# Teaching Systemic Risk: An In-Class Simulation for Diverse Audiences

William C. Wood
DOI: 10.4018/IJRCM.2015100104
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## Abstract

This article shows how an in-class simulation can be used to teach the joint failure probability of statistically independent failures, and then to teach the more complex problem of system or “common-mode” failure. The technique has many potential applications, but here focuses on bank failures as a readily accessible application. This teaching simulation has been successfully presented to diverse audiences since 2011. The original audience consisted of high school, community college and university instructors and the case has since been taught to additional continuing education groups and 400-level Economics students.
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## Introduction

The concept of systemic risk is challenging to understand and analyze. Even beyond understanding, an even greater challenge is to teach the concepts to audiences as diverse as high school, community college, and university learners. This article is a teaching case study of systemic risk, illustrating a teaching simulation that has been successfully presented to diverse audiences since 2011 (For example, see Stavros Center, 2011). The original audience consisted of high school, community college and university instructors and the case has since been taught to additional continuing education groups and 400-level Economics students.

The objectives of the simulation are simple: first, to teach the calculation of the joint probability of multiple statistically independent failures; and second, to show how system risk makes the calculated probabilities inaccurate. The specific context is systemic financial risk, but the concept is much broader. Consider these three cases in which system risks, or “common-mode failures,” resulted in significant hazards to economic well-being, health and safety:

• A fire under a nuclear power plant’s control room simultaneously disabled primary and backup safety systems, creating the threat of a catastrophic accident (Kazarians, Siu & Apostolakis, 1985).

• All of the engines of an airliner over the Atlantic failed because of the same defective maintenance procedure, threatening the total loss of lives of all those aboard (NTSB, 1984).

• Seemingly sound financial institutions faced failure because of insufficient accounting for the risks of derivative assets failing simultaneously (Bullard, Neely & Wheelock, 2009).

The in-class simulation described in this article dramatizes the idea of systemic risk and how radically systemic probabilities can differ from probabilities that assume independent failures.

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## The Bank Failure Simulation

In this simulation, there are five banks. Banks A, B, C and D are well run, with a probability of failure equal to 1 in 1,024. This number is chosen for convenience, as the probability of flipping ten “tails” in a row using a fair coin. Bank F, on the other hand, is a problem bank with failure probability equal to 0.5—the same as a single flip of “tails” with a fair coin. In this stylized example, bank regulators are justified in believing the probability of the entire system failing is infinitesimal or at least acceptably low.

As long as the failure is isolated to Bank F, there is little to worry about. Since the joint failure probability of statistically independent failures is their simple product, the probability of the whole system failing after Bank F does is 1/1024 x 1/1024 x 1/1024 x 1/1024, or 9 x 10-13. Since this is less likely than the probability that an individual would be struck by a meteorite, and then struck by lightning, and then win the lottery, bank regulators would seem justified in neglecting the risk. Their job is to handle the isolated failure of Bank F, an easy task using deposit insurance and possibly a merger with a sounder financial institution. However, if there is an undiagnosed systemic risk, the entire system might fail with a probability as high as 0.5.

Bank A, the soundest bank in the system, has an independent failure probability of 1/1024 – but to add a systemic risk element, this simulation assumes that the bank also would fail if 80 percent of the other banks in the system failed. (The idea would be that a shortage of liquidity would make the bank unable to meet its obligations if many of its financial partners failed.) Bank B also has an independent failure probability of 1/1024, but the simulation assumes Bank B would fail if 60 percent of the other banks failed. In a similar fashion, Bank C would fail if 40 percent of the other banks failed and Bank D would fail if 20 percent of the other banks failed. With these systemic risk assumptions, the single failure of Bank F (20 percent of the banks in this small five-bank system) would also cause Bank D to fail – but then with 40 percent of the banks having failed, Banks C and B would follow. At this point, 80 percent of the banks have failed and the seemingly strong Bank A follows.

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