QuoteOriginally posted by: exotiq5.) In efficient markets, must the price processes of all tradeable assets be Markovian? I think so. If the market has a memory that affects the future, then there will presumably be a delay in prices reaching their efficient value. Since I have buckets of evidence from US equities and their options that the market does have such a memory, I guess this must put me in the camp of the non-believers.

QuoteIn efficient markets, must the price processes of all tradeable assets be Markovian? As to the logic of this statement I do not agree - for two reasons:1. Even in non-stochastic dynamic models with perfect foresight - e.g. overlapping generations models - you can find general equilibria with cycles in asset prices (see Gale, D. 1973. Pure Exchange Equilibrium of Dynamic Economic Models. Journal ofEconomic Theory, 6, 12-36, Grandmont, J.-M. 1985. On Endogenous Competitive Business Cycles. Econometrica, 53, 995-1045, and a full line of related litterature). And in general equilibrium there are no arbitrage profits. The point is: Systematic behaviour in asset prices can be an equilibrium phenomenon even in the most simple models - so there is good reason to think that systematic movements in asset prices may be compatible with general - and thus a fortiori arbitrage - equilibrium.2. In a stochastic environment systematic behaviour in asset reurns may also be explained by systematic variations in risk premiums (so that properly risk adjusted returns does not exhibit such systematics).As to the concept I would prefer to see informational efficiency as an equilibrium concept: I would define a general equilibrium to be informational efficient with respect to specific information if the equilibrium would survive as an equilibrium if this specific information was revealed to all agents. In economics we are used to utilise an equilibrium concept as an abstraction to capture some general features of the economy under idealised conditions and accept that this is not a perfect description of the world. Also the chosen equilibrium concept will depend on what we want to investigate. The question "Are the market prices informational efficient" does not make more sense than "Is the economy in equilibrium" - only much more specific questions can make empirical sense, and there are many non-exclusive and interesting ways to phrase these. And as I pointed out above: There is no reason to see systematic movements in asset returns as evidence of informational inefficiency (unless you - tautologically - use this as part of the definition).Olejasz

Apart from the fact that "all" information is defined as whatever information happens to be reflected in securities prices (and the problem of coordinating who reflects what is intractable), the main problem with the concept of market efficiency, is that the objective and outcome of markets cannot ultimately be measured as to its efficiency.At the most basic level, you can never say that a man who baked and ate a bagel, when he could have baked and eaten a doughnut, chose the more efficient path. All mankind could choose to hibernate in holes for three years, and no alien would sneer at our stupidity. Similarly, there is no right price for a currency exchange rate or interest rate, but rather any number of exchange rates and interest rates are equally valid, particularly in light of the fact that the largest participants are non-profit organizations (governments).If everyone wishes to hold euros in their basements, we can simply print more euros and fewer dollars, or we can do away with either currency entirely, and then move interest rate spreads in the opposite direction when people change their minds. There are currently people in possession of large quantities of worthless pre-euro local currencies. While the exchange rate of zero seems like the right one, it hardly seems like it is the only one we could have chosen.And while markets may command a huge amount of information, it is likely that over the course of an entire day with millions of trades, not a single trader is aware of the daily exports of pencils manufactured in Malaysia to Italy, for example.

Market efficiency means there is no more an unlimited role for middlemen in securities markets than there is for automobile manufacturers in the car markets. There is no reason why an unlimited number of people should expect they can walk up to the stock market and make money like a cash window, just as there are people who hold no similar expectation from the car market.The difference is, no college professor who built a car in his garage, tried to sell it, and lost money, would come up with some crazy theory of car-market efficiency!You can always expand the market for cars, like that guy who built the two-wheeled scooter, or by building a cheaper car, or something. Similarly, you can always expand the market for securities, by finding something new to trade, by bringing a new company to market, or by trading from Wyoming where the lower sales tax on your paper clips enables you to lift an offer which would have otherwise gone unfilled.Combining the two, you could say a guy with a cheaper futures quote service could pay to have one more pound of marginal metal ore extracted from the ground, sell it to a bidder who otherwise wouldn't have gotten filled, where that bidder then builds a car and sells it a price which a buyer - who happens to work at the mine - could not otherwise have afforded to pay, so that they all stay in business when they otherwise would have become self-sufficient potato farmers or eaten out of trashcans. And now the trash rots, or is eaten by bacteria instead.Of course, even if these people then all make 10,000,000% and become billioniares, that 10,000,000% will be called "the market return," and some academic will say that it is impossible for them to "beat the market return" in the long run. Similarly, if someone were to measure the pace of a marathon, he would discover that runners, on average, cannot beat the marathon. And yet marathon records are broken every year.

I actually think the phrase "market efficiency" means close to nothing.Markets are markets that's all. They incorporate randomness, but they also incorporate structure - the best way to understand structure is to get deeply involved."Efficiency", as well as prediction, is subjective. Those who spend too much time on data and time series etc, and model without causal relationships find it very "efficient."

Mathematically, EMH is that market is a martingale. I have not seen a paper yet that would devise a criterion to test it (in the statistics terms), but it's not impossible. By the way, martingales could be non-Markovian easily (and most of them are).