Comment on Open thread, Aug. 10 - Aug. 16, 2015

Tue, 11 Aug 2015 14:53:55 GMT

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.

Does that violate your "risk-adjusted terms" assumption?

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.

Discuss