24 January 2013

Lotteries and Skew

Rhymes With Cars & Girls | Why people buy lottery tickets

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. [...] 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.
Empirical question: poor people buy more lottery tickets. Do poor people have more negative skew?

On the one hand, they have less of a safety net to fall back on in terms of savings, human capital, family, etc. On the other hand, they have less to lose. (If you're only marginally employed to begin with, losing your job is not as big of a blow; losing your lease is not as damaging as losing your mortgage, etc.)

I think it would interesting to take this skewness concept and run it through Prospect Theory. I have a feeling a lot of things that look irrational with regards to skew preferences would appear more reasonable if you didn't assume linear utility functions, equal weights on gains and losses, etc. (Which, for all I know, the "several papers" Falkenstein mentions may not assume. But I'm not taking the time to track them down and find out.)


  1. Poor people buy more (literal) lottery tickets, but rich people buy more stocks. Which, relatively speaking, is the bigger investment in 'skewness'? You're right, there's an empirical question in here....