When does it make sense to get insurance?

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Crusader
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When does it make sense to get insurance?

Post by Crusader »

I am going on an international trip soon, which made me start thinking about getting emergency health insurance, or not, and I am not quite sure how to make a decision, but I am leaning towards not getting it. The general principle I am asking about has general implications beyond health or even insurance, and I would like to have a system that will allow me to make these kind of decisions consistently.

If we look at it purely in terms of numbers, you have:

p = probability that something will go wrong (e.g. 1/1000)
Lm = monetary loss if not insured (e.g. $10000)
Li = intangible loss if not insured that the insurance would prevent, both short term and long term (let's assume none here)
C = cost of insurance (e.g. $20)

For these numbers, the cost of insurance is too expensive, because the breakeven cost would be:

(Lm + Li) * p = $10000 * 1/1000 = $10

so it is better to not get it.

The problem is in the Li term. For something like life insurance, it is pretty high (you cannot work for the rest of your life -> how do you put a number on that? I guess you sum up all the lost income and future medical bills. But, for something like emergency travel insurance, I think it's pretty low (they only pay the hospital bill and that's it), assuming you can afford the hospital bill.

What do you guys think? Is my analysis right?

I also suspect that because insurance companies always have to make a profit, the answer to this question is very likely to be "no, don't get insurance" all the time. In fact, mathematically, it's the same as playing the lottery.

Alphaville
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Re: When does it make sense to get insurance?

Post by Alphaville »

this is massively wrong and not how you buy insurance, but i don’t have time to lay out in how many ways.

but let’s skip all that—since you’re canadian and your healthcare is covered by taxes, i’d ask your government what sort of emergency evacuation plans and other protections do they have for travelers. begin with the insurance you already might have.

now ask yourself in a neutral/abstract scenario, if you were in the situation of needing $10k to prevent serious damage and disability, how far $10 in your pocket would take you? (you’re an individual, not a population.) if you don’t have the savings, you need insurance.

read “fooled by randomness.” invisible russian roulette generators abound :D
Last edited by Alphaville on Sat Oct 03, 2020 10:55 am, edited 1 time in total.

rube
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Re: When does it make sense to get insurance?

Post by rube »

Edith Keeler might give an more sophisticated answer.

risk = probability x severity

My main focus would be on the severity, in this case mostly "cost". I don't insure my cellphone as it's cheap to replace. No real issue. I don't have a "dental" insurance that is costing me 200 Euro's a year but only payout max. 500 Euro's a year.
I do have a fire insurance for our house though. The probability is very low I ever need it. Way lower than I lose my cellphone, or have a dental bill of 500 euro. But I don't want to lose half a million Euro's in case my house burns down, for an insurance that is costing me only 200 euro a year or so. I am fine that the insurance company takes a profit here.

If you are travelling to a low cost area, including the hospitals, you might be fine without. But for many (high cost) countries, like the USA, I would personally not do this and take a travel insurance with a high deductable but which would protect you in case of extremely high cost. Not sure what it would cost for you though. In my country, it's not very expensive.
But this is all very much depending on local/personal circumstances.

Crusader
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Re: When does it make sense to get insurance?

Post by Crusader »

@Alphaville, from the synopsis of "Fooled by Randomness":
Other misperceptions of randomness that are discussed include:
...
Skewed distributions. Many real life phenomena are not 50:50 bets like tossing a coin, but have various unusual and counter-intuitive distributions. An example of this is a 99:1 bet in which you almost always win, but when you lose, you lose all your savings. People can easily be fooled by statements like "I won this bet 50 times". According to Taleb: "Option sellers, it is said, eat like chickens and go to the bathroom like elephants", which is to say, option sellers may earn a steady small income from selling the options, but when a disaster happens they lose a fortune.
I guess this is what you are referring to. I am not convinced. You need to take calculated risks in life because the expected benefit you get is much higher than if you don't. Why leave the house at all? You could be hit by a car or lightning.

Crusader
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Re: When does it make sense to get insurance?

Post by Crusader »

@rube

That's how intuitively I thought about it as well, but the only difference between your cellphone and house burning down example is the relative size of the numbers. Why would this change anything in the analysis? (other than "peace of mind", which is a purely emotional concept)

Alphaville
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Re: When does it make sense to get insurance?

Post by Alphaville »

screw the synopsis (by who?) and read the thing. it’s all about being blind to catastrophe—until it happens. it’s about the successful trader with a good track record who one days blows up. it’s about the weight of many small wins vs the weight of *one huge loss*

and of course everyone dies. that’s not the point.
Last edited by Alphaville on Sat Oct 03, 2020 11:05 am, edited 1 time in total.

Crusader
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Re: When does it make sense to get insurance?

Post by Crusader »

@Alphaville
I just read the Wikipedia article.

Anyway, continuing on with my thought process, taking my "optimize the expected value" to the extreme, if someone said: I will flip a coin and if it lands on tails, I will give you all your savings + $1, and if it lands on heads, I will take all your savings from you, I would have to take that bet. Which I am sure I wouldn't.

I think there is no objective answer here and depends on personal preference. I just don't know how to personally determine this preference.

Alphaville
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Re: When does it make sense to get insurance?

Post by Alphaville »

i don’t know of you’re talking about the general concept of insurance, or the specific instance of needing insurance for your trip.

generally speaking, having insurance against disaster is a good thing.

if you can self-insure, i,e. have enough resources to absorb a shock, you’re gold.

if you can’t self insure, then buying (good) insurance makes sense, as it spreads the risk among the pool. (but some insurance is indeed wack)

if you can’t self-insure and can’t afford to buy insurance, then you’re in what’s called a “vulnerable population.”

but yes, everyone dies in the end. the question is how do you live until that happens. :D

daylen
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Re: When does it make sense to get insurance?

Post by daylen »

It really should depend on your reserves. If you can take the worst-case outcome and recover without much hassle then you're self-insured. Otherwise, the worst-case may result in financial ruin forcing a lifestyle change you are not willing to take.
Last edited by daylen on Sun Oct 04, 2020 10:25 pm, edited 1 time in total.

Crusader
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Re: When does it make sense to get insurance?

Post by Crusader »

Yes, my question is exactly this (and I am curious as to how different people answer this question): at what point do you determine that you can effectively "self-insure" and recover from a specific "disaster"?

In my coin tossing example, if the person gave me $1.01 on heads and took $1.00 on tails, I would absolutely take that bet (because I can recover from a $1 loss). So that's the other extreme.

Alphaville
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Re: When does it make sense to get insurance?

Post by Alphaville »

you don’t insure individuals though, you insure populations.

a more fitting scenario is, in a population of 10,000, there’s a 1/10,000 risk of suffering in damages of 10,000.

the population agrees that none of them can absorb a $10k loss, so each puts up $1. the person who organizes the pool and holds the money charges a service fee of 10¢.

when the bird of doom takes a dump on the unlucky individual head, the organizer pays up $10k and profits $1000.
Last edited by Alphaville on Sat Oct 03, 2020 11:43 am, edited 2 times in total.

ZAFCorrection
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Re: When does it make sense to get insurance?

Post by ZAFCorrection »

Maybe this is already implied and I am just not seeing it in the OP, but your expectation values are all integral(x*p(x)). So think about what your distribution is when throwing out numbers. Your later reference to Taleb makes me think you might already be thinking along those lines.

As for the number you are willing to self insure, that's pretty much up to your own psychology. If someone is willing to pay your whole medical bill so you can be their slave for life, theoretically you might be willing to take that bargain. Or maybe it would even hurt to part with one dollar more than the premium.

Crusader
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Re: When does it make sense to get insurance?

Post by Crusader »

Alphaville wrote:
Sat Oct 03, 2020 11:32 am
you don’t insure individuals though, you insure populations.
Unless I don't know what you mean, this doesn't make my question any less pertinent.

You can think of the "population" as every dollar that comes into my account that is being contributed into the insurance fund, but every time a disaster happens, it happens to me. If you go to an outside source for this (an insurance company), they will necessarily make a profit and this will be more costly than you not needing their help. At what point do you determine that you don't need their help? Does it relate to the amount of the disaster, for example.?

Alphaville
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Re: When does it make sense to get insurance?

Post by Alphaville »

Crusader wrote:
Sat Oct 03, 2020 11:44 am
If you go to an outside source for this (an insurance company), they will necessarily make a profit and this will be more costly than you not needing their help.
no, when i collect insurance i personally make a “profit,” relative to my premiums. the insurance company profits *from the whole pool.*

the profit of the insurance company is not based on me personally, it’s based in the premiums and payouts from/to the population.

again, insurance is a way for individuals to pool their risk. it’s not an individual duel. the rates and solvency of the insurance business are adjusted by government to prevent scams.
Last edited by Alphaville on Sat Oct 03, 2020 11:55 am, edited 1 time in total.

Crusader
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Re: When does it make sense to get insurance?

Post by Crusader »

ZAFCorrection wrote:
Sat Oct 03, 2020 11:39 am
Maybe this is already implied and I am just not seeing it in the OP, but your expectation values are all integral(x*p(x)). So think about what your distribution is when throwing out numbers.
If I actually calculate the expected value, of course I will determine that the money the insurance company wants is always higher than the expected value of the expenses. But of course, yes, I am always thinking of a distribution curve of, in this medical insurance case, (amount needed for a hospital bill) * (probability of that happening). The sum of these is your expected value.

But at one point you say: this particular bet (I think it is easier to think of the curve as a discrete graph of different events and not continuous) is too much for me to take, I will pay for someone else to take this risk.

@Alphaville, I agree with everything you said and I still don't see where you see the issue/flaw with my question.

Alphaville
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Re: When does it make sense to get insurance?

Post by Alphaville »

Crusader wrote:
Sat Oct 03, 2020 11:55 am

@Alphaville, I agree with everything you said and I still don't see where you see the issue/flaw with my question.
your criticism seems to be (did i misunderstand?) that the insurer’s profit invalidates any and all insurance purchases.

i see the profit of the insurer as covering their cost of assuming and managing the risk, plus the need to stay solvent should risks change (eg unexpected earthquake).

in a fully efficient and honest and nearly omniscient group of people, we could just all pay to a common savings to bail ourselves out and the payouts would be exactly equals to to premiums and the fund would always be solvent.

but such a thing doesn’t exist...

Crusader
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Re: When does it make sense to get insurance?

Post by Crusader »

Ok, let me try from a different angle. Let's say I have a house. I understand that stuff can break in this house (e.g. my fridge, let's call this event A), causing unexpected expenses. If stuff breaks, I have enough money to buy a new fridge. This is a risk I am willing to make when buying a house. I have effectively "insured myself" against such an occurrence, I don't need outside help. But, this house is in Hawaii, and there is a chance that a volcano will wipe out my house at any time (let's call this event B). I don't have enough money to buy another house and I would end up homeless, so then I pay an amount of money into a pool of money that is managed by an insurance company (i.e. outside help), at a cost that is higher than if I had "a lot" of money to not need their help.

How do I determine whether a given event falls into the "event A" or "event B" category?

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Sclass
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Re: When does it make sense to get insurance?

Post by Sclass »

daylen wrote:
Sat Oct 03, 2020 11:13 am
It really should depend on your reserves.
This is the approach I’ve taken. I look at insurance as a “bump filter”. You get bumped and it smooths out the impact over time. Depending on how big a bump you can take, you insure appropriately.

Looking back I’ve never been hit with a big enough bump. Luck I guess. I’ve paid out a lot of premiums and made people rich for doing nothing. There was one time I was uninsured between jobs and got hit with a big medical bill. It was exactly the amount I would have paid in monthly premiums that I’d turned down the prior year. One of those uh huh moments.

When negotiating a package for my last business I had a literal eye opener. We were offered vision insurance at $15 a month so our employees would get free glasses once a year. Nobody even blinked. Our HR VP just took it and I said “wait, why don’t we just reimburse employees $150 for an eye exam and glasses once a year? WTF am I paying for?” HR said it wouldn’t look as good if the benefit was handled internally. We looked better if we said we offer a free vision plan...which wasn’t really free because our entire package was bundled into an employee’s compensation budget.

My takeaway has been if I’m paying insurance I may be in above my head. Kind of like my sister buying six year bumper to bumper service agreements on a BMW she really cannot afford.

Health insurance is a big exception but I’ve recently started buying the cheapest policy available and being willing to pick up the difference.
Last edited by Sclass on Sat Oct 03, 2020 12:25 pm, edited 1 time in total.

rube
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Re: When does it make sense to get insurance?

Post by rube »

Event A or even B: that's the severity part you"ll need to determine.

@crusader: daylen answered your question to me largely. And again: it is the severity here that makes the difference (for you as a person).

Alphaville
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Re: When does it make sense to get insurance?

Post by Alphaville »

Crusader wrote:
Sat Oct 03, 2020 12:09 pm

How do I determine whether a given event falls into the "event A" or "event B" category?
i think you just did. you determined that the house was worth insuring but the fridge wasn’t.

similarly, i used to have liability-only car insurance because i could replace or let go of the vehicle, but owing the city a quarter million dollars for hitting a lamp post would be debtor’s prison.

and i pay for health insurance because, while it’s pricey, cancer treatment or trauma surgery and rehabilitation are much pricier and could wipe me out or put a serious dent on my resources, and diet and exercise do not cure all.

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