Academic journal article Risk Management and Insurance Review

# Computing Value at Risk: A Simulation Assignment to Illustrate the Value of Enterprise Risk Management

Academic journal article Risk Management and Insurance Review

# Computing Value at Risk: A Simulation Assignment to Illustrate the Value of Enterprise Risk Management

## Article excerpt

INTRODUCTION AND MOTIVATION FOR THE ASSIGNMENT

The following assignment was created for use in an undergraduate risk management course, or perhaps a short assignment in an MBA course. The purpose of the assignment is to introduce the students to simulation using ©Risk modeling software, to provide them with an opportunity to compute the Value at Risk (VaR) for a combined set of risks facing a firm, and to illustrate some of the value concepts associated with a firm adopting an enterprise-wide view of the risks that it faces.

Through the assignment, the students are introduced to the following important concepts. First, they observe that the smaller the number of iterations in the simulation, the more the variation that occurs in the results when running a simulation. This result illustrates the limitations that firms face in estimating their risk exposures if they have limited observations or experience of their own.

Second, they learn how the interactions of individual risk exposures combine to influence the overall risk profile of the firm. They observe that the sums of various summary statistics (e.g., median and VaR) across the individual risk categories are greater than the comparable parameters for the total losses. This is an example of the portfolio effect of pooling of risks. Pooling these risks leads to some level of risk reduction which is being ignored if the parameters for each risk factor are estimated separately and then added together. In other words, a value of an enterprise-wide view is that these pooling benefits are not ignored. The students are also introduced to the value that negative correlation among risks can generate when risks are assessed at the enterprise-wide level. VaR and other risk estimates for total losses when individual risks are negatively correlated will be lower than the value estimated when the risks are statistically independent (uncorreIated). This result highlights the concept of natural hedges.

Finally, they learn that summary statistics like VaR are just point estimates, and values above the VaR are certainly possible. The assignment illustrates that, in fact, these possible outcomes above the VaR can be substantially above the VaR number. They see that when the distribution is positively skewed, as several of the risk distributions in this assignment are, it is especially important not to ignore the "tail" of the loss distribution.

The assignment has been a valuable learning and instructional tool in the MBA risk management classes where it has been used. The information below should be readily adaptable by other instructors for use in their courses. The questions that are assigned to the students are presented below with suggested answers. The necessary data are provided in an Excel workbook that can be downloaded from the Web (see Appendix C) or requested from the authors.

INTRODUCTION TO SIMULATION AND VAR

Simulation

Many business decisions can be evaluated using an analytical model. An analytical model is an equation that uses observed or hypothetical values of certain inputs to determine the values of outputs of interest to the firm's management. For example, consider a manufacturing firm with two identical machines. Each machine produces 100 units per day. The manager can use an analytical model to determine the likely impact on daily production of adding a third machine. The model would look like this: M × 100 = units of production, where M equals the number of machines.

Analytical models often are less useful for evaluating scenarios involving uncertainty as to the exact form of the model. The analyst may have a reasonable assessment of the analytical models that fit frequency and severity associated with a particular risk, but these separate models may not result in a clear analytical model for the distribution of total losses. As an alternative example, assume the machines referenced above do not always produce 100 units per day. …

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