This is precisely why I absolutely always get house and car insurance but never ever pay for an extended warranty.

House (if you have a mortgage) and car insurance are not optional. The bet you'd be making by not having them has much higher stakes.

I haven’t carried collision insurance for decades. There was one exception where I financed an electric car at 0% for a while. Obviously, the lender required comprehensive insurance, most of the cost of which I viewed as the finance charge and paid off the loan and dropped collision coverage once the balance got low enough to make the imputed interest rate unattractive.

You need liability insurance (until you’re ridiculously wealthy perhaps), but fire/structure coverage and collision coverage are much more optional if the home/car value is low enough relative to your net worth.

You can get minimal "liability-only" car insurance (at least in the USA) and still be legally covered.

Called third party in New Zealand, I assume it's basically the same thing.

Likewise, I have car insurance but not contents insurance for my house. I can just buy a bed and a laptop if my (rented) home burns down, everything else is really non essential and can be picked up again slowly.

Living is coastal Florida it makes no sense. My goal is to pay off my mortgage and drop home owners insurance.

Absolutely correct. Measured in log wealth (call it growth, or utility, or whatever you want), insurance is sometimes a net gain -- even if the straight arithmetic expectation would indicate it's a loss.

I forget who, but one person I respect a lot in risk management said that "the only surprising thing about insurance is that people don't get more of it."

But of course, it's not always a net gain. And even a rule of thumb like "for expensive things insure, otherwise don't" has problems. That rule would have lead me to get unemployment insurance, but doing the numbers I realised it would be a net loss, even considering the Kelly criterion.

You have to make the computations each time to bet rationally.

> the only surprising thing about insurance is that people don't get more of it.

That's a weird formulation. To me, the most surprising thing is that people insure... wrong things. I mean, there are exactly two reasons to take insurance:

1. The economical effects of the event you insure against are beyond your comfort zone.

2. You are for some reason confident that the insurance company has miscalculated your risk profile.

Now, I ignore the second one. The question is, why people take travel insurances that cover lost sunglasses? I mean, to me, it would be obvious that the equilibrium is that people choose so high deductibles that they just can afford/are comfortable with, which means cheaper insurances for two reasons: Insurance company pays out less money and needs to do less work per paid out dollar. But high deductible insurances are almost non-existent.

> The question is, why people take travel insurances that cover lost sunglasses?

I think the answer could be a quite mundane appeal to 'bundling'. i.e. I get very comprehensive travel insurance when travelling to the US due to the punitive cost of healthcare (your (1)). This comphrensive insurance can often cover unrelated and unneeded items, but it's hard to slice and dice the coverage exactly.

You're right, of course. I think the formulation was aimed more at general life events that we don't even think of as insurable. I can't recall any concrete examples from that person, whoever it was, but one thing I've long wanted is insurance against bad weather on family outings planned well in advance. Some days when I have more important meetings to get to farther away, I would also like insurance against unexpected traffic jams and other holdups.

Essentially, we make all these tiny little bets every day, and while it's possible to hedge them[1], it's complicated compared to just straight-up money-based insurance.

[1]: I can for example reserve a table at a fancy restaurant halfway to the important meeting, so if I get stuck on my way and miss the meeting I can at least get a nice meal out of it, at the cost of the table reservation.

Yep. If you can survive catastrophic loss (for some appropriate definition of survive), then insurance is always a losing proposition.

> always a losing proposition

It is not always, and in fact there are common cases where it has significant positive expected outcomes.

Let's assume that you have sufficient wealth (say $40MM) that you can pay for a massive medical bill out of pocket. Let's furthermore say that you know, due to a hereditary illness in your family, that you have 90% chance you will be on the hook for a very large (say $1MM) bill when you're in the age range 20-30.

An american health insurance company legally cannot charge you more just because of preexisting conditions or family history, so health insurance will be a winning proposition for you.

Similarly, if you have information that the insurance company does not have, then you can "win" at other forms of insurance. If you have an ex-boyfriend who is prone to stealing bikes or setting homes on fire, then insurance covering those will have a higher expected value to you, and the insurance company is unlikely to account for that increased risk.

If you happen to know you're a bad driver, but have never been in an accident (only close calls), you might look normal on paper, and thus get a rate that has positive expected returns for you.

Said another way, insurance is not always a losing proposition. It can be a winning proposition if the insurance company doesn't understand the risks correctly or if laws prevent the company from accounting for certain risks.

Another easy counterfactual is an insurance company's public financial disclosures where the payouts > collected premiums.[0] Not sure I'd argue there was a moral information hazard, but, in retrospect, it's favorable risk transfer per $ for the insured.

[0] https://www.reuters.com/business/life-insurers-adapt-pandemi...

It isn't if you know your own risk is significantly worse than the average buyer. This is called adverse selection.

It's a really interesting (to me) example of how a trade can be mutually beneficial when there's no obvious difference (like trading an excess of chickens for something you lack). The odds on the bet are/can be the same for both sides yet getting insurance can make sense as can selling insurance.

There is an obvious difference though. As an individual, you provide a small amount to a collective pool kept by a third-party. You can't do much with the effective amount, but the combined wealth of all of an insurers premiums is quite a large amount of money.

As an insurer, you're essentially a deposit-only bank with some special cases that allow you to withdraw (make a claim). You have a large amount of money that you can now invest and make actually meaningful profits. What you trade for that is the assurance that should someone require a large sum of money for a loss, you will pay for it.

I don't really now where people get the idea that insurance companies are just sitting on the stacks of cash they pull in from premiums. You have a minimum reserve you have to keep to assure you have enough to cover claims, just like a bank doesn't have your cash on hand all the time. (You all should watch It's a Wonderful Life sometime.) The long run expected gain from a "properly priced" insurance product is net zero (in reality its usually a loss). They make money off your money, not directly off selling insurance.

I dunno, for-profit insurance has always struck me as something predatory by nature. The only functional difference between the two sides is that the sellers of insurance have capital to absorb loss--sure, there's some overhead in organization and risk calculation, but fundamentally it's leveraging the wealth of a few people so they can extract some wealth from many more.

>fundamentally it's leveraging the wealth of a few people so they can extract some wealth from many more

The insurance company isn't paying you out of the coffers of their wealthy owners. They're paying you out of the coffers from you and all your fellow insurance buyers' premiums. The primary transfering of money is from the little guy--- to the little guy. Any massive profits come from skimming a tiny bit of that at a very large scale. And competition pretty much dictates that that won't be predatory.

What I mean is that some group of people earns dividends from the profit of the insurance company (stockholders or private owners), the insurance company earns profit by charging each little guy more than they are expected to cost.

When I say 'inherently predatory', I don't mean that every insurance company is doing the equivalent of loan sharking, I mean that the concept of mandatory participation in a system that then also makes its own determination of how much wealth is reasonable to take from you in exchange for its service seems fundamentally immoral.

You know, when I write it like that, this applies to life in basically any situation --

* fully-capitalist (have to work, a market you have no control over determines your value)

* fully-communist (have to work, a government you have no control over determines your value)

* completely anarchist (have to work, the conditions of the world around you determine how much work you need to do to stay alive)

So I think what I'm actually saying might just be 'life isn't fair' which is kinda banal.

You can think of an insurer as someone who provides a service of pooling resources together to help those who got unlucky. That service is worth something and is not necessarily predatory.

I think the idea of that service being all three of mandatory, not owned by its participants, and profit-driven is what causes it to feel inherently predatory -- that there exist companies which take on risk on behalf of entities who cannot take on that risk (and therefore must participate), and then profit by charging those entities more than they are expected to cost and using the pool of wealth created as investment funds for which only owners of that company derive benefit.

The service is obviously not worthless--some entity has to assess risk, coordinate, and administrate--but it is predicated on terms that make it (I would assert) immoral to transfer more than is necessary from those that participate in the service to those that own the service.

I'm not sure I understand how Kelly applies to insurance, as by definition the Kelly of any -EV bet is 0. Can you elaborate on how to do a Kelly calculation with a wager of negative expected value? Or what am I missing?

A theoretical bet from this analysis in real life can be any situation where your outcome depends on result of a random event.

Every time you don't take insurance you're betting all your wealth on there being no ruin- level disaster.

The Kelly bet for any negative arithmetic EV is 0 when you are fully in control of the bet size. Sometimes you're forced to bet, and then you might want to hedge your bet to avoid large losses which will set you back more than the insurance, when you look at it from a growth perspective.

In other words, when you are choosing between "a loss" and "no loss", then the correct Kelly bet is of course "no loss".

However, when you are choosing between "a loss" and "a different loss", which is the case when it comes to insurance, then you need to whip out your slide rule and do the numbers.

This is an example I used with another group of people in another context:

----

Let's say you get the opportunity to try to hover a helicopter close to ground, for whatever reason. There's a real pilot next to you who will take control when you screw up (because hovering a helicopter is hard!)

However, there's a small (2 %) chance you will screw up so bad the other pilot won't be able to recover control and you crash the helicopter. You will be fine, but you will have to pay $10 k to repair the helicopter, if that happens.

You can get insurance before you go, which will cover $6 k of helicopter damage (so even with insurance, you have to pay $4 k in addition to the insurance premium if you crash), but cost you $150 up front.

Do you pay a $150 premium to reduce an unlikely (2 %) loss of $10 k down to a still sizeable $4 k?

----

If we do the arithmetic expectations, we'll find that with insurance, the expectation is negative $200 if you don't go for the insurance, and negative $230 with the insurance. So always skip the insurance, right?

Not so fast. That is correct if we had effectively infinite money in the bank. If we have an infinite amount of money in the bank, we can repeat that "no insurance" bet over and over and get the arithmetic expectation.

In practise, we don't always have an effectively infinite amount of money compared to the losses in question, so we need to consider how the growth of what we have is affected by the losses.

----

The answer then, according to the Kelly criterion, is "it depends". Specifically, it depends on how much money you have in the bank.

If you have more than $35 k in the bank, then the $10 k loss is small enough to not affect the growth of your money significantly. If you have less than that, the $10 k loss is sizeable enough that it's worth spending $150 to reduce it down to $4 k.

Going the other way around, if you have $20 k in your bank, you should be willing to spend as much as $186 on the insurance, to protect against the risk of halving your available money.

----

In terms of how the calculation is done: I find it easiest to do it the way Bernoulli did it back in the 1700's when he invented the mathematical formulation of the Kelly criterion: use the geometric expecation. (This is equivalent to the arithmetic expectation of the log.)

Here's the equation set up to compute what wealth is needed to decline the insurance in the helicopter example: https://www.wolframalpha.com/input?i=solve+w%5Ep+*+%28w+-+L%...

(Hopefully the symbols are obvious, but in case they are not:

- w = current wealth

- L = loss with no insurance

- p = probability of no adverse event

- q = 1 - p = probability of adverse event

- c = premium of insurance

- d = deductible of insurance)

It's strange to me how you overcomplicate it all by thinking about growth instead of utility of money. Once you switch everything becomes easier and more intuitive. You will also see why Kelly is not a good guideline for most cases as it's utility that matters (by the very definition of it) and not growth.

I commented elsewhere already, but I have a blog post where I go through some examples of applications of the Kelly Criterion, including two that are related to insurance: https://blog.paulhankin.net/kellycriterion/

You're really betting your net worth with odds of say p 0.995 = net worth - insurance payment p 0.005 = 0 (or worse)

It is not the same. The Kelly criterion is for when your capital is required to make you money; without capital you can't make bets so you'll be ruined forever. Without insurance you risk losing all your money, but if you have a day job, you'll eventually make it back again.

It is the same. It takes the same time for your savings to go from $1 k to $10 k as it does from $10 k to $100 k.

In other words, if you have $10 k in savings, and then skip the insurance and go down to $1 k, you might end up retiring with $10 k. Whereas if you do take the insurance and your savings stay at roughly $10 k, you can retire with $100 k – given the exact same day job, etc.

Your savings compound. That's the only requirement of the Kelly criterion, regardless of everything else.

> Your savings compound. That's the only requirement of the Kelly criterion, regardless of everything else.

The use case of the Kelly criterion is to determine the optimal size of your capital to put at risk, where the profit you're expecting to make is linearly related to that size.

In your example you have savings which will bring in some percentage no matter what. And you have the choice of taking an insurance or not. Taking the insurance would cut your profit, but most likely not in the linear way that the Kelly criterion assumes when it calculates the optimal bet size.

This paper discusses that exact issue:

Insurance makes wealth grow faster Ole Peters, Alexander Adamou https://arxiv.org/abs/1507.04655

Which given how much people underestimate how easy it is to lose it all starts to make it make a lot of sense

Do what you can to avoid financial ruin.