In an essay on risk, Nobel Laureate Kenneth Arrow asks us to consider the difference between gambling versus regularly paying premiums to an insurance company. The mathematical probabilities indicate that we will lose money in both instances. In the case of gambling, it is statistically impossible to expect more than break even because the house edge tilts the odds against us. In the case of insurance, the premiums we pay exceed the statistical odds that our house will burn down or that we will be burglarized.
Why do we enter into these losing propositions?
We gamble because we are willing to accept the large probability of a small loss in the hope that the small probability of scoring a large gain will work in our favor. We buy insurance because we cannot afford to take the risk of losing our home to fire, or our life before our time. That is, we prefer a gamble that has certain odds on a small loss and a small chance of a large gain versus a gamble of uncertain but potentially ruinous consequences for our family by saving cost and going without insurance.
In practice, however, insurance is available only when the Law of Large Numbers is observed. This law requires that the risks to be insured must be both large in number and independent of one another, like successive deals in a game of poker. It also means that insurance will only be available when there is a rational way, for the insurance company, to calculate the odds of loss. Consequently, the number of risks that can be insured against is far smaller than the number of risks we take in the course of a lifetime.
In business, we seal a deal by signing a contract or by shaking hands. These formalities prescribe our future behavior even if conditions change in such a way that we wish we had made different arrangements. At the same time, they protect us from being harmed by the people on the other side of the deal. Contracts protect us from unwelcome consequences even when we are coping with uncertainty. Outside of business, people guard against uncertain outcomes in other ways. They call a limousine service to avoid the uncertain ability of getting a cab or having to rely on public transportation. They have burglar alarms installed in their homes. Yes, reducing uncertainty can be a costly business.
How Much Information Is Enough?
Have you ever noticed that the way you make decisions involving gains and decisions involving losses may be different? Where significant sums are involved, would you reject a fair gamble in favor of a certain gain? Or, if the choice was different and involved loss, would your decision remain the same? Also, are your decisions significantly swayed depending on the size of an expected gain or loss?
Academics believe that we display risk-aversion when we are offered a choice in one setting and then turn into risk-taking when we are offered the same choice in a different setting. We tend to ignore the common components of a problem and concentrate on each part in isolation. We have trouble recognizing how much information is enough and how much is too much. We pay excessive attention to low-probability events accompanied by high drama and overlook events that happen in routine fashion. If true, why is this so?
A 1979 paper on Prospect Theory describes an experiment showing that subjects were first asked to choose between an 80% chance of winning $4,000 and a 20% chance of winning nothing versus a 100% chance of receiving $3,000. Even though the risky choice had a higher mathematical expectation (80% times $4,000 equaling $3,200), 8 out of 10 subjects chose the $3,000. These people were risk-averse. Then the subjects were offered a choice between taking the risk of an 80% chance of losing $4,000 and a 20% chance of breaking even versus a 100% chance of losing $3,000. Now, 9 out of 10 chose the gamble, even though its mathematical expectation of a $3,200 was once again larger than the certain loss of $3,000. When the choice involved losses, the subjects were risk-takers, not risk-averse.
These results, although understandable, are inconsistent with the assumptions of rational behavior. The answer to the question should have been the same regardless of the setting in which it was proposed. From the experiment, the authors conclude, "it is not so much that people hate uncertainty, but rather, they hate losing."
University of New Orleans economics professor Edward Miller cites various psychological studies showing that the magnitude of an expected outcome significantly influences our decisions. "Occasional large gains seem to sustain the interest of investors and gamblers for longer periods of time than [when experiencing] consistent small winnings. That response is typical of investors who look on investing as a game and who fail to diversify; [because] diversification is boring. Well-informed investors diversify because they do not believe that investing is a form of entertainment."
If you were expecting this newsletter to discuss how probability works or how to predict the future, you may have come away disappointed. My intent was to focus on how people make decisions under conditions of uncertainty and how we live with the decisions we have made. Hopefully, the concepts touched upon will help you develop a more thoughtful approach in evaluating future risks you will face and those risks you will decide to take.