## Is Equity Pairs Trading Profitable Due to Cointegration?

**A new financial research paper related to:**

**#12 – Pairs Trading with Stocks**

**Authors:** Farago,Hjalmarsson

**Title: **Stock Price Co-Movement and the Foundations of Pairs Trading

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3114058

**Abstract:**

We study the theoretical implications of cointegrated stock prices on the profitability of pairs trading strategies. If stock returns are fairly weakly correlated across time, cointegration implies very high Sharpe ratios. To the extent that the theoretical Sharpe ratios are "too large," this suggests that either (i) cointegration does not exist pairwise among stocks, and pairs trading profits are a result of a weaker or less stable dependency structure among stock pairs, or (ii) the serial correlation in stock returns stretches over considerably longer horizons than is usually assumed. Empirically, there is little evidence of cointegration, favoring the first explanation.

**Notable quotations from the academic research paper:**

"The purpose of the current paper is to evaluate whether cointegration among stockprices is indeed a realistic assumption upon which to justify pairs trading. In particular, we derive the expected returns and Sharpe ratios of a simple pairs trading strategy, under the assumption of pairwise cointegrated stock prices, allowing for a flexible specification of the stochastic process that governs the individual asset prices. Our analysis shows that, under the typical assumption that stock returns only have weak and fairly short-lived serial correlations, cointegration of asset prices would result in extremely profitable pairs trading strategies. In a cointegrated setting, a typical pairs trade might easily have an annualized Sharpe ratio greater than ten, for a single pair, ignoring any diversification benefits of trading many pairs simultaneously. Cointegration of stock prices therefore appears to deliver pairs trading profits that are "too good to be true."

The existence of cointegration essentially implies that the deviations between two nonstationary series is stationary. The speed at which the two series converge back towards each other after a given deviation depends on the short-run, or transient, dynamics in the two processes. If there are relatively long-lived transient shocks to the series, the two processes might diverge from each other over long periods, although cointegration ensures that they eventually converge. If the transient dynamics are short-lived, the two series must converge very quickly, once they deviate from each other. In the latter case, most shocks to the series are of a permanent nature and therefore subject to the cointegrating restriction, which essentially says that any permanent shock must affect the two series in an identical manner.

To put cointegration in more economic terms, consider a simple example of two different car manufacturers. If both of their stock prices are driven solely by a single common factor, e.g., the total (expected long-run) demand for cars, then the two stock prices could easily be cointegrated. However, it is more likely that the stock prices depend on firm-specific demands, which contain not only a common component but also idiosyncratic components. In this case, the idiosyncratic components of demands will cause deviations between the two stock prices, and price cointegration would require that the idiosyncratic demands only cause temporary changes in the stock prices. That is, cointegration imposes the strong restriction that any idiosyncratic effects must be of a transient nature, such that they do not cause a permanent deviation between the stock prices of different firms.

In the stock price setting considered here, most price shocks are usually thought to be of a permanent nature. For instance, under the classical random walk hypothesis, all price shocks are permanent. Although current empirical knowledge suggests that there are some transient dynamics in asset prices, these are usually thought to be small and short lived. In this case, if two stock prices are cointegrated, there is very little scope for them to deviate from each other over long stretches of time. Thus, when a transient shock causes the two series to deviate, they will very quickly converge back to each other. Such quick convergence is, of course, a perfect setting for pairs trading, and gives rise to the outsized Sharpe ratios implied by the theoretical analysis.

The theoretical analysis thus predicts that cointegration among stock prices leads to statistical arbitrage opportunities that are simply too large to be consistent with the notion that markets are relatively efficient, and excess profits reasonably hard to achieve. Or, alternatively, the serial correlation in stock returns must be considerably longer-lived than is usually assumed, with serial dependencies stretching at least upwards of six months. However, such long-lived transient dynamics imply a rather slow convergence of prices in pairs trades, at odds with the empirical evidence from pairs trading studies.

In the second part of the paper, we evaluate to what extent there is any support in the data for the predictions of the cointegrated model.

__The theoretical and empirical analysis together strongly suggest that cointegration is not a likely explanation for the profitability of pairs trading strategies using ordinary pairs of stocks. Pairs trading is based on the idea of stock prices co-moving with each other, and that deviations from this co-movement will be adjusted and reverted, such that prices eventually converge after deviating. Profitability of such strategies is consistent with cointegration, but cointegration is not a necessary condition for pairs trading to work. Instead, it is quite likely that pairs trading profits arise because over shorter time spans, asset prices on occasion move together. This could, for instance, be due to fundamental reasons, such as a common and dominant shock affecting all stocks in a given industry.__"

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