# Why does the Weak Form of Market Efficiency and Markov Property hold?

This question is to do with a paragraph in Hull (Options and other Derivatives) He explains that Stock Prices usually follow a Markov Property, where the current price of the stock contains all the information of the past, and that the path taken by the Stock is irrelevant.

He gives an example saying: "All investors watch stock prices closely. Suppose that a pattern is discovered in a Stock Price that always gave a 65% chance of steep price rises. Therefore, Investors would attempt to buy the stock immediately, and the demand for the stock would rise. This would lead to an immediate increase in price and the observed effect would be eliminated, as would any trading opportunities."

I don't get why the observed effect would be eliminated? Didn't the Stock Price actually rise as was predicted? I.e, if the price was expected to rise in the first place, wouldn't the strategies have worked?

• If the prediction is: "65% of the time stocks will rise on the 15th of September" then the stocks will rise on the 14th of September! And so on. – Alex C Oct 15 '17 at 17:07

The weak form of the efficient market hypothesis (EMH) just says that the market is efficient to all prior information contained within price. By definition, the weak form of EMH obeys the Markov property such that the current state contains more information about the future state than all prior states combined. Thus, the weak form EHM is alone sufficient to show that market prices do indeed follow a random walk. Note that while the weak form potentially allows fundamental analysis and insider information as means of predicting future price, it rules out technical analysis as a possible predictor.

To your example, the arbitrage mechanism is the implied mechanism for how and why historically significant price signals should not persist into the future. Suppose there was a price signal which historically gave $(\textbf{past tense})$ a 65% chance of a steep price increases over some finite $(\textbf{future past})$ time horizon. Arbitrageurs' (i.e., traders, basically) knowledge of the existence of a predictable and significant pattern would then alter the nature of the signal causing it to become less predictable in the future. In this case, competition to be the first arbitrageur would result in buying in anticipation of the completion of the pattern. When you compound the actions of many arbitrageurs, the pricing anomaly is eventually eliminated. When you introduce machines to the mix, predictable price patterns are identified and arbitraged at speeds which defy human ability. In all cases, trading in anticipation of a predictable pattern causes price to evolve differently than in the past.

So, to your question: yes, price would've risen as predicted albeit more quickly and thereby differently, eventually to point where the pattern becomes unpredictable in the future.

In all of this, I think it's important to remember that the theory assumes that free lunches are consumed instantly, so that no free lunches exist across any finite time period. Reality, however, is different from the theory because it does take time and effort to identify and arbitrage opportunities for excess profit, but by that time the lunch is no longer free. So the theory is just an approximation, albeit a good one.

Its best to think of market efficiency from 2 perspectives - the statiscian's and the trader's. The statiscian's market efficiency incorporates a lot of simplyfying assumptions (e.g. frictionless markets), while the trader's denotes the absence of opportunities with a risk/return profile in excess of the market (in practice, this would incorporate all the financial and time costs that drag on performance).

Think of it within the context of a market exchange. The market makers who facilitate trades would want to protect themselves against adverse selection from traders who knew about this "inefficiency". If there were repeated patterns that caused everyone to buy, market makers would quickly learn to adjust prices in anticipation of the imbalanced trading, which eliminates those opportunities.

The price would rise, but your opportunity as a trader to benefit from this information would be limited.