Why people buy lottery tickets
January 23, 2013 4 Comments
Falkenstein on ‘skewness‘:
There are several papers asserting that investors like positive skew to their returns. This is because empirically investors tend to be highly undiversified, and have a bias towards highly volatile stocks, and so they seem to want big lottery-type payoffs (incidentally, this is the exact opposite to what Nassim Taleb states is common, that people prefer payoffs that have high modes and low means–negative skew).
I don’t have a fancy model but I do have two cents. This preference for ‘skewness’ (positive convexity) is perhaps perfectly explainable as a hedge. Not a hedge to the rest of a financial portfolio (by assumption/observation, it clearly isn’t), but to life. The natural state of life is to be negatively-convex (in a lot of things).
You have a job. It pays you $X/year. Sure, maybe down the road you’ll be at 1.15X. But will you ever be at 100X? Clearly not. On the down-side though – you could simply lose your job altogether. Your upside is pretty modest – your downside is huge. That’s negative-’skewness’ and you experience it in your main/only source of income by default.
Or take something like Social Security. You’re paying into Social Security. I guess down the road you’ll get a check. It might be a little bigger than you expected (who knows). It might be just about what you might expect. Or there might be a big overhaul, it might get raided, and/or huge inflation, and you get effectively $0. Again: minimal upside, huge potential downside.
You have a girlfriend. Maybe you’ll get married (yay? sort of). Or maybe she’ll just dump you and leave you a drunken wreck.
You have kids. Presumably they’ll end up ok (computer programmers). Maybe something a little more impressive. Or maybe they turn out to be meth addicts…
You’re a doctor. Doctoring is good. But your friends are in Tech. Maybe your friends were right. If you overexposed yourself to doctorness, that’s huge trouble for you. If Tech explodes big-time, you’ve missed out…
Add in the use of leverage (usually going hand in hand with societal improvement/technology/progress) – buying a house with a mortgage, a bunch of complicated child-care to allow the spouse to get a second job, moving to a higher-echelon of school district so your kids can go to a Good School – and the sense of being ‘negatively-convex’, or having sold vol, or being short protection, or having sold a bunch of insurance, or however you want to think of it – must only multiply.
You may, while all this is going on, always suspect/fear that you ‘sold vol too cheaply’. Was it really worth it to pony up for the extra-fancy-school-district house? You’re not sure – you’re uncertain. Uncertainty in one direction doesn’t help you much. But uncertainty in the other direction hurts you a lot…
That’s the way of it. So what do you need to balance all that out, the negative-convexity and the uncertainty about whether the exposure made sense (your ‘ model’, for life)? You need insurance. Often, of course, literally (e.g. homeowner’s insurance). But perhaps just in the metaphorical sense of needing positive-convexity, from anywhere: you need lottery tickets. You need positive convexity to balance out the negative convexity you walk around saddled with all the time.
So you ‘overpay’ (compared to what models suggest) for optionality, for anything with a ‘lottery-ticket-like-payoff’. But the models didn’t take into account your natural negatively-convex existence, did they? (Or do they?)
Taleb, meanwhile, is analyzing banks. (Or thinks he is.) I guess. (Again: I’ve never read Taleb.) Banks, as a business, are typically in the natural position of having sold vol, being negatively-convex, and all that. So to Taleb, analyzing bank trading and their VaR and such, he gets, I guess, the impression that they ‘want to be negatively-skewed’. But it’s really that they have to be negatively-skewed, they just try to do it as smart as they possibly can. (Which of course is a recipe for sometimes getting it spectacularly wrong.)
But that is not the motivation of individuals. Individuals are naturally negatively-skewed – they’re already ‘bank-like’, and don’t necessarily want to be if they can help it. So, they buy lottery tickets. The financial markets offer many of them.