General Insurance #1-2-3-4

This course is probably your first exposure to many of the insurance and risk terms that we cover this semester. I expect you will find that will be surprised at how you look at many terms and ideas regarding the insurance product are vastly different after going through this class. For example, I like to start out asking the students to provide their pre-class definition of risk. Many of them say “it’s the chance of something bad happening,” or “the possibility of a negative outcome.” You’ll find that these definitions are actually incorrect. While you’ll find three definitions of different types of risk on slide 3, please start thinking of risk as: 

Risk: The possibility of a deviation between actual and expected outcomes.

This definition contains the same elements as the definition given in slide 3 “uncertainty concerning the occurrence of a loss,” but let’s look at the deviation needed between actual and expected outcomes.  The following example really sets the groundwork for fully understanding Risk and the elements necessary to make the insurance product work successfully.

Assume that you own a house that has a 1/100 probability of total fire loss. You cannot predict whether your house will burn. Perhaps you then become a property investor and own 100 homes. You may assume that if your 1/100 probability is correct that you will have one loss. However, with such a small sample size, you could easily have 2 losses, meaning your expectation deviated 100% from the number of actual losses. Then perhaps you become a mega property investor and own 1000 similar homes. Keep in mind, we need all of these homes to be homogeneous for that 1/100 probability to be remotely accurately. Should you own 1000 homes, you should expect 10 losses. Should an extra loss occur (11 losses) when your expectation deviated only 10% from the number of actual losses. Continue this exercise with more houses, say 100,000, when you will expect 1,000 losses. One extra loss would lead to a deviation of only .1% from expected losses. Thus, is illustrated how the concept of insurance utilizes the law of large numbers (sample must be unbiased, without adverse selection, etc.) and units must be homogeneous to match the 1/100 probability of loss. Ultimately, risk (the deviation between actual and expected losses) is reduced! 

Let’s think briefly about the variables that may interrupt this process. Let’s say that instead of you owning all of these homes, we open up this process to MTSU students in this class. If there is only 1 student, it would be impossible to predict or plan for the outcome of that single house. We’d just probably buy insurance on the house if we were the owner. Now, let’s assume that there are 100 students in this class, each having identical homes in the same geographic area. Let’s also say that each home is worth $100,000. We should expect one of those houses to burn. So, we’d all agree to put $1,000 in a pot, and we’d have $100,000 available to pay for whoever the unlucky one of use is who incurs the fire. Everyone is happy and the owner of the house that burned “gets” the funds to rebuild his house as it was.

That’s sounds great, UNLESS we are off on our prediction. What happens to the pot if we actually have TWO houses burn, versus one? Obviously, we don’t have enough money in the pot to pay for two losses. We could have charged $2,000 per person, but perhaps none of us would have been willing to spend that much in premiums. So, let’s look exactly at the RISK in this deviation:  We expected one loss; we had two losses, so that’s a 100% deviation between actual and expected outcomes. How should we proceed with this scenario?

The only reasonable way to make this pot be large enough to cover our losses is to increase our sample size. So, the next line in the above table shows that we add more houses to our pool, let’s say 1,000 homeowners join our pool. We would then expect to have 10 losses and we would charge premiums accordingly. However, if we are off in our projection by 1 loss, then we are only off by 10% (the percentage difference between 10 and 11 is 10%). So we have reduced the risk, which is actually just that deviation between actual and expected losses.

Consider the problems that may occur in this scenario. Suppose a student joins our class who has a history of having multiple fire losses, or even worse, whose house is already on fire! Would you be willing to let him join the pool? Would you want to ask anyone who wants to join the pool if they have had prior fire losses? Would you think that the rules for joining the pool should prevent someone from joining if they are severely upside down on their mortgage? Clearly, we’d want the pool of homeowners to have similar loss probabilities if they are all paying that $1000 annual premium.   

I hope this example sparks some ideas in your mind about how to structure that pool of homeowners’ risks to charge just the right amount of premium that will cover any losses that may occur. You’ll find that the slides in this chapter take you through the basic classifications of risk and the costs and benefits of having this pool work successfully.