I took a graduate level measure-theoretic probability theory class. The professor had this rant about how "buy low, sell high" was a bad idea, it's all about how long you stay in the market. He had a mathematical proof that, if I recall correctly, only held if the random process is monotonically increasing in expectation, which of course is not guaranteed.
trading, frictional costs, and the asymmetric psychology of selling winners and riding losers are a better explanation for why buy low, sell high is a bad heuristic to aspire to.
