Nasty or nice – playing the tail

Insurance and gambling have much in common. They both involve uncertainty and money and the rational consumer will, on average, lose money through the interaction. Both business models involve leveraging the tail of probability distributions (one nasty and one nice).

The tail of a distribution includes the very bad and very good possible outcomes, that typically have a very low frequency of occurring. Having your house burn down is a very bad outcome, but fortunately happens very infrequently. Winning the lottery is very good, but unfortunately in this case is also very unlikely for any particular individual.

Managing the nasty tail

A rational person who wants to avoid the unlikely but catastrophic risk of  losing their house to fire will be prepared to pay more than just the average cost of the loss of the house in order to avoid the risk. Typically, we humans are risk averse (a wild generalisation given the research into utility and decision making that has led to behavioural finance and behavioural economics, but probably good enough for now). Insurance provides:

  • genuine decrease in risk and indemnification of losses against the loss event happening
  • peace of mind even if no loss is ever experienced, which has real value in terms of clearing the mind to think about other more important and more controllable personal and business matters
  • reduction in the amount of capital / liquid assets individuals and businesses need to keep against unforeseen events. This capital can be better used and invested elsewhere

Contrary to the popular view, insurance has value even if you never claim.

Gearing to the nice tail

Gambling can be dangerous and addictive. It can also be entirely rational to gamble within certain parameters.

Many people with a little mathematical, statistical or economic backgrounds view gambling as foolish because on average, those playing against “the house” will lose. Playing the game has a negative “expected value” since on average more money is spent than is one. (Casions regularly pay out approximately 97% of the money they take in, safe in the knowledge that most of the money they pay out will be return straight to the casino. The casino has several bites at your wallet. Playing ten times over reduces the effective payout to below 75%.)

A negative expected value is not sufficient to make it irrational to play the game. Insurance has a negative expected value for the insured but for the reasons mentioned above it is rational to use an appropriate amount of insurance.

The step that comes closer to making gambling irrational is that the gambler is paying to take on risk. Insurance is all about paying a premium to reduce risk. If humans are naturally risk-averse, how can it be rational to pay a premium to take on risk?

This brings into sharper focus the problems around the generalisation that humans are risk averse. I’ll try to explain how it can be rational to gamble under some parameters as an example of how risk-seeking behaviour (paying to take on risk) can be rational.

Entering the national lottery twice a year (you and your spouse’s birthday, for example) will cost around R7 per year. If you start this when you get married, using very rough numbers, it will almost certainly cost you less than R500 over your entire life. That R500 is not going to change your life in any meaningful way, but it does provide the chance of a completely life-changing event. You could pay off your house and cars, stop working, travel the world, donate to your favourite charities and provide for your children’s health and education. You now have upside exposure to that very unlikely, buy very desirable outcome.

Provided you don’t live your life expecting to win the Big One, and provided you don’t buy a hundred tickets every month to improve your chances at the expense of food on the table for your family, this can be an entirely sensible decision.

Other tails

Gold miners can’t control the gold price. In order to plan operations and capital investment, they should be hedging gold production at some level. The downside tail of very low gold prices is an unbearable risk that limits the ability of the organisation to be an efficient gold miner.

Gold exploration companies, on the other hand, are geared to the upside tail. Expenses are relatively fixed, and the chance of success isn’t great, but the payoff is they literally strike gold is fantastic.

Entrepreneurs are putting themselves out into the risky world, hoping to catch a wild ride up a huge positive tail.

Management diversifying a business because all their personal interests are too tightly focused in a single company, in a single industry, in single part of the value chain are hoping to avoid nasty tail events (or trying to diversify away from a dying business, or simply empire building rather than returning cash to shareholders, but that’s several separate posts altogether).

The lesson

The distribution of what can happen is important. Forget about the MBA mean and standard deviation mirage. Those measures conceal more information than they provide. Understood the most likely events and the extremes, understand how they affect your business and understand how the perception of these issues affects the decisions of those around you.

Published by David Kirk

The opinions expressed on this site are those of the author and other commenters and are not necessarily those of his employer or any other organisation. David Kirk runs Milliman’s actuarial consulting practice in Africa. He is an actuary and is the creator of New Business Margin on Revenue. He specialises in risk and capital management, regulatory change and insurance strategy . He also has extensive experience in embedded value reporting, insurance-related IFRS and share option valuation.

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