Friday, April 14, 2006

Self-insuring whenever possible – not necessarily for those in the know, after all…

Large segments of America, for one reason or another, may be underinsured. This may be attributable to a number of root causes, such as extreme poverty or social strictures – for instance, the Amish prefer to engage in implicit community insurance (which is likely underfunded). Nonetheless, the common financial mantra is that on average, people generally overinsure themselves against certain particularly salient risks (travel insurance that protects against dying in a plane crash, for instance), and have a tendency to overinsure in general. So, the supposedly sophisticated investor turns his nose up at mutual funds in favor of private equity, hedge funds, and commodities, and turns down all but the most vital of insurance, in favor of self-insurance whenever possible. This is not entirely incorrect -- I certainly minimze many forms of insurance, and make my deductibles as high as I can tolerate. However, I’d argue that the extra shrewd may, under certain circumstances, find ways to pick up insurance and not feel like Mr. Main Street after all.

I break this post into three segments, two of which, I and III, are nothing new:

I.Why insurance is probably overpriced and oversold – people reasonably familiar with human psychology, behavioral economics, and/or the insurance industry can skip this.

II.Why the shrewd investor who can afford to self-insure, may still want to seek out insurance under certain conditions.

III.A primer of the underlying concepts that are needed to understand how insurance works – _really_ nothing new here for people who’ve taken Econ 101/202, except my summary/excerption of some wikipedia concepts.

I.A qualitative description of how insurance works, and why people frequently buy too much of it – see below for a more detailed intro.

People buy insurance because they dislike taking large risks, even if on average, they’d make a profit if they could take on such risks over and over (roughly speaking, this makes them unwilling to take on bets with positive expected value). Making a profit in this fashion isn’t always viable for a single individual, such as when you buy a single extremely expensive machine for one’s business. Say there’s a one-in-a-thousand chance that if the machine breaks, you’ll have to replace it – but because you can’t afford to do so, you’ll go bankrupt. Instead, you buy insurance against breakage, which costs you far less than the replacement value of the machine. However, you are charged a premium by the insurance company that’s enough to make them a profit. How do both parties end up with a win win scenario? Well, the insurance company wins because they _can_ play the game over and over again by insuring lots and lots of people in situations similar to yours, and thus, they’re not worried about a single broken machine bankrupting them (as long as the machines don’t all break at the same time). And, they charge a high enough rate that on average, they make money and you lose money in the 999 cases where your machine doesn’t break – and even if one in a thousand machines breaks, they still make just enough money off the elevated premium on the other 999 machines to more than break even. You of course don’t mind the fact that you’re paying that extra slice because you now won’t go bankrupt (at least from the machine breaking, anyway).

Here’s the thing – for smaller amounts at risk, you typically don’t want to buy insurance. After all, if you self-insure for small amounts that you can afford to absorb yourself, you get to pocket the premium. In some cases, this may be simply impossible, such as when one engages in a lucrative, one-time activity that also has a high risk of limb amputation (not exactly a repeatable game, at least for values >4 or so).

Nonetheless, people frequently fail to properly understand this critical expected value-vs-risk principle that ought to drive decisions about insurance, and as a result, they buy excessive amounts. There are a number of reasons for this, and a few examples follow.

Insurance is an intensely quantitative business, and the average person is nowhere nearly as mathematically sophisticated as the pricing actuaries working for BigLifeInsuranceCo (arguably, insuring for this reason may be a valid choice to outsource to a specialist). Furthermore, in many insurance segments, people who set foot in insurance offices have to contend with an intensely broker-driven, sales-oriented business. Finally, people have a tendency to overestimate particularly salient risks – even though the probability of dying in a plane crash is miniscule, people inevitably and repeatedly shell out big bucks for practically worthless crash insurance.

The average person may not want to cancel his or her health insurance policy, but typically, by raising deductibles just short of the pain point, one can make oneself much better off financially. I could go on, but I haven’t even gotten to the actual focus of my commentary – namely, that while most people fail to realize that they should self-insure whenever practicable, many smarty-pants fail to realize that they may be even better off seeking out specific forms of excess insurance.

II.Why financially sophisticated, quantitatively comfortable, fairly wealthy people may still want to buy more insurance than they think they should:

1.Perhaps the insurance industry is similar to the airline industry (which has made barely any money/arguably has made no money (net of direct government subsidies) over the course of their history), and thus, you can rip them off. On an empirical basis, this is probably not true, except perhaps in certain sub-industries in certain states. A weaker claim that might hold -- in certain highly competitive markets where insurers are competing on price for market share, they may in the short run price below the level of acceptable long-term profits. Signs of this may involve intensive ad bombardment, desperate insurance salesmen, geckos, etc.

2.Take advantage of principal-agent problems:
Brokers are typically not also owners, and they are frequently incentivized to produce up-front business and premiums – in poorly run insurance companies, they may be able to fudge risk, or else get paid while the going is good, and then skedaddle. If a contract is expected to pay w/very low probability, and stretches over a long period of time, it is hard for managers in a poorly run organization to overrule a broker who sells you insurance too cheaply. I’m not arguing for wink-wink, nudge-nudge agreements w/your broker. However, it is possible that while broker-driven insurance businesses overall may have more fingers in the profit pie, leaving less for the consumer, a consumer with good negotiation skills going to an improperly incentivized broker-driven insurance business may be able to get a legal steal. GEICO tries to deal w/this problem by backloading commissions, and reducing emphasis on volume – probably not a good place to test this theory.

3.Maybe Johnny can time the market, after all:
Examine historical behavior of E & O (errors & omissions) insurance pricing for executives in large, publicly traded companies. In a rising bull market, where there is little incentive for investors, regulators, journalists, and insurers to rock the boat, and the most incentive for executives to conceal material information or engage in abuse accounting, the historical levels of errors and omissions may seem to have fallen to a new low. Yet, it is at these frothy times that actual levels of liability are rising to all-time heights – so that insurers w/poor memories may lower and re-lower premiums on the assumption that liabilities have reached a permanently low plateau – not realizing that in fact, they are about to get slammed. Even if you’re not an executive, it may pay off to avoid/seek out similarly over/undervalued forms of insurance during bull markets and economic upturns, or vice versa.

4.Even if insurance companies on average extract profits from risk averse individuals in a given industry, you can still beat the markets. There's an asymmetric information and/or adverse selection issue -- if you have private information about your bad genetics that on expectation, make your health far worse than that of someone with your publicly available health profile (eg, cholesterol gets disclosed to insurance companies, but certain genes do not, except insofar as your agent asks you about family disease histories), then definitely get the cushiest reasonably priced insurance plan possible. (The corollary to this is that the insurance industry probably has to price even more aggressively overall to compensate for this, making insurance for the average person that much worse a deal.)

5.Another argument by anecdote:
Most law firms don't vary the pricing of insurance policies by individual worker -- yes, you can choose different plans, but except for various subsidies that may go up if you're a secretary vs an associate vs a partner, everyone pays the same marginal amount for switching to the PPO from the HMO. In this scenario, even if you are publicly sickly, as long as pricing overall for the entire firm is close enough to fair, you can again free ride by opting for the cushiest policy. Unless your firm is tiny, I doubt your increased medical costs will drive up firmwide costs enough to impact you much. The lesson here is to seek out other examples of artificially fixed price insurance if you’re way above the norm for risk, and to avoid such insurance -- or else seek it through non-fixed-price sources. (As always, every argument I makes only definitely applies if all else is held equal. Even if you’re remarkably healthy, and your company does not explicitly subsidize your health insurance, you still may not be able to save money by going out on your own, because the company’s greater ability to negotiate rates for a big bloc of insureds comes into play.)

6.An observation:
Some insurance companies are actually willing to take on expected value negative bets. They're willing to bet that they can reinvest your upfront premiums so that on average, they'll be ahead when, at random intervals, various policies need to pay out.

Caveat: once events take place in the future (rather than just multiplying probabilities by outcomes for lots of present events), one could argue that I could manipulate this argument by using different discount rates. I'd point out that lots of insurance 10-K's show that by (presumably liberal) assumptions, the cost of their float (the money they get up front) is still negative. As a cynical/rational person, I'd assume that other than Buffet’s, most companies are overly optimistic in reporting expected losses on policies, so if anything, the cost of float to them is even higher. (Whether this translates into skinnier premiums for you, or fatter bonuses for brokers is a different story.)

Insofar as the companies that are most willing to believe that they can successfully reinvest your money before your policy pays out, are easily identifiable, try to do more business with them. Hopefully, their greater shrewdness (if their belief is justified) doesn’t hurt you when they price your business, and their idiocy (in case they overvalue their investing skills) doesn’t extend to bankrupting the firm.

7.Another low-payoff variant:
Say that you’re a housewife/househusband (and a fairly inactive one with a nanny at that, so you’re not providing implicit unpaid/untaxed economic services to the household). If you can sign up on your spouse’s company health plan, despite the coinsurance for out of network visits common to most plans, because of the low opportunity cost for your time, you can use the plan far more than the average person. This is unlikely to make much money, however, and if anything, probably just argues for your being more active an economic contributor to household income. More generally, when you have low opportunity costs (and don’t plan to change that fact) – it may make sense to buy of certain types of insurance – assuming that you have the money to do so.

I should probably generalize my comment in point #6 to all strategies that depend upon seeking out poorly managed insurance companies: such strategies leave you worse off to some degree because such companies are also the most likely to go bankrupt and leaving you holding the bag. Any savings you can get must be carefully weighted against such risks, and you may want to consider some fairly crappy hedging by purchasing long-lived put options on the fairly crappy company you buy insurance from, or else avoid implementing these suggestions entirely. I post these mostly as a set of thought-provoking comments, and do not anticipate that the average individual will do anything different -- hopefully, he or she will walk away a little better informed.

III.A brief overview of a few insurance-related concepts:
My loose description of loss aversion, which may be another significant factor that causes people to pay too much for insurance.
Say people are irrationally sensitive to the way a particular set of choices is framed, so that two things w/identical effect -- losing $X vs failing to get an $X bonus, where all else is held equal – are treated very differently simply because they are described, or framed differently. Another rough example of this is when someone is asked “How much money will you accept to double your cancer risk,” vs “How much would you pay to halve your cancer risk, assuming that it were actually twice as high as it is right now,” not realizing that giving different answers would be inconsistent. (To be closer to correct, I’d also have to also state for the second scenario, that the respondent had just been made wealthier by the amount of money given in the response to the first question, etc.)
Expected Value, courtesy of wikipedia:

In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value"). Thus, it represents the average amount one "expects" to win per bet if bets with identical odds are repeated many times. Note that the value itself may not be expected in the general sense; it may be unlikely or even impossible. A game or situation in which the expected value for the player is zero (no net gain nor loss) is called a "fair game."For example, an American roulette wheel has 38 equally possible outcomes. A bet placed on a single number pays 35-to-1 (this means that you are paid 35 times your bet and your bet is returned, so you get 36 times your bet). So the expected value of the profit resulting from a $1 bet on a single number is, considering all 38 possible outcomes:

which is about -$0.0526. Therefore one expects, on average, to lose over five cents for every dollar bet.
Risk Aversion, from an interactive economics tutorial:
This use of the expected value is based on the Law of Large Numbers, which is a statement about what happens when a game is repeated over and over and over again. If a game can be repeated many times, good luck and bad luck tend to wash out.
What happens, though, if the game isn't going to be repeated over and over? What if it's only played once, or a few times, in your life? What if the stakes are very high, so that you are gambling with something that you really do not want to lose? That's when risk aversion comes in.
Risk averse means being willing to pay money to avoid playing a risky game, even when the expected value of the game is in your favor.
N.B.: This post was originally inspired by the intended post of a comment on, where the blogger mentions self-insurance only tangentially – unfortunately, I ended up sticking my comments onto a different post of his about Social Security -- my bad.


At 4/26/2006 8:09 AM, Blogger Miserly Bastard said...

One small concept that is missing in your otherwise thorough discussion of the insurance connundrum is the moral hazard problem, namely that once insured, the insured party has a tendency to engage in more risk-seeking behavior because he bears a disproportionately small amount of the risk (i.e., the deductible), but he will often bear the upside of that risk-seeking behavior.

So insurance companies try to re-align the moral hazard problem, by, for example, encouraging risk-avoiding behavior by offering discounts on things like cars w/ airbags, anti-theft devices, defensive driving courses, etc.

At 4/26/2006 11:46 AM, Blogger cellardoor said...

I suspect you're right -- I got a little too stuck on the "how to pick them off rather than get picked off" mentality, and failed to pay much attention to the elements of insurance that can clearly be non-zero-sum games. Yes, there are plenty of fairly cheap and/or fairly personally beneficial actions or objects to buy, that will simultaneously lower your premiums (sometimes substantially).

A side note to my insurance discussion is that if you have a very annoying/bad landlord who regularly engages in documentably illegal/actionable-for-damages acts, you may still want to outsource the suing of him/her for damages to a big insurance company (and collect fairly quickly). Renter's insurance is fairly good for this purpose. The flip side to this is higher future premiums.

My practical solution to the raised premium problem is threefold:

1.You presumably will be able to/will want to move within the year, and if you can demonstrate to your agent the egregiousness of your old landlord's improper conduct (lots of lawsuits involving parties other than yourself and poor maintenance, condo conversions rejected by the AG's office, illegal and unsafe hotel running out of your improperly zoned apartment building, etc, it is possible that you could renegotiate a better premium. I have the least confidence in this idea.

2.Realize, mentally, that the $ cost of renter's insurance is very low, and even if doubled, the expected loss of taking on such an insurance policy is still capped at the total premium price. This is typically true, and emotionally doable, but is also an inconsistent way to think about your finances -- which, of course, isn't the end of the world.

3.The very safe solution in my particular case is to have my girlfriend take out the next renters policy -- and also move into one of the few really dinky buildings owned by a landlord who typically owns far nicer buildings (eg, the Bank of America tower, the Wall Street Journal building, etc), and is thus highly exposed to bad publicity.

At 7/21/2006 11:53 AM, Blogger cellardoor said...

I've been asked by a party who shall remain nameless, to clarify that the above is tongue in cheek :P


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