Conditional probabilities and evil insurers

By Felix Salmon
July 30, 2009
Mike Konczal picks up on a great Taunter post about conditional probabilities, which comes with a nasty sting in the tail. When you buy health insurance, the main thing you're concerned about is tail risk: you want to be sure that in the unfortunate event you have stratospheric medical bills, the insurance company will be there to pay them.

The problem here is that you can't be sure of that.

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Mike Konczal picks up on a great Taunter post about conditional probabilities, which comes with a nasty sting in the tail. When you buy health insurance, the main thing you’re concerned about is tail risk: you want to be sure that in the unfortunate event you have stratospheric medical bills, the insurance company will be there to pay them.

The problem here is that you can’t be sure of that. Indeed, by Taunter’s math, if you have stratospheric medical bills (this is where the conditional probability comes in), the chances of the insurance company paying them are quite possibly no higher than 50-50. The term of art for an insurer not paying an insured’s medical bills is “rescission”: the insurer rescinds the policy rather than pay the bills.

Here’s James Kwak:

The legal basis for rescission is that when you sign an insurance application, you are warranting that the information on the application is true; if it turns out not to be true, the insurer can get out of your insurance contract. It’s particularly nasty in practice because the insurer does not immediately investigate your application to determine if it is accurate before selling you the policy (that would be impractically expensive); instead, the insurer waits – years, in many cases – until you actually need expensive health care, and then does the investigation, which at that point is worth it because of the payments the insurer could potentially avoid. Also, you can lose your coverage for innocent mistakes, which are easy to make since the application form asks you if you have ever seen a doctor for any one of a long list of medical conditions that you are certain not to recognize or understand. (In a Congressional hearing, the CEO of a health insurer admitted that he did not know what several of the conditions listed on his company’s application were.)

Kwak’s parenthetical about how insurers can’t examine applications before they’re approved on the grounds that that would be “impractically expensive” misses the true evil here: the insurer wants to cash the insurance-premium checks of people who made fraudulent applications. Those are the most valuable insureds of all, because the minute they make claims which cost more than their premiums, their policies can be immediately rescinded. As Taunter puts it, you are free to play, you just aren’t free to win. And that’s why you get people being denied breast-cancer surgery on the basis of having had acne in the past.

This is a huge problem with any private-sector health insurance: it’s essentially impossible to gauge the quality of that insurance until it’s too late.

More generally, as Konczal says, this applies to other insurance policies too: CDS, for instance, or even hurricane insurance. In general, if you’re making a series of small payments now on the grounds that you will be paid a large sum of money if something bad happens, you’re running some large and unhedgeable counterparty risk. Which just goes to confirm what everybody deep down suspects: that a significant part of the money we spend on insurance policies is wasted.


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I can’t speak for health insurance, but I know Life Insurance has a 2 year statute of limitations. Once you are through that window, it doesn’t matter if you’ve lied through your teeth on your app.

The point is that Insurance is a contract. There is no reason that the following conditions couldn’t be included in such contracts: es/2009/07/the-public-plan-you-wont-have -access-to.php

“The most important part of the bills that actually exist—the part that will impact the lives of most Americans—are the new regulations on insurers.

The administration is proposing:

— A ban on discriminating against people with pre-existing conditions.

— Caps on out-of-pocket spending.

— No cost-sharing for preventive care.

— No “rescission” of coverage for people who get seriously ill.

— No gender discrimination.

— No caps on coverage, either lifetime or annual.

— Extension of family coverage for kids up to the age of 26.

— Guaranteed insurance renewal.”

The thing is to have a third party with enough clout to negotiate such a deal, say the Federal Govt. The govt could even propose its own competing plan if it couldn’t get the deal that it wants. In the end, the govt will step in where the private market of insurance doesn’t cover enough. In some cases, the govt itself offers insurance where it tends to often get stuck with the tab. So, there’s nothing new about that discovery.

The only reason that you would favor my idea as opposed to employer insurance and a total govt plan is if:
1) You think that the employer based option doesn’t have the clout to get the best deal, and it hides the cost of health care from the recipients of it, causing expenses to be less than efficient.
2) The single payer plan will save money over the current mess, but will end up costing us quite a bit more than its advocates claim as politicians will be loathe to increase taxes or cut services. Its better to have a market make those type of decisions, especially if the govt can negotiate effectively the basic conditions.

The analogy to CDS is inapt. While both issues relate to conditional probabilities, health insurer rescission is far more troublesome (and sinister) than counterparty risk. A CDS counterparty can’t refuse payment because you filled out the paperwork wrong (unless you actually filled out the paperwork wrong, which in the case of a CDS contract seems unlikely). Rescission is more akin to a conditional put option. If you filled out the paperwork wrong, the insurer can choose to tear-up the contract. Obviously the insurer wants to collect as many of these options as it can, so it makes it’s no surprise (though certainly not forgivable) that they do everything they can to make it likely that you’ll inadvertently make a mistake on the application.

There is however an good analogy to be made between counterparty risk in CDS and counterparty risk (by which I mean inability to pay, rather than unwillingness to pay) in insurance contracts. When you buy insurance (health/life/property), a good chunk of what you are insuring against are idiosyncratic risks: the risk that YOU will need healthcare or that YOUR family will need coverage in case you cease to be or that YOUR property will be damaged. These idiosyncratic risks are pretty much uncorrelated with the insurer’s wherewithal to pay.

But there are also systematic risks that impact both your need of coverage and the wherewithal of the insurer to provide it. In property insurance, this is the (implicit) part of your insurance that covers you for damage incurred in a large, widespread catastrophe. If you live along the I95 corridor, this might be a 1,000-year hurricane or winter storm. In the west, it might be that 8.5 earthquake that comes around once in a very blue moon. For life and health insurance, the key systemic risk is the next pandemic flu. And of course, there are systemic risks that impact all of these: major geopolitical unrest, nuclear war, another Dinosaur-killing comet, alien invasion, etc.

I throw in these latter examples to illustrate a point. For major systemic risks, no one expects their counterparty to perform. They expect their government to. Which basically means we’re all self-insured against systemic risks.

And counterparty risk on a CDS contract works pretty much the same way. You’re paying for protection against idiosyncratic risk, but you better not be counting on too much systematic risk protection. Which is why it’s so puzzling that anyone was ever willing to pay even a couple bps for super senior protection on a well diversified basket of credits. This smells very much like buying a end-of-the-world insurance from someone of this world.

With respect to counterparty risks in cat insurance, presumably one can put on the same hedge GS did for AIG with respect to their CDS counterparty risk, as in

Posted by tomrus | Report as abusive

The problem with the analysis is that it pretends almost 100% of the policy rescissions occur because applicants do not know they are not telling the truth.

Simply put, the individual insurance market is difficult because of adverse selection. Typically, people seeking coverage realize they have risk and are seeking to pass it off to the insurer. Furthermore, they understand rates will go up (or coverage will not be available) if they disclose medical conditions on their applications. Unfortunately, many outright lie and most will bend (forget) the truth to minimize their premiums.

If we put the burden on the carriers to spend the time and money to track down the applicants medical records before they accept a policy, I would expect doing so would easily cost hundreds of dollars for each application. Since rejected applicants would not pay any premiums, the millions of dollars in investigative costs would need to be passed on to actual customers.

While there certainly have been cases of abuse of rescission, the current system relies on information provided by the lowest cost source of information on the health of the applicant – the applicant.

Posted by Brad Ford | Report as abusive