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Stock price ratios have long been used by finance practitioners as a relative value metric. A popular argument for this widespread use is that stock price ratios tend to revert to their long-run mean so that substantial deviations from historical averages could successfully be arbitraged away. In this work, we lay out the theoretical conditions for the ratio of stock prices to be a stationary process. In particular, we theoretically relate price ratio stationarity to economic mean reversion in profitability (as measured by dividends or earnings price ratios) across securities. We further test our theoretical predictions using a popular example of 'close' stocks.
