I stumbled across a site that claims
"given a long enough forecast horizon H, all assets with positive volatility have an unbiased expected return that is negative".
They base this on the formula:
Expected log return over Horizon periods = (1- Horizon/Sample)*(Sample Arithmetic Avg) + Horizon/Sample *(Sample Geometric Average)
(which I found comes from this paper) and the logic that since Arithmetic>Geometric, for large enough Horizon, this will become negative.
I can't find a flaw in their logic, but this seems to run counter to our intuitions about the stock market. It implies that over a long enough time horizon, the market portfolio has a negative expected return, which also implies that it will approach zero.
Do all risky assets have negative expected returns as the time horizon approaches infinity? If not, what's the flaw in the argument? If so, how do you reconcile that with our experience and intuitions about risky assets?