A Dynamic Analysis of Stock Price Ratios

Abstract

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 would 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 trend stationary process. In particular, we establish that, in the context of our model, market completeness entails stationary price ratios. We also theoretically relate statistical 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 standard unit root tests and cointegration analysis on a popular example of stocks. To illustrate the implications of the theoretical work, we provide a simple empirical exercise where we analyze the time series behavior of the Coca Cola and Pepsi stock price ratio. These two stocks provide us with a straightforward example of relative pricing between close substitutes. Our results have important implications for practitioners who seek to apply pairs-trading investment strategies in the stock market as they gives clear economic intuition to this popular practice. Indeed, as long as theoretical requirements are met, an investment strategy that exploits short-term error deviations of stock prices of close firms apart from their long run (cointegrated) relation, e.g., matching stocks by minimizing the sum of squared deviations between normalized stock prices as in Gatev, Goetzmann, and Rouwenhorst (2006) should produce significant risk-adjusted returns.