Gambling vs Insurance

I came across a post over at Falkenblog (a fairly interesting blog that I just recently started reading) that discussed the paradox of people's proclivity both to gamble and to buy insurance. Eric Falkenstein writes,

People clearly like to gamble, and are willing to pay a premium for the exposure to random payoffs with large skew. This is contrary to the usual assumption that people are risk averse, and necessitate a positive expected return to take a gamble. 

Early on in utility theory, Friedman and Savage (1948) seized on this anomaly to argue that the curvature of an individual's utility function differs based upon the amount of wealth the individual has. This curving utility function would thereby explain why an individual is risk-loving when he has less wealth (e.g., by playing the lottery) and risk-averse when he is wealthier (e.g., by buying insurance)... 

The basic problem is that 

1) People pay to buy insurance. 

2) People pay to gamble.

It's still a puzzle, though every so often a new paper shows up to solve it.

Falkenstein's paradox made me think back to my very post here at The Crimson Cavalier, "On Insurance and Flat Tires" (for a refresher, I found a nail in the sidewall of my tire, and I was able to get the tire replaced for free, because I'd bought the "Tire Protection Plan", something I almost never do). In that post, I argued:

It is rare for the average individual or investor to do even basic expected value math (Expected loss = Probability of loss x Amount of potential loss) to determine what price they should be willing to pay for insurance. Insurance companies know this, and profit massively from it. Why, then, do people do this? Well, for the same reason that I'm an incredibly happy man this morning, that's why...

Frankly, it's biological--or, at least, psychological. We as humans are hard-wired for "loss aversion". While it may seem counter-intuitive, losing $100 causes us more pain than gaining $100 yields pleasure. It's bizarre, but it's true. Therefore, avoiding a $100 loss (or a $150 loss in the case of my flat tire) is actually more exciting than stumbling into a $100 gain. Yes, you heard right. I'm happier this morning than I would be if I'd come back to my car and seen a 100 dollar bill sticking out of my tire.

I think that this dynamic is key to deciphering Falkenstein's insurance/gambling paradox. I would argue that the reasons we buy insurance and the reasons we gamble are in fact one and the same.

When insurance pays to cover the costs of our crisis events, the excitement (or relief) that we feel at not having to pay to recover our loss more than compensates the added premium we paid along the way. Gambling is much the same. In both cases, we feel an incredible rush when we receive an unexpected gain. Not having to pay for a loss feels to us very much the same as an unexpected gain.

Ultimately, the decision to purchase insurance is not as simple as "risk-aversion", nor is the decision to gamble as simple as "risk-seeking". Rather, both decisions entail very complex psychological preferences with respect to our mental coding of gains and losses--our brains do some very strange accounting when it comes to unexpected financial results. (I'll link again now to the paper I linked to in my first post on insurance, in case you suffer from severe insomnia or masochistically enjoy reading dense academic treatises).

Of course, not all people suffer from this paradox. I, for one, avoid purchasing insurance whenever possible, but do enjoy gambling--you could call me a bit of a risk-taker, though I of course prefer to just think of myself as a coolly rational trader. Others will conversely avoid gambling and purchase insurance whenever possible. But the willingness to both gamble and purchase insurance should not be read as irrational or even necessarily inconsistent--it's just a reflection of our complex psychological wiring and the way we code gains and losses. I'll see you in Vegas.

[Falkenblog]

On insurance and flat tires

This morning, as I was climbing back into my car with my wife Meggie following our 4-mile run, I spotted a large nail sticking out of the sidewall of one of my tires--brand new tires I'd bought barely a month ago. Not just in the tread, but in the sidewall, making patching impossible and replacement mandatory. Great.

As I drove home, Meggie called the tire shop to set up an appointment. It was then that I realized that I'd had the amazing foresight to buy the Tire Protection Plan when I'd bought my tires. $70 extra on $700 tires gave me free replacement for the life of the tires, if something like a nail in the sidewall came along. Hooray! All is well.

The trader in me had to laugh. In fact, he's still laughing. Hysterically. For years now in the options markets, I've made a living by selling insurance (in the guise of option volatility) to investors who overvalue it. It's good business, provided you are well-trained in the art (note: not science) of risk management. The fact is, especially in times of great uncertainty, investors and consumers unconsciously place incredibly high values on insuring against unpalatable outcomes. Following the schizophrenic markets lately, all manner of talking heads--including men whom I respect greatly, like Nassim Taleb--are advising investors to "protect their tail risk", and buy insurance. This, even when the cost of doing so has nearly doubled (at one point, it had in fact tripled) in just four months. Frankly, it's madness.

It is rare for the average individual or investor to do even basic expected value math (Expected loss = Probability of loss x Amount of potential loss) to determine what price they should be willing to pay for insurance. Insurance companies know this, and profit massively from it.

Why, then, do people do this? Well, for the same reason that I'm an incredibly happy man this morning, that's why. As you might expect, I almost never buy the protection plans pitched by car rental companies, appliance salesman, tire shops, or (my personal favorite because of their incredibly absurd premiums on low-value goods) Best Buy. I'm frequently arguing with Meggie (your typical risk-averse consumer) about why she shouldn't spend money on various insurance products (life insurance happens to come up frequently). I'm still not really sure why I bought the Tire Protection Plan this time around. But I do now better understand why many people do.

Frankly, it's biological--or, at least, psychological. We as humans are hard-wired for "loss aversion". While it may seem counter-intuitive, losing $100 causes us more pain than gaining $100 yields pleasure. It's bizarre, but it's true. Therefore, avoiding a $100 loss (or a $150 loss in the case of my flat tire) is actually more exciting than stumbling into a $100 gain. Yes, you heard right. I'm happier this morning than I would be if I'd come back to my car and seen a 100 dollar bill sticking out of my tire.

Yes, there are of course other valid reasons to buy insurance (if, for example, the magnitude of the potential loss is so great that you won't have enough cash to cover it, then you may have no choice but to buy insurance), but this mental accounting trick explains a great portion of why people OVERvalue insurance. Does this all mean that I'm going to start buying the protection plans more frequently? Good Lord, no. As I say often to people, they build big buildings in Las Vegas because of thinking like that. But it certainly makes me understand why many people do.

(If you're a real nerd like me and want to read more on this topic, check out Richard Thaler's "Mental Accounting Matters" here: http://www.som.yale.edu/faculty/keith.chen/negot.%20papers/Thaler_MentalAccounting99.pdf. It's a real page-turner.)