Synthetic Event Analysis

Jim MeVay and Chris Turner

Stress-testing portfolios of risk positions to see how they would behave under hypothetical changes in market values has become an increasingly popular tool in the risk manager's bag of tricks. It is usually done by assuming an extreme movement in an underlying risk factor such as interest rates, and then assuming a variety of bumps and twists along a particular yield curve. These types of stress assumptions, however, are often unrealistic.

The first difficulty with stress testing is that it is usually arbitrary. When calculating the impact of an increase in exchange rates on a portfolio, for example, should a rate be bumped 10 percent, 20 percent or even 50 percent? Obviously, the "right” amount of perturbation will depend on the market in question. Determining the right amount to change a market factor is a judgment call—and often a haphazard guess at that.

Even if one is willing to accept the challenge of determining the right amount to perturb a market price, the arbitrary nature of the shifts almost inevitably violate economic relationships, such as covered interest arbitrage. As a result, traditional scenario analysis involving several market factors will create interest rates and exchange rates that cannot be observed in practice. Applying traditional stress testing to a portfolio dependent on these factors will create changes in market value that may be meaningless.

The qualitative aspects of what measures to apply and how turn out to be more challenging than building the actual quantitative tools. Some more creative approaches to the problem include proxy analysis, multivariate statistical evaluation and synthetic event-risk formulation.

Scenario analysis

In response to the lack of realism in stress testing, scenario analysis takes a different tack. Rather than attempt to guess an unfavorable event that may happen in the future, historical stress testing uses market upsets that have already occurred. There is an assortment of events to choose from—the stock market collapse of 1987, the breakdown of the European exchange rate mechanism in 1992, the bond market meltdown of 1994, and the peso crises of 1994 and 1995, to name a few. In scenario analysis, the price changes that occurred during these historical stress periods are applied to recent market prices to create a hypothetical slate of new market prices. The current portfolio is then revalued using these market prices.

Using these "blasts from the past” to evaluate catastrophic risk has several advantages. Since these events have already occurred, no one can argue that they are unrealistic. Furthermore, they provide a good demonstration of the true power of the portfolio effect. During the Mexican peso crisis, for example, emerging markets assets and currencies sold off badly, but European currencies sharply rebounded. Carefully diversifying a portfolio, both across asset classes and geographic regions, may be the best way to immunize it against such catastrophes. Indeed, the fundamental lesson of historical stress testing, at least thus far in modern capital markets history, is that there has been no such thing as a global catastrophe.

Proxy analysis

Another alternative is proxy analysis, or using a stress event to create a hypothetical scenario. Historical stress testing is problematic because there has not been a catastrophe for every single market or asset class, so the results lack specificity. Consider a firm whose portfolio is dominated by a Chinese renminbi exposure. Clearly the Mexican peso crisis has some relevance for this company, as it could be thought of as a representative emerging-market disaster.

The risk of such a concentrated position could be captured simply by using the peso event as a template. To do this, the risk manager would simply transpose the major devaluation from the Mexican peso to the relevant currency. This scenario captures the major characteristics of the peso stress event, but applies them to a hypothetical event relevant to the portfolio's largest position and can suggest a potential magnitude of risk.

Multivariate scenarios

Another approach is to integrate correlations between market factors into the scenario analysis. This involves using historical data to calculate summary statistics of volatilities and correlations. We can then create an arbitrary scenario in one market and calculate the likely behavior of the other markets to which a portfolio might have exposure.

Consider a simple case in which one has a predominantly U.S. dollar interest rate portfolio and a few assets that depend on Deutsche mark interest rates. If one wants to do a scenario analysis on this portfolio, he or she might simply apply a 20 percent shift at all points along both the U.S. dollar and the Deutsche mark yield curves. But this would be unrealistic, since it ignores the historical relationships between these markets.

One approach that better captures the relationship considers what would happen to the Deutsche mark curve if U.S. dollar rates rose 20 percent. Although one can apply complex economic models to this problem, a purely statistical approach captures most of the relevant behavior. Consider one point on both curves, the six-month U.S. dollar LIBOR and Deutsche mark LIBOR rates. Over the last 10 years, the correlation between the percentage changes in the six-month U.S. dollar and Deutsche mark LIBOR rate is about .28, while the volatility of the U.S. dollar and Deutsche mark LIBOR rates has been roughly 19 percent and 17 percent, respectively.

The first thing that should be noted from these statistics is that the scenario increase of 20 percent is more likely in six-month U.S. dollar than in six-month Deutsche mark LIBOR. Furthermore, scaling a correlation of .28 shows that the markets tend to move in the same direction about two-thirds of the time, so that we might want to reduce further the rate increase applied to Deutsche mark LIBOR.

If we are willing to believe that these interest rates are normally distributed, we can get much more specific. The rules of this distribution then tell us that a 20 percent increase in the U.S. dollar rate should lead us to expect somewhat more than a 5 percent increase in the Deutsche mark rates. In addition, the relatively low correlation between the rates tells us that the largest likely move in the Deutsche mark rate, at a 95 percent confidence level—a two-standard-deviation move—is only 14 percent. Needless to say, we could also examine the impact of a 20 percent move at each point along the U.S. yield curve on German LIBOR rates using discrete correlations.

The risk of recurring events

Risk managers face another related problem: the world of finance is dominated by the periodic release of economic data or recurring events. The markets often hold their collective breath before these events and economists expend great energy trying to forecast the outcomes. Risk managers are most likely to earn their pay by evaluating risk during these critical periods.

The value-at-risk approach loses much of its applicability under these conditions because the methodologies currently available assume that the distribution of changes in market prices is stable. Some markets, however, have experienced sharp deviations from recent market volatility in reaction to events such as an economic data release or a Federal Reserve action.

To deal with this problem, many risk managers have turned to stress testing and scenario analysis during these transition periods. But we need not discard value-at-risk completely—we can use it to create scenarios based explicitly on the recurring nature of these events.

Consider the impact of Federal Reserve interest rate moves on long-term rates. It's a relatively easy matter to gather statistics on the dates of the meetings and coincident changes in the interest rate markets for the past several years. The yield on 10-year Treasury bonds for the last 12 years is illustrated in Figure 1 with the dates of the FOMC meetings indicated by circles.

Using these data, we can conduct an analysis of the interest rate changes around the meetings. We calculated the percentage change in yields from the day before the meeting until the day after the meeting. The bar chart inset into the figure describes the distribution of these changes. As indicated in the chart, the most common occurrence is no change in rates over FOMC meetings. After some meetings, however, there are several relatively large increases or decreases in rates, depending generally on the direction the Fed pushes short-term interest rates.

More explicitly, we can use the data to estimate the maximum likely increase in rates, for a given confidence interval, over the next FOMC meeting. In this case, we are assuming that the percentage changes in rates observed over previous FOMC meetings are representative of changes we are likely to see in the future. If we are willing to make this assumption, then the maximum change in rates we are likely to see over the next FOMC meeting at a 99 percent confidence level is slightly more than 3.5 percent.

Note that this analysis makes no distinction between periods in which the Fed has a bias toward pushing short-term rates up from those in which its bias is to push rates down. An enhancement can be made by assessing consensus market sentiment for a particular rate change, segregating data for these periods, and creating subdistributions for use under a particular sentiment consensus in the future. Another possible expansion of this analysis could also involve recording additional market factor changes, such as for currencies and commodities, that occurred over the periods studied to assess total portfolio behavior under these events.

Although great strides have been made in creating quantitative analytics for purposes of measuring risk, the usefulness of the results have been mixed because of qualitative anomalies in the risk exposures to be measured. The challenge for the future is to understand adequately the nature of the risks facing a manager and to construct creative approaches that are relevant to those risks.