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What is the difference between RWH and EMH?

In efficient market, the price will be fully reflected by available information.

If there is no news, the price would be unchanged. If there is a news, the price would immediately adjust to a new price reflecting the price. This is the same as the idea of RWH.

However, it is not necessary for efficient efficient market to have random walk prices. I do not totally understand the difference between two hypothesis.

Also, when will the stock prices follow martingale property in efficient market? Only in risk-neutrality?

Which one is the better model for EMH?

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EMH: An asset always trades at its fair value. That is, all information is continuously being priced in.

RWH: The asset price is not predictable and follows a random walk.

So RWH is a hypothesis which is consistent with EMH. If every piece of information is being priced in continuously, and you cannot predict what information will become available, then from your standpoint the price follows a random walk.

On martingales: The stock itself is never a martingale in an efficient market. That is a popular misconception. If that were true, the risk premium for the stock would be negative and you would invest in riskless assets instead. Even the discounted stock price shouldn't be a martingale, because, again, that would imply that the risk premium is 0 and again the riskless asset would be a better choice.

However, the discounted stock price under risk-neutral dynamics is a martingale if the market is arbitrage-free.

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  • $\begingroup$ is that possible for efficient markets to have non-random walk price? $\endgroup$ – Claire Aug 15 '15 at 15:45
  • $\begingroup$ @Claire I believe no, because that would imply you can predict the movement of the price, which implies that you have some information which the rest of the market does not. That is inconsistent with the idea of EMH. $\endgroup$ – Slug Pue Aug 15 '15 at 15:48

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