Prospective book-to-market ratio and expected stock returns
                                                    ∗                 †                        ‡
                                        Kewei Hou            Yan Xu            Yuzhao Zhang
                                                              Feb 2016
                    We propose a novel stock return predictor, the “prospective book-to-market”, as the present
                 value of expected future demeaned book-to-market ratios. We find that the aggregate prospective
                 book-to-market ratio can significantly predict stock market return, with adjusted R-squared be-
                 tween 5.0% and 5.8% out-of-sample. In addition, a high-minus-low investment strategy based on
                 prospective book-to-market ratio generates significant monthly alpha ranging from 13.4 to 20.8
                 basis points across various factor models, and the return spread is also shown to be non-redundant
                 as an alternative value factor in pricing cross-section of stock returns.
                   ∗Fisher College of Business, The Ohio State University, 2100 Neil Avenue, Columbus, OH 43210, USA; phone:
                 +1 614 292 0552; fax: +1 614 292 7062; email: hou.28@osu.edu.
                   †Faculty of Business and Economics, University of Hong Kong; Pokfulam Road, Hong Kong; phone: +852 2859
                 7037; fax: +852 2548 1152; email: yanxuj@hku.hk.
                   ‡Rutgers Business School, Rutgers, The State University of New Jersey, Newark, NJ 07102, USA; Phone: +1
                 973 353 2727; fax: +1 973 353 1006; email: yzhang@business.rutgers.edu
         Prospective book-to-market ratio and expected stock returns
         We propose a novel stock return predictor, the “prospective book-to-market”, as the present
       value of expected future demeaned book-to-market ratios. We find that the aggregate prospective
       book-to-market ratio can significantly predict stock market return, with adjusted R-squared be-
       tween 5.0% and 5.8% out-of-sample. In addition, a high-minus-low investment strategy based on
       prospective book-to-market ratio generates significant monthly alpha ranging from 13.4 to 20.8
       basis points across various factor models, and the return spread is also shown to be non-redundant
       as an alternative value factor in pricing cross-section of stock returns.
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                1    Introduction
                In this paper, we propose a new stock return predictor, through decomposing the book-to-market
                ratio into permanent and transitory components. Our decomposition relates the present value
                of demeaned stock return to the temporary component of the book-to-market ratio, the present
                value of demeaned book-to-market, and the present value of demeaned return on equity. When
                expected return moves with each or all of these three terms, future stock return can be predictable
                when the investor observes new information about book-to-market ratio. Specifically, we focus
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                on the ‘prospective book-to-market’, , defined as the expected sum of all future book-to-market
                around its long run trend. When the expected sum of future book-to-market is above its long run
                trend, it signals that either the expected return is above its long run trend, or the market value
                is temporarily underpriced than the book value and is expected to rise in the future. Indeed, we
                find that the prospective book-to-market is particularly useful in predicting next period returns.
                    Empirically, we model the prospective book-to-market by assuming a simple autoregressive
                form of book-to-market ratio then estimate its infinite sum while taking into consideration of the
                historical average. Similar to ?, which utilize the difference of persistence in state variables to
                better predict stock returns, in our setup the superior predictive power of the prospective book-
                to-market depend on the persistence of book-to-market ratio and its current level relative to the
                long run trend.
                    Our data include returns and book-to-market on three different levels: market, industry port-
                folios, and cross-section of individual firms. In out-of-sample tests, we use only the currently
                available information to ensure there is no look-ahead bias. There are two parameters to esti-
                mate: for the long run trend, we simply use the historical sample average to proxy for it. The
                estimation of autoregressive coefficient of book-to-market ratio deserves further elaboration. For
                both market and industry portfolios, we rely on simple autoregression as the measure for the
                persistence. Other than the OLS, we also conduct robust regression to minimize the effect of
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                outliers in the return predictability tests.
                   1The naming of this term is analogous to ?, although in a different setting.
                   2In the meantime, we are aware that we will suffer the well-known “? bias” that occurs when a sample size is
                small especially at the early stage of out-of-sample period. This bias constitutes another difficulty: that our point
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           We find that our prospective book-to-market ratio is a significant return predictor at the
         market, industry, individual stock level. At the market level, the prospective book-to-market
         ratio produces out of sample adjusted R-squared between 5.0% and 5.8%, in contrast to the
         conclusion of ? that market returns can not reliably be predicted out of sample. Moreover, as
         shown in ?, these out-of-sample R-squared implies substantial economic gains for the investor.
           In industry level time series tests, we show that the prospective book-to-market ratio predicts
         48industryportfolio returns. Moreover, using a zero cost long-short strategy, industry prospective
         book-to-market ratio is shown to generate a significant monthly spread of 2.3%∼2.4% in risk-
         adjusted returns across industries, but the original book-to-market ratio fails to do so, consistent
         with ?.
           At the individual firm level, as firm by firm estimation of the persistence in book-to-market
         ratios is very imprecise with shorter sample period, we use a straightforward pooling OLS re-
         gression at industry level then assign to individual stocks within that industry. Interestingly, we
         observe a lot of cross-industry difference in the persistence parameter, which creates additional
         degrees of heterogeneity in book-to-market ratios when we sort firms into portfolios to develop a
         highly profitable investment strategy. To demonstrate the forecasting power of our new predictor,
         welong (short) firms when the expected sum of future book-to-market ratio is higher (lower) than
         its historical average, after controlling for firm size. This strategy generates significant monthly
         alphas ranging from 13.4 to 20.8 basis points, over models with q-factors, Fama-French 3 factors,
         3 factors augmented with momentum factor, Fama-French 5 factors, and 5 factors augmented
         with momentum factor.
           WeprovidetimeseriesspanningtestsbyregressingthereturnsofthestandardHMLfactorand
         the alternative annually formed HML factor with updated price information on our prospective
         book-to-market factor. We find that these two versions of HML factors are spanned by our
         prospective factor, but not the other way around. Finally, we contribute to the debate whether
         HML is a redundant factor in the existing factor models. Although these two annually formed
         HMLfactors are indeed redundant in the Fama-French 5 factor model, the prospective factor is
         estimates will be imprecise in the early sample period, thereby contaminating the return predictability results. We
         thus also employ other econometric tools to address such bias, for example, the recursive mean least squares.
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