests.
It is hoped that this article has demonstrated how risk control frameworks that rely on VAR can be dangerous and may not protect an institution from an unacceptable loss. Risk frameworks based around stress testing actually offer far greater protection against large losses and are easier to understand as well.
This week's Learning Curve was written by Philip Best, managing principal, at The Capital Markets Company in London.
