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Price Risk Management
Unfortunately, neither historical VaR nor traditional price risk management tools tell us anything regarding the probability of losses over the next 24 hours for our current portfolio holdings. By contrast, forward-looking (parametric and simulation) VaR models apply statistical measures, such as standard deviation and correlations, to current portfolio holdings to estimate probability distributions of losses for a particular holding period (i.e., 24 hours). Subsequently, forward-looking VaR models can effectively account for how the addition of a particular position to current portfolio holdings will either reduce or increase portfolio risk (due to its negative or positive correlation to the existing portfolio).6
PITFALLS OF VALUE AT RISK
Although value at risk is a valuable tool, it does not provide a comprehensive solution to the problem of managing price risk. This is because VaR does not address how much we could lose during a given holding period, only the maximum that we are likely to lose. For example, while VaR defines an excessive loss for our particular trading account as $30 million and tells us that we have a 5 percent chance of enduring such a loss over the next 24 hours, it says nothing about how severely any particular daily loss will exceed this $30 million threshold.
Another flaw in VaR models is that they assume serial independence: whatever happened today has no impact on tomorrow’s trading. Because all of the trading systems discussed in this text owed their success to the market’s propensity to either trend or revert to the mean, serial independence is a flawed assumption.
The assumption of serial independence leads to VaR’s inability to account for excessive event clusterings. For example, the fact that we exceeded our daily VaR threshold yesterday says nothing about the likelihood of VaR being exceeded again today. In fact, excessive event clusterings can be one of the distinguishing traits of a strongly trending market. This is perhaps best exemplified by the 1995 Mexican peso crisis, during which the market experienced 9 days beyond 20 standard deviations from the mean.
A subtler problem relating to cumulative losses is that VaR only attempts to predict the likelihood of violating a particular confidence level, such as 95 percent. Consequently, VaR cannot account for cumulative losses that never achieve the chosen VaR confidence threshold. This problem of cumulative daily losses below the VaR threshold is another example why traditional price risk management tools such as historical studies of worst peak-to-valley drawdowns, are an essential adjunct to VaR analysis.
MECHANICAL TRADING SYSTEMS
Perhaps one of the most dangerous and flawed assumptions inherent in all VaR models is the ability of traders to close out positions without significant slippage. VaR literally “assumes away” liquidity risk, which is especially dangerous when we remember that this assumption of liquidity is being paired with an attempt to measure the probability of our trading account enduring an excessive and statistically improbable daily loss. We need only to imagine a commodity market in “locked limit” or recall the illiquidity of global equity markets on October 19, 1987, to see the disastrous potential of assuming away liquidity risk.
Finally, VaR assumes that correlation history is predictive. Just as we saw in the examination of VaR and liquidity, the pairing of historical correlations with a price shock event could lead to potentially fatal assumptions regarding price risk of a particular portfolio. In fact, one of the major distinguishing traits of a price shock event is the breakdown of historically stable correlations. This is perhaps best exemplified by the breakdown of the historically stable exchange rate relationship between the British pound and German deutsche mark during the Exchange Rate Mechanism (ERM) crisis in September 1992 (see Figure 8.1).
FIGURE 8.1 Daily chart of spot DM-pound preceding and during the 1992 ERM crisis.
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Price Risk Management
Stress testing attempts to address many of the flaws inherent in VaR exercises. Value at risk tries to quantify the likelihood of our portfolio’s breaching of a particular loss threshold over a specified time horizon, but says nothing regarding the degree of severity of a particular loss. Stress testing attempts to quantify how bad the unlikely event could get, but—for the most part—fails to examine the probability of the particular event’s occurrence. As such, stress tests are ideal complements to VaR analyses.
A comprehensive examination of stress testing methodologies is beyond the scope of this text.7 However, an example will explain the basic concept and its utility. One of the simplest and most popular types of stress tests is known as scenario analysis. In scenario analysis, we apply to our current portfolio holdings either a hypothetical scenario, such as a 100 basis point rise in interest rates, or an actual historical scenario, such as the stock market crash of 1987, to determine our portfolio’s vulnerability. Once our stress test has identified such portfolio hot spots, we can reduce these exposures by reducing position exposures or purchasing options.