Why do you have explain anomalies ? They are anomalies that is the point you can't. This theory isn't new I speculation is old as the hills and has never change in my life time of markets 34 years or the next 34.

Well, first of all, "anomalies" are efficient market "anomalies" in typical usage, and since efficient market theory is demonstrably wrong, those anomalies might have explanations. In the framework I develop, most do. Second, knowledge of why an anomaly occurs is EXTREMELY important, for it helps one know when to exit trades and strategies.

Wich kind of anomaly?

This comment doesn't make sense by itself; it responded to a comment on LinkedIn. The question was "Why do I need to know about anomalies?"​ My answer, not well stated was (1) anomalies in the EMT sense are opportunities to profit, and (2) knowing why they happen makes it easier to know when they'll stop being profitable.

Steve, interesting read. Thanks.

Thank you RALPH VINCE for being decades ahead of the rest. http://www.ralphvince.com/optimalf.pdf

Market efficiency is related to market memory, which is also measurable.

Would like to discuss market memory - I'm thinking about writing an article about it. Interested: marketpatternresearch@gmail.com

Good graph teaser, simply comparing a 22 well chosen DJIA stocks with an unadjusted Pairs Trading System seems somehow leaving to many open questions.

I've been working on methods described in the paper for a very long time, it's almost a evolution of behavioral patterns. (Stuart School of Business'94-'96

Market efficiency = market memory .

Pairs trading results depends on selection bias of basket. Else my stat arbs would have retired long time ago

That "Gambling Theory" has relevance within the context of your analysis is interesting. However, people gamble in Vegas, and have a ton of fun doing it. the idea that cash is secondary to a concept isn't what buys me other companies. So.....forget it. This is bullshit.

Efficient Market Hypothesis (EMH) is a bad theory but it is the best we have. It is very inspiring to see that someone proposes alternative ideas aiming to resolve the biggest (IMO) weakness of EMH - assumption of rational investors. Thank you. However, EMH will not go away that easy.

Price distorters proposed can be separated in to two groups: factors affecting market efficiency and just random events moving price. As a result, they perfectly fit in to EMH.

Pairs trading (PT) examples do not disproof but support EMH. EMH claims that abnormal returns are impossible on efficient market but real markets are not perfectly efficient. Market efficiency is not absolute and not constant. After strong (negative) events markets become less efficient. PT strategy flourishes on high volatility, which results from higher uncertainty, that is lower market efficiency. Global historical decline in PT returns demonstrates increase in market efficiency.

@Tim Thanks for your thoughtful comments and your compliments. I certainly agree that EMH will stay with us. In my view, it's strength is simplicity and tractability. It says that markets are (almost) always fairly priced, meaning that no deviations from fairness are sufficiently predictable to be consistently profitable. As to the specific example of PT, the price distorters I have in mind are not random (that is, "unpredictable") events and strategies. They are regular enough to make the strategy profitable, to wit, the predictable fact that more players (up to a point) make the strategy more profitable (! positive feedback), that certain market events will have a predictable impact (decimalization will reduce profitability), and that the rise of factor strategies will make a naive PT strategy lose its profitability. On this latter point, consider the Grossman-Stiglitz paradox, that a market doesn't magically become "efficient" - somebody has to make it that way.

Even in this interpretations, "price distorters" and POPP in general fit perfectly in EMH.

EMH allows abnormal returns for any trading strategy if this strategy is able to identify and exploit market inefficiency. PT looks for mispricing which can be illustrated by your fig 1. Greater divergence of opinions - greater possible mispricing - greater profit when mispricing will be fixed. PT reduces market inefficiencies, so there is a reward. Over time, this kind of inefficiency disappear, as too many people keep an eye on this opportunity, so trading strategy stops working. We saw it with arbitrage, which is assumed to be non-existent now. We see it with statistical arbitrage right now. Markets become more efficient.

In a "perfect" market, there will be no divergence of opinions, as a result, no winner's curse and no trading strategies. At the same time, there will never be a perfectly efficient market, as some price distorters, e.g. transactions costs, will always remain.

Also, I'd like to stress that any trading strategy (TS) never crashes. Phase D in POPP is impossible for TS. As time goes, TS slowly reduces profits and finally stops earning money and starts slowly losing money due to transaction costs. If TS is consistently losing a lot of money, then we can turn over buy/sell orders and TS becomes profitable. It is extremely difficult to lose a lot of money if you follow TS and use proper risk management.

Portfolio insurance crashed in 1987.

For "Grossman-Stiglitz paradox". It starts from a false assumption, that markets are efficient. They are not. They have higher or lower level of efficiency and it is not constant.

Markets become more efficient through:

1) Regulators activities. Transparent markets, unlimited access for all willing to trade, allowing short trading, reasonable taxation regime.

2) Speculators activities. Constant Pursuit of Profit pushes them to look for market inefficiencies and fix them as speculators get rewarded for that.

US market is the most efficient market in the world as it is the most open and it has the highest number of speculators "doing research" in a constant pursuit for profit. If anyone looks for "easy and big" money - welcome to developing countries. Wild-Wild-East - lower efficiency, more often mispricing, more opportunities for profit.

Here you can find some examples https://www.researchgate.net/publication/263327309_Can_time_difference_deter_arbitrage_opportunities

Due to time constraints, I cannot respond fully to your note. I'll read your research and attempt to respond later. I will say this now. If markets have "higher or lower efficiency" but an "efficient market" is a false assumption, how do you know that a market can have higher or lower efficiency? You can conclude that markets offer different profit opportunities in venue and time, but to relate that with efficiency seems to be aiming at a vacuous target. Markets are not efficient, period, if there are PREDICTABLE ways to win.

Final comment (for now): In my framework, markets have different profit opportunities at different points of their "life cycles," that is, they are never efficient. But sometimes profit opportunities are not large enough to be tradable. The main question is: how predictable are these profit opportunities? My answer - quite predictable in situations I identify in my writings.

The problem is in binary approach efficient/non-efficient. If we step away from this restriction, then most anomalies fit EMH nicely.

If one year TS, e.g. PT, earns more money then year before, then market is less efficient than before. If profit opportunities become too small (less than transaction cost) then markets become more efficient then before.

Here I completely agree with you, existence (and size) of abnormal returns is a measure of market inefficiency.

Markets asymptotically approach efficiency but never reach that absolute. The same way as normal distribution density curve never touches zero. Theoretically any number is possible but we don't care after three sigma. The same way, classics said "markets efficient" assuming some (reasonably high) level of efficiency.