The purchase or non-purchase of insurance could be either rational or irrational depending on how you view the question. I find that when faced with a situation like this it helps to create a 2×2 matrix and look at the characteristics of each cell that results.
In this case the matrix is constructed on the parameters of owning insurance or not, and having the insured event occur or not. For example, suppose someone has income of $80,000 per year and the option of buying $1,000,000 of life insurance or not. The premium is $1,000. (They are young and healthy.)
The outcomes are:
- No Insurance no death
- No insurance and death
- Insurance and no death
- Insurance and death
Assuming we want to look at only one year and not the net present value of all future potential income, then the contents of each of the cells (the meaning) is:
- No Insurance no death: Gain = Income = $80,000
- No Insurance but die: Gain = The premium = $1,000
- Insure and no death: Gain = Income minus premium = $79,000
- Insure and die: Gain = Insurance Proceeds minus premium = $999,000
Clearly, conditions 1) and 3) are negligibly different. While conditions 2) and 4) are profoundly different. The rational buyer at this point needs to ask themselves two questions.
First, what are the odds of death occurring? Let us suppose that the 1000 to 1 pricing of the bet the insurer offers will be in their favour. (You can be very sure of that.) Maybe the real odds are 2500 to 1 or even higher. Am I being stupid betting on an immensely improbable outcome. Maybe, but not until I can answer the second question.
What are the odds that my survivors would be indifferent to receiving outcome 2 or outcome 4? They would take either one of them and not care. I expect that the odds of indifference are enormously greater than the odds of death. Practically, they are infinite.
So we decide that the rational decision is that I should not buy insurance because it enriches insurance companies, but the practical decision is that while improbable that I will collect, it is vastly improbable that life would go on as before if I merely stored the premiums but I died.
People have difficulty with decisions that are ambiguous. If people continually compare outcomes, they will almost always love that they did not pay premiums. Every morning they get up and say, “Good thing I did not buy life insurance yesterday, I did not need it.” They could be right 10,000 times and only wrong once and still be a big loser. People are sometimes trapped in the idea that many successes is better than a single failure.
The paradox is that people cannot be fully rational and fully right at the same time. Smart people base their decisions on what they can accept as an outcome. In our example, “Insure” is affordable under all conditions while “Do not insure” is affordable only if you live.
There are two ways to be insurance poor. Pay too much premium or have too little to claim when the event occurs.
Don Shaughnessy is a retired partner in an international public accounting firm and is presently with The Protectors Group, a large personal insurance, employee benefits and investment agency in Peterborough Ontario.