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Thursday, November 17, 2005

The Theory of Insurance

I think people would better understand the complicated topic of insurance if they learned a little more about it. For example, why do people get insurance? Here's a brief summary on the theory of insurance.

Insurance is there to protect against unexpected large losses. For example, homeowner's insurance protects against loss from fire, wind damage, and theft. You don't use homeowner's insurance to protect against the food in your refrigerator going bad... it's a trivial loss. And you don't use homeowner's insurance to pay for repainting your house. Though it is quite expensive, it's not an unanticipated cost. Through insurance, you replace an uncertain large loss with certain smaller losses.

How is insurance priced? There's the net premium, which covers the cost of the expected loss. For example, if you had a 0.1% chance of having a $100,000 loss tomorrow, the net premium would be $100. However, you wouldn't be able to purchase this insurance for $100, as the insurance company has its own expenses, overhead, and profit requirements. The gross premium, which is higher, accounts for that.

Despite the fact that you're paying more for insurance than the expected value of your loss, it's still an advantageous transaction for both parties. The reason for this situation is a concept called utility of wealth. Your first dollars are the most important to you, as they provide food, clothing, and shelter. Beyond that, the money purchases less and less important things. You're willing to give $120 out of the last, least important dollars in order to protect you against a loss that would take away your important first dollars. In other words, you are risk-averse. If you have a net worth of $100,000, you would not be willing to bet $100,000 on the flip of a coin, as the benefit of another $100,000 isn't as large as the penalty of losing $100,000. The person with a net worth in the billions of dollars, however, might bet that amount on a visit to the casino, on less than even odds.

If you think to the insurance you have, you might see some coverage for non-insurable events. A yearly checkup at the doctors, or semiannual teeth cleaning at the dentist, really aren't insurable events, as they're anticipated. Roughly speaking, you could pay on your own two $50 dentist bills a year and pay $100 less for your dental insurance.

That's not to say it's bad for insurance to offer these types of coverage. For one, it's a selling point for the insurance product. (Independent agents tend to drive what features get put in companies' products, by demanding these features in companies' next generation products.) Consider a product targeted to seniors; if it offers a "free" MedicAlert (a.k.a. "I've fallen, and I can't get up!") subscription, it would possibly have a competitive advantage. And benefits such as these might be expected to lower costs. Preventative care, like an annual checkup, can lead to finding diseases early, when they are easier, safer, and cheaper to treat. (Before you nod your head in agreement, note that it's also a theory on how HMOs reduce costs. Weigh that fact when you try to decide how big the impact really is.)

Update: A couple of other points I'd like to make:

First, you don't "waste your money" if you buy insurance and don't need to file a claim. That would be like betting red in roulette, and complaining that you wasted your money every time the ball landed on black or green. Your premium purchases insurance protection, which is of value in and of itself, even if subsequently ending coverage gives you no money in return.

Second, the local newspaper (like many others) has an anonymous comment column, where readers contribute brief comments. It's remarkable how many of them juxtapose their health insurance premiums and executive pay. "My premium is going up 12%, and the CEO is getting a $20 million bonus." These two items have nothing to do with each other! Health insurance premium rates are reviewed by the state, and are adjusted based on a combination of actual experience and trend.

One kind of insurance, long term care insurance, had premium levels regulated by the lifetime loss ratio (the present value of claims divided by the present value of premiums), with the ability to raise rates if the lifetime loss ratio exceeded the standard set by state regulation. You will note that overhead does not factor into that equation. A company could give each of its employees a $20 million bonus, and that would not allow the company to justify a rate increase.

And, do check the comments for a nice addition from The Probligo.

3 Comments:

At 6:02 PM, Blogger The probligo said...

Good simple summation.

There is one aspect that you have missed in the description of getting from true premium to gross premium.

Also factored into the gross premium is "past claim history".

This takes two parts -

First is the claim history of the statistics group the insurance company uses. So, for example if you are 45 y-o your car insurance will generally be cheaper than for your 18 y-o son. That difference is based upon group claim distributions.

Second is the personal claim history. If over the past 5 years you have claimed for the writeoff of three cars, it is likely that the insurance company will write you inviting you to seek insurance from another company. That offer will be accompanied by a hefty increase in your personal premuim.

There is also the "unexpected loss" recovery. To illustrate, expect that there will be a major premium increase for those who move back to NO for example, or the Louisiana coastline. There will be an element of "cross-subsidisation" from the rest of the company's market, but that must be limited so that income is not lost from other "less risky" areas.

Those same principles would apply to health insurance. Consider what is likely to happen to health insurance premiums if the fears of an avian flu pandemic are realised.

 
At 2:01 AM, Blogger Greg said...

I didn't really cover that part of insurance, how one calculates the risk of loss. Your description is good. Another element is the natural cycle of the market. Competition tends to force premiums down, until experience turns bad, and everyone realizes that they can't keep up these low premiums.

It's hard to picture how pandemic flu would affect health costs. If the flu is something like in Stephen King's The Stand, it would kill efficiently and not generate a lot of expenses. I doubt that would be the case, and the U.S. health care system could treat the results of the flu, keeping most of those infected alive, but possibly at great cost.

 
At 2:13 AM, Blogger The probligo said...

"... and the U.S. health care system could treat the results of the flu, keeping most of those infected alive, but possibly at great cost."

Interesting comment. When the kitchen gets hot, call in the government.

Leaving that argument aside, it is no more than a red herring...

First, there has to be a treatment. Not necessarily a cure but some means of maximising the probability of survival.

If that treatment is going to cost, say, USD1500 per person and it has the effect of halving the death rate from 50% to 25% then the cost to the insurance company per survivor will go from USD3000 to USD2000.

Now the insurance company has a problem. Do they charge every insured their $1500 in advancein the hope that there will not be a better cure for less before the pandemic starts? Or do they follow standard practice and try and recover the $2000 from the survivors?

Or do they, as has been the case with much property insurance and terrorism losses, just decide that the next flu pandemic is not insurable. In the perfect capitalist society, that would be a perfectly acceptable outcome.

The reality check, and this returns to the hot kitchen, is that very few people might be able to afford the $1500 per person for their family - $7500 for an average family? - plus the cost of living without income for a period from two weeks to a couple of months.

So, social security or public health does have its place as "provider of last resort". But what if, in response to continual pressure from the electorate, the government has been downgrading the health system to the point where it can no longer cope with a catastrophy of this scope. Reality check again - no one in their right mind would try.

Just hope that you might be one of the lucky ones. And bear in mind that if the death rate is too high, the lucky might be the dead.

Final note -

There was an excellent tv series some years back - four seasons if I recollect - that came out of British production. It was called "The Survivors", and it compares with the current crop of unreality Survivor Guatemala programmes as much as da Vinci's sketch of a bicycle compares with the 69 Corvette. Google it. There is probably a web page for it somewhere. It scared the S***T out of me.

 

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