By Albert J. Beer
After many years of teaching, I have discovered that nothing gets the attention of students more effectively than the threat of money coming out of their own pockets. I have shamelessly taken advantage of this vulnerability to illustrate some fundamental principles of Insurance, Risk Management and Actuarial Science.
Like most colleges, all St. John’s University students are issued a multi-purpose Identification Card known as a StormCard. As the campus website explains: “The StormCard is your personal connection to University services, purchases and access control. In addition to serving as your college ID, the StormCard provides the ability to set up debit accounts for purchases at the campus book store, dining facilities, computer labs, copiers, printers and selected vending machines. Purchases may also be made for personal training and various ticket events! The StormCard also provides access to campus gates, buildings and events. In addition, your StormCard is your pass for entry into the residence halls.”
Therefore, every student becomes well aware of two things:
- The StormCard is an essential part of college life; and
- It is expensive to replace.
More precisely, the University policy is as follows: “The fee for your first StormCard replacement is $25. After the first replacement there is a graduated replacement fee. The graduated fee consists of the $25 replacement fee plus a $25 fee for each lost replacement StormCard up to a maximum fee of $100.”
With these universally known facts as background (knowledge that is sometimes painfully acquired!), I propose during class that we form an insurance company with all 21,000 St. John’s students as prospective “policyholders.” The insurance policy would cover the cost of replacing lost or stolen StormCards whereby, for a fixed annual premium, we would reimburse the student as follows:
- First replacement card: $25
- Second replacement card: $50
- Third replacement card: $75
- Fourth and subsequent replacement cards: $100
We generally begin with an open discussion among the students concerning whether they think that they and their fellow students would be interested in such a policy and, if so, how much premium would they be willing to pay. I generally seed the discussion by throwing out possible premiums—would you pay $5 a year?…$3 a year?.....nothing? This is an excellent opportunity to explain that there is no “right answer” and I often introduce the concepts of risk aversion and utility curves.
With the help of campus security I have obtained data from several years on the number of students who have replaced one, two, three and four or more StormCards. Based upon this information, I show how it is easy to determine the basic statistics (expected value and variance) for the amount of replacement fees that are paid annually. (For my actuarial students, we often develop separate estimates for the number of students who will replace cards [Frequency] and the average cost per replacement [Severity].)
As a simplistic example, the data might show that in 2014, 21,000 students generated $42,000 of replacement fees (“Loss”). This would form the basis of an initial estimated $2 “Pure Premium” which would be intended to represent that part of the annual cost per student to cover “Losses.”
Of course, estimating the expected losses paid by our “insurance company” is only the first step in determining an appropriate premium. This is the time when we discuss building a pricing model by introducing concepts such as risk load, administrative expenses and profit. The risk load discussion can be as simplistic or as sophisticated as you and your class prefer. As a purely hypothetical example, presume the data set reveals:
|Year||Students||Actual Fees Paid||Indicated Pure Premium|
|2010||21,295||$ 41,525||$ 1.95|
|2011||21,321||$ 43,250||$ 2.03|
|2012||21,345||$ 42,050||$ 1.97|
|2013||21,546||$ 45,600||$ 2.12|
|2014||21,792||$ 42,725||$ 1.96|
Seeing this variability in results stimulates interesting discussions among the “student owners” about the risk of needing to provide additional capital to fund poor loss years!
At this point I remind the class that this would not be a university sponsored program and it would be very unlikely that all students would be required to purchase our product. Since our data is based on the entire population, we would need to make some modifying assumptions about the subset of students who would become policyholders. Some interesting discussion points that I like to introduce include:
- Asymmetric Information: Isn’t it likely that many students who tend not to lose their cards may forgo buying the policy? In that case, the actual average cost per student that we would incur would likely be much higher since many of the $0 cost student’s results would not enter into the calculation.
- Adverse selection: It doesn’t take long for the class to conclude that students who tend to lose things (including their StormCard!) would have much higher expected fees to be paid than those students who are more careful. If we developed one fixed premium for every student based upon the overall average experience, we would be “undercharging” (on an expected cost basis) the chronic fee-payer and “overcharging” the more diligent student. Suddenly, they grasp (and demand!) a classification system that reflects different likelihoods of filing a claim(s). The most common initial suggestion is to charge anyone who has a history of losing a card more. (It is enlightening to hear how young adults change their initial thinking about the “fairness” of raising auto insurance rates after an accident when they put it in this context. The extension to life and health coverage is obvious. Also, recently the issue of using credit scores in insurance pricing has been a highly controversial topic and I find that discussing this issue in the context described here is an excellent way to broach the reality of these complex actuarial/social/economic concepts.) Putting aside fairness, it is easy to show that a competitor who had different rates for students who had varying likelihoods of filing a claim (or multiple claims) would attract all the better risks and leave us with all the worse-than-average risks paying our “average” rates. (Imagine a New York State automobile insurance company charging a statewide average rate to every prospective policyholder. Where do you think all the seventeen year olds with speeding tickets would be insured?)
- Behavior Risk: Would the existence of this insurance change behavior? If students didn’t need to worry about paying multiples of $25 anymore, would they be less careful in the way they handled their StormCard? Would we as an insurance company suffer much different (worse?) experience than that evidenced historically? (The class is generally intrigued to find that there is some very interesting research that suggests that the existence of automobile insurance negatively affects driving behavior.)
- Environmental Risk: What if St. John’s increased the fees during the year and our policy simply provided “indemnification of fees” without being specific? Lesson learned: be sure to design your policy wording carefully.
It should surprise no one that subtle, complex topics are much more easily grasped by students when they can personally relate to the issues. I have certainly not perfected the exercise and each semester I try to incorporate additional material that I think would be of value to their careers and of interest to them. For example, this coming semester I plan on introducing the concept of Predictive Modeling/Data Mining. After they “convince” me that a classification system is essential, I will ask the question “How can we find out who are the better risks? Actuarial majors or literature majors? Men or women? Right handed people or lefties?”
I have found that the greatest advantage of this simplistic exercise is that you can modify the complexity and focus of the discussion based on your audience. As you might imagine, my actuarial classes tend to be more quantitatively oriented but I have also had enjoyable experiences in other classes involving students from vastly different educational backgrounds. The potential application is limited only by your imagination! I can easily see this used to stimulate high school students who have had little or no insurance/risk management/actuarial exposure.
The issues discussed here are only a few of the concepts that flow from the initial proposition. You will find that the paths of the discussions are difficult to predict but invariably they lead to fascinating conclusions and an engaged audience.
Albert J. Beer, FCAS, MAAA, is Michael J. Kevaney/ XL chair and professor of risk management, insurance and actuarial science in the Peter J. Tobin College of Business at St. John’s University in New York, N.Y. He can be reached at firstname.lastname@example.org.