This paper documents that the earnings yield and book-to-price combine to predict equity returns in a way that is consistent with the rational pricing of risk. It is well known that earnings yields predict returns in the cross-section, consistent with standard formulas that show that the earnings yield equals the required return when there is no expected earnings growth beyond that from retention. With growth, those same formulas show that the earnings yield is increasing in the required return but decreasing in the growth. So, if growth is risky and requires a higher return, the determination of the required return from a given earnings yield is problematical. The paper shows that book-to-price facilitates the determination: for a given earnings yield, book-to-price indicates additional return associated with expected growth. The finding provides a rationalization of the well-documented book-to-price effect in stock returns: book-to-price indicates the risk in buying earnings and earnings growth. However, growth identified by a high book-to-price as yielding a higher return is quite different from "growth" typically attributed to a low book-to-price as yielding a lower return. Accordingly, the notion of "growth" versus "value" is redefined.
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Penman, Stephen, and Francesco Reggiani. "Returns to Buying Earnings and Book Value: Accounting for Growth and Risk." Review of Accounting Studies 18, no. 4 (December 2013): 1021-1049.
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