Then a person placing a dumb trade is creating a mispricing, which will be consumed by some market agent.
Well, that looks like an "offering to buy a stock for $1 more than its current price" scenario. You can easily lose a lot of money by buying things at the offer and selling them at the bid :-)
But let's imagine a scenario where everything is happening pre-tax, there are no transaction costs, we're operating in risk-adjusted terms and, to make things simple, the risk-free rate is zero. Moreover, the markets are orderly and liquid.
Assuming you can competently express a market view, can you systematically lose money by consistently taking the wrong side under EMH?
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Yes, we have to be quite careful here.
Let's take penny stocks. First, there is no exception for them in the EMH so if it holds, the penny stocks, like any other security, must not provide a "free" opportunity to make money.
Second, when you say they are "a poor investment in terms of expected return", do you actually mean expected return? Because it's a single number which has nothing do with risk. A lottery can perfectly well have a positive expected return even if your chance of getting a positive return is very small. The distribution of penny stock returns can be very skewed and heavy-tailed, but EMH does not demand anything of the returns distributions.
So I think you have to pick one of two: either penny stocks provide negative expected return (remember, in our setup the risk-free rate is zero), but then EMH breaks; or the penny stocks provide non-negative expected return (though with an unusual risk profile) in which case EMH holds but you can't consistently lose money.
My "risk-adjusted terms" were a bit of a handwave over a large patch of quicksand :-/ I mostly meant things like leverage, but you are right in that there is sufficient leeway to stretch it in many directions. Let me try to firm it up: let's say the portfolio which you will use to consistently lose money must have fixed volatility, say, equivalent to the volatility of the underlying market.
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: