Markov property supposes a stochastic process, i.e. a random function. And we're back to the random walk of Burton Malkiel and the famous answer of Buffet. If the markets were random said Buffet, why am I so rich and he is so poor ! Indeed the issue is that most TA people believe (rightfully or not) that prices are not random. And most trend followers http://www.turtletrader.com/ try to take advantage of that non randomness.
Anyone who has ever traded knows to let the winners run (non randomness expressing that winners will be bigger winners) and to cut the losses short (non randomness expressing that losers will be worse losers). They also know that losers average losers and that catching a falling knife always hurts, etc... all that is the rationale for trading, i.e. the non (total) randomness.
Of course, one can think the markets are random and decide not to trade (often based on TA), nor to actively invest (selecting stocks based on FA) and decide to throw darts on charts or listings as the best decision process. The latter often resort to passive index investing (with some success).
My two cents, not being a specialist of Markov processes...
