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The EMH states that stocks are traded at its fair values. This means there is no arbitrage strategy in efficient markets.

However, if the market is no arbitrage, can we conclude the market is efficient? I am confused about the relationship between these two. Can someone give a example that satisfies NO arbitrage but not the EMH?

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Existence of arbitrage opportunities does not lead to market as inefficient.

Samuelson has defined relationship between existence of arbitrage opportunities and market efficiency. He said:

if market adjust quickly to arbitrage opportunities to return back to normal without cost of any other investor and through market mechanism then market can be said efficient. But if price differences persist (or arbitrage opportunities) for a long period then market is not efficient

So both arbitrage opportunities and market efficiency can exist together. It is how quickly market responds to arbitrage opportunities that distinguishes between an efficient or inefficient market.

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It seems reasonable that no-arbitrage doesn't necessarily imply EMH. If we are talking pure arbitrage opportunities, like offsetting the same contract on 2 exchanges, futures cash and carry, BS options no-arbitrage, etc. Mainly, for derivative products it's very easy to do the arbitrage trade. However, this means that you are assuming the underlying product is priced at fair-value.

So in theory you could have some person who is beating the index by buying /selling products not priced at fair value. However, you can still satisfy the no-arbitrage property by correctly pricing all the derivatives on that product.

There are many more examples that could satisfy no-arbitrage and not EMH.

For what it's worth the weak EMH is a plausible claim. In this case the no-arbitrage clause would be easily satisfied.

The semi-strong EMH doesn't make sense in practice. For a market to adjust prices to new information instantaneously is impossible. Information would have to dissipate from it's source to every other market participant simultaneously. Since current technology doesn't allow for this we end up with a some participants being fast, and others being slow. The fast guys end up making their money from this inefficiency, even if it only lasts for microseconds.

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  • $\begingroup$ NA is a necessary condition for an equilibrium in the financial markets. If there is an arbitrage opportunity, then demand and supply for the assets involved would be infinite, which is inconsistent with equilibrium. If there is no arbitrage strategy, the market should be in equilibrium. why this case is not a efficient market? $\endgroup$
    – HAHAHA
    Aug 16, 2015 at 20:42
  • $\begingroup$ Arbitrage only takes care of cases where two assets are substantially equivalent. That's only a small fraction of the mispricings that could occur. Suppose you believe that GOOG is overpriced compared to stocks in general. There is no way to set up an arbitrage to eliminate this mispricing. You can short GOOG and go long the S&P but that is most defintely not a risk free position, i.e. not an arbitrage. When arbitrage applies it is very powerful, but that's not common. $\endgroup$
    – Alex C
    Aug 17, 2015 at 4:46
  • $\begingroup$ @Claireee, Alex C really answers your question. Because a future on GOOG only depends on: price of GOOG, time to expiration, and the risk-free rate. The no-arbitrage principle could apply here with GOOG still being overpriced relative to the market. Thus violating the EMH. $\endgroup$
    – meh
    Aug 17, 2015 at 13:13

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