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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,” our results suggest 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.