Ever get stuck in the details of an insurance offer? With a thousand different kinds of health insurance and warranty offers for all kinds of products out there, here’s a rational framework from our guest poster, Stuart, on how to decide what insurance to buy.
I happen to think insurance is a fascinating industry, and I’m not alone. My friend Stuart – a math wizard and analytics genius – share his perspective on how to think rationally about what insurance is worth buying. Here’s Stuart on the subject:
How To Think About Insurance
I like to think about insurance as a bet. You pay a premium, and in exchange, you don’t have to pay some future uncertain cost.
Of course, this is a simplified model. Sometimes you still have to pay some of those costs, like copays and deductibles, like in health insurance. Sometimes the government requires you to make the bet, like in car insurance. And sometimes the cost avoided is a bit abstract – no matter how many life insurance premiums you pay, you’re still going to die.
But the model is useful because it’s how insurance companies think. Let’s say I’m going to start selling a super-simple version of travel insurance. I’ll charge you a premium, and in exchange, if you lose your bags I’ll pay for it.
To figure out how high my premium should be, I hire a bunch of very smart people and calculate that on average 15% of travelers will lose their bags and be owed $100 in claims, while the other 85% of travelers I won’t have to pay anything to.
As a result, I must set my premium to be at least $15 – otherwise, I’d be paying out more in claims than I’m making in premiums, and I won’t be an insurance company for very long. Indeed, factor in the salaries and offices and so on for all those very smart people, and the fact that I want to turn a profit, and I’m probably setting my premium closer to $25.
The more mathematical way of putting it is, the cost of the claims ($C) multiplied by the probability of those costs occurring (P) is each customer’s expected claim value ($C x P). And so my insurance company needs to make sure that for each customer, I’m taking in more in premiums than the customer’s expected claim value, or, in other words:
Cost of Premium > (Cost of claim) x (Probability of claim)
Put in these terms, my travel insurance looks like a raw deal for you! You’re paying $25 so that on average, you can avoid paying $15. In the long run you are just losing $10 every time you buy my insurance, and that $10 goes straight to me to pay for my overhead and profit.
On a fundamental level, this is always true no matter what insurance you buy. Health insurance, car insurance, pet insurance – all of it, by definition, has to be profitable in aggregate for the insurance company, or else they wouldn’t be able to offer it. And that means that also by definition, every customer’s insurance policy is on average, a money-loser.
So why, then, would you ever buy insurance?
Well, as it turns out, there’s three good rational reasons to buy insurance:
- Reason 1: Your probability of incurring claim costs (P) is higher than average;
- Reason 2: Your claim costs ($C) are higher than average;
- Reason 3: Financial catastrophe, aka the nonlinear value of money
Reason 1: You Believe Your Probability of Experiencing The Event Is Higher Than Average
The first reason to buy insurance is if your probability of incurring claim costs is higher than average. Suppose you come to buy travel insurance from me. You know that I assume my customers will lose their bags 15% of the time. But you’re flying a special airline, one notorious for losing its customers’ bags. In fact, this airline loses its customers’ bags a shocking 50% of the time. Now buying my insurance will be a great deal for you: you’re paying $25 to avoid paying an expected value of $50.
In the real world, insurance companies guard against this in a variety of ways. For car insurance, they ask a bunch of questions to try to figure out your exact probability of getting into a crash. For flood insurance, they prepare exhaustive statistical analyses of the likelihood of flood damage. And of course, it’s almost always considered insurance fraud if you intentionally incur claim costs (e.g., burn down your home, intentionally lose your luggage, etc.).
But at the end of the day, an insurance company simply doesn’t have the manpower to ensure a perfectly customized quote for every single customer. It has to make some statistical assumptions about you, and that means that overcharging some customers and undercharging others. You want to be one of the ones undercharged.
Reason 2: Your Claim Costs Are Higher Than Average
The second reason to buy insurance is if your expected claim costs are higher than average. Suppose that you’re looking to buy my travel insurance again, but this time, you’re transporting priceless cargo 1,000 times as valuable as before. There might still only be a 15% chance that you lose your bags, but if you do, now I’m on the hook to pay you $100,000. Here buying insurance is a total steal for you – you’re paying $25 to avoid paying, on average, $15,000.
In the real world, insurance companies guard against this by imposing limits on the maximum claim amounts they’re liable for. But the point remains the same. If you are confident that your costs would be much higher than what the insurance company thinks your costs are, and that it would be covered under your policy, then you should buy the insurance.
Reason 3: Financial Catastrophe, aka Nonlinear Value of Money
Finally, the main reason people buy insurance is because the value of money isn’t linear. By which I mean, sometimes owing $250,000 isn’t just 1000 times worse than owing $250 – it’s even more.
Health insurance is perhaps the best example of this. Almost all of us pay out more in health insurance premiums than we get back in terms of benefits, because most of the health care we need is cheap. But if something catastrophic happens and you owe $250,000 in medical bills, well, owing that much money warps your life in unfathomable ways. You have to liquidate your savings and retirement accounts. You have to mortgage your home or sell your car. You have to move. And all of this comes on top of being so sick you need $250,000 in care in the first place.
In other words, you’re buying insurance against the possibility of a financial burden so awful that it trumps the cold expected value calculations I described above. Sure, buying health insurance, on average, you’ll be losing money. But the catastrophic downside financial risk is so severe that you are more than happy to “overpay” to avoid it.
With these rules in mind, finally, we can talk about the kinds of insurance I recommend and don’t recommend by this metric. Keep in mind that each type of insurance is still very different.
- Health insurance: Yep, as discussed above, for Reason 3.
- Car insurance: For liability, it’s legally mandated, but would be a good idea for Reason 3 anyway. For collision, it comes down to how much of an impact losing your car would be on your personal finances.
- Home insurance: Yep, for Reason 3, and it’s usually required by your mortgage lender. But you need to carefully consider for yourself the value of earthquake, flood, and hurricane insurance, many of which are often excluded from home insurance policies due to too many Reason 1 and Reason 2 situations.
- Travel insurance: Don’t do it. This is a good example of where none of the above considerations apply. Your odds of losing your luggage will not meaningfully differ from the statistical average. Even if you’re carrying super-valuable cargo, the insurance policy will almost certainly be capped. And most of us do not carry luggage of such value that we would be financially devastated by losing it. Additionally, many credit cards offer a certain level of lost luggage protection for free.
- Pet insurance: If you are the kind of person that would without hesitation drive yourself into deep debt for your pet, then pet insurance makes sense for Reason 3. Also, the industry is far less developed than human health insurance, so there are many more opportunities for arbitraging their premium rates under Reasons 1 or 2. (For instance, you might not get charged as much as you should for insuring a constantly-sick pet.) Absent one of those considerations, I don’t recommend it.
- Life insurance: This depends, and I recommend JP Livingston’s article here. If you’re the sole breadwinner for a family, you definitely want it for Reason 3. If your family can get by without your income, it’s probably not. Child life insurance policies are never worth it unless your child is the primary income stream for the family. And whole life insurance is 1% of the time a reasonable and sound component of estate planning, and 99% of the time a scam preying on the elderly.
- Phone insurance (e.g., AppleCare): Probably not. That being said, my wife and I got AppleCare on our new phones because of our toddler, who likes to a) play with our phones, and b) break things – thus qualifying for Reason 1.
- Credit insurance: You shouldn’t be carrying credit card debt; you doubly shouldn’t be carrying so much that you might not pay it back; and you triply shouldn’t be carrying so much that failure to pay it would be financially catastrophic.
Summary in 30 Seconds
TL;DR: Insurance companies will always set premiums to be greater than the expected cost for an average customer. So I don’t buy insurance unless I have unusually likely or unusually high costs relative to the average customer, or if I’m insuring against financial catastrophe.
What insurance decisions are you trying to make right now? Do you buy things like phone insurance and pet insurance? Share your thoughts in the comments.