A Risk Professional's Survival Guide. Rossi Clifford

be seen later, while statistics provide an intuitive and elegant way to define risk, it nonetheless offers an incomplete way to fully understand risk due to inherent limitations on standard statistical theory and applications that do not always represent actual market behaviors. This does not imply that we should abandon statistical applications for assessing risk, but that a healthy dose of skepticism over accepting a purely analytical assessment of risk is a prerequisite to good risk management. As a starting point, basic statistical theory presents a convenient way of thinking about risk. Figure 2.1 depicts a standard normal probability distribution for some random variable x. The shape of the distribution is defined by two parameters, its mean or central tendency centered on 0 and the standard deviation, σ. If risk can be distilled to a single estimate, standard deviation is perhaps the most generalized depiction of risk, as it measures the degree to which outcomes stray from the expected outcome or mean level. More formally, standard deviation is expressed as shown in Equation 2.1.

(2.1)

Figure 2.1 Standard Normal Distribution and Area Under the Curve

      where p_i represents the probability of outcome i, and μ is the mean of the variable x. The variable x could reflect the returns from a product or service for a company, the compensation to an employee for a particular job, or the amount of collateral damage from a terrorist attack, for example. Despite the difference in the variable of interest, the one common aspect for all of these risks is that they can be measured by the standard deviation. Further, risks can be managed based on the tolerance for risky outcomes as may be represented by the distance of a specific set of outcomes from their expected level.

To further reinforce the concept of standard deviation as a measure of risk, consider the returns for the firm shown in Table 2.1. There are nine different annual return outcomes representing x in Equation 2.1. The average of these scenarios is 11.3 percent. The deviations of each outcome from that mean (m μ) are shown as (x – μ)² and that result is multiplied by each outcome’s probability. The sum of these probability-weighted squared deviations represents the variance of the firm’s annual returns. Taking the square root of the variance yields the standard deviation of 5.91 percent. That would mean that 68 percent of the firm’s potential return outcomes should lie between (11.3 – 5.91) and (11.3 + 5.91) or 5.39 and 17.21 percent, respectively.

Table 2.1 Example Calculation of Standard Deviation of Firm Annual Returns

      Take the case of a company that faces whether to engage in a certain business activity or not. The firm obtains a set of historical data from the last several years of returns on similar products provided by other competitors. Suppose now the mean return for the product is 15 percent with a standard deviation of 5 percent. Using the information from the standard normal distribution in Figure 2.1, the company can begin to shape its view of risk. First, the distribution of returns takes on a similar symmetric shape as the standard normal curve shown in Figure 2.1. Under such a distribution, outcomes that deviate significantly from the average come in two forms: some that create very large positive returns above the 15 percent shown on the right-hand side of the distribution, and some that create corresponding returns smaller than 15 percent. The company realizes that returns less than 15 percent (its cost of capital) would drain resources and capital away from the firm, thus destroying shareholder value. In this context, only returns below 15 percent create risk to the company. The company now focuses on the left-hand tail, paying particular attention to how bad returns could be. The distribution’s y-axis (vertical) displays the frequency, or percentage of time, that a particular return outcome would be observed. According to the standard normal distribution, approximately 68 percent of the time returns would be between plus and minus 1 standard deviation from the mean. In this case we should find returns between 10 and 20 percent occur about 68 percent of the time. But moving out two or three standard deviations in either direction would capture 95 and 99.7 percent of the occurrences, respectively. However, with the focus only on low-return events, the company only needs to understand the frequency of these occurrences in assessing its project risk. In this example, outcomes that generate returns between 10 and 15 percent occur about 34 percent of the time. If the company were to look at adverse outcomes that are –2 standard deviations away from the mean, then returns between 5 and 15 percent would occur about 47.5 percent of the time. At this point, the company would need to think about what would happen if they were to observe a return of 10 percent versus 5 percent. If, for instance, the company had information to suggest that if returns reached 5 percent it would have to shut down, this would pose an unacceptable level of risk for the firm that it would want to guard against. As a result, it might establish a threshold that it will engage in products where there is a 97.5 percent chance that returns would not fall below 5 percent. Notice that since half of the outcomes fall above a 15 percent return and that 47.5 percent of the outcomes fall between 5 and 15 percent (one half of the 95 percent frequency assuming +/–2 standard deviations from the mean), then the portion of the area under the distribution accounting for returns worse than 5 percent would be 2.5 percent.

      Such use of statistics provides risk managers with easy-to-apply metrics of how much risk may exist and how much risk should be tolerated based on other considerations such as the likelihood of insolvency. But blind use of statistics can at times jeopardize the company should actual results begin to vary significantly from historical performance. In such cases formal measures of risk as based on statistical models must be validated regularly and augmented when needed by experience and seasoned judgment. Such considerations bring to mind the need to characterize risk management in situational terms for the existence of uncertainty in any risk management problem implies that circumstances specific to each problem can and will affect outcomes that might not be precisely measured using rigorous analytical methodologies based on historical information.

       Situational Risk Management

      As the phrase implies, situational risk management is a way of assessing risk that takes into account the specific set of circumstances in place at the time of the assessment. It could include the market and economic conditions prevailing at the time, the set of clients or customers of a set of products posing risk, their behavior, business processes, accounting practices, and regulatory and political conditions, among other factors to take into consideration. And complicating the problem a bit more is the need to take these factors into account in projecting potential future outcomes. All of this may seem daunting to the risk manager who is facing how to assess risk based on the unique situation of the particular problem.

      If we could teleport back to 2004 into a major mortgage originator’s risk management department, it might provide some insights into the nature of situational risk management. Consider the heads of risk management of two large mortgage originators facing whether to expand their mortgage production activities. Both firms face extraordinary pressures on their businesses due to commoditization of prime mortgages that are typically sold to the government-sponsored enterprises Fannie Mae and Freddie Mac. As a result, prices for these loans have squeezed profit margins to a point that other sources of revenue are required for the long-term sustainability of the franchise. As a result, one of the companies, X Bank (a mortgage-specializing thrift) decides that it needs to compete with other major players in loans that feature riskier combinations than they have traditionally originated. X Bank has over time acquired other smaller thrifts and banks focused on mortgage lending and this has led to a number of deficiencies and gaps in the way mortgage loans are underwritten. Fortunately, the economic environment has been extremely favorable, with low interest rates and high home price appreciation contributing to low default rates. These conditions thus have masked any problems that might cause X Bank higher losses for the time being. The other bank, Z Bank faces the same conditions; however,