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Why No-Arbitrage Does Not Guarantee Market Efficiency

Article Quant Q&A · Author: HAHAHA
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Summary

The document asks whether the absence of arbitrage implies the efficient-market hypothesis and presents two responses arguing that the concepts are distinct. A market can avoid arbitrage while an underlying asset is still argued to be mispriced relative to some notion of fair value. Derivatives linked to that asset may nevertheless be consistently priced to avoid arbitrage, illustrating the distinction between derivative pricing relationships and broader informational efficiency.

The discussion also describes efficiency in terms of how quickly prices respond to exploitable opportunities or new information. Persistent pricing discrepancies may indicate slow adjustment, while rapid adjustment is associated with efficiency, though the responses differ in emphasis and make broad claims rather than providing formal tests. The examples are conceptual, including derivative pricing and differences in participant speed. The document does not define a precise efficiency measure or resolve the debate over how the efficient-market hypothesis should be interpreted in practice.

Key ideas

  • No-arbitrage pricing conditions do not by themselves establish that underlying assets reflect all available information.
  • Derivatives can satisfy pricing relationships even when participants disagree about the underlying asset’s fair value.
  • The speed with which prices adjust to opportunities is presented as relevant to market efficiency.
  • Differences in participant speed can allow short-lived opportunities to persist.
  • The discussion is conceptual and does not provide a formal test of efficiency.

Tags

ArbitrageMarket microstructureDerivatives pricingEquities
Full text
# Does No arbitrage(NA) imply efficient markets (EMH)?


# Does No arbitrage(NA) imply efficient markets (EMH)?












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?

## Answer by Neeraj (score 2)

https://quant.stackexchange.com/a/19375

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.

## Answer by meh (score 0)

https://quant.stackexchange.com/a/19347

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.