Gifford Fong, president of Gifford Fong Associates, explains how risk managers must draw upon three critical risk measurement tools in order to build a realistic, multidimensional view of the risks lurking in their portfolios.

The history of risk management has been, until recently, inextricably linked to the development of individual markets. And as these individual markets developed, highly sophisticated and specialized techniques for measuring risk grew alongside them. For example, in the fixed income arena, duration, modified duration and effective duration rapidly gained favor as the risk measurement methods of choice. Likewise, in the equity realm, beta coefficients and fundamental betas were introduced as a means of assessing the risk of stock portfolios. But while both these measures work well in their own, original habitats, neither is easy to interpret if applied in other environments.

Furthermore, the highly specialized-and segmented-approach to market risk management has been fostered by the compartmentalized organizational structure that characterizes most financial institutions. Money managers, for example, are most often classified according to narrow market areas or instrument types, such as municipal bonds, mortgage-backed securities or U.S. small-cap stocks. Similarly, trading operations are segregated according to market type and often evaluated solely according to departmental performance.

So it is no surprise that holistic, portfolio-wide methods of managing risk have not evolved naturally. Instead, top managers who have been rattled by risk management gaffes of years past-such as Barings, Orange County and the Askin portfolio-are now laying out substantial research and development efforts and money. Their goal: the development of effective risk management methods and systems that can comfortably incorporate complex, niche-specific financial products into a comprehensive view of an entire portfolio's risk.

In order to create a seemingly paradoxical risk measurement technique capable of providing both a macro estimate of total exposure and a detailed look at how various sub-types of risk interact, it is necessary to combine three basic risk measurement methods which, when taken together, can help clearly identify-and prioritize-all the risk factors that may impact a portfolio. I call this method the multidimensional approach. In this article I will provide a rough outline of how multidimensional risk management works and why it provides a more comprehensive picture of portfolio-wide risk than any one technique used alone.

The building blocks

The three basic building blocks of the multidimensional approach are sensitivity analysis, value-at-risk and stress testing. While most managers already use one or more of these techniques, the key to multidimensional risk management is to ensure that all these methods are used in concert with one another. Consider the plight of the meteorologist, who must determine the risk of foul weather for the Labor Day weekend. In order to make the most accurate predictions, he does not rely on a single method. Instead, he uses a variety of forecasting tools and weaves their forecasts together.

Sensitivity analysis, for the weatherman, represents the basic weather factors such as wind velocity and barometric pressure. Value-at-risk is equivalent to a weather satellite, which can provide a macro snapshot of storm activity at any given point in time. And stress testing is similar to weather forecasting simulation where both the likely and the extreme projections are evaluated. Each dimension provides a different perspective; taken together, they provide a useful, multifaceted analysis for risk management.

The risk factors

Any portfolio of derivatives, securities or other contracts is exposed to a vast array of risk factors. Furthermore, these risk factors can interact with each other. For example, a substantial change in the U.S. equity market as expressed by a movement in the S&P 500 might very well have effects in other markets. Consider the following broad categories of risk that might affect a portfolio: market risk, option risk, prepayment risk, credit risk, liquidity risk, operations risk, regulatory risk and event risk.

Of course, it is possible to quantify only some of the risks listed above. Market risk, option risk, prepayment risk and even credit risk can all be quantified to various degrees. Other types of risk, however, cannot be easily expressed. For example, forecasting political and regulatory risks is necessarily more an art than a science. Nor can operational errors, administrative gaffes, poor judgment and fraud be accurately predicted. In these cases it is necessary to incorporate some sort of qualitative, judgmental process as part of regular risk evaluations.

How sensitive is it?

Once an array of broad risk factors have been considered, it is important to determine just how sensitive a portfolio might be to movements in the specific, quantifiable risk factors identified. For example, there are five principal risk factors which can affect the value of fixed income derivatives. First, there is the interest rate level, which represents fluctuations in the term structure. Second, consider the changing rates of benchmark maturities, which are specific maturity points along the term structure against which changes in interest rates can be measured. Next, there are the spreads of various instruments over government rates, which might include corporate bond quality sectors, swap spreads and MBS spreads that reflect the yield premium attributable to specific, nongovernmental securities. And finally, there is interest rate volatility and changing currency exchange rates.

By comparing the change in the value of each representative security relative to the change in each risk factor, the sensitivity to each can then be determined. However, in the case of many securities, it is important not to assume automatically that there is a linear relationship between one unit of change in a particular risk factor and the percentage change in the price of the security under consideration. Many derivatives, for example, contain embedded options that must be factored into the price sensitivity measure.

Therefore, when determining the relationship between changes in the price of a security and changes in a particular market factor, it makes sense to include both a linear and a quadratic measure of exposure in the calculations. For example, in the interest rate market, a linear exposure would be analogous to dollar duration and a quadratic exposure would be like dollar convexity.

Finally, because many swaps and other instruments start out with a low-or even null-value, it may be wise to measure changes in price in terms of their dollar value rather than in terms of percentage variation.

Thus by developing an equation that includes both linear and quadratic exposures and corrections for security-specific risks, it is possible to develop sensitivities to individual market factors for all the instrument types in the portfolio. With this information, it is possible to create portfolio-wide sensitivities to various market factors by combining weighted averages for the individual securities. This data gives the necessary information to prioritize the many risks that might conceivably affect a portfolio.

Value-at-risk

Value-at-risk (VAR) provides a look at the maximum decline in portfolio market value that can be expected within a given time interval-such as two weeks-and to a given level of certainty, such as 95 percent. This is a very useful number and, to ensure maximum accuracy, I recommend that users include variances and correlations in their VAR calculations drawn from current derivatives market prices, rather than relying on historical data. For example, in the swaps market, use interest rate volatility quotes that are calculated from current market valuations of swaptions. Volatilities obtained in this way are often called implicit or implied volatilities, and they reflect the market's estimate of future volatilities. Only when such implicit volatilities are unavailable for a given market factor should a historical variability be used.

Also, it is important to determine the probable variance of price changes in your portfolio. For example, are the price changes in the portfolio normally distributed, or highly skewed? Determining the degree of skew in a portfolio will help determine which value-at-risk methodology will work best. For example, the popular RiskMetrics methodology includes the assumption that price changes will be normally distributed; while this method is very convenient and cost-effective, it can provide meaningful data only for portfolios where prices tend to be normally distributed over time.

Value-at-risk can be calculated for individual securities, portfolio sectors and the total portfolio. It can also be calculated according to the various sources of risk, permitting only a selected number of market factors to fluctuate. However, it is important to keep in mind that by "slicing and dicing" value-at-risk according to either individual security or risk source, these sub-totals of risk will not necessarily add up exactly to the total, portfolio-wide risk for all relevant market factors. That is because of the effects of correlation between the different market factors and natural hedges among the various instruments within the portfolio.

Stress testing

Value-at-risk does provide a broad overview of a portfolio's risks to a relatively high degree of certainty. But what about the other 5 percent or 1 percent of the time? Catastrophic market movements such as the 1987 stock market crash will not fall within the bounds of the probable, maximum-loss forecast by VAR. Indeed, even under the best of circumstances on two or three trading days per year a portfolio's loss-or gain-will exceed what has been predicted by VAR. Stress testing, which consists of specifying a scenario of extreme and unfavorable market movements over a specific time interval and evaluating what happens to the portfolio under these circumstances, can provide a preview of what to expect in the case of extreme adversity.

Stress testing is particularly useful for a number of reasons. First, worst-case scenarios can be skewed to include shifts in market factors to which an earlier, sensitivity analysis has already demonstrated the portfolio will be vulnerable. Second, scenario analysis can easily incorporate path-dependent events, such as cash flows on CMOs. Third, scenario analysis does not hinge on any particular assumptions, as does VAR. And, finally, scenario analysis has an intuitive appeal. It is much easier to explain the results of a stress test than to explain why a particular VAR number is good or bad.

Moving ahead

Because the study of portfolio-wide risk is still relatively new, it remains in some respects more an art than a science. But although the weatherman isn't always correct, most of us still prefer to listen to a forecast before deciding whether or not to plan a trip to the beach or to haul an umbrella to work. And just as the weatherman uses all his prognosticating tools together to create an overall forecast, the effective risk manager should consider adopting a multidimensional analytical framework.

Step #1: Identify all your critical risk factors.

Step #2: Use sensitivity analysis to determine which risk factors will have the greatest effect on your portfolio. For example, will a 20 percent change in the dollar-yen rate have a greater impact on your portfolio than a 20 percent change in the one-year U.S. Treasury rate? Each security should be analyzed for sensitivity to all relevant risk factors, and then portfolio-wide sensitivities to each market factor can be determined by combining the weighted averages of sensitivity calculations for each security.

Step #3: Use value-at-risk to provide a broad overview of how your portfolio might change value, over a specific time horizon and to a specified level of certainty (for example, 95 percent or 99 percent). Be sure to determine the probable variance of the price changes in your portfolio, and select your value-at-risk method accordingly.

Step #4: Use scenario analysis to test your portfolio's response to extreme market conditions. Of particular interest should be testing your portfolios to large changes in market factors to which you are particularly sensitive.