Economists and Mathematicians are often believed to be in a better position when making decisions on finances. Their training in all things numbers would give them an edge in making smart decisions and being able to capitalize on what they have to build greater wealth. However, this training can backfire, especially in the unique case of buying insurance.
This realisation came to me when I read an article about what insurance we should get. Its recommendation for readers is to use the concept of expectations to inform our decision-making on what and how much insurance to buy.
Expectations: A Mini Lesson In Economics
What do we mean by the concept of ‘expectations’? In economics, the “expected costs” of an uncertain activity are given (simplistically) by the cost of event C multiplied by the probability of the event happening P.
Expected Cost = C x P
To illustrate, let’s use the example of the expected cost of getting an emergency cesarean-section at a public hospital.
Cost of a Emergency C-Section
Probability of the event (especially for a breech baby)
Expected Cost (C x P)
50% x $10,000 = $5000
The reason why the expected cost is lower than the costs is that when we calculate expected cost, we actually average out the costs across time; and since the cost is occasionally avoided, the overall average cost actually falls.
Issues with the Concept of Expected Costs
As illustrated by the example above, mummies would probably intuitively know the issue with this concept. Mothers know that this expected cost doesn’t make sense - they either have an emergency C-Section, or don’t.
Schwarzman, author of the book, “What It Takes: Lesson in the Pursuit of Excellence”, similarly illustrates this problem: Schwarzman was discussing a case study regarding how much money should one spend diving for gold assuming they could calculate the expected value of gold buried underwater.
“I read the case,” I (Schwarzman) said. “But it seems to be nonsense. If this is what the class is going to be, it’s basically got no practical application to someone like myself.”
Jay stared at me. “Tell me, Mr. Schwarzman, why would that be?”
“Because this case about expected value is premised on having an infinite number of dives to find the gold. I don’t have an infinite number of dives in my life. When I dive, I have to have a 100 percent probability of finding the gold, because otherwise this whole enterprise can bankrupt me.
Therein lies the problem of using expected values; it requires repeated plays, with the costs averaged out over time for it to make sense. Unfortunately, we cannot use expected values because we don’t have infinite lives (unless the Matrix was real!) to reduce the costs of the event NOT happening over repeated games. We don’t have an expected value of falling sick or going to the hospital. We are either sick or not sick. The cost to an individual is the entire cost of illness, or $0.
Does this mean that expected values are meaningless?
No. It is important to understand them, not for an individual, but for the population.
Let us consider, illness. Hospitalization bills can run up a hefty sum. To self-insure means we would need to make a guess of the estimated bill in advance and set that amount aside. We might also have repeated admissions over the course of a lifetime, and this could be costly for us since that money will need to be sitting in some low returns-low risk asset to ensure they are available at any time. So we would have to set aside a sizeable amount just to ensure we are well-protected.
However, an insurer has the opportunity to average out the cost, or at least use expected values. By insuring a large group of people, the insurer can ‘relive’ life many times over. Furthermore, because he controls the premiums paid, he is able to pool the resources across the group. As a result, the individuals who do not fall sick help to subsidize the costs of those who are sick. In other words, the insurer can actually set aside "C x P" per person.
Does this mean healthy people lose out? In a way, yes. A healthy person may not need insurance! But, will you know if you are healthy and never need insurance? Can you predict the future? You cannot. Hence, insurance helps to mitigate the risk, on the off chance you are actually the unfortunate sick person.
The key takeaway from this exercise is to recognize that what is true for a population, is not always true for an individual. Expected values depend on repeated lives AND the ability to share costs over the different lives. An individual cannot. An insurer can. The problem with statistics is that what is true for a population, or a group of people, is not true for an individual. So take expected costs, or average costs, with a pinch of salt. You might be the outlier in that population.
This is why we insure ourselves.
What Should We Insure Ourselves From?
You might be wondering, what then are the events we should insure for?
The answer is simple: Costly, infrequent events.
Again, the logic goes back to the principles of expected costs.
Firstly, costly events can wipe out our savings. We should aim to avoid such costs. But when it is impossible to avoid entirely, such as hospitalization, the next best alternative is to insure, in order to protect ourselves.
Secondly, infrequent events make it hard for us to predict, or even to face repeated opportunities for events to occur, in order to smoothen out the costs. As such, these events make it worthwhile to insure.
Ultimately, it is important to note that insurance is an expense until it becomes a valuable asset. And it is something that you buy when you don’t need it, such that when you do need it, it is available. How do you then ensure the appropriate level to spend on insurance? That requires a planning process to ascertain needs, and how much you’d like to protect yourself. Don’t forget, insurance is meant to protect against an uncertain event, which might not happen. So balance between protecting yourself and living a full life.