Risk economies of scale in the finance and insurance industries: Placing the right emphasis in introductory business statistics

Most undergraduate and graduate business programs include a required introductory course in statistics with statistical inference as the primary focus. Developing the proper understanding of statistical inference techniques requires an ambitious ramp-up effort devoted to the study of proability theory, discrete and continuous probability distributions, and the central limit theorem. Mastering this large amount of demanding material in a short time poses a significant challenge to most students. As a result, students resort to formula lists they apply without proper understanding. Frequently, even the best performing students in the class are incapable of applying simple statistical concepts soon after the course is over. Acquiring lifelong knowledge requires understanding. This paper illustrates how simple properties of the sum of independent identically distributed random variables account for risk economies of scale which are at the foundations of the finance and insurance industries. By highlighting this simple, yet extremely important result, students stand a better chance of achieving lifelong recollection and understanding of one of the most significant quantitative results in business.