Joseph Gerakos and Juhani T. Linnainmaa
Market reactions to tangible and intangible information revisited
Critical Finance Review | Volume 5, Issue 1 (2016), tbd

Daniel and Titman(2006) posit that the value premium is due to investors overreacting to intangible information. They therefore decompose five-year changes in book-to-market ratios into stock returns and a residual that is a proxy for tangible information based on accounting performance (“book returns”). That is, their decomposition is the following identity:   label{eqn:dt_decomp}
   underbrace{dbm(t,t-5)}_{ textrm{change in log-BE/ME}}  equiv  ;  ;  underbrace{r^B(t,t-5)}_{ textrm{book return}} -  underbrace{r(t,t-5)}_{ textrm{stock return}}.
Consistent with their thesis, they find that it is only when stock prices move in response to intangible information—the return component orthogonal to book returns, obtained by regressing stock returns on book return and lagged book-to-market—that returns reverse. They conclude that the book-to-market ratio forecasts returns because it is a good proxy for the intangible return.

Problems with the decomposition

We show that changes in book-to-market ratios cannot be decomposed into book and stock returns. A simple example illustrates the problem. Suppose a firm has $1 in book value of equity and $2 in market value of equity, and so its book-to-market ratio is {1}/{2}. If the firm now issues $1 worth of additional equity, both the book and market values of equity increase by $1, and the book-to-market ratio increases to {2}/{3}. Because the Daniel-Titman decomposition factors out stock returns—which are neutral with respect to net issuances and dividends—from changes in the book-to-market ratio, book return captures this increase in full by being distorted upward by log({2}/{3}) – log({1}/{2}) ≈ 29%.

Book return combines return-on-equity with a nonlinear bundle of past book-to-market ratios and contemporaneous stock returns, net issuances, and dividends. This problem occurs because changes in market and book values of equity are additive and not multiplicative when firms pay dividends or issue or retire equity. Hence, it is not possible to factor out stock returns from changes in the book-to-market ratio without creating a book return correlated with past book-to-market ratios, stock returns, net issuances, and dividends.

Approximation of the error in the decomposition

A cross-sectional regression of the book return on the return on equity measures the approximation error in book returns. For the Daniel-Titman decomposition to hold, such a regression should have an R2 of one. Instead, we find an average R2 is 0.57, implying that two-fifths of the cross-sectional variation in book returns is due to the approximation error induced by factoring out stock returns from changes in the book-to-market ratio. These results are not surprising given that firms rarely conform to the model under which the Daniel-Titman decomposition would hold. A majority of firms issue or repurchase equity or pay dividends during the typical five-year period, thereby introducing approximation error into book returns.

How big is the approximation error if we view book return as being equal to the return on equity plus noise? 
  r^B(t,t-5) =  textrm{roe}(t,t-5) +  textrm{approximation error}.
Among growth firms—the lowest quintile of firms in the BE/ME distribution—the average five-year return on equity is 0.77, the average approximation error is  – 0.15, and the standard deviations of return on equity and the approximation error are 0.71 and 0.60. Among value firms the average five-year return on equity is 0.33, the average approximation error is 0.08, and the standard deviations are 0.40 and 0.32. These numbers show, first, that the average approximation error flips sign as we move from growth to value and, second, that the standard deviation of the approximation error nearly equals that of the return on equity.

Net issuances and dividends

To illustrate the importance of net issuances and dividends in the evolution of book-to-market ratios, we decompose changes in the book-to-market ratio into changes in the book and market values of equity. Among all-but-microcaps, net issuances and dividends explain one-third of the cross-sectional variation in changes in the book value of equity, and one-quarter of the variation in changes in the market value of equity. These sources of variation are important in return regressions. Without a control for net issuances, changes in the book value of equity barely correlate with future returns. The reason is that the book value of equity can increase either because the firm is profitable or because it issues new equity. But profitable firms have high returns and firms issuing equity have low returns. Therefore, changes in the book value of equity alone are not informative about future returns.

The approximation error in book returns makes Daniel and Titman (JF 2006) projection of stock returns on book returns ill-suited for delineating between tangible and intangible returns. Even in an economy in which accounting performance is fully disconnected from firm valuations, stock returns are correlated with book returns in the Daniel and Titman decomposition. Furthermore, net issuances and dividends are counted as book returns, and their signs depend on whether a firm is classified as value or growth. If a growth firm, for example, issues equity, this action shows up as a high book return. That is, the firm appears to have good tangible performance just because it issued equity. Value firms that issue equity, in contrast, look worse than their peers that do not issue equity. Given that book returns are substantially polluted, cross-sectional differences in book returns have little economic content and provide no insight into the source of the value premium.

Tangible versus intangible information

Questions regarding the effects of tangible and intangible information are interesting but difficult to resolve empirically. We show that the data are at odds with the argument that book-to-market predicts returns because “it is a good proxy for the intangible return” (Daniel and Titman (2006) p. 1605). Current book-to-market fully subsumes intangible-return proxy's ability to predict the cross-section of average returns. This analysis suggests that book-to-market does not predict future returns because it is a good proxy for the intangible return. Instead, it appears that the intangible return is a good proxy for the current book-to-market ratio. It also suggests that there is more to book-to-market's predictive power than its correlation with what Daniel and Titman call the intangible return. We also show that Daniel and Titman conclusions reverse when we change the tangible-information proxy from book return to the change in the book value of equity. Under this specification the tangible returns reverse. We do not suggest that this is the correct conclusion. Rather, we view it as an example of the difficulty in separating the effects of tangible and intangible information.

The question of why book-to-market ratios correlate with future returns remains important. Fama and French (JF 2008) show that recent changes in book-to-market ratios carry more information about expected returns than historical book-to-market ratios, but their results shed no light on what this information might entail. Gerakos and Linnainmaa (2013) use Fama and French (JF 2008) decomposition to divide the HML factor into two parts, and suggest that these parts carry different prices of risk. They show that book-to-market ratios' ability to explain variation in future returns traces back to changes in the market value of equity, and suggest that these changes are important because they pick up changes in expected returns. If a stock's expected return increases, its instantaneous return is negative, thus turning it into a value stock, and vice versa.