We are so skewed!

Note that I didn’t say “screwed” but skewed. Well, it wouldn’t have made a difference because today’s post is about how we get screwed by skewness. 

But I’m getting ahead of myself. The other day I asked myself why would anyone buy lottery tickets? The return profile is atrocious! The average payout is probably only about 50% of the money raised. In a hypothetical lottery with a one in a million chance for a $500,000 prize and a ticket price of $1.00, your expected return is -50% in one week, which means essentially -100% compounded over a year. The standard deviation is $500, so 50,000% relative to the $1 investment. And that’s on a weekly basis, which translates into over 360,000% annualized. What’s worse, that jackpot payout is usually stretched over many years or decades with a much lower lump-sum payment. And it’s subject to income taxes, so the after-tax return is even bleaker! If Vanguard or Fidelity or Schwab offered a mutual fund with return stats like that everybody involved would be facing federal indictments!

Then why not invest the lottery ticket money in stocks? No one can tell me that they’re afraid of equity risk (about 10-15% annualized) when they buy lottery tickets with 360,000% annualized risk. Nowadays you can buy stocks or equity mutual funds in very small amounts. Our 529 account has a $25 minimum investment and you can buy single stocks on Robinhood. Then what’s the appeal of a lottery? In one word: Skewness, see the Wikipedia definition. In particular, positive skewness!

Positive Skewness: higher probability of large positive outcomes (e.g. lottery). Negative skewness: higher probability of large negative outcomes (e.g. stock market). Source: Wikipedia

Positive Skewness means that the likelihood of large positive outliers is much higher than that of large negative outliers. Case in point, a lottery ticket: Your worst return is -$1, or whatever the price of the lottery ticket may be.  The largest positive outlier might be in the hundreds of millions.  Continue reading “We are so skewed!”