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Compulsory health insurance and deductible optimization

While the time to change your health insurance is now over, I wanted to share with you an observation I did regarding the compulsory health insurance in Switzerland.


I decided to optimize my deductible. Many health insurance companies offer different monthly primes depending on the deductible you choose. If your deductible is high, your prime will be lower, because the insurance company only begins to pay after you have exhausted your deductible. Anyhow, once your deductible is exhausted, you still have to pay 10% of the remaining costs, with a limit of 700 CHF per year (for an adult), this is what the Swiss call 'quote part'.


Taking this into account, I took the work of plotting in my computer the total health costs for the user as a function of the total health cost incurred.


Case 1: If you are perfectly healthy and never go to the doctor, the total cost incurred is zero, and the health insurance cost for the user is the fixed term, i.e., just the 12 monthly primes. Of course you're best choice is to go for the highest deductible (2500 CHF), which goes along with the lowest monthly primes.


Case 2: If you are in bad health and go often to the doctor or have a major operation, the total cost incurred will be very high, and you will be better off with the lowest deductible (300 CHF), because despite the higher monthly primes, once you have passed the 300 CHF deductible, 90% of the rest will be covered by the insurance.


Case 3: ... for most of us, we will be somewhere in between. But does it mean that the optimal deductible is somewhere between the minimum 300 and the maximum 2500 CHF? In most cases, No!


After plotting the curves for my insurance (Assura) I noticed that 300CHF was the optimal deductible if I incurred total costs over 2000 CHF in the year, and 2500 CHF was the optimal deductible if I incurred less than 200CHF cost in health during the year. 


i.e., ... all the other deductibles (500, 1000, 1500, 2000 CHF) would never be optimal!! No matter how high the health costs incurred, with an intermediate franchise, at the end of the year, you would end up paying more than if you had gone for the minimum or for the maximum deductible. Of course, only one of the two will be optimal ... but even if you choose "the wrong one", you would still pay less than with any of the intermediate deductibles !! 


And it is not an exception. I repeated the same exercise with 3 different insurance companies (Assura, Concordia, Swica), collecting their data for the monthly primes for all possible deductibles [*]:  for the four of them the conclusion was the same : the intermediate deductibles were never optimal, no matter what the total health cost incurred were. 


To sum up: never choose an intermediate deductible. Go for 300 CHF if in bad health, or 2500 CHF if in good health. Here in good health means that you expect to incurr in health costs for less than around two thousand francs in the year. Even if you expect no costs, choose a deductible of 2500 CHF. Even if in the end you end up having major operations with high cost involved, you will stay pay less at the end of the year that if you had opted an intermediate deductible of, let's say, 1000 CHF. Surprising, but true!!


As said, I have only done the complete calculation for four insurane companies,. ... but I presume that it must be the same for most of them.


So then, this raises the ethical/legal/practical question of "Why do these companies offer intermediate deductibles?" How can it be legal, knowing that no matter what, the cost for the user who chooses them is never going to be optimal?


Any hints?


Cheers,


[*] The raw data for this analysis were obtained from: http://www.priminfo.ch/praemien/praemien_dat/CH.pdf





The text you are quoting:

While the time to change your health insurance is now over, I wanted to share with you an observation I did regarding the compulsory health insurance in Switzerland.


I decided to optimize my deductible. Many health insurance companies offer different monthly primes depending on the deductible you choose. If your deductible is high, your prime will be lower, because the insurance company only begins to pay after you have exhausted your deductible. Anyhow, once your deductible is exhausted, you still have to pay 10% of the remaining costs, with a limit of 700 CHF per year (for an adult), this is what the Swiss call 'quote part'.


Taking this into account, I took the work of plotting in my computer the total health costs for the user as a function of the total health cost incurred.


Case 1: If you are perfectly healthy and never go to the doctor, the total cost incurred is zero, and the health insurance cost for the user is the fixed term, i.e., just the 12 monthly primes. Of course you're best choice is to go for the highest deductible (2500 CHF), which goes along with the lowest monthly primes.


Case 2: If you are in bad health and go often to the doctor or have a major operation, the total cost incurred will be very high, and you will be better off with the lowest deductible (300 CHF), because despite the higher monthly primes, once you have passed the 300 CHF deductible, 90% of the rest will be covered by the insurance.


Case 3: ... for most of us, we will be somewhere in between. But does it mean that the optimal deductible is somewhere between the minimum 300 and the maximum 2500 CHF? In most cases, No!


After plotting the curves for my insurance (Assura) I noticed that 300CHF was the optimal deductible if I incurred total costs over 2000 CHF in the year, and 2500 CHF was the optimal deductible if I incurred less than 200CHF cost in health during the year. 


i.e., ... all the other deductibles (500, 1000, 1500, 2000 CHF) would never be optimal!! No matter how high the health costs incurred, with an intermediate franchise, at the end of the year, you would end up paying more than if you had gone for the minimum or for the maximum deductible. Of course, only one of the two will be optimal ... but even if you choose "the wrong one", you would still pay less than with any of the intermediate deductibles !! 


And it is not an exception. I repeated the same exercise with 3 different insurance companies (Assura, Concordia, Swica), collecting their data for the monthly primes for all possible deductibles [*]:  for the four of them the conclusion was the same : the intermediate deductibles were never optimal, no matter what the total health cost incurred were. 


To sum up: never choose an intermediate deductible. Go for 300 CHF if in bad health, or 2500 CHF if in good health. Here in good health means that you expect to incurr in health costs for less than around two thousand francs in the year. Even if you expect no costs, choose a deductible of 2500 CHF. Even if in the end you end up having major operations with high cost involved, you will stay pay less at the end of the year that if you had opted an intermediate deductible of, let's say, 1000 CHF. Surprising, but true!!


As said, I have only done the complete calculation for four insurane companies,. ... but I presume that it must be the same for most of them.


So then, this raises the ethical/legal/practical question of "Why do these companies offer intermediate deductibles?" How can it be legal, knowing that no matter what, the cost for the user who chooses them is never going to be optimal?


Any hints?


Cheers,


[*] The raw data for this analysis were obtained from: http://www.priminfo.ch/praemien/praemien_dat/CH.pdf


ajimenezpDec 9, 2014 @ 19:05
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Re: Compulsory health insurance and deductible optimization
Post 1

Wow! Many thanks for this. Very helpful indeed!

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Wow! Many thanks for this. Very helpful indeed!


isaac b, Dec 9, 2014 @ 20:51
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Post 2

Hi,


Just because the intermediate deductible is not the optimal solution at any incurred cost does not mean it cannot be a good decision. At the beginning of the year, you don't know what your costs will be. Given this uncertainty, it is possible for the intermediate deductible to give the lowest expectation value of the cost to the user.


At the end of the year, of course, you will always be able to calculate that you 'should have gone with the lowest / highest (depending how ill you were) deductible' - but only with the benefit of hindsight.

The text you are quoting:

Hi,


Just because the intermediate deductible is not the optimal solution at any incurred cost does not mean it cannot be a good decision. At the beginning of the year, you don't know what your costs will be. Given this uncertainty, it is possible for the intermediate deductible to give the lowest expectation value of the cost to the user.


At the end of the year, of course, you will always be able to calculate that you 'should have gone with the lowest / highest (depending how ill you were) deductible' - but only with the benefit of hindsight.


adam_jeff, Dec 10, 2014 @ 11:46
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Re: Compulsory health insurance and deductible optimization
Post 3

Hi,


Maybe my explanation was not clear enough, but you have not fully understood. The important thing is that, even without the benefit of hindsight, we can say that the choice of an intermediate deductible will NEVER be optimal, no matter what the total health costs incurred will be at the end of the year.


Without knowing what those total costs will be, we can already say that the optimal deductible will be either 300 CHF or 2500 CHF. Never one of the intermediate deductibles. Of course, which of those two (300 or 2500) will end up being the optimal we can only say at the end of the year. But even if we choose the wrong one among those two, our cost will still be lower than with any of the intermediate ones.


You can see this by looking at the graphs. Look at the lower envelope. In both cases (Assura and Concordia) we see that up to a cost of ~2000 CHF, the optimal deductible is 2500 CHF (lower envelope is the yellow line); and above ~2000 CHF, the optimal deductible is 300 CHF (lower envelope is the blue line).


One can see, that no matter what the value of the variable in the horizontal axis, the lowest value in the vertical axis will never be given by one of the other deductibles (green, red, cyan, magenta).


 


I hope it is all clear now.

The text you are quoting:

Hi,


Maybe my explanation was not clear enough, but you have not fully understood. The important thing is that, even without the benefit of hindsight, we can say that the choice of an intermediate deductible will NEVER be optimal, no matter what the total health costs incurred will be at the end of the year.


Without knowing what those total costs will be, we can already say that the optimal deductible will be either 300 CHF or 2500 CHF. Never one of the intermediate deductibles. Of course, which of those two (300 or 2500) will end up being the optimal we can only say at the end of the year. But even if we choose the wrong one among those two, our cost will still be lower than with any of the intermediate ones.


You can see this by looking at the graphs. Look at the lower envelope. In both cases (Assura and Concordia) we see that up to a cost of ~2000 CHF, the optimal deductible is 2500 CHF (lower envelope is the yellow line); and above ~2000 CHF, the optimal deductible is 300 CHF (lower envelope is the blue line).


One can see, that no matter what the value of the variable in the horizontal axis, the lowest value in the vertical axis will never be given by one of the other deductibles (green, red, cyan, magenta).


 


I hope it is all clear now.


ajimenezp, Dec 10, 2014 @ 12:46
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Re: Compulsory health insurance and deductible optimization
Post 4

Sorry, actually the claim "But even if we choose the wrong one among those two, our cost will still be lower than with any of the intermediate ones" is wrong.


What is true is that, no matter what your health costs are, even if you could know them in advance, choosing an intermediate deductible would never be the optimal choice.


 


 

The text you are quoting:

Sorry, actually the claim "But even if we choose the wrong one among those two, our cost will still be lower than with any of the intermediate ones" is wrong.


What is true is that, no matter what your health costs are, even if you could know them in advance, choosing an intermediate deductible would never be the optimal choice.


 


 


ajimenezp, Dec 10, 2014 @ 13:00
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Post 5

No, I understood your point, but mathematically, just because a certain deductible is not optimal for any value of the healthcare costs, does not mean it cannot be optimal overall.


For example, although the deductible2500 line is the lowest for low costs, it is the highest for a large range of costs. Now imagine that we take 100 people and we give them a range of healthcosts: we distribute them evenly over the x axis of your graph. If they all take the 2500 deductible, the average cost per user might end up quite high, because the 2500 deductible is the most expensive for quite a lot of people. If they all took the 300 deductible, the people with high costs would be better off but the people with no costs would be paying more, so again the average might be high. It's possible that the average might be lowest for an intermediate deductible.


Of course, in reality the 100 people would not be evenly spread. Probably, the largest number would have zero costs, a few would have very large costs, and so on. Without knowing this distribution of probabilities of health costs, we cannot conclude which is the best deductible to take: it might even be one of the intermediate ones.

The text you are quoting:

No, I understood your point, but mathematically, just because a certain deductible is not optimal for any value of the healthcare costs, does not mean it cannot be optimal overall.


For example, although the deductible2500 line is the lowest for low costs, it is the highest for a large range of costs. Now imagine that we take 100 people and we give them a range of healthcosts: we distribute them evenly over the x axis of your graph. If they all take the 2500 deductible, the average cost per user might end up quite high, because the 2500 deductible is the most expensive for quite a lot of people. If they all took the 300 deductible, the people with high costs would be better off but the people with no costs would be paying more, so again the average might be high. It's possible that the average might be lowest for an intermediate deductible.


Of course, in reality the 100 people would not be evenly spread. Probably, the largest number would have zero costs, a few would have very large costs, and so on. Without knowing this distribution of probabilities of health costs, we cannot conclude which is the best deductible to take: it might even be one of the intermediate ones.


adam_jeff, Dec 10, 2014 @ 15:53
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Re: Compulsory health insurance and deductible optimization
Post 6

Can I ask ? To wich insurer are you insured ? And what is your experience about this insurer ?

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Can I ask ? To wich insurer are you insured ? And what is your experience about this insurer ?


Alexandre B, Dec 31, 2014 @ 00:27
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Post 7

I think there is also some other aspects you may take into account.


I did not see you considering the 700 CHF contribution to medicine.


In addition, with some insurance companies your bills are automatically paid by the insurance company and you do not have to go through a long recovery period.


This is also important besides the cost of the insurance.


If you want to have a free choice of doctors, that you do not want to go to a GP first and then to a specialit, etc.


Cost is one aspect but one may would like to have flexibility as well.


 

The text you are quoting:

I think there is also some other aspects you may take into account.


I did not see you considering the 700 CHF contribution to medicine.


In addition, with some insurance companies your bills are automatically paid by the insurance company and you do not have to go through a long recovery period.


This is also important besides the cost of the insurance.


If you want to have a free choice of doctors, that you do not want to go to a GP first and then to a specialit, etc.


Cost is one aspect but one may would like to have flexibility as well.


 


Reka Y, Dec 31, 2014 @ 12:46
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Re: Compulsory health insurance and deductible optimization
Post 8

I think there is also some other aspects you may take into account.

I did not see you considering the 700 CHF contribution to medicine.

In addition, with some insurance companies your bills are automatically paid by the insurance company and you do not have to go through a long recovery period.

This is also important besides the cost of the insurance.

If you want to have a free choice of doctors, that you do not want to go to a GP first and then to a specialit, etc.

Cost is one aspect but one may would like to have flexibility as well.

 


Dec 31, 14 12:46

In the graphs, I have considered the 10% of the quote part, which can be up to 700 CHF. All this is taken into account in the plots.


 


The matter of whether you pay and are reimbursed later, or the insurance company pays directly, has nothing to do with what was discussed here. The conclusions still apply independently of the reimboursement modality.

The text you are quoting:

In the graphs, I have considered the 10% of the quote part, which can be up to 700 CHF. All this is taken into account in the plots.


 


The matter of whether you pay and are reimbursed later, or the insurance company pays directly, has nothing to do with what was discussed here. The conclusions still apply independently of the reimboursement modality.


ajimenezp, Mar 4, 2019 @ 21:09
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Re: Compulsory health insurance and deductible optimization
Post 9

An interesting read and the same rules will apply for complementary (mutuel) health insurance plans.

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An interesting read and the same rules will apply for complementary (mutuel) health insurance plans.


Slava Sviridovs, Mar 5, 2019 @ 09:42
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