Yes, and I sometimes think about the inverse - that people like to hate on lottery players (which I'm not) with a clever sounding argument like E[X] < 1, so don't play, you'll lose.
But this fails to acknowledge the harder to model 'but I can pay £1 to play, I won't miss it, who cares, it's insignificant, and on the tiny chance I win, the win is significant'. I.e. 'but Var[X] is massive'.
You have a coin, and each time you don't get heads the payout doubles. Get heads and get the payout. What do you pay to play this?
It turns out that you can't work out an E[X] for this, as it's a series that doesn't converge. But also if you go around and ask people what they'd pay, surprisingly they don't say infinity. Expectation is thus not the last word in decision making.
Turns out utility is a thing that matters, and we can come up with some thoughts on it (von Neumann-Morgenstern etc).
I'm not sure it's that surprising, the expectation is only infinity if you think the person making the payout has the capacity to pay an infinite amount. The second you think this amount is finite (which must always be the case in reality), then the expectation becomes finite and probably quite small.
I agree in the more general point, expectation is not always the best tool for extremely rare / extremely significant scenarios.
In general money has a diminishing utility, your first dollar is worth more to you than your millionth dollar. In order for it to be worth it to play a -EV lottery not only does you utility graph need to be nonlinear, it cannot decrease monotonically. At some point your nth dollar needs to be worth more (to you) than your first dollar. For example, you have one dollar and a life saving drug for your terminal disease costs 1 million dollars. You would see a sudden spike in utility at the 1 million dollar mark. It would be rational to play the lottery in this case.
Another possibility is that the event of winning money or even just the thought of possibly winning that money gives you more value than simply having the money alone, and this tips the scale. This would be like the opposite of insurance. For some people the experience of losing, or worrying about the possibility of losing money is so negative that it still makes it worth it to buy insurance.
Your millionth dollar might have less marginal utility, but you were never going to win 10^6 -1 dollars anyway. So really to consider marginal utility you need 'margins' as wide as the payouts. (Really stretching/breaking the meaning of marginal, but hopefully you see what I mean.)
There is also time. You may be able to afford the lawsuit that will come from the owner of the car you wrecked. But having your insurance company handle that, something they have developed expertise in, can be worth the cost.
I think that is not necessary, and is a choice we have to make for our society.
For example, for health, do we want "sicker" persons to pay more, leaving healthy people the choice to not pay ? Or should we make it mandatory for everyone to pay what they can afford, and insure everyone, even high risks people ?
For cars, it might be a little different, but I think I'd rather have a system where everyone pays the same, and insurance is mandatory (although it's not as critical as health care).
"Sorry to hear you got cancer, here's your cheque. Please don't bother us anymore, as we terminate our contract. All the best."
Health care is more like a flatrate plan where some people receive much more intensive service.
Many forms of insurance include a cap to reduce the insurer's risk, but that doesn't mean such a cap is necessary for it to be called insurance. The height of the premium can be defined by law, but it's still an insurance premium.
Pensions can be hard to understand because longevity risk is a bit counterintuitive, but depending on how they work in your country they can definitely be a form of insurance.
Depending on your country this catalog is also shrinking and pushed into private insurance. Since there is such variability between countries and their systems these discussions become 'hard' to have because something that is normal for one guy works the opposite in the other guy's country.
In Germany I had dental covered by the state. Like you said, fixed percentage of my income covered all that (and all the other health insurance needs with a catalog of services). No need to think about it. Except someone actually decided on that catalog based on monetary concerns and calculations. Also while there is a fixed health insurance cost as a percentage of your salary, there are different actual insurance companies and they add a variable premium to this which they 'compete on' for clients. This is the public system which must cover you and you can go fully private (and never be admitted back into the public system if you do) which gives you "better service" (like private rooms being standard at the hospital and such).
Then they added private insurance on top for some stuff that wasn't covered by the public dental plan any longer. In Canada just a regular filling needs to be paid out of pocket and I really want private/employer extra insurance. Different for kids where I pay out of pocket for a white filling but Amalgam would be covered. I don't even know if this is the same in other provinces maybe.
Pension: Germany has a pyramid scheme and it collapsed a while back. Not enough payers any longer and suddenly they had to tax people's pensions. People who they told need not worry about their pension ever. Suddenly they were told they would need to pay tax on their pensions and oh btw. you should really have started paying into private pension like a decade or so ago. From after tax income. They do have various private insurance schemes that lower your taxable income but the fees are sky high and returns meager. It's a way to shuffle money into insurance companies. Thank's government! And other than that, you can get ~800 EUR of tax free interest/dividends per year. Everything else is taxed at 25%.
This is way different in Canada again where Old Age Security and your pension are not covering you and everyone knows. People either work longer because they can't afford extra insurance or have an RRSP (kinda like a 401k) they pay into. You know you will be taxed on this later but you aren't now. And all your money grows tax free in that account. Never pay a single dollar of taxes on those dividends over the years. And a non pension tax free savings account on top of that. Sure it's after tax income in there but you can take it out any time. No need for any insurance company fees either if you don't want to. Sure you can buy mutual funds and such but you arent forced to just to be tax exempt.
The system did just fine, but was plundered by politics. During the German reunification, the people from the former Eastern Germany were added to the public pension fund without ever having anything payed in. This drastically increased the amount of recipients without bringing in additional money.
Politics decided that. They also decided to not put any tax money in the pension pool to re-balance it.
No matter how you design a pension fund: If you bring in an additional country as recipients without any additional capital, that pension fund won't survive.
[1]: https://www.bpb.de/politik/innenpolitik/rentenpolitik/290963...
The complicating issue here being that you’ll eventually pay income tax rates on those dividends instead of (usually) lower dividend tax rates. If your income is high when you retire, you might pay more in taxes this way with the deferral. And it’s hard to know in your 20s and 30s what your income will be when you retire. But as a form of insurance, you should still build that nest egg.
Now here in Canada you pay something like half of your tax rate and its different whether they're "eligible" or not and such things. But all that is only outside of tax sheltered accounts and at least on my end I don't make enough to worry about calculating that. Then again at least here in Canada you also need to be aware of the whole withholding tax thing on US stocks and the implications for your dividends coz the US recognizes RRSPs as tax sheltered but not TFSAs...
Of course I won't really know whether I maybe make more in retirement than I do now but I personally believe that I will definitely make less than I do now. And if I really do earn more in retirement than I do now then I am probably very well off an it will in part be because my RRSP and TFSA contributions were able to grow without loosing 25% of the dividends all the time. So if compounding then does its thing and make me rich (I doubt I'll actually be rich from that though) then I'm fine with being taxed on it then.
It's not so much about whether you'll make less or not, but if you'll make enough less to land in a lower tax bracket to take advantage of the deferral. And avoid dying and having to pay tax on it all at once (unless you can shift it to your spouse, but then they may have a high income problem too, negating the benefit of the deferral).
RSPs can be great, but I think they're oversold to the working class as a tax advantage.
Different question since you seem not to like tax deferral. What makes you not like tax deferral and compounding on the extra ~25% of dividends you keep?
I can't do much about when I'll die. I do advocate for 'living now' btw. If you can do that 'trip around the world' now or put money into a pension fund, do it now. Don't wait, have kids and tell yourself you'll do it when you retire. That day may never come or you might not be up to it any longer for various reasons.
This is the wrong analysis. While it's true that when you withdraw you pay taxes at the marginal rate, you also need to realize that your contributions are before tax. When you're withdrawing, you're not paying income tax rates on the gains/dividends, you're paying income tax that you previously deferred. The gains are still tax free.
That's not true. The taxation of pensions in Germany is a gradual shift accompanied by a parallel shift to tax-free payments into the pension funds.
Please stop that FUD.
Really the issue is people with incurable conditions. Universal health care is there for them. Private insurance fucks them over.
I.e. they keep you in the healthy, fit and young group until you get cancer, and then they move you over to the $7,000/month group.
The current system just averages that out. Your rates are higher than they have to be when you're young, but your rates are lower than they have to be when you're old. It negates the risk by lumping everyone together. Your form of insurance doesn't do much to reduce risk because you can always be moved to another category. The insurer really just becomes a middleman between you and your medical providers then, if the goal is to allow people to pay for what they use. It's basically an HSA.
How could it be both?
And if it was beneficial, how could you describe the people to whom it was beneficial as "healthy and fit"? Aren't they really just people who the screening failed to identify as unhealthy?
When you're young you want to think only abt yourself, when you're old you want younger people to think abt you so :D
What about people that are not as well educated as you are, and thus don't know that too much sugar is bad for them ? Should they pay more ? What about overweight people that are from a genetic pool of people that are more subject to this issue ?
Sometimes it's hard to know if a disease comes from lifestyle or other factors.
It seems to me a lot of this is about responsibility to society, but that only goes one way. If it's my responsibility to pay into social Healthcare, why is it not their responsibility to not be a heavy smoker, or morbidly obese, or a heavy drinker? It seems to me that the moral tables are turned around in this argument, where I'm a bad person for not wanting to pay, but they arnt bad people for doing things that virtually garuntee they will need payouts.
Then, to quantify the people in that gray zone, it becomes a question of which variables to we include? Sure, alcohol is bad, and junk food is bad. But what is junk food precisely? And if you run ultra-marathons, it surely doesn't matter as much. If you live in a city with higher pollution, if you drive a cheaper older car with a worse safety rating, if you work two jobs and thus have higher stress levels, on and on.
And if we're talking about social healthcare, do you really want a faceless bureaucracy to be tasked with calculating those risks and putting a price on all your life choices?
But for geico (primarily auto), where’s the float? I thought it was like a pyramid scheme: this years payments pay out this year’s claims. There would be minimal float for the future except to cover black swan events like a hurricane hitting a state every 10 years, and that might be what Reinsurance is for (something else BH does a lot of, and probably self-deals a lot). Float would be great for the insureco, but any insurer charging anything more annually than average annual claims will lose all their business.
What are you basing the assumption that insurance companies are working with low margins on? There are many competitors, sure, but what reason is there to believe that they must compete on price?
And yet my car insurance quotes only ask me my age, gender, and what car I drive. They presumably also use my history of car accidents, serious legal issues like DUIs, and car insurance claims (all nonexistent in my case) as input. This strikes me as a comically low amount of information to place me in a risk pool.
https://en.wikipedia.org/wiki/Redlining
https://web.archive.org/web/20170317143050/https://fairhousi...
If they can, they'll use it: that is why black box car insurance exists.
“Oh wait, I almost never drive, but when I do, I’m either drunk or speeding. Well, I’ll sign up with this insurance company which offers me a discount because I drive so little!”
If you try to ise 10 pieces of information with 10 possible values each, that could give you 10 billion risk pools, i.e. individual person. Alternatively 33 Yes/No questions alsp let you identify an insividual person on planet earth.
Having "individual" insurance has no real meaning, because at that point its not spreading risk.
- That bit of info you give can be used to infer other info. Also it's possible those first three things explain most of the variation. We've all heard that young men in their 20s crash their cars a lot, I get the feeling it's true though I've never checked.
- You only need the risk groups to be granular enough that it isn't totally obvious that people are different risks (footballers and grannies).
But I don't think there is any solution. The further out on the "tail" you go, the more the total risk depends on the accuracy of information and assumptions you have. If there is an extremely large potential loss that is extremely unlikely, then the average becomes unknowable since the probability estimate in particular could be off by orders of magnitude. Nuclear power plants would be sort of the archetype of that, I think.
I mean, I reason like this to justify what I actually observe - that insurance companies don't want to insure things without strict limits. Despite reinsurance existing.
Isn’t that pretty much handled by reinsurance?
In the U.S. at least, you don't need to insure your own car. You just need liability insurance that will pay out to someone else if you're at fault in an accident.
That's why Buffet bought National Indemnity, btw. He wanted the float which, for him, was a cheap way of financing investment.
Not a very folksy move, truth be told.
- Some events are low probability but high cost. You're unlikely to crash your car, but if you do, it might cost you a heck of a lot to fix. Nearly everyone is in this situation, so it makes sense for everyone to pay a little at a time and give that pot to whoever ends up crashing.
- The insurance pool cares about the average outcome, ie average cost. They need to collect more than this. The insurance buyer cares about the extreme case, where they end up crashing. So in there we have space for a trade. Yes they care about the extremes too of course, since they wouldn't want a bunch of payouts at the same time, but that's something actuaries have thought extensively about.
- You want people in the pool to be similar risks. If they aren't and they know they aren't the low risk people will decide they don't need to insure, leaving everyone else with a higher average cost. Also, the high risk people will see a good deal and join. Adverse selection.
- If the thing you're insuring isn't a catastrophic cost, you're less likely to want to pay over the odds. Maybe your £200 phone doesn't need a £30 annual insurance, because you have lots of money to buy a new phone. If you're really rich maybe that car crash scenario doesn't matter for you either (but of course there are laws about insurance).
- The insurance company holds a free float. All the premiums are coming in, but only pay out now and again. That gives some room for investing the free float.