The traditional view of insurance is that it is a “win-lose” proposition.
There are three reasons that insurance would exist:
- Asymmetric information – one party knows something that the other doesn’t.
- Irrationality – one party (typically the insurance purchaser) is dumb.
- Risk aversion – the buyer of insurance knows they are making a losing bet, but are willing to do this as a way to be more “conservative.”
This thinking would imply that buying home insurance is a losing proposition and that most people do it because they don’t evaluate the odds correctly or they are irrational and afraid.
Insurance according to this narrative is not about wealth creation, but irrationality and some wealth preservation.
This paper from Ole Peters and Alexander Adamou provides a different explanation:
Here we provide an alternative explanation whose basis is dynamics: activities resembling insurance are likely to emerge whenever multiple entities are faced with managing resources in an environment of noisy non-additive growth.
This returns, of course, to the notion of ergodicity. Here’s a brief refresher on ergodicity (feel free to skip it if you’re familiar with the concept):
In scenario one, which we will call the ensemble scenario, one hundred different people go to Caesar’s Palace Casino to gamble. Each brings a $1,000 and has a few rounds of gin and tonic on the house (I’m more of a pina colada man myself but to each their own). Some will lose, some will win, and we can infer at the end of the day what the “edge” is.
Let’s say in this example that our gamblers are all very smart (or cheating) and are using a particular strategy that, on average, makes a 50% return each day, $500 in this case. However, this strategy also has the risk that, on average, one gambler out of the 100 loses all their money and goes bust. In this case, let’s say gambler number 28 blows up.
Will gambler number 29 be affected? Not in this example. The outcomes of each individual gambler are separate and don’t depend on how the other gamblers fare.
You can calculate that, on average, each gambler makes about $500 per day and about 1% of the gamblers will go bust. Using a standard cost-benefit analysis, you have a 99% chance of gains and an expected average return of 50%. Seems like a pretty sweet deal right?
Now compare this to scenario two, the time scenario. In this scenario, one person, your card-counting cousin Theodorus, goes to the Caesar’s Palace a hundred days in a row, starting with $1,000 on day one and employing the same strategy.
He makes 50% on day 1 and so goes back on day 2 with $1,500. He makes 50% again and goes back on day 3 and makes 50% again, now sitting at $3,375. On Day 18, he has $1 million. On day 27, good ole cousin Theodorus has $56 million and is walking out of Caesar’s channeling his inner Lil’ Wayne.
But, when day 28 strikes, cousin Theodorus goes bust. Will there be a day 29? Nope, he’s broke and there is nothing left to gamble with.
The central insight?
The probabilities of success from the collection of people do not apply to one person. You can safely calculate that by using this strategy, Theodorus has a 100% probability of eventually going bust. Though a standard cost-benefit analysis would suggest this is a good strategy, it is actually just like playing Russian roulette.
The first scenario is an example of ensemble probability and the second one is an example of time probability. The first is concerned with a collection of people and the other with a single person through time.
This thought experiment is an example of ergodicity. Any actor taking part in a system can be defined as either ergodic or non-ergodic.
In an ergodic scenario, the average outcome of the group is the same as the average outcome of the individual over time. An example of an ergodic system would be the outcomes of a coin toss (heads/tails). If 100 people flip a coin once or 1 person flips a coin 100 times, you get the same outcome. (Though the consequences of those outcomes (e.g. win/lose money) are typically not ergodic)!
In a non-ergodic system, the individual, over time, does not get the average outcome of the group. This is what we saw in our gambling thought experiment.
In practice, pretty much all situations we face in our lives are non-ergodic and this same logic translates to insurance.
We do not live 100 simultaneous lives, we live one life through time. Anything we do which contains the risk of ruin (or large losses) then must be avoided to maximize long-term wealth growth.
Take the example of insuring an old Phoenician trader insuring their ship for a perilous voyage. Let’s say the ship travels safely in 95 out of 100 voyages and is lost in the other ﬁve.
If you think about in terms of an ensemble average, 100 different traders each taking one voyage, then you would say that “on average,” the voyage goes fine and it doesn’t make sense to buy insurance.
Just as with cousin Theodorus, you are not an average of many individuals. You are a single individual living through time.
One trader taking 100 voyages over time is likely to experience multiple huge losses of wealth each time his ship fails to return and so there is a price at which insurance makes a lot of sense.
The two mental pictures – many parallel cooperating trajectories versus a single trajectory unfolding over a long period – are at odds. In general, we cannot equate the performance of expectation values with the performance of a single system over time.
A price range exists where both the shipowner and the insurer should sign the insurance contract. Within a certain range, the insurance increases the time-average growth rates of both of their wealth. Both insurer and insured end up wealthier in the long run!
It does make sense that some types of insurance are a result of behavioral biases and asymmetric information. Not any price is a fair price, but for most insurance contracts, there is some range that is beneficial to both parties in the long run. Both parties will do better in the long run, which constitutes an explanation of the existence of insurance markets without people needing to be “irrational” or having privileged information.
As the Farmer’s Fable shows, this not only is beneficial to each party but systemic risk is reduced and systemic growth supported.
Last Updated on January 28, 2022 by Taylor Pearson