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“It is a peculiar frailty of human reactions that many are prone to believe that a cynical, 'tough' perspective is more likely to be 'realistic' than a more objective, complex, and constructive one.”
- E. Fromm


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When Insurance Makes Wealth Grow Faster

The traditional view of insurance is that it is a “win-lose” proposition.

There are three reasons that insurance would exist in the traditional way of thinking about it:

  1. Asymmetric information - one party knows something that the other doesn’t.
  2. Irrationality - one party is dumb and simply not calculating the odds correctly.
  3. 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 or they are risk averse.

Setting aside the first two cases and assuming we have two "rational" and equally informed parties, insurance then is a behavioral error on the part of the insurance buyer as a result of being too risk averse.

A 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.

Another way of saying "an environment of noisy non-additive growth" is to call it an environment that is non-ergodic.

Here’s a brief explanation from my post 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 which, 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. They are, in the authors' words "environment of noisy non-additive growth."

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.

Let's say there's 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, the trader is not an average of many individuals. They 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. From Peters and Adamou again:

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 wealths. 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.

Each of us can only get the results that we get, we can’t get the average of results of a large group and cannot go back in time to change the results once received!

A lot of investors tend to think in terms of expected value. Consider a coin toss game where you are offered a 50% return if the toss comes up heads or a 40% loss if it comes up tails, but you have to play for a minimum of 100 tosses.

The expected return of any one toss looks attractive at +5%. Would you do it?

Well, the bad news is that the time-average returns, at the median, result in your capital approaching zero.

If we do the simulation with 200 players doing one toss of the coin, sure enough the average will come out with capital rising steadily by the 5% expected return.

There is an average terminal capital of $404, a 400% return. Seems great right?

However, if we flip it and play the game with one player and 200 tosses of the coin, the individual trends towards zero every time.

The median player that starts with $100, doesn't end up with $404. They ends up with $12 after only 40 tosses!

Coin Toss Simulation +50% vs -40%. 200 Players. 40 Tosses.

In effect, most people are losing everything and a few people are getting really lucky and pulling up the average.

It's also important to note that this luck cannot go on indefinitely and, over the long run, everyone's wealth trends down. Notice player 5 (light green line) starts with an astounding run up to $20,000, but proceeds to promptly lose almost all of it.

Is the lesson here that you shouldn't take positive expected value bets? No!

The lesson is it's possible to over-bet on a positive EV bet so you should size your bets appropriately!

This is exactly what insurance can allow you to do. The Phoenician trader that only owns two ships effectively has very large bet sizes. They have to risk half their portfolio on each trip. Using insurance effectively lets them to manage their bet size in a way that actually allows them to increase their expected long-term wealth.

When should you use insurance then? As a starting point, Kelly Criterion developed by John Kelly at Bell Labs is a methodology for calculating bet sizes that can be helpful in determining how much to bet (and thus where it makes sense to use insurance as a way to reduce your bet size).

As a more basic rule, the general idea of insurance that you should use it when the thing being insured represents a large portion of your net worth works fairly well (and the insurance is correctly priced, of course).

While we can never know the exact future expected value or risk of an investment/bet, I think it's a reasonable rule of thumb to say that something that represents a majority of your portfolio is likely too large a bet size.

You can play with this Kelly Criterion calculator yourself, but to give one example: an investment/bet with a 10 to 1 payout that you have a 70% chance of winning spits out a bet size of ~33% of your assets at half Kelly (never go full Kelly). That's insanely favorable odds and most investors will never see a bet that good in their life times. Based on that, my rough rule of thumb is you probably never want to go over 25-33% of assets into any one bet (and usually much less than that).

P.S. The Farmer’s Fable is a great example that shows how this dynamic is not only beneficial to each party, but systemic risk is reduced and systemic growth supported.

The Best of What I’ve Been Consuming

Decentralized Autonomous Organizations (DAOs) are the most recent “hot” topic in crypto-land. The concept however has been around since at least 2015. (If you’re not familiar, I recommend this post on What is a DAO? as a helpful, brief introduction).

I’m very excited to see how DAOs evolve and develop and I think it’s not hyperbolic to say that it is the biggest innovation in corporate governance since the development of the limited liability corporation.

This post is a good look at the current state of DAOs and how they are evolving.

DAOs are the native corporate structure of these crypto economies.

Instead of being incorporated in Delaware or the Cayman Islands, DAOs are incorporated in Discord servers and blockchains. DAOs provide an internet-native way of pooling capital, making collective decisions, and capturing value.


Community DAOs are the next evolution in online communities. It’s like if subreddits had a shared bank account, a token, and governance mechanisms. They’ll become the new social networks. And the best way to learn is by actively contributing.

It Might Be Passive, But It Ain't Income

I’d say I don’t normally get triggered very easily, but there are a few things that will do it.

Most commonly, putting the toilet paper on the roll incorrectly.

Second, most commonly is any time I hear the phrase “passive income”.

One common example of “passive income” is selling options. (As a reminder, selling a call option as mentioned here is selling the right, but not the obligation, to buy a stock at a specific price called the strike price).

The idea is that it’s a way to generate “extra income” from your existing stock positions but it has a few problems.

Suppose you own a $50 stock. Imagine you sold the $45 strike call for $5. Imagine the scenarios:

  • Stock goes up: Let’s say it goes to $60.
    • $10 profit on stock holdings.
    • Call option you are short goes up by $10.
    • You are assigned on your call option, your stock is called away, leaving you with no position. P/L =0

  • Stock falls but remains above the strike: Let’s say it goes to $47.
    • $3 loss on stock holdings.
    • Call option you shorted falls to $2. You earn $3 on that leg.
    • Again, you are assigned on your call option, your stock is called away, leaving you with no position. P/L =0

  • Stock falls below the strike: Let’s say it goes to $40.
    • $10 loss on stock holdings.
    • Call option you shorted expires worthless. You earn $5 on that leg.
    • Since the call is worthless, you still own the stock and you have a net loss of $5.

A few things to observe:
  1. You can only lose. This makes sense. You sold an option at its intrinsic value. Visually:

So when you sell a call against your stock position, you are now saying “I prefer total downside and limited upside”.

While this has immediate utility if your financial advisor is suggesting you sell covered calls, I think it’s also generalizable.

I would argue that most things marketed as “passive income” are effectively selling “total downside and limited upside”. Caveat emptor.


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The Interesting Times is a short note to help you better invest your time and money in an uncertain world as well as a digest of the most interesting things I find on the internet, centered around antifragility, complex systems, investing, technology, and decision making. Past editions are available here.
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