Why Cointegration Can Coexist with Market Efficiency
Summary
The document explains why cointegration among asset prices does not necessarily conflict with market efficiency. Market efficiency concerns whether future returns can be predicted reliably from available information, while cointegration describes a stable statistical relationship among nonstationary price series. Shared factors or economic links can create such cross-asset relationships even when individual future returns remain uncertain.
Examples include factor-style relationships among assets and the expectation that the same stock traded on different exchanges should have linked prices. The discussion frames cointegration as a cross-sectional relationship rather than proof of predictable profits over time. It offers intuition and examples, but no formal tests or empirical results; cointegration alone does not establish a profitable trading strategy or demonstrate that markets are efficient.
Key ideas
- Market efficiency concerns the predictability of returns, while cointegration describes long-run relationships among price series.
- Assets can share common factors and remain cointegrated without making their future returns reliably predictable.
- Equivalent securities traded in separate venues should have linked prices under market efficiency.
- Cointegration by itself does not demonstrate a profitable strategy.
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Full text
# Does cointegration contradict the market efficiency? # Does cointegration contradict the market efficiency? It is generally assumed that market prices follow random walks, implying market efficiency. However, one could find that some combinations of the "random walks" are cointegrated. Does this contradict market efficiency? How should it be interpreted? ## Answer by Kenneth Chen (score 1, accepted) https://quant.stackexchange.com/a/30083 There's no contradiction. Intuitively speaking the Market Efficiency Hypothesis has more to do with "predictability". In all of its three senses, it's more or less a translation of "you cannot make positive return consistently", in other words, as long as you're in the market, the next realization of return is no more than random draw, i.e. returns are non-predictable. Now that's what we would call things happening along the time line. But if we fixed the time point, and go into cross-sectional data, then there's a good chance to find relationship that is both statistically significant as well as give you good explanation power(in terms of fitting data). The easiest one you can think of is CAPM: $$r_i - r_f = \beta_i(r_m - r_f)$$ well, this might be leap of faith..But this is nothing more than a cointegration relationship.. So that does this say then? It means that you cannot predict what happens tomorrow(EMH), but you whatever it happens tomorrow, there could possibly exists a relationship across assets.(Cointegration) Remember the randomness are for all assets, but there could some underlying factors which drive all the returns, which then gives you a factor model. So as an example, you buy and sell the same stock for one share, I don't know what the stock price is going to be tomorrow, but I sure know that my payoff is even. And that's it. ## Answer by Richard Hardy (score 1) https://quant.stackexchange.com/a/30076 Cointegration does not contradict market efficiency. On the contrary, lack of cointegration where it is due would contradict market efficiency. For example, if the same stock had noncointegrated prices across different exchanges (e.g. NYSE vs. NASDAQ), only one of them could reflect all available, relevant information, and the others would not. Why is this a relevant argument? From Investopedia: > Market efficiency refers to the degree to which stock prices and other securities prices reflect all available, relevant information.
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