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Yes, I mean expected return. If you hold penny stocks, you can expect to lose money, because the occasional big wins will not make up for the small losses. You are right that we can imagine lotteries with positive expected return, but in the real world lotteries have negative expected return, because the risk-loving are happy to pay for the chance of big winnings.
Why?
Suppose we have two classes of investors, call them gamblers and normals. Gamblers like risk, and are prepared to pay to take it. In particular, they like asymmetric upside risk ("lottery tickets"). Normals dislike risk, and are prepared to pay to avoid it (insurance, hedging, etc). In particular, they dislike asymmetric downside risk ("catastrophes").
There is an equity instrument, X, which has the following payoff structure:
99% chance: payoff of 0 1% chance: payoff of 1000
Clearly, E(X) is 10. However, gamblers like this form of bet, and are prepared to pay for it. Consequently, they are willing to bid up the price of X to (say) 11.
Y is the instrument formed by shorting X. When X is priced at 11, this has the following payoff structure:
99% chance: payoff of 11 1% chance: payoff of -989
Clearly, E(Y) is 1. In other words, you can make money, in expectation, by shorting X. However, there is a lot of downside risk here, and normals do not want to take it on. They would require E(Y) to be 2 (say) in order to take on a bet of that structure.
So, assuming you have a "normal" attitude to risk, you can lose money here (by buying X), but you can't win it in risk-adjusted terms. This is caused by the market segmentation caused by the different risk profiles. Nothing here is contrary to the EMH, although it is contrary to the CAPM.
Thoughts:
By itself, no. But this is diversifiable risk and so if you short enough penny stocks, the risk becomes acceptable. To use a historical example, realizing this (in the context of junk bonds) is what made Michael Milken rich. For a while, at least.
This certainly exists, though it's more complicated than just unwillingness to touch skewed and heavy-tailed securities.
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