Pascal's Wager and the Making of Prudent Decisions: Insurance

Last week, we examined how the logic behind Pascal’s Wager can lead investors towards the prudent choice regarding a portfolio’s equity allocation. Today, we’ll change gears a bit and consider how the concepts in Pascal’s Wager can be helpful in certain advanced planning situations, specifically concerning decisions about whether or not to purchase insurance.

Consider a young, healthy couple with a newly born baby. They have a mortgage, a small 401(k) plan, and the equivalent of about six months of spending accumulated in a money market account. They are trying to decide if they should purchase life insurance.

The couple knows that the odds of either one of them dying in the near future are probably less than 100:1. Thus, they know that if they purchase life insurance, the great likelihood is that they’ll be transferring assets from their pockets into the pockets of the insurance company. What should they do?

Pascal provides the answer: the consequences of leaving a spouse and child with insufficient assets to provide the desired quality of life are unthinkable. Thus, even though the odds seem to suggest that the couple shouldn’t purchase insurance, the prudent decision is to do so.

Again, per the argument in Pascal’s Wager, we see that the consequences of our decisions should dominate the probability of outcomes. A similar example relates to long-term care insurance.

It’s estimated that at least 60% of people over age 65 will require some sort of long-term care services. Medicare and private health insurance programs don’t pay for the majority of the long-term care most people need, such as help in dressing or using the bathroom. Yet, long-term care is often overlooked as a crucial planning tool. Unfortunately, very few of our nation’s baby boomers have a policy that will cover the costs of long-term care. Let’s see how Pascal’s Wager can help us decide whether the purchase of long-term care insurance is appropriate. Consider the following example.

Mr. and Mrs. Smith are both 65 years old. They have financial assets of about $6 million. A Monte Carlo analysis reveals their portfolio has a high likelihood of providing sufficient assets to maintain their desired lifestyle even if the couple never has a need for long-term care. If one, or both, do eventually require long-term care for an extended period, however, the portfolio has a significant likelihood of being strained or even depleted. The Monte Carlo analysis also reveals that the costs of a long-term care insurance policy will not significantly reduce the odds of success.

The following table demonstrates various long-term care scenarios, and the odds that a portfolio will have sufficient assets to cover the need.

If no insurance is needed, the cost of purchasing a long-term care policy increases the odds of running out of money by just 3 percentage points (from 94% to 91%).

On the other hand, if long-term care is needed, and no insurance is purchased, the odds of running out of money increase by 20 percentage points. The odds of success fall from 94% to 74%. That’s almost seven times the 3 percentage point increase in likelihood of failure caused by the purchase of insurance. It seems clear that the purchase of the insurance is the prudent decision.

The same lesson also applies to decisions to buy other types of insurance, be it disability, flood, earthquake, or personal liability (specifically umbrella policies, which are relatively inexpensive).

Next week, we’ll look a few more examples in which Pascal’s Wager can be applied to financial decisions.

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