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Expected versus Ex Post Profitability in the Cross-Section of Industry Returns.

Numerous recent studies document that firm profitability positively predicts the cross-section of stock returns in North America, Asia, and Europe (e.g., Fama and French, 2006, 2015, 2017; Novy-Marx, 2013; Ball et al., 2015; Hou, Xue, and Zhang, 2015). Motivated by this evidence, investment companies and information providers such as Dimensional Fund Advisors, AQR, and MCSI offer profitability-based products (e.g., Trammel, 2014; Kalra and Celis, 2016). Although these studies all use historical (ex post) measures of profitability, the underlying theory predicts a positive relation between expected returns and expected profitability in the cross-section. In this article, we propose a novel method of forecasting profitability out of sample and investigate whether expected profitability contains important asset pricing information not captured by ex post profitability.

We estimate expected profitability with forecast combination methods to extract information from a panel of candidate predictors. Combination forecasts are weighted averages of individual forecasts and benefit from a diversification-like effect. If the prediction errors of individual forecasts are imperfectly correlated, combination forecasts can be more accurate out of sample than even the best individual forecast (for a recent survey, see Timmermann, 2006). Consistent with the diversification benefit, prior studies show that combination forecasts significantly improve the predictability of economic time series such as output or stock returns out of sample (e.g., Stock and Watson, 2004; Rapach, Strauss, and Zhou, 2010; Detzel and Strauss, 2018). By choosing weights based on historical forecast performance, combination forecasts can also, over time, effectively extract relevant information from a set of candidate predictors.

To use combination forecasts, aggregating individual stocks into portfolios is necessary to obtain regular-frequency time series with low idiosyncratic noise. For our asset-pricing tests, these portfolios must plausibly have variation in returns attributable to variation in predicted profitability that is orthogonal to ex post profitability. Based on this criterion, we follow Detzel and Strauss (2018) and forecast profitability of industry portfolios as opposed to characteristic-sorted portfolios. The latter have little cross-sectional variation in returns that is uncorrelated with the sorting characteristic (e.g., Lewellen, Nagel, and Shanken, 2010). Industry selection is further central to many real-world equity strategies and is therefore interesting to asset managers and investors. Value-weighted industries also have relatively low transaction costs as they put little weight on small-cap stocks. This benefit increases the likelihood that investors can actually capture cross-sectional patterns in industry returns.

Several of the studies cited here compare the performance of different measures of profitability in predicting returns. Contributing to this body of research, we evaluate the performance of expected versions of different profitability measures. Using our combination forecast methods, we construct out-of-sample predicted-profitability measures for operating profit (OP), gross profit (GP), operating cash flow (CF), and net income (NI). (1)

To construct our set of candidate predictors, we first include all four profitability measures given that they are all driven by the same underlying state variables. Our remaining candidate predictors, which are motivated by theory and prior evidence, include: industry-level real investment, stock returns, and book-to-market (BM) ratios, as well as the cross-sectional average (aggregate) of the industry-level predictors and their recursively estimated principal components.

We apply our out-of-sample forecasts of profitability to construct portfolio-rotation strategies that buy portfolios with the highest predicted profitability and short portfolios with the lowest predicted profitability. Testing whether these portfolios outperform asset pricing factors based on ex post profitability assesses whether expected profitability contains significant incremental asset pricing information. To ensure investors can capture the alphas we find, we correct our strategies for transaction costs and evaluate their performance using a generalized alpha that accounts for these costs following Novy-Marx and Velikov (2016). This method involves estimating effective transaction costs for individual stocks and applying them to our trading strategies. These strategy transaction costs precisely capture variation in transaction costs over time and across portfolios.

Following Hou et al. (2015), we use quarterly accounting data, which are the timeliest available, but limit the sample period due to data availability. Data over the five-year period 1975:1-1979:4 serve as an initial training sample for our combination forecasts, and we recursively expand this training sample each quarter to generate the subsequent quarter's forecasts. We assess forecast and trading-strategy performance for the out-of-sample period from 1980:1 to 2015:4.

We summarize our findings as follows. Over 1980:1-2015:4, the industry-specific, aggregate, and principal-components-based predictors significantly predict each measure of profitability at the quarterly frequency for each industry. On average, each industry's prior-quarter (ex post) profitability predicts current-quarter profitability with in-sample [R.sup.2]s of 3% to 33% depending on choice of OP, GP, CF, or NI. Adding the other industry- and aggregate-level predictor variables increases adjusted [R.sup.2]s to 18% to 52%. This increase is significant at the 1% level for all four profitability measures and nearly all industries. Similarly, adding the principal components of each profitability measure, which captures cross-industry predictive information, further significantly increases predictability for most industries' profitability with adjusted [R.sup.2]s increasing to 20% to 61% on average. Overall, the in-sample evidence shows that industry-level, aggregate-level, and cross-industry accounting and market variables forecast industry profitability.

Our choice of out-of-sample combination forecast method, discounted mean-squared forecast error (DMSFE), assigns weights to individual forecasts that are inversely related to their historical mean-squared forecast errors (MSFEs). The DMSFE method therefore effectively extracts relevant forecasting information from our set of candidate predictors over time. On average, DMSFE forecasts have 6% to 25% lower out-of-sample mean-squared forecast errors than a simple autoregression benchmark for each industry's profitability, depending on the choice of OP, GP, CF, or NI. Clark and West (2007) statistics indicate that these forecast error reductions are significant for 66% to 93% of industries. Thus, our combination forecasts are relatively precise estimates of expected profitability compared to the ex post values of OP, GP, CF, and NI.

The long legs of the industry-rotation strategies based on predicted profitability earn large average excess returns, ranging from 9.7% to 11.2% per year. Conversely, the short legs earn 2.3% to 3.5% less per year on average. With the exception of the GP-based strategies, the long legs earn significant alphas of about 3% per year with respect to the Hou et al. (2015) model, which includes a factor based on ex post profitability. Controlling for transaction costs reduces this figure to 2.3% to 2.6% per year, but the statistical significance remains. (2) In contrast to the long legs, the alphas for the short legs of our predicted-profitability strategies are generally insignificant. These results are interesting given that alphas are generally stronger on the short legs of anomaly strategies where arbitrage costs are higher (e.g., Stambaugh, Yu, and Yuan, 2012). Moreover, impediments to short selling would not prevent a real investor from capturing the net-of-costs alphas on our strategies.

We also form long-short strategies based on ex post OP, GP, CF, and NI. In contrast to the predicted-profitability strategies, the ex post strategies do not earn significant alphas with respect to the Hou et al. (2015) model. Moreover, with the exception of strategies based on predicted GP, the long legs of the predicted-profitability strategies (and the long-short strategies based on predicted OP and CF) each earn significant alphas with respect to a four-factor model that consists of the Hou et al. (2015) market, size, and investment factors along with our long-short strategy based on ex post profitability. Thus, predicted profitability contains significant asset pricing information that is not captured by ex post profitability.

Although prior studies such as Novy-Marx (2013) and Ball et al. (2015) find differences in how well the ex post version of each metric predicts the cross-section of returns, we find that performance is qualitatively similar for strategies based on predicted OP, CF, and NI. In contrast, strategies based on predicted GP perform similarly to those based on ex post GP. This is not surprising given that GP--revenues minus cost of goods sold (COGS)--omits time-varying expenses such as sales, general, and administrative, and is the most persistent measure of profitability. Hence, industries with the highest GP typically have the highest expected GP as well. This finding is also related to Kisser (2014), who finds that the gross profitability premium is largely driven by persistent differences in operating leverage. Firms with low variable costs such as low COGS will have persistently high operating leverage and GP, all else equal.

The main contribution of this study is to evaluate the role of expected profitability in the cross-section of returns. Our study is related to Detzel and Strauss (2018) who use combination forecasts to predict industry returns out of sample with the cross-section of industry BM ratios and form trading strategies based on these predicted returns. In contrast to their study, we use a different set of predictor variables with a different economic motivation and sort industries based on predicted profitability, not predicted returns. This study is further related to the broader literature that tries to forecast stock returns out of sample (e.g., Goyal and Welch, 2008; Rapach et al., 2010; Kelly and Pruitt, 2013). Rather than predict returns, we predict profitability out of sample, which results in cross-sectional variation in expected returns.

This article proceeds as follows. Section I explains the theoretical importance of expected profitability. Section II describes our data and combination forecast methods. Section III presents our combination forecasts of industry profitability. Section IV describes the construction of our forecast-based trading strategies and analyzes their performance. Section V concludes.

I. Theoretical Motivation of Expected Profitability

To illustrate the theoretical role of expected profitability in asset prices, we present a simple extension of the Hou et al. (2015) q-theory

model. There are two periods, (t = 0, 1), and each firm i chooses time 0 investment ([I.sub.i0]) to maximize firm value:

[mathematical expression not reproducible] (1)

where assets evolve according to:

[A.sub.i1] = [I.sub.i0] + (1 - [delta])[A.sub.i0]. (2)

The [A.sub.it] ([[PI].sub.it]) denote assets (profitability) for firm i at time t. Firm i takes the depreciation rate & and expected return [E.sub.0]([r.sub.i1]) as given. The parameter a > 0 yields convex adjustment costs of investment. The [[PI].sub.it] are assumed to be constant with respect to [A.sub.it], but the model would produce similar predictions with diminishing marginal returns ([[delta][[PI].sub.it]/[delta][A.sub.i1]]< 0) and [alpha] = 0 (e.g., Wu, Zhang, and Zhang, 2010).

The first-order condition for the problem given by Equation (1) yields the following relation between the expected return ([E.sub.0]([r.sub.i1])) and each ex post investment ([I.sub.i0]/[A.sub.i0]) and expected future profitability ([E.sub.0]([[PI].sub.i1])):

[E.sub.0]([r.sub.i1]) = [[E.sub.0]([[PI].sub.i1])/1+a([I.sub.i0]/[A.sub.i0])]-1. (3)

We depart from Hou et al. (2015) by applying a first-order Taylor approximation to Equation (3) centered around market-expected profitability and real investment (E([[PI].sub.M1]), [I.sub.M0]/[A.sub.M0]), which yields constants [c.sub.0], [c.sub.[PI]], and [c.sub.IA] such that:

[E.sub.0]([r.sub.i1]) [approximately equal to] [c.sub.0] + [c.sub.[PI]]([E.sub.0]([[PI].sub.i1])) + [c.sub.IA]([I.sub.i0]/[A.sub.i0]), (4)

where [c.sub.[PI]] > 0 and [c.sub.IA] < 0.

Letting I denote an arbitrary industry and [w.sub.i0] the (market value) weight of firm i in industry I, it follows by Equation (4) that the industry expected return is given by:

[mathematical expression not reproducible] (5)

where [[PI].sub.I1] ([I.sub.I0]/[A.sub.I0]) denotes value-weighted average industry profitability (investment). Equation (5) formalizes the intuition that if firm-level ex post investment and expected profitability jointly predict returns in the cross-section, then so should portfolio-level weighted-average investment and expected profitability, with the same signs. This is an important implication for our empirical tests, which rely on the use of industry portfolios.

This one-period model can be extended to a dynamic multiperiod setting with similar intuition and implications. (3) It is also worth noting that this prediction holds whether expected returns are rational or irrational. The q-theory depends only on firms' responding optimally to whatever discount rates the capital market gives them. Why investors demand higher expected returns for stocks with high expected profitability is an interesting question, but one that we believe is beyond the scope of this article. Kozak, Nagel, and Santosh (2018) argue that answering these questions requires structural models of investor beliefs. (4)

II. Data and Methodology

A. Return and Accounting Data

We obtain monthly return and market capitalization data on the value-weighted Fama-French (1997) 30 industry returns from the website of Kenneth French. (5) We exclude one industry (Smoke) because it has long gaps with insufficient accounting data to compute our profitability metrics. Hence, our analysis is based on 29 industries. We obtain individual-stock data from the Center for Research in Security Prices (CRSP). Following Hou et al. (2015), we use Compustat quarterly accounting data to construct OP, GP, CF, and NI. (6) Compustat quarterly provides the timeliest accounting information that is broadly available, which is important for real-time forecasting exercises. However, the availability of Compustat quarterly data for each of our profitability measures results in a sample beginning in 1975:1. Chen Xue provided us monthly return data on the 2 x 3 x 3 size/investment/profitability portfolio used to construct the Hou et al. (2015) size, investment, and profitability factors ([r.sub.ME], [r.sub.IA], and [r.sub.ROE]) through December 2015. Thus, our sample period is 1975:1-2015:4.

Each quarter, we calculate firm-level characteristics as follows. Investment (INV) is the percentage change in book assets over the prior four quarters following Hou et al. (2015). GP is revenues minus COGS as in Novy-Marx (2013). Following Ball et al. (2015), OP is GP minus selling, general, and administrative expenses (SG&A). (7) IN is earnings before extraordinary items following Hou et al. (2015). Following Hirshleifer, Hou, and Teoh (2009), we calculate CF by deducting accruals from operating income. The Appendix provides additional details about the calculations of CF and OP. In the spirit of Ball et al. (2015), we deflate the firm-level variables OP, GP, CF, and NI by lagged assets. Before aggregating the firm-level data to the industry level, we winsorize each profitability metric at the 0.5 and the 99.5 percentile by quarter. To ensure comparability across profitability metrics, a given firm-quarter needs to have all required data for each of the four metrics to be included in the sample.

We calculate value-weighted averages by industry-quarter to obtain industry-level profitability measures and other characteristics (motivated by Equation 5). Because the resulting performance metrics are based on ratios, they are comparable across time and industries regardless of the number of firms in a given industry-quarter.

Given that the focus of our analysis concerns the ability of out-of-sample forecast methods to simulate a real-time situation that a portfolio manager may face, it is important for accounting data to be both available and timely. Following Hirshleifer et al. (2009), Lewellen (2015), Hou et al. (2015), and Detzel and Strauss (2018), we match accounting data with returns using a four-month lag after the fiscal-quarter-end. (8) Specifically, we match accounting data from the calendar quarter ending in month t (March, June, September, or December) with the one-quarter-long return over months t+5 through t+7 (August to October, November to January, February to April, or May to July, respectively). For example, we match accounting data from quarter four of year t with the return over the months May through July of year t+1. Most firms have a fiscal-quarter-end that corresponds with the calendar-quarter-end resulting in exactly a four-month accounting lag. We refer to the three-month windows February to April, May to July, August to October, and November to January as return quarters 1, 2, 3, and 4, respectively. Thus, when we specify that the sample is 1980:1-2015:3 in tests where the dependent variables are returns, the return sample covers February 1981 to October 2015, which represents N = 143 return quarters. The associated accounting data sample is October 1979 to June 2015, which represent N=143 calendar quarters.

We construct quarterly frequency versions of the Hou et al. (2015) factors by compounding the monthly returns on the 2 x 3 x 3 size/investment/profitability portfolios over the return quarters used for the industry returns and then defining [r.sub.ME], [r.sub.IA], and [r.sub.ROE] the same way as Hou et al. (2015) do for the monthly factors.

For each of the 29 Fama-French (1997) industries we use, Table I presents the time-series averages of the end-of-quarter values of: 1) the market capitalization of the industry (in $billions), 2) the number of firms in the industry, and 3) the value-weighted cross-sectional average market capitalization of the firms within the industry (in $billions). The sample is 1980:1-2015:4 (N = 144). The first two variables come directly from the 30-industry data file on Kenneth French's website. We construct the value-weighted average of firm market capitalizations by replicating the Fama-French (1997) industries with CRSP and Compustat data following the corresponding industry data description on Kenneth French's website.

Table I shows that industry sizes vary significantly, from $10.4 billion with 31.5 firms on average in Txtls, to $1.5 trillion with 967.7 firms on average in Fin. However, the value-weighted average market capitalizations, which range from $1.9 billion in Txtls to $69.5 billion in Hshld, show that the representative firm in each industry is large capitalization (large cap). For comparison, the time-series average of the 50th-percentile New York Stock Exchange (NYSE) market value taken from Kenneth French's website (the Fama-French, 1993 big-cap/small-cap cutoff) is $1.12 billion. The large-cap nature of industries also makes them relatively easy to trade and trade with relatively low transaction costs, which we show later.

Table II reports select summary statistics for our four ex post industry-level profitability metrics OP, GP, CF, and NI. Inspection of the means and standard deviations for all four metrics reveals considerable variation within and across industries. On average, the standard deviations of industry profitability are greater than the respective means, reflecting considerable time variation.

The third column for each metric ([bar.[rho]]) shows the average correlation of the profitability measure in the column heading with the other three measures within an industry. For most industries, there are positive correlations between each measure and the other three, which range from 0.19 (for CF) to 0.46 (for GP) on average. CF has the weakest correlation with the other three measures, reflecting the weak correlation of accruals (the difference between CF and OP) with the remaining profitability metrics.

Table III presents cross-industry averages of the correlations between each pair of profitability metrics. Consistent with [bar.[rho]] from Table II, all three measures have significant positive correlations with each other. Because these correlations are also less than one, each measure contains relevant but nonredundant information that is potentially useful in a forecast combination model. The highest correlation is between OP and GP (0.76) and the lowest is between CF and NI (0.30). The primary difference between each measure is the number of expenses they reflect (e.g., GP and OP differ only by SG&A). The correlations across profitability measures become weaker as the number of expenses the measures have in common decreases.

B. Transaction Cost Data

In this article, we evaluate the performance of trading strategies net of transaction costs. We closely follow Novy-Marx and Velikov (2016) to compute strategy-trading costs in two steps. First, we estimate effective one-way stock-level transaction costs (spreads or bid-ask spreads) using daily CRSP return data following Hasbrouck (2009). (9) Second, we use these stock-level spread estimates to compute portfolio-level costs.

The Hasbrouck (2009) approach expands on the intuition of the Roll (1984) model of log stock price dynamics:

[V.sub.t] = [V.sub.t-1]\ +[[??].sub.t] (6)

where [V.sub.t] is the efficient value of a stock price, [V.sub.t] is the trade price, [Q.sub.t] = +1 (-1) if the trade is a buy (sell), [[??].sub.t], is a random public shock to the efficient value, and c is the effective one-way transaction cost. It follows from Equation (6) that:

[DELTA][P.sub.t] =c[DELTA][Q.sub.t]+[[??].sub.t] (7)

Hasbrouck (2009) estimates c via Bayesian methods applied to an augmented daily frequency version of Equation (7): (10)

[DELTA][P.sub.t] =c[DELTA][Q.sub.t]+[beta][r.sub.m,t]+[[??].sub.t], (8)

where [r.sub.m,t] denotes the market return on day t. Hasbrouck (2009) shows this is an accurate measure of transaction costs as it has a 96.5% correlation with effective spreads based directly on Trade and Quote (TAQ) data.

The Hasbrouck (2009) procedure yields missing observations that are needed to compute trading-strategy costs. In each month t, we assign to each stock i missing an estimate of effective spread that of the stock j with the closest match in terms of market capitalization and idiosyncratic volatility, which are the main observable determinants of transaction costs. (11) Specifically, each month we rank all stocks' market values and idiosyncratic volatilities, referring to the ranks as [rankME.sub.i] and [rankIVOL.sub.i], respectively. Then we assign to stock i the estimated spread of stock j with the smallest value of [square root of [([rankME.sub.i] - [rankME.sub.j]).sup.2] + [([rankIVOL.sub.i] - [rankIVOL.sub.j]).sup.2]].

For the long leg of a portfolio, we use stock-level transaction costs [c.sub.i,t] to compute transaction costs for the leg via:

[TC.sub.Long,t]=[[N.sub.t].summation over (i=1)]|[w.sub.i,t]-[[??].sub.i,t-1]|*[c.sub.it], (9)

where [N.sub.t] = the number of stocks at time t, [w.sub.i,t] is the weight of stock i in the leg at time t after rebalancing, and [mathematical expression not reproducible] is the weight of stock i in the leg at time t before rebalancing (with [r.sub.it] denoting the return on stock i in period t). The transaction costs for the corresponding short leg ([TC.sub.short,t]) are defined similarly. The net-of-costs return on a portfolio ([r.sup.net.sub.t]) are defined by:

[r.sup.net.sub.t] = [r.sup.gross.sub.t]-[TC.sub.Long,t]-[TC.sub.Short,t], (10)

where [r.sup.gross.sub.t] denotes the return on the portfolio before transaction costs. We estimate the [w.sub.i,t] of the Fama-French (1997) industry portfolios following the methodology described on Kenneth French's website and the [w.sub.i,t] for [r.sub.ME], [r.sub.IA], and [r.sub.ROE] following Hou et al. (2015).

The primary limitation of the Hasbrouck (2009) spread measure is that it does not consider the price impact of very large trades. However, it is an upper bound of trading costs for small trades because it assumes market orders. Overall, this measure captures the marginal cost of a strategy for small traders. Because we use value-weighted industries, our portfolios are dominated by large stocks as shown in Table I that are less subject to large price impacts.

Panel A of Figure 1 presents the distribution of time-series means of the estimated effective transaction costs of the value-weighted Fama-French (1997) 29 industry portfolios. The industry transaction costs range from 23 to 54 basis points and average 33 basis points. This range and average are similar to those reported by Detzel and Strauss (2018) for the Fama-French (1997) 48 industries (35 basis points on average, ranging from 20 to 69 basis points). These low transaction costs reflect the value-weighted nature of industries. Panel B of Figure 1 depicts the four-quarter moving average trading costs of the Hou et al. (2015) size ([r.sub.ME]), investment ([r.sub.IA]), and profitability ([r.sub.ROE]) factors over our out-of-sample period 1980:1-2015:3 (return quarters). The transaction costs for all three factors are nontrivial, ranging from about 0.3% per quarter to about 1.2%. The transaction costs also decline over the sample period, reflecting a secular decline in equity transaction costs over time (for details about these patterns in transaction costs, see Detzel and Strauss, 2018). Throughout most of the sample period, [r.sub.ROE] has the highest turnover and transaction costs, followed by [r.sub.IA], and finally [r.sub.ME]. Overall, the transaction costs of the Hou et al. (2015) factors are relatively high compared to the cost of trading industry portfolios.

C. Forecasting Methodology

We investigate whether expected profitability has important asset pricing implications not captured by the commonly used lagged ex post profitability. To forecast industry profitability, we use a combination forecast approach. Since the seminal work of Bates and Granger (1969), forecast combinations are viewed as a simple and effective way to improve forecasting performance over that offered by individual models. Combination forecast methods perform well in settings where a large number of predictors could potentially forecast a variable and economic theory is absent concerning the exact specification. Many studies show combination forecasts significantly improve out-of-sample predictability of gross domestic product (GDP), employment growth, housing prices, and stock returns (e.g., Stock and Watson, 2003, 2004; Timmermann, 2006; Rapach and Strauss, 2009, 2012; Rapach et al., 2010; Detzel and Strauss, 2018).

The basic building block for our combination forecasts are bivariate autoregressive distributed lag (ARDL) predictive regressions estimated recursively in real time for each industry i. (12)

[[PI].sub.i,t+1]=[[alpha].sub.X,i][[PI].sub.i,t]+[[gamma].sub.X,i][X.sub.i,t]+[[??].sub.i,t+1], (11)

where [PI] is a measure of profitability (OR GP CF, NI) for industry i, and [X.sub.i,t] is a potential predictor of industry i profitability (besides [[PI].sub.i,t]). The potential predictors include the four measures of actual profitability (OR GP, CF, NI), as well as investment (INV), BM, and stock returns (RET). The four measures of profitability should each help predict each other because they are all driven by the same underlying state variables. RET and BM should help predict profitability given that stock prices appreciate when expected profitability increases, and vice versa. Investment is a candidate predictor of profitability because firms invest more in anticipation of profitability.

Following Detzel and Strauss (2018), we consider both industry-level and market-level measures of each variable as well as five principal components of the forecasted profitability metric to capture potentially important cross-industry information. Market-level predictors are computed as simple averages across the 29 industries and are denoted ([bar.X]). The five principal components of each profitability measure (denoted [PC1.sub.[PI]],... [PC5.sub.[PI]]) are estimated recursively across industries using only data up to time t in Equation (11). To avoid a profusion of predictor variables, in forecasting each measure of profitability, we use only the lagged principal components of the profitability measure used in Equation (11). Thus, for example, in forecasting OP for the food industry (FD), we use the following candidate predictors for [X.sub.i,t]:

(1) [GP.sub.FD], [CF.sub.FD], [NI.sub.FD], [INV.sub.FD], [BM.sub.FD], [RET.sub.FD];

(2) [bar.OP], [bar.GP], [bar.NI], [bar.CF], [bar.INV], [bar.BM], [bar.RET];

(3) [PC1.sub.OP], [PC2.sub.OP], [PC3.sub.OP], [PC4.sub.OP], [PC5.sub.OP].

A combination forecast ([[??].sub.c.sub.i,t+1|t]) at time t for industry i's time t+1 profitability is simply a weighted average of out-of-sample forecasts from Equation (11):

[[??].sub.c.sub.i,t+1|t] (12)

where [PI] denotes one of the four profitability measures (OP, GP, CF NI), c denotes the weighting method, and ([[alpha].sup.t.sub.X,i],[[??].sup.t.sub.X,i], [[??].sup.t.sub.X,i]) are estimates of Equation (11) based on data available through time t. (13)

Different combination forecasts are defined by the choice of weighting schemes {[w.sup.c.sub.i,t]}. The different combination forecast weights can be simple functions such as an equal-weighted mean or functions of prior forecast performance that give low weight to forecasts that have large past errors. There is generally no ex ante optimal combination method for a given time series; it is an empirical question (e.g., Timmermann, 2008). We use DMSFE, which is a relatively simple and intuitive combination method based on MSFE--the most commonly used loss function in forecast evaluation. This procedure follows Bates and Granger (1969) and Stock and Watson (2004) and can be estimated by:

[w.sup.DMSFE.sub.i,t]=[[[phi].sup.-1.sub.i,t]/[[SIGMA].sup.n.sub.j=1][[phi].sup.-1.sub.j,t]], (13)

where:

[[phi].sup.-1.sub.i,t]=[t-1.summation over (s=1)][[theta].sub.t-1-s][([OP.sub.i,s]+1-[[??].sub.i,s+1]).sup.2] (14)

We choose [theta] = 0.9 to discount forecast errors further back in time. By discounting past observations more heavily, DMSFE works relatively well if the data-generating process is time varying. However, the cost of discounting is a lower effective sample size and therefore higher volatility of estimated weights, which reduces forecast accuracy all else equal. (14)

III. Forecasting Results

A. In-Sample Results

In-sample regression statistics in Table IV test the contribution of our individual-industry, aggregate, and principal-components-based predictors in forecasting profitability. For each profitability metric ([PI]), which corresponds to a separate panel, columns labeled (1) show the adjusted [R.sup.2] for an autoregressive (AR1) benchmark:

[[PI].sub.i,t+1] = [[alpha].sub.i] + [[beta].sub.i] [[PI].sub.i,t] + [[??].sub.i,t+1], (15)

where the only predictor is the lagged profitability measure for industry i. Columns labeled (14) show the adjusted [R.sup.2] when adding the other profitability metrics, [BM.sub.i,t], [INV.sub.i,t], and [RET.sub.i,t], and their market-level aggregates (collectively referred to as [X.sub.i,t]) to the AR benchmark:

[[PI].sub.i,t+1] = [[alpha].sub.i] + [[beta].sub.i] [[PI].sub.i,t] [[gamma].sub.i][X.sub.i,t] + [[??].sub.i,t+1] (16)

Columns labeled (19) show the adjusted [R.sup.2] from models of the form given by Equation (16), but adding the five principal components of the profitability measure ([PC1 [PI],t],...* [PC5 [PI],t]) to [X.sub.i,t] in addition to the [X.sub.i,t] predictors used for the model in the columns labeled (14).

Inspection of Columns (1) in Table IV shows that, on average, each profitability measure besides CF is predicted by its own lag, with nontrivial [R.sup.2]s ranging from 0.19 (for OP) to 0.33 (for GP). The simple AR benchmark for CF has an [R.sup.2] of only 0.03. (15) Adding the other 13 predictors in Columns (14) increases adjusted [R.sup.2] by 0.11 (for NI) to 0.20 (for OP). Moreover, for OP, GP, CF, and NI, these differences have significant F-statistics at the 5% level for 29, 28, 23, and 24 of the 29 industries, respectively. Thus, for each profitability measure, the other industry-level and aggregate profitability, return, valuation, and investment measures all evidently contain important predictive information for future profitability.

Inspection of Columns (19) in Table IV show that including the principal components of the profitability measures further increases adjusted [R.sup.2] by 0.02 (for CF) to 0.08 (for OP and GP) on average. Depending on measure, these differences are significant for 4 to 22 industries. This evidence indicates that cross-industry profitability helps predict future profitability.

Overall, the in-sample analysis presented in Table IV demonstrates that our set of candidate industry-level, market-level, and cross-industry predictors contain significant predictive information for forecasting profitability relative to lagged profitability (captured by the AR benchmark). In the next section, we investigate whether this predictive information can be exploited out of sample.

B. Out-of-Sample Results

In-sample return predictability can break down in real time because of parameter instability and does not offer real-time evidence of predictability because of a look-ahead bias (e.g., Goyal and Welch, 2008). Hence, we investigate the out-of-sample performance of the combination forecasts for the four profitability metrics relative to the AR benchmark. The AR benchmark captures the predictability of future profitability by lagged ex post profitability. Following Stock and Watson (2004), Panel A of Table V reports the ratio of MSFE for the combination forecast to MSFE for the AR benchmark. A ratio below one indicates that the combination forecast outperforms the AR benchmark; for example, a value of 0.90 indicates the combination forecast reduces MSFE by 10%.

The combination forecasts of OP reduce MSFE relative to the AR benchmark by 25% on average. This difference is significant for 27 industries. Average MSFE ratios for GP (0.94), CF (0.94), and NI (0.97) indicate smaller forecast improvements; however, they are still significant for most industries (16 to 21 at the 5% level). Although the AR 1 forecasts are based only on lagged profitability, they are still a measure of expected future profitability. Intuitively, they represent an intermediate step between lagged ex post profitability and our combination forecasts. Panel B of Table V presents MSFE ratios of our combination forecasts relative to the lagged ex post profitability benchmark. The combination forecasts significantly outperform the lagged ex post profitability measure in forecasting OP, GP, and NI. On average, MSFE declines 35%, 34%, and 49%, respectively, and this difference is significant for the vast majority of industries. CF is harder to predict, with an average MSFE reduction of 8%, but these reductions are still significant for most industries. Overall, the out-of-sample tests provide evidence that our combination forecasts are relatively accurate proxies of expected profitability relative to forecasts based only on lagged profitability.

The reader may wonder why the MSFE reduction in the combination forecast relative to the AR benchmark is so large (25% vs. 3% to 6%) for OP. At an intuitive level, we can think of forecast improvements relative to the AR benchmark as deriving from a combination of relatively low autocorrelation and ease of predictability. The forecast [R.sup.2] of the AR benchmark will be high, and therefore hard to improve upon, if autocorrelation is high. GP deducts the fewest time-varying expenses from revenues and, as a result, has the highest autocorrelation of the profitability measures. OP deducts other operating expenses from GP, rendering it less persistent. The combination forecasts take advantage of this lower persistence and forecast OP better than the AR. However, as CF and NI deduct more time-varying expenses and adjust for accruals, the resulting measures evidently become harder to predict in real time.

Table VI presents the time-series average of the weight the combination forecasts place on each of the forecasts. Inspection of the weights over the full sample shows that they range from 3.5% to 9.8%. For comparison, an equal-weighted combination forecast would impose weights of 5.6% = 1/18. This relatively narrow range implies that most variables contribute explanatory power to the forecasts and no variable dominates with a large weight. In particular, all three groups of predictors--aggregate, industry-level, and cross-sectional--contribute to predicting industry profitability. Inspection of the weights over the second half shows similar patterns as the full sample, with weights ranging from 3.3% to 9.5%

IV. Trading Strategies Based on Return Forecasts

In this section, we assess the performance of real-time industry-rotation strategies based on predicted profitability from our combination forecasts. This exercise measures whether expected profitability contains economically significant asset pricing information relative to the commonly used ex post profitability.

A. Industry-Rotation Portfolio Construction

To control for investment, as suggested by Equation (5), for each return quarter from 1980:1 to 2015:3, we construct predicted-profitability factors ([??]) from a 3 x 3 sort based on industry-level investment (INV) and one of our industry-level predicted-profitability measures ([??] = [??], [??], [??], or [??]). We allocate 10, 9, and 10 industries in the low, medium, and high investment groups, respectively. Next, within each investment group from the first sort, we identify the two highest and two lowest industries based on predicted profitability within this quarter. We take the equal-weighted portfolio of the 6 (2 + 2 + 2) value-weighted industries with the highest (lowest) predicted profitability to form the long (short) leg. This approach closely follows the construction of the (ex post) profitability factor [R.sub.ROE] of HOU et al. (2015), which is constructed from a quarterly 2 x 3 x 3 sort on size, investment, and profitability. (16) Similar to [??], the long (short) leg of [r.sub.ROE] consists of the six portfolios with high (low) profitability from each of the 2 x 3 size/investment groups. For comparison, we also construct two other profitability factors using the same construction as [??]. First, we form ex post profitability factors ([r.sub.[PI]]) using lagged ex post profitability instead of the combination forecasts. Second, we form factors using the AR1 forecasts ([r.sub.AR1]) from Table V instead of the combination forecasts.

B. Industry-Rotation Portfolio Performance Results

We evaluate the performance of strategies using the Hou et al. (2015) four-factor model, which contains a profitability factor and, like our strategies, is based on more timely data than the alternative Fama and French (2015) model. In the presence of transaction costs, however, four-factor intercepts do not in general represent obtainable returns. Hence, we measure abnormal net-of-costs returns with the generalized [[alpha].sub.net], of Novy-Marx and Velikov (2016). The [[alpha].sub.net], has the same units as the standard factor model intercept [alpha] but properly accounts for transaction costs in measuring how access to a given asset expands the investment opportunity set relative to the Hou et al. (2015) factors (see Novy-Marx and Velikov, 2016, for details).

Panel A of Table VII presents performance statistics for each benchmark ex post profitability factor ([r.sub.[PI]]). Each factor's long leg earns higher average returns (Sharpe ratios) than its short leg by 1.1% to 3.5% (0.11 to 0.27) per year. For comparison, the market Sharpe ratio over this sample is 0.49. However, neither the long nor the short leg earns any abnormal returns with respect to the Hou et al. (2015) model. As expected, inspection of [[beta].sub.ROE] shows that the long legs of each factor correlate significantly more with the profitability factor [r.sub.ROE] than the short legs. Untabulated results further show that the inferences of Panel A remain unchanged if we replace [r.sub.ROE] with our predicted-profitability factors. (17) Thus, the industry-level ex post profitability measures do not appear to add significant asset pricing information to the stock-level ex post profitability used to construct [r.sub.ROE] or the corresponding predicted-profitability measures.

Panel B of Table VII reports similar performance statistics as Panel A but using AR1-based factors ([r.sub.AR1]). Long strategies for OP and NI produce significant alphas of 2.0% and 2.4%, and long-short strategies also earn significant alphas of 3.7% and 4.1% for OP and CF, respectively. Comparing the results in Panels A and B reveals that using the AR1 forecasts of profitability appear to contribute incremental asset pricing information relative to lagged ex post profitability.

Table VIII presents performance statistics for the factors ([??]) that are based on predicted profitability using real-time combination forecasts. Panel A shows that average gross excess returns are relatively high for the long legs ranging from 9.8% (for [??]) to 10.5% (for [??]) per year. Moreover, with the exception of [??], the long leg of each predicted-profitability factor earns a significant [[alpha].sub.gross] of about 3% per year with respect to the Hou et al. (2015) model. Sharpe

ratios for each long portfolio, ranging from 0.62 (for [??]) to 0.72 for ([??]), are all higher than the market Sharpe ratio of 0.49. The transaction costs of our strategies reduce average and abnormal return estimates slightly, but [[alpha].sub.net], for the long legs of [??], [??], and [??] are still statistically significant and about 2.5% per year each. This decrease in alphas from correcting for transaction costs is not large because of the relatively low cost of trading value-weighted industry portfolios compared to the Hou et al. (2015) factors as documented in Figure 1. In contrast, the long leg of [??] earns statistically and economically insignificant [[alpha].sub.gross] and [[alpha].sub.net] The corresponding short legs of the strategies generate insignificant [[alpha].sub.gross] and [[alpha].sub.net] The lack of significantly large short [[alpha].sub.gross] renders the long-short [[alpha].sub.gross] insignificant for [??] and [??] despite significant long [[alpha].sub.gross] on the latter. The small short [[alpha].sub.gross] also renders the long-short [[alpha].sub.net] insignificant for all four profitability measures.

Panel B of Table VIII presents similar performance statistics as Panel A but using the corresponding ex post profitability factor ([r.sub.[PI]]) in place of [r.sub.ROE] The highly significant [[beta].sub.[PI]] coefficients show that each predicted-profitability factor is highly correlated with the corresponding ex post profitability factor. However, the significance of [[alpha].sub.gross] is unchanged relative to Panel A. Long [[alpha].sub.gross] for [r.sub.[??]], [r.sub.[??]], and [r.sub.[??]] significant, along with [[alpha].sub.gross] for the long-short [r.sub.[??]] and [r.sub.[??]]. These results indicate that the predicted-profitability strategies significantly outperform their ex post profitability counterparts.

Panel C of Table VIII presents results similar to Panel A but using AR1-based profitability factors in place of [r.sub.ROE] The significance of [[alpha].sub.gross] is hardly different from Panel A. Long [[alpha].sub.gross] for [r.sub.[??]], [r.sub.[??]], and [r.sub.[??]] is significant, along with [[alpha].sub.gross] for the long-short [r.sub.[??]], [r.sub.[??]], and [r.sub.[??]], although the latter is only marginally significant. Comparing Table VII with Table VIII reveals a pattern that parallels the out-of-sample forecast performance in Table V. Although the ex post profitability strategies do not earn any alpha with respect to the Hou et al. (2015) model, some of the AR 1 -based strategies do. Thus, strategies based on the combination forecasts generally improve performance relative to the AR1 forecasts.

Overall, the results from Table VIII show that, consistent with theory, expected profitability predicts the cross-section of returns and this predictability is not explained by commonly used ex post measures of profitability. Moreover, investors facing transaction costs earn positive abnormal returns relative to the Hou et al. (2015) four-factor model by trading industries based on predicted [??], [??], and [??]. Unlike most asset pricing anomalies, the abnormal returns on our predicted-profitability strategies are concentrated in the long leg. Thus, short-sale costs and constraints, which are responsible for a large percentage of empirically observed [alpha], do not explain the performance of our strategies (e.g., Stambaugh et al., 2012).

C. Industry-Rotation Portfolio Composition and Cumulative Returns

Figure 2 shows the percentage of quarters in which each industry is chosen in the long or short leg of each of our predicted and lagged-actual profitability strategies. The x-axes are sorted by average profitability from smallest on the left to highest on the right. As expected, for each metric, industries with the highest average profitability are selected more often in the long legs of both sets of strategies, because these industries frequently have the highest predicted and actual profitability, and vice versa for the short legs. One important implication of the high correlation between the frequencies with which industries are chosen in the predicted and ex post profitability strategies is that the alpha of the predicted-profitability strategies does not arise because of a timeinvariant lucky choice of industries. Were this not the case, the ex post profitability strategies that invest most heavily in the same industries would earn abnormal returns as well.

The correlation between average and both predicted and actual profitability is highest for GP, which means that the strategy based on GP is nearly identical to that based on [??]. This persistence explains why [r.sub.[??]] does not earn significant abnormal returns in Table VIII. In contrast, predicted profitability is less correlated with average profitability for OP, CF, and NI, resulting in an opportunity for strategies based on [??], [??], and [??] to outperform the respective ex post profitability strategies.

The persistence of GP--revenues minus COGS--is not surprising given that it omits important time-varying expenses that affect the economic notion of profitability such as SG&A, research and development, and interest expenses. Two firms with the same true profitability, but a different mix of SG&A relative to COGS, will have the same expected returns in theory but different predicted returns based only on GP. Thus, even if an econometrician forecasts GP well, she will not necessarily generate a spread in expected profitability or returns by sorting on predicted GP; she may only succeed in predicting a spread in the mix of cost structure, for example, COGS versus SG&A. Related, Kisser (2014) finds that the gross profitability premium is largely driven by persistent differences in operating leverage. Firms with low variable costs, such as COGS, will have persistently high operating leverage and GP, all else equal. If our results for other measures of profitability were driven by persistent differences in operating leverage, then our strategies based on ex post profitability would perform as well as those based on predicted profitability, which they do not.

Figure 3 depicts the time series of the cumulative value of $ 1 invested in the long and short portfolios based on predicted and ex post profitability over 1980:1-2015:4. The plots clearly illustrate that the long portfolios for predicted [??], [??], and [??] outperform both the market and their ex post counterparts for most of the sample period. The cumulative values of the long predicted-profitability strategies range from $97.1 for [??] to $165.6 for [??]. Moreover, with the exception of the [??] strategy, the difference in cumulative values between the long predicted and ex post profitability strategies ranges from an economically large $27.9 (for CF) to $105.1 (for NI). Conversely, consistent with the previous results, the long [??] strategy effectively has the same level of performance as the ex post GP strategy. For comparison, the total cumulative value of the investment in the market over this time is $46.5. The short legs of the ex post and predicted-profitability strategies underperform the market and end with similar cumulative values.

V. Conclusion

Several recent studies emphasize the theoretical relevance of expected profitability in explaining the cross-section of returns (e.g., Novy-Marx, 2013; Fama and French, 2015; Hou et al., 2015); however, their empirical tests use lagged ex post profitability. The results in this article provide evidence that expected profitability contains important information for explaining the cross-section of returns that is not captured by ex post profitability.

We use combination forecast methods to construct estimates of expected profitability for the Fama-French (1997) 30 industries for four profitability metrics: OP, GP, NI, and CF. In-sample and out-of-sample tests show that the combination forecast methods provides relatively accurate estimates of expected profitability. We use these predicted-profitability metrics to form realtime industry-rotation strategies that buy industries with the highest out-of-sample predicted OP, GP, CF, and NI. With the exception of those based on GP, these strategies earn a significant alpha with respect to the Hou et al. (2015) four-factor model of approximately 2.5% per year net of transaction costs. Moreover, we show that industry-rotation strategies based on ex post profitability do not generate a significant alpha and are significantly outperformed by predicted-profitability strategies in explaining the cross-section of industry returns.

Although prior studies find variation in how well the ex post versions of different profitability measures predict the cross-section of returns, we find that the predicted version of OP, CF, and NI generate strategies with similar abnormal returns relative to the Hou et al. (2015) model. Hence, the choice of using predicted profitability versus ex post profitability appears more important than the choice of which profitability measure to use, with the exception of GP.

Appendix: Variable Definitions

For ease of exposition, the firm and quarter subscripts are omitted from Compustat variable names in parentheses. We calculate the market-value-weighted industry average by quarter to obtain the industry-level measures of BM, CF GP, INK NI, OP, and RET.
Name           Definition

[BM.sub.iq]    BM ratio for firm i in quarter q. To measure book value
               of equity, we follow Novy-Marx (2013) and use Compustat's
               stockholder's equity (SEQ), if available; or common
               equity (CEQ) plus the carrying value of preferred stock
               (PSTXQ), if available; or total assets (ATQ) minus total
               liabilities (LTO) as the numerator.
[CF.sub.iq]    CF from operations for firm i in quarter q, scaled by
               one-quarter lagged assets ([ATQ.sub.iq-1]/4). Following
               Hirshleifer et al. (2009), [CF.sub.iq] is calculated as
               the difference between earnings and accruals. Earnings is
               operating income after depreciation (OIADPQ). Accruals is
               the change in noncash current assets (ACTQ - CHEQ), minus
               the change in current liabilities (LCTQ), excluding the
               change in short-term debt (DLCQ) and taxes payable
               (TXPQ), minus depreciation and amortization expense
               (DPQ). Hence, Accruals = [DELTA](ACTQ - CHEQ)
               - [DELTA](LCTQ + DLCQ + TXPQ) - DPQ. Following Ball et
               al. (2016, p. 44), we replace missing values in balance
               sheet accounts with zeros when computing accruals.
[GP.sub.iq]    GP for firm i in quarter q, scaled by one-quarter lagged
               assets ([ATQ.sub.iq-1]/4). Following Novy-Marx (2013), we
               calculate gross profit as the difference between revenues
               (REVTQ) and cost of goods sold (COGSQ).
[INV.sub.iq]   Investment for firm i in quarter q, calculated as the
               percentage increase in assets over the past 12 months
               ([ATQ.sub.iq] - [ATQ.sub.iq-4])/[ATQ.sub.iq-4].
[NI.sub.iq]    NI before extraordinary items (IBQ) for firm in quarter
               q, scaled by one-quarter lagged assets
               ([ATQ.sub.iq-1]/4).
[OP.sub.iq]    OP for firm i in quarter q, scaled by one-quarter lagged
               assets ([ATQ.sub.Piq-1]/4). In the spirit of Ball et al.
               (2015), we define [OP.sub.iq] as (REVTQ - COGSQ - XSGAQ
               + XRDQ), if XRDQ is available; or we replace it with XRDQ
               from the previous quarter; or we set XRDQ = 0.


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Andrew Detzel, Philipp Schaberl, and Jack Strauss (*)

For helpful comments and suggestions, we thank Bing Han (Editor) and an anonymous referee as well as conference participants at the 2015 Front Range Finance Seminar.

(*) Andrew Detzel is an Assistant Professor of Finance in the Daniels College of Business at the University of Denver in Denver, CO. Philipp Schaberl is an Assistant Professor of Accounting in the Monfort College of Business at the University of Northern Colorado in Greeley, CO. Jack Strauss is a Professor and the Miller Chair of Applied Economics in the Daniels College of Business at the University of Denver in Denver, CO.

(1) Our order in the text and tables of the profitability measures reflects the order of their introduction in the literature, with OP, the most recently introduced, first.

(2) The reductions in alpha from correcting our strategies for transaction costs are not large because of the relatively low cost of trading value-weighted industries compared to trading the Hou et al. (2015) factors.

(3) The resulting model would predict that expected returns are positively related to expected profitability over all future periods in addition to that of period t+1.

(4) We did, however, try several tests motivated by existing rational models. For example, we investigated whether the predicted-profitability factors we construct later are innovations in intertemporal capital asset pricing model (ICAPM) state variables following Maio and Santa-Clara (2012), and whether our factors are significantly correlated with consumption growth following Jagannathan and Wang (2007). We did not find any reliable results. Our results are also not in conflict with the conclusions of Lam, Wang, and Wei (2016), which are only about gross profitability. For instance, Lam et al. (2016) find that macroeconomic risks only partially explain the gross profitability premium, and investor sentiment helps explain a substantial amount of the remaining premium.

(5) Kenneth French's website is available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. Untabulated tests show that our main inferences are unchanged using the Fama-French (1997) 48 industries as well.

(6) Ball et al. (2016) find that cash-based operating profitability (COP) performs well in predicting the cross-section of returns, but the data for this variable are not available at a quarterly frequency for our sample period. However, CF is conceptually similar to COP because both COP and CF are measures of operating profit minus a measure of operating accruals.

(7) In Compustat, the variable for selling, general, and administrative expenses (XSGAQ) includes research and development expenses (XRDQ). Hence, we deduct (XSGAQ-XRDQ) from gross profit to obtain operating profit. More detailed variable definitions are provided in the Appendix.

(8) The US Securities and Exchange Commission (SEC) requires publicly traded companies to submit Form 10-Q within 45 days (at most) after fiscal-quarter-end. The exact deadline for filing 10-Q reports varies by the category of filer. Specifically, large accelerated filers (>$700 million) and accelerated filers (between $75 million and $700 million) have to file form 10-Q within 40 days, whereas and nonaccelerated filers (<$75 million) have 45 days. However, in practice, not all firms follow these deadlines, hence our choice of the conservative information release reporting lags of four months, which is also used by Hirshleifer et al. (2009).

(9) Hasbrouck (2009) provides SAS code to estimate effective spreads at http://people.stern.nyu.edu/jhasbrou/. This code runs directly on the WRDS server after only changing relevant file paths.

(10) The Bayesian methods are necessary because [Q.sub.t] is unobservable.

(11) See Novy-Marx and Velikov (2016) for more details. Idiosyncratic volatility is defined as the standard deviation of residuals from a capital asset pricing model (CAPM) based on the prior 90 days of a given stock's returns.

(12) ARDL is perhaps the most common benchmark framework in forecasting variables that possess a strong autoregressive structure (e.g., Stock and Watson, 2003; Rapach and Strauss, 2009). We also investigate the effect of seasonality in earnings by allowing four lags of profitability in Equation (11). However, incorporating seasonality comes with the cost of estimating more parameters, which leads to potential overfitting that reduces out-of-sample performance. In untabulated tests, allowing for four lags of profitability reduces the out-of-sample performance of the combination forecasts relative to those from Equation (11), both on average and for most industries. Thus, the cost of overfitting appears more important for forecasting quarterly industry-level profitability than warranted by the benefits of incorporating seasonality.

(13) To be clear, we use expanding estimation periods that apply data from the beginning of the sample through time t to produce forecasts for time t + 1, as opposed to rolling estimation periods that recursively drop the oldest observation.

(14) Untabulated results show our main inferences are unchanged using no discounting ([theta] = 1). The choices of [theta] = .9 and [theta] = 1.0 are common in the literature (e.g., Rapach and Strauss, 2008, 2012; Stock and Watson, 2004).

(15) With only one predictor and a sample size of n = 144 the adjusted [R.sup.2] statistics shown in columns (1) must be within 0.01 of the unadjusted [R.sup.2] statistics, which are equal to the squared autocorrelation coefficient of the corresponding profitabilities. The average adjusted [R.sup.2] from columns (1) correspond to autocorrelations ranging from approximately [square root of 0.03] = 0.17 (for CF) to [square root of 0.33] = 0.57 (for GP). While nontrivial, these figures show the persistence of quarterly industry profitability is far from perfect.

(16) We do not use a size sort because we are using value-weighted industries instead of individual stocks.

(17) In these untabulated tests, the alphas of the ex post profitability factors are all insignificant except for the alpha on the long leg of the ex post CF-based factor, which is 2.13% per year and only marginally significant (t = 1.88).
Table I. Industry Size Characteristics

For each of the 29 Fama-French (1997) industries we use, this table
presents the time-series averages of the end-of-quarter values of: 1)
the market capitalization of the industry (in $billions), 2) the number
of firms in the industry, and 3) the value-weighted cross-sectional
average market capitalization of the firms in the industry (in
$billions). The sample period is 1980.1-2015.4 (n = 144).

               (1)           (2)           (3)
          Avg.    Rank   Avg.    Rank   Avg.   Rank

Food      245.8   10     101.8   15     40.1     9
Beer      144.5   15      14.3   28     29.8    10
Games      99.3   23     107.9   12     22.4    14
Books      68.1   24      59.4   24     10.1    21
Hshld     205.8   11      90.1   17     69.5     1
Clths      60.2   25      67.8   21      7.1    25
Hlth      908.3    3     454.8    4     45.2     6
Chems     184.7   13      83.3   18     17.9    16
Txtls      10.4   29      31.5   26      1.9    29
Cnstr     103.2   21     162.7   10      7.0    26
Steel      56.5   26      66.0   22     10.7    18
FabPr     186.2   12     182.5    8     28.6    11
ElcEq     100.4   22      77.8   19     63.1     3
Autos     122.3   17      63.7   23     20.6    15
Carry     120.6   18      30.8   27     22.9    13
Mines      43.0   27      40.3   25      6.9    27
Coal       11.3   28       7.4   29      2.4    28
Oil       636.7    5     203.2    6     69.0     2
Util      359.2    8     151.7   11      8.7    22
Telcm     544.6    7     107.7   13     43.5     7
Servs     814.8    4     504.5    3     49.1     5
BusEq     919.4    2     564.5    2     62.5     4
Paper     135.0   16      74.2   20     10.6    19
Trans     173.9   14     102.9   14     10.2    20
Whlsl     111.8   19     180.5    9      7.9    24
Rtail     576.5    6     240.9    5     42.7     8
Meals     104.6   20      91.3   16     15.6    17
Fin     1,482.5    1     967.7    1     26.8    12
Other     299.2    9     186.5    7      8.6    23

Table II. Summary Statistics for Industry Performance Metrics

This table presents three statistics for industry-level operating
profit (OP), gross profit (GP), cash flows (CF), and net income (NI).
The first two are time-series averages (Mean) and standard deviations
(SD). The third [bar.[rho]], shows the average correlation between the
profitability measures defined in the header with the remaining three
measures within an industry. The row labeled Average presents the
average of each statistic across industries. The sample period is
1980:1-2015:4. See the Appendix for detailed variable definitions.

                 OP                          GP
          Mean   SD     [bar.[rho]]   Mean   SD     [bar.[rho]]   Mean

Food      0.20   0.17      0.25       0.55   0.19      0.37       0.25
Beer      0.20   0.07      0.32       0.51   0.12      0.27       0.22
Games     0.16   0.09      0.43       0.34   0.08      0.49       0.17
Books     0.20   0.15      0.40       0.52   0.15      0.52       0.21
Hshld     0.23   0.12      0.37       0.68   0.12      0.45       0.22
Clths     0.23   0.24      0.51       0.68   0.20      0.59       0.23
Hlth      0.26   0.15      0.19       0.58   0.15      0.39       0.23
Chems     0.19   0.06      0.41       0.33   0.07      0.47       0.18
Txtls     0.15   0.18      0.27       0.36   0.17      0.29       0.17
Cnstr     0.18   0.08      0.50       0.37   0.11      0.56       0.18
Steel     0.15   0.06      0.84       0.22   0.07      0.83       0.14
FabPr     0.18   0.06      0.55       0.35   0.06      0.58       0.16
ElcEq     0.19   0.09      0.30       0.39   0.07      0.43       0.18
Autos     0.14   0.12      0.31       0.28   0.13      0.36       0.16
Carry     0.14   0.09      0.31       0.24   0.08      0.36       0.12
Mines     0.14   0.09      0.69       0.20   0.10      0.71       0.15
Coal      0.15   0.07      0.61       0.20   0.09      0.55       0.16
Oil       0.19   0.06      0.80       0.27   0.06      0.77       0.20
Util      0.12   0.04      0.56       0.17   0.05      0.52       0.13
Telcm     0.18   0.08      0.63       0.35   0.12      0.68       0.19
Servs     0.26   0.15      0.01       0.56   0.11      0.20       0.25
BusEq     0.26   0.15      0.31       0.51   0.13      0.29       0.21
Paper     0.20   0.12      0.34       0.35   0.11      0.38       0.19
Trans     0.14   0.13      0.27       0.26   0.12      0.28       0.16
Whlsl     0.14   0.10      0.36       0.47   0.12      0.36       0.13
Rtail     0.16   0.34      0.09       0.70   0.27      0.13       0.20
Meals     0.20   0.23      0.16       0.34   0.23      0.24       0.25
Fin       0.14   0.06      0.60       0.33   0.10      0.56       0.17
Other     0.20   0.07      0.64       0.31   0.12      0.66       0.21
Average   0.18   0.12      0.41       0.39   0.12      0.46       0.19

          CF                          NI
          SD     [bar.[rho]]   Mean   SD     [bar.[rho]]

Food      0.13     -0.02       0.11   0.03      0.24
Beer      0.21      0.10       0.09   0.03      0.26
Games     0.13      0.20       0.06   0.03      0.31
Books     0.11      0.22       0.08   0.05      0.38
Hshld     0.15      0.31       0.10   0.03      0.33
Clths     0.14      0.28       0.13   0.05      0.50
Hlth      0.11      0.03       0.11   0.03      0.36
Chems     0.10      0.27       0.07   0.03      0.34
Txtls     0.15     -0.10       0.06   0.04      0.10
Cnstr     0.10      0.24       0.07   0.03      0.38
Steel     0.08      0.65       0.05   0.04      0.80
FabPr     0.07      0.35       0.07   0.03      0.49
ElcEq     0.12      0.13       0.08   0.02      0.28
Autos     0.10      0.09       0.05   0.02      0.28
Carry     0.09      0.12       0.05   0.03      0.25
Mines     0.14      0.46       0.06   0.08      0.69
Coal      0.20      0.30       0.05   0.10      0.43
Oil       0.07      0.67       0.07   0.04      0.72
Util      0.15      0.17       0.04   0.03      0.37
Telcm     0.09      0.48       0.05   0.05      0.59
Servs     0.12     -0.09       0.10   0.03      0.16
BusEq     0.08      0.16       0.10   0.04      0.38
Paper     0.08      0.05       0.08   0.02      0.21
Trans     0.07     -0.06       0.06   0.03      0.16
Whlsl     0.05      0.07       0.07   0.02      0.22
Rtail     0.08     -0.15       0.08   0.02     -0.04
Meals     0.12     -0.16       0.10   0.03      0.15
Fin       0.10      0.36       0.06   0.03      0.37
Other     0.13      0.32       0.05   0.05      0.29
Average   0.11      0.19       0.07   0.04      0.34

Table III. Average Correlations

This table presents the within-industry correlations between different
profitability metrics averaged across the 29 Fama-French (1997)
industries. All correlations are statistically significant at the 5%
level or better. The sample period is 1980:1-2015:4. See the Appendix
for detailed variable definitions.

                                 GP     CF     Nl

Operating profit (OP)            0.78   0.32   0.54
Gross profit (GP)                       0.33   0.48
Cash flow from operations (CF)                 0.30

Table IV. In-Sample [R.sup.2] Statistics from Predictive Regressions

This table presents in-sample adjusted [R.sup.2] statistics for
predictive regressions of the industry profitability metric shown in
the panels labeled OP (operating profit), GP (gross profit), CF (cash
flow), and NI (net income). The row labeled Average provides the
average of the adjusted [R.sup.2] statistics across the 29 Fama-French
(1997) industries. In the columns labeled (1), the lagged profitability
metric is the only predictor. In the columns labeled (14), the
following 14 predictors are included: lag of industry OP, GP, CF, NI,
book-to-market (BM), investment (INV), and returns (RET) as well as
their market-level aggregates. In the columns labeled (19), the first
five principal components of the profitability metric on the left-hand
side are added in addition to the 14 predictors. The principal
components are taken across the 29 industry time series for that
metric. The columns labeled (14-1) present the difference between the
[R.sup.2] statistics in Columns (14) and (1), and the columns labeled
(19-14) present the difference between the [R.sup.2] statistics in
Columns (19) and (14). For Columns (14-1), significance is determined
by an F-test that the coefficients on the 13 predictors included
besides the own lag of the dependent variable are jointly zero. For
Columns (19-14), significance is determined by an F-test that the
coefficients on the five principal components are jointly zero. The
sample period is 1980:1-2015:4 (N = 144). See the Appendix for detailed
variable definitions.

                           Panel A. OP
Industry    (1)     (14)   (14-1)        (19)   (19-14)

Food        0.17   0.29    0.12 (***)    0.59    0.30 (***)
Beer        0.04   0.19    0.15 (***)    0.18   -0.01
Games       0.14   0.22    0.08 (**)     0.44    0.22 (***)
Books       0.10   0.31    0.21 (***)    0.38    0.07 (***)
Hshld       0.01   0.16    0.15 (***)    0.18    0.02
Clths       0.31   0.59    0.28 (***)    0.87    0.28 (***)
Hlth        0.23   0.41    0.18 (***)    0.48    0.07 (***)
Chems       0.22   0.35    0.13 (***)    0.37    0.02 (*)
Txtls       0.00   0.24    0.24 (***)    0.30    0.06 (***)
Cnstr       0.22   0.44    0.22 (***)    0.52    0.08 (***)
Steel       0.66   0.72    0.06 (***)    0.73    0.01
FabPr       0.40   0.57    0.17 (***)    0.59    0.02 (**)
ElcEq       0.05   0.38    0.33 (***)    0.44    0.06 (***)
Autos       0.02   0.10    0.08 (**)     0.08   -0.02
Carry       0.10   0.16    0.06 (**)     0.32    0.16 (***)
Mines       0.30   0.41    0.11 (***)    0.42    0.01
Coal        0.43   0.52    0.09 (***)    0.54    0.02 (**)
Oil         0.46   0.61    0.15 (***)    0.60   -0.01
Util        0.02   0.27    0.25 (***)    0.32    0.05 (**)
Telcm       0.17   0.32    0.15 (***)    0.37    0.05 (**)
Servs       0.05   0.52    0.47 (***)    0.61    0.09 (***)
BusEq       0.20   0.34    0.14 (***)    0.46    0.12 (***)
Paper       0.02   0.33    0.31 (***)    0.54    0.21 (***)
Trans      -0.01   0.21    0.22 (***)    0.41    0.20 (***)
Whlsl       0.00   0.17    0.17 (***)    0.20    0.03 (*)
Rtail       0.06   0.87    0.81 (***)    0.95    0.08 (***)
Meals      -0.01   0.30    0.31 (***)    0.31    0.01
Fin         0.44   0.51    0.07 (***)    0.52    0.01
Other       0.61   0.71    0.10 (***)    0.72    0.01
Average     0.19   0.39    0.20          0.46    0.08

                    Panel B. GP
Industry     (1)     (14)   (14-1)       (19)   (19-14)

Food        0.34   0.46     0.12 (***)   0.58   0.12 (***)
Beer        0.23   0.38     0.15 (***)   0.43   0.05 (**)
Games       0.10   0.12     0.02         0.33   0.21 (***)
Books       0.24   0.48     0.24 (***)   0.63   0.15 (***)
Hshld       0.19   0.41     0.22 (***)   0.45   0.04  (**)
Clths       0.35   0.60     0.25 (***)   0.75   0.15 (***)
Hlth        0.77   0.86     0.09 (***)   0.88   0.02 (***)
Chems       0.47   0.61     0.14 (***)   0.69   0.08 (***)
Txtls       0.04   0.33     0.29 (***)   0.39   0.06 (***)
Cnstr       0.58   0.68     0.10 (***)   0.75   0.07 (***)
Steel       0.69   0.74     0.05 (***)   0.75   0.01 (*)
FabPr       0.52   0.67     0.15 (***)   0.70   0.03 (***)
ElcEq      -0.01   0.32     0.33 (***)   0.37   0.05 (**)
Autos       0.00   0.33     0.33 (***)   0.34   0.01
Carry       0.18   0.23     0.05 (**)    0.40   0.17 (***)
Mines       0.39   0.49     0.10 (***)   0.52   0.03 (**)
Coal        0.36   0.42     0.06 (**)    0.44   0.02 (*)
Oil         0.60   0.72     0.12 (***)   0.72   0.00
Util        0.16   0.44     0.28 (***)   0.47   0.03 (*)
Telcm       0.49   0.67     0.18 (***)   0.75   0.08 (***)
Servs       0.56   0.74     0.18 (***)   0.75   0.01 (**)
BusEq       0.48   0.62     0.14 (***)   0.82   0.20 (***)
Paper       0.05   0.34     0.29 (***)   0.60   0.26 (***)
Trans       0.04   0.34     0.30 (***)   0.59   0.25 (***)
Whlsl       0.16   0.46     0.30 (***)   0.49   0.03 (**)
Rtail       0.06   0.85     0.79 (***)   0.95   0.10 (***)
Meals       0.06   0.28     0.22 (***)   0.40   0.12 (***)
Fin         0.74   0.78     0.04 (***)   0.79   0.01 (*)
Other       0.79   0.84     0.05 (***)   0.84   0.00
Average     0.33   0.52     0.19         0.61   0.08

                          Panel C. CF
Industry   (1)     (14)   (14-1)         (19)    (19-14)

Food        0.01   0.13   0.12 (***)     0.16    0.03
Beer       -0.01   0.00   0.01          -0.02   -0.02
Games       0.04   0.06   0.02           0.12    0.06 (**)
Books       0.00   0.23   0.23 (***)     0.22   -0.01
Hshld       0.00   0.19   0.19 (***)     0.19    0.00
Clths       0.01   0.24   0.23 (***)     0.28    0.04 (**)
Hlth        0.02   0.11   0.09 (**)      0.08   -0.03
Chems       0.03   0.27   0.24 (***)     0.30    0.03 (*)
Txtls       0.02   0.02   0.00           0.05    0.03 (*)
Cnstr       0.01   0.23   0.22 (***)     0.24    0.01
Steel       0.19   0.53   0.34 (***)     0.53    0.00
FabPr      -0.01   0.31   0.32 (***)     0.32    0.01
ElcEq      -0.01   0.13   0.14 (***)     0.15    0.02
Autos       0.01   0.15   0.14 (***)     0.13   -0.02
Carry      -0.01   0.05   0.06 (*)       0.09    0.04 (*)
Mines       0.05   0.26   0.21 (***)     0.27    0.01
Coal        0.00   0.12   0.12 (***)     0.10   -0.02
Oil         0.23   0.49   0.26 (***)     0.52    0.03 (*)
Util        0.01   0.01   0.00           0.04    0.03
Telcm       0.09   0.34   0.25 (***)     0.33   -0.01
Servs       0.01   0.21   0.20 (***)     0.21    0.00
BusEq       0.06   0.25   0.19 (***)     0.27    0.02
Paper      -0.01   0.11   0.12 (***)     0.14    0.03
Trans       0.00   0.06   0.06 (**)      0.06    0.00
Whlsl       0.00   0.04   0.04           0.07    0.03 (*)
Rtail       0.03   0.24   0.21 (***)     0.29    0.05 (**)
Meals       0.00   0.18   0.18 (***)     0.20    0.02
Fin         0.03   0.14   0.11 (***)     0.16    0.02
Other       0.01   0.18   0.17 (***)     0.24    0.06 (**)
Average     0.03   0.18   0.15           0.20    0.02

                  Panel D. NI
Industry    (1)    (14)   (14-1)      (19)   (19-14)

Food        0.15   0.18   0.03        0.24    0.06 (***)
Beer        0.30   0.36   0.06 (**)   0.40    0.04 (**)
Games       0.11   0.24   0.13 (***)  0.30    0.06 (**)
Books       0.35   0.50   0.15 (***)  0.51    0.01
Hshld       0.21   0.37   0.16 (***)  0.39    0.02
Clths       0.39   0.61   0.22 (***)  0.63    0.02 (**)
Hlth        0.15   0.39   0.24 (***)  0.42    0.03 (**)
Chems       0.28   0.42   0.14 (***)  0.43    0.01
Txtls       0.14   0.19   0.05 (*)    0.18   -0.01
Cnstr       0.22   0.29   0.07 (**)   0.37    0.08 (***)
Steel       0.60   0.67   0.07 (***)  0.68    0.01
FabPr       0.67   0.77   0.10 (***)  0.78    0.01 (*)
ElcEq       0.10   0.24   0.14 (***)  0.24    0.00
Autos       0.35   0.41   0.06  (**)  0.44    0.03 (**)
Carry       0.39   0.49   0.10 (***)  0.50    0.01
Mines       0.40   0.47   0.07 (***)  0.49    0.02 (*)
Coal        0.03   0.21   0.18 (***)  0.24    0.03 (*)
Oil         0.58   0.66   0.08 (***)  0.67    0.01
Util        0.10   0.13   0.03        0.22    0.09 (***)
Telcm       0.33   0.55   0.22 (***)  0.55    0.00
Servs       0.23   0.26   0.03 (*)    0.26    0.00
BusEq       0.64   0.70   0.06 (***)  0.72    0.02 (**)
Paper       0.46   0.55   0.09 (***)  0.55    0.00
Trans       0.14   0.27   0.13 (***)  0.34    0.07 (***)
Whlsl       0.39   0.42   0.03 (*)    0.44    0.02 (**)
Rtail      -0.01   0.29   0.30 (***)  0.32    0.03 (*)
Meals       0.37   0.50   0.13 (***)  0.50    0.00
Fin         0.36   0.47   0.11 (***)  0.46   -0.01
Other       0.16   0.31   0.15 (***)  0.43    0.12 (***)
Average     0.30   0.41   0.11        0.44    0.03

(***) Significant at the 0.01 level.
(**) Significant at the 0.05 level.
(*) Significant at the 0.10 level.

Table V. OOS Performance of Combination Forecasts of Profitability
Relative to AR1 and Lagged Actual Benchmark

For each profitability measure level operating profit (OP), gross
profit (CP), cash flows (CF), and net income (NI), this table presents
the out-of-sample (OOS) mean-squared forecast error (MSFE) of the
combination forecasts divided by the MSFE of benchmark forecasts. In
Panel A, the benchmarks are OOS forecasts from a first-order
autoregressive (AR1) model. In Panel B, the benchmark forecasts are the
one-quarter lag of the profitability measure. The row labeled Average
denotes the average of the MSFE ratios across the 29 industries. The
OOS period is 1980:1-2015:4. Statistical significance for the MSFE
ratios are based on the Clark and West (2007) MSFE-adjusted statistic,
which tests the null hypothesis that the combination forecasts have
equal expected squared forecast error as the benchmark forecast against
the alternative that the combination forecast has a lower expected
squared forecast error.

Industry   Panel A. Relative to AR1                           Panel B.
                                                              Relative
                                                              to Lagged
                                                              Ex Post
           OP          GP           CF           NI           OP

Food       0.56 (***)  0.91 (***)   0.95 (**)    0.98         0.41 (***)
Beer       0.97 (***)  0.98 (*)     0.99         1.00 (**)    0.97 (*)
Games      1.02 (**)   1.00         1.01         0.99 (*)     0.91 (***)
Books      0.56 (***)  0.96 (***)   0.95 (***)   0.96 (***)   0.35 (***)
Hshld      0.92 (***)  0.98 (***)   0.91 (***)   0.95 (***)   0.89 (***)
Clths      0.89 (***)  0.98 (***)   0.87 (***)   0.96 (***)   0.71 (***)
Hlth       0.61 (***)  0.86 (***)   0.96 (**)    0.95 (***)   0.42 (***)
Chems      1.01        0.87 (***)   0.92 (***)   1.00 (**)    0.96 (**)
Txtls      0.42 (***)  0.70 (***)   0.96         0.99         0.21 (***)
Cnstr      0.87 (***)  0.95 (***)   0.95 (***)   1.00         0.74 (***)
Steel      1.00 (*)    1.00         0.77 (***)   0.99 (*)     1.01
FabPr      0.89 (***)  0.96 (**)    0.93 (***)   0.99         0.87 (***)
ElcEq      0.83 (***)  0.95 (***)   0.95 (***)   0.96 (***)   0.73 (***)
Autos      0.61 (**)   0.98 (***)   0.99         0.99 (*)     0.62 (***)
Carry      0.97 (**)   0.99 (***)   0.96 (*)     1.00 (**)    0.94 (***)
Mines      0.91        0.98 (*)     0.85 (***)   0.96         0.80 (***)
Coal       0.88 (**)   0.99 (*)     0.92 (***)   0.95 (**)    0.91 (***)
Oil        0.73 (***)  0.96 (***)   0.82 (***)   0.99 (**)    0.63 (***)
Util       0.79 (*)    0.91 (***)   1.01         0.94 (***)   0.71 (***)
Telcm      0.81 (***)  0.93 (***)   0.89 (***)   0.94 (***)   0.75 (***)
Servs      0.58 (***)  0.99 (***)   0.94 (***)   1.00         0.40 (***)
BusEq      0.39 (***)  0.84 (***)   0.93 (***)   1.00         0.21 (***)
Paper      0.60 (***)  0.73 (***)   0.97 (**)    0.86 (***)   0.39 (***)
Trans      0.81 (***)  1.00 (***)   1.01         0.99 (***)   0.59 (***)
Whlsl      0.87 (***)  0.91 (***)   0.98 (***)   1.00         0.75 (***)
Rtail      0.27 (***)  0.83 (***)   1.01 (*)     1.00 (***)   0.86 (***)
Meals      0.18 (***)  1.04 (***)   0.99 (***)   0.99 (**)    0.89 (***)
Fin        0.96 (*)    0.98 (***)   0.90 (***)   0.98         0.91 (***)
Other      0.94 (***)  0.98 (***)   0.88 (***)   0.97 (***)   0.91 (***)
Average    0.75        0.94         0.94         0.97         0.65

Industry     Panel B. Relative to Lagged Ex Post
           GP           CF           NI

Food       0.60 (***)   1.00         0.48 (***)
Beer       0.68 (***)   1.05         0.51 (***)
Games      0.83 (***)   0.93 (***)   0.45 (***)
Books      0.52 (***)   1.08         0.63 (***)
Hshld      0.42 (***)   0.86 (***)   0.340 (***)
Clths      0.37 (***)   1.17         0.63 (***)
Hlth       0.45 (***)   0.77 (***)   0.37 (***)
Chems      0.52 (***)   0.51 (***)   0.45 (***)
Txtls      0.27 (***)   1.02         0.79 (***)
Cnstr      0.78 (***)   1.06         0.49 (***)
Steel      0.94 (**)    0.64 (***)   0.53 (***)
FabPr      0.64 (***)   0.82 (***)   0.38 (***)
ElcEq      0.70 (***)   0.94 (*)     0.36 (***)
Autos      0.94 (**)    1.02         0.32 (***)
Carry      0.88 (***)   0.99         0.53 (***)
Mines      0.94 (**)    0.69 (***)   0.75 (***)
Coal       0.99         1.01         0.75 (***)
Oil        0.77 (***)   0.58 (***)   0.45 (***)
Util       0.84 (***)   1.24         0.57 (***)
Telcm      0.76 (***)   0.55 (***)   0.61 (***)
Servs      0.74 (***)   1.01         0.35 (***)
BusEq      0.55 (***)   0.86 (***)   0.30 (***)
Paper      0.36 (***)   0.82 (***)   0.30 (***)
Trans      0.65 (***)   0.98         0.76 (***)
Whlsl      0.46 (***)   0.98 (*)     0.36 (***)
Rtail      0.40 (***)   1.17         0.35 (***)
Meals      0.65 (***)   1.04         0.37 (***)
Fin        0.55 (***)   0.90 (***)   0.55
Other      0.94 (**)    0.96 (*)     0.68 (***)
Average    0.66         0.92         0.51

(***) Significant at the 0.01 level.
(**) Significant at the 0.05 level.
(*) Significant at the 0.10 level.

Table VI. Average Predictor Weights from DMSFE Combination Forecasts

In this table, each column reports the average weight of the individual
forecasts in the out-of-sample combination forecast of the
profitability measure defined by the column heading (see Equation 12).
Each forecast corresponds to a row and is defined by 1 of the 19
predictors from Table IV, which corresponds to X in Equation (11). The
first seven predictors listed are market-level: industry returns (RET),
operating profit (OP), gross profit (GP), cash flow (CF), net income
(N[GAMMA]), book-to-market ratio (BM), and investment (INV). The next
five listed are the principal components (PCi) of the industry-level
profitability measure defined by the column heading. The remaining
seven predictors listed, which are denoted by a subscript i, are the
industry-level versions of the seven market-level variables listed
above. The averages are first taken over time and then across
industries. The units are percentages so that the entries in each
column sum to 100. Columns labeled Avg. report the average of the
weights from the columns labeled OP, GP, CF, and Nl. Rows labeled Min.
and Max. report the minimum and maximum values from each column. We
report results over the full out-of-sample period 1980:1-2015:4 as well
as the second half of the sample 1993:1-2015:4.

              1980:1-2015:4                 1993:1-2015:4
Variable      OP   GP   CF   NI   Avg.   OP    GP    CF    NI    Avg.
                                 Aggregate Predictors

RET           5.3  5.6  4.7  4.7  5.1    5.2   5.1   5.2   6.6   5.5
OP            5.3  5.5  9.8  5.5  6.5    5.5   5.5   5.2   4.6   5.2
GP            5.2  5.4  4.6  4.5  4.9    5.5   5.2   5.0   3.7   4.4
CF            9.2  5.8  5.1  9.7  7.5    5.1   4.2   5.9   5.4   5.3
NI            4.0  3.5  9.8  4.0  5.3    5.4   5.3   7.7   7.2   6.4
BM            5.9  6.7  5.9  8.8  6.8    5.8   5.2   7.3   5.3   5.9
INV           5.3  5.4  4.6  4.7  5.0    5.4   5.2   5.2   5.3   5.3

                              Principal Component Predictors
PC1           5.9  5.3  6.7  7.6  6.4    5.7   5.4   5.0   4.6   5.2
PC2           4.6  4.7  4.4  4.1  4.4    5.1   4.2   5.3   6.4   5.3
PC3           5.3  5.5  4.7  4.7  5.0    6.1   6.5   6.2   6.4   6.3
PC4           5.2  5.3  4.7  4.8  5.0    5.5   5 1   5.3   5.7   5.4
PC5           5.4  5.5  4.9  4.9  5.2    5.5   5.5   5.3   5.3   5.4

                              Industry-Level Predictors
[RET.sub.i]   6.5  6.0  7.2  7.4  6.8    6.4   6.9   6.4   4.1   6.0
[OP.sub.i]    --   5.8  4.8  4.8  5.1    --    6.9   5.0   5.5   5.8
[GP.sub.i]    5.8  --   3.9  3.7  4.5    5.9   -     3.9   6.2   5.3
[CF.sub.i]    5.2  5.6  --   6.4  5.7    4.9   3.9   --    5.5   4.8
[NI.sub.i]    5.3  6.0  4.7  --   5.3    6.1   3.3   5.3         4.9
[BM.sub.i]    5.3  5.8  4.8  5.0  5.2    4.1   9.5   5.3   6.5   6.3
[INV.sub.i]   5.3  6.6  4.7  4.6  5.3    6.8   7.1   5.5   6.0   6.4
Min.          4.0  3.5  3.9  3.7  4.4    4.1   3.3   3.9   3.7   3.8
Max.          9.2  6.7  9.8  9.7  7.5    6.8   9.5   7.7   7.2   7.8

Table VII. Performance of Real-Time Industry-Rotation Strategies Based
on Ex Post Profitability and AR1 Forecasts

In Panel A, each column presents performance statistics for the long,
short, and long-minus-short (L-S) real-time industry-rotation
strategies based or each of the four measures of ex post profitability:
operating profit (OP), gross profit (GP), cash flows (CF), and net
income (N[GAMMA]). The statistics include average gross excess returns
(E([r.sup.e.sub.gross])), annualized Sharpe ratios, and estimated
[[alpha].sub.gross], [[beta].sub.mkt], [[beta].sub.ME],
[[beta].sub.IA], and [[beta].sub.ROE] from the Hou et al. (2015)
four-factor model [r.sup.e.sub.gross,t] = [[alpha].sub.gross] +
[[beta].sub.MKT] * [MKT.sub.t], + [[beta].sub.ME], * [r.sub.ME,T] +
[[beta].sub.IA] * [r.sub.IA,t] + [[beta].sub.GROSS] * [r.sub.ROE,t] +
[[epsilon].sub.T]. Panel B presents similar statistics as Panel A but
using the returns on autoregressive (AR1)-based strategies instead of
ex post profitability strategies. The t-statistics are presented in
parentheses below the coefficient estimates. The sample period in both
panels is return quarters 1980:1-2015:3 (N = 143).

                         Panel A. Performance of Strategies Based on
                         Ex Post Profitability
Variable                               OP
                          Long         Short           L-S

E([r.sup.e.sub.gross])     9.40          6.96          2.44
[[alpha].sub.gross]        0.74         -2.05          2.80
                          (0.62)       (-1.15)        (1.33)
[[beta].sub.mkt]           1.00 (***)    1.04 (***)   -0.04
                         (26.94)       (18.96)       (-0.62)
[[beta].sub.ME]            0.14 (***)    0.28 (***)   -0.14
                          (2.83)        (3.85)       (-1.64)
[[beta].sub.IA]           -0.04          0.41 (***)   -0.46 (***)
                         (-0.58)        (3.90)       (-3.63)
[[beta].sub.ROE]           0.14 (**)    -0.19 (**)     0.33 (***)
                          (2.41)       (-2.10)        (3.15)
Adj. [R.sup.2]             0.88          0.79          0.16
Sharpe ratio               0.58          0.38          0.22

                            Panel A. Performance of Strategies Based on
                                  Ex Post Profitability
Variable                               GP
                          Long          Short          L-S

E([r.sup.e.sub.gross])     9.78          6.30           3.48
[[alpha].sub.gross]       -0.56         -1.73           1.17
                         (-0.46)       (-0.84)         (0.47)
[[beta].sub.mkt]           1.03 (***)    0.96 (***)     0.07
                         (27.60)       (15.22)         (0.87)
[[beta].sub.ME]            0.08          0.17 (**)     -0.09
                          (1.57)        (1.98)        (-0.87)
[[beta].sub.IA]            0.02          0.44 (***)    -0.41 (***)
                          (0.34)        (3.56)        (-2.75)
[[beta].sub.ROE]           0.32 (***)   -0.22 (**)      0.54 (***)
                          (5.38)       (-2.14)         (4.35)
Adj. [R.sup.2]             0.87          0.70           0.16
Sharpe ratio               0.61          0.35           0.27

                         Panel A. Performance of Strategies Based on
                               Ex Post Profitability
Variable                             CF
                          Long          Short        L-S

E([r.sup.e.sub.gross])     9.44          7.14         2.30
[[alpha].sub.gross]       -0.43         -1.63         1.20
                         (-0.38)       (-1.02)       (0.68)
[[beta].sub.mkt]           0.96 (***)    1.11 (***)  -0.15 (***)
                         (27.70)       (22.76)       -2.80)
[[beta].sub.ME]            0.16 (***)    0.09         0.07
                          (3.49)        (1.41)       (0.95)
[[beta].sub.IA]            0.07          0.22 (**)   -0.15
                          (1.11)        (2.34)       -1.39)
[[beta].sub.ROE]           0.27 (***)   -0.11         0.38 (***)
                          (4.80)       (-1.41)       (4.32)
Adj. [R.sup.2]             0.88          0.83         0.18
Sharpe ratio               0.62          0.39         0.25

                        Panel A. Performance of Strategies Based on
                              Ex Post Profitability
Variable                             NI
                          Long          Short         L-S

E([r.sup.e.sub.gross])     8.48          7.35          1.13
[[alpha].sub.gross]       -1.19         -0.43         -0.76
                         (-0.98)       (-0.26)       (-0.38)
[[beta].sub.mkt]           1.04 (***)    0.98 (***)    0.06
                         (27.86)       (19.48)        (1.02)
[[beta].sub.ME]            0.13 (**)     0.20 (***)   -0.07
                          (2.57)        (2.93)       (-0.84)
[[beta].sub.IA]            0.09          0.34 (***)   -0.25 (**)
                          (1.28)        (3.46)       (-2.08)
[[beta].sub.ROE]           0.16 (**)    -0.22 (***)    0.38 (***)
                          (2.58)       (-2.70)        (3.81)
Adj. [R.sup.2]             0.88          0.80          0.12
Sharpe ratio               0.51          0.43          0.11

                         Panel B. Performance of Strategies Based on AR1
                             Forecasts of Profitability
Variable                                OP
                         Long          Short         L-S

E([r.sup.e.sub.gross])    9.74           8.22          1.52
                          2.01 (**)     -1.71          3.72 (*)
                         (2.00)        (-0.93)        (1.87)
[[beta].sub.MKT]          0.97 (***)     1.02 (***)   -0.05
                        (31.66)        (18.18)       (-0.83)
[[beta].sub.ME]           0.12 (***)     0.37 (***)   -0.26 (***)
                         (2.86)         (4.94)       (-3.13)
[[beta].sub.IA]          -0.10 (*)       0.48 (***)   -0.58 (***)
                        (-1.67)         (4.41)       (-4.94)
[[beta].sub.ROE]          0.08 (*)      -0.12          0.20 (**)
                         (1.69)        (-1.32)        (2.08)
Adj. [R.sup.2]            0.91           0.78          0.22
Sharpe ratio              0.61           0.44          0.14

                        Panel B. Performance of Strategies Based on AR1
                            Forecasts of Profitability
Variable                                 GP
                         Long           Short         L-S

E([r.sup.e.sub.gross])    9.49           7.22          2.26
                         -0.93          -1.06          0.13
                        (-0.76)        (-0.48)        (0.05)
[[beta].sub.MKT]          1.01 (***)     1.00 (***)    0.01
                        (26.85)        (14.71)        (0.08)
[[beta].sub.ME]           0.10 (*)       0.14         -0.04
                         (1.97)         (1.55)       (-0.39)
[[beta].sub.IA]           0.04           0.44 (***)   -0.40 (**)
                         (0.55)         (3.31)       (-2.49)
[[beta].sub.ROE]          0.34 (***)    -0.22 (**)     0.56 (***)
                         (5.53)        (-2.00)        (4.18)
Adj. [R.sup.2]            0.87           0.68          0.14
Sharpe ratio              0.60           0.39          0.17

                         Panel B. Performance of Strategies Based on AR1
                         Forecasts of Profitability
Variable                                     CF
                         Long         Short           L-S

E([r.sup.e.sub.gross])    8.91          6.30           2.61
                          0.27         -3.85 (**)      4.12 (*)
                         (0.23)       (-2.03)         (1.96)
[[beta].sub.MKT]          0.94 (***)    1.02 (***)    -0.08
                        (26.43)       (17.59)        (-1.31)
[[beta].sub.ME]           0.11 (**)     0.34 (***)    -0.22 (**)
                         (2.37)        (4.31)        (-2.58)
[[beta].sub.IA]           0.05          0.35 (***)    -0.30 (**)
                         (0.72)        (3.08)        (-2.38)
[[beta].sub.ROE]          0.15 (***)    0.01           0.14
                         (2.70)        (0.14)         (1.36)
Adj. [R.sup.2]            0.87          0.76           0.10
Sharpe ratio              0.59          0.34           0.25

                        Panel B. Performance of Strategies Based on AR1
                        Forecasts of Profitability
Variable                               NI
                          Long          Short           L-S

E([r.sup.e.sub.gross])    10.87          8.01          2.86
                           2.42 (**)     0.71          1.71
                          (2.05)        (0.41)        (0.87)
[[beta].sub.MKT]           0.96 (***)    1.01 (***)   -0.06
                         (26.39)       (18.90)       (-0.94)
[[beta].sub.ME]            0.12 (**)     0.17 (**)    -0.05
                          (2.37)        (2.33)       (-0.65)
[[beta].sub.IA]           -0.14 (*)      0.37 (***)   -0.51 (***)
                         (-1.96)        (3.59)       (-4.35)
[[beta].sub.ROE]           0.23 (***)   -0.34 (***)    0.56 (***)
                          (3.86)       (-3.86)        (5.72)
Adj. [R.sup.2]             0.87          0.79          0.29
Sharpe ratio               0.69          0.44          0.26

(***) Significant at the 0.01 level.
(**) Significant at the 0.05 level.
(*) Significant at the 0.10 level.

Table VIII. Gross and Net Performance of Industry-Rotation Strategies
Based on Predicted Profitability Using Combination Forecasts

Panel A presents performance statistics for the long, short, and
long-minus-short (L-S) real-time industry-rotation strategies based on
each combination forecast of profitability: operating profit ([??]),
gross profit ([??]), cash flows ([??]), and net income ([??]). The
statistics include average gross excess returns
(E([r.sup.e.sub.gross])), annualized Sharpe ratios, and estimated
[[alpha].sub.gross] [[beta].sub.MKT], [[beta].sub.ME], [[beta].sub.IA],
and [r.sub.ROE] from the Hou et al. (2015) four-factor model:
[r.sup.e.sub.gross,t] = [[alpha].sub.gross] + [[beta].sub.MKT] *
[MKT.sub.t], + [[beta].sub.ME] * [R.sub.ME,T] + [[beta].sub.IA] *
[r.sub.IA,t] + [[beta].sub.ROE] * [r.sub.ROE,t] + [?.sub.t], (18) as
well as annualized net-of-costs average excess returns E([r.sub.net])
and Novy-Marx and Velikov (2016) generalized net-of-costs
[[alpha].sub.net] (which are non-negative by construction). The rows
labeled TO and T costs report average turnover and transaction costs (%
quarter). Panel B presents similar statistics as Panel A, but using the
long-short industry-rotation strategy return ([r.sub.[PI]]) based on
the lagged ex post version of the profitability measure defined in the
column heading instead of [r.sub.ROE]: [r.sub.gross,t] =
[[beta].sub.gross] + [[beta].sub.MKT] * [MKT.sub.t + [[beta].sub.ME] *
[r.sub.ME,t] + [[beta].sub.IA] * [r.sub.IA,t] + [[beta].sub.[PI]] *
[r.sub.[PI],t] + [?.sub.t] (19) Panel C presents performance statistics
similar to those in Panel B but using an autoregressive (ARl)-based
strategy ([r.sub.AR1]) instead of [r.sub.[PI]]. The t-statistics are
presented in parentheses below the coefficient estimates. The sample
period in both panels is return quarters 1980:1-2015:3 (N = 143).

                                  Panel A. Four-Factor Model
Variable                                [??]
                         Long           Short           L-S

E([r.sup.e.sub.gross])   10.52            6.97           3.54
[[alpha].sub.gross]       3.03 (***)     -2.12           5.15 (***)
                         (3.04)         (-1.18)         (2.69)
[[beta].sub.mkt]          0.95 (***)      1.04 (***)    -0.09
                        (31.00)         (18.82)        (-1.56)
[[beta].sub.IA]           0.12 (***)      0.24 (***)    -0.12
                         (2.98)          (3.30)        (-1.55)
[[beta].sub.IA]          -0.13 (**)       0.46 (***)    -0.59 (***)
                        (-2.16)          (4.30)        (-5.16)
[[beta].sub.ROE]          0.10 (*)       -0.19 (**)      0.29 (***)
                         (1.96)         (-2.15)         (3.04)
N                         0.91            0.79           0.23
Adj. [R.sup.2]            0.68            0.38           0.34
[r.sup.e.sub.net]         9.76           -7.95           1.81
[[alpha].sub.net]         2.54 (***)      0.17           2.71
                         (2.82)          (0.10)         (1.59)
TO                       57.9            65.0           61.5
T costs                   0.19            0.24           0.43

                               Panel B. Controlling for the Ex
                               Post Profitability Strategy
[[alpha].sub.gross]       3.14 (***)     -0.53           3.67 (***)
                         (3.56)         (-0.44)         (3.26)
[[beta].sub.MKT]          0.94 (***)      1.01 (***)    -0.07 (*)
                        (32.71)         (25.54)        (-1.94)
[[beta].sub.ME]           0.13 (***)      0.16 (***)    -0.03
                         (3.38)          (2.96)        (-0.54)
[[beta].sub.IA]          -0.07            0.20 (**)     -0.27 (***)
                        (-1.23)          (2.40)        (-3.56)
[[beta].sub.[PI]]         0.14 (***)     -0.57 (***)     0.71 (***)
                         (3.59)        (-11.09)        (14.80)
Adj. [R.sup.2]            0.91            0.88           0.68

                             Panel C. Controlling for the AR] Strategy
[[alpha].sub.gross]       3.13 (***)     -0.02           3.15 (***)
                         (3.53)         (-0.02)         (3.28)
[[beta].sub.mkt]          0.94 (***)      1.01 (***)    -0.07 (**)
                        (32.62)         (28.53)        (-2.16)
[[beta].sub.ME]           0.15 (***)      0.07           0.08 (*)
                         (3.66)          (1.46)         (1.73)
[[beta].sub.IA]          -0.05            0.06          -0.12 (*)
                        (-0.88)          (0.85)        (-1.77)
[[beta].sub.ARI]          0.14 (***)     -0.69 (***)     0.83 (***)
                         (3.49)        (-13.78)        (18.82)
Adj. [R.sup.2]            0.91            0.91           0.77

                        Panel A. Four-Factor Model
Variable                                [??]
                          Long           Short          L-S

E([r.sup.e.sub.gross])    9.68           7.37           2.30
[[alpha].sub.gross]      -0.58          -1.01           0.43
                        (-0.49)        (-0.46)         (0.16)
[[beta].sub.mkt]          0.99 (***)     1.01 (***)    -0.02
                        (26.95)        (14.91)        (-0.21)
[[beta].sub.IA]           0.08           0.12          -0.04
                         (1.54)         (1.30)        (-0.39)
[[beta].sub.IA]           0.02           0.42 (***)    -0.40 (**)
                         (0.31)         (3.20)        (-2.51)
[[beta].sub.ROE]          0.35 (***)    -0.19 (*)       0.54 (***)
                         (5.93)        (-1.76)         (4.13)
N                         0.87           0.68           0.14
Adj. [R.sup.2]            0.62           0.40           0.17
[r.sup.e.sub.net]         9.07          -8.15           0.92
[[alpha].sub.net]         0.12           0.00           0.00
                         (0.12)
TO                       23.1           27.2           25.1
T costs                   0.15           0.19           0.35

                             Panel B. Controlling for the Ex
                             Post Profitability Strategy
[[alpha].sub.gross]       0.85           1.52          -0.68
                         (0.87)         (1.36)        (-0.80)
[[beta].sub.MKT]          0.94 (***)     1.03 (***)    -0.08 (***)
                        (29.47)        (28.07)        (-3.07)
[[beta].sub.ME]           0.08 (*)       0.03           0.05
                         (1.82)         (0.68)         (1.20)
[[beta].sub.IA]           0.12 (*)       0.11           0.01
                         (1.79)         (1.43)         (0.18)
[[beta].sub.[PI]]         0.30 (***)    -0.69 (***)     0.99 (***)
                         (8.78)       (-17.74)        (33.77)
Adj. [R.sup.2]            0.89           0.90           0.90

                        Panel C. Controlling for the AR] Strategy
[[alpha].sub.gross]       1.21           0.87           0.34
                         (1.25)         (0.91)         (0.72)
[[beta].sub.mkt]          0.96 (**)      0.98 (***)    -0.02
                        (29.97)        (31.20)        (-1.55)
[[beta].sub.ME]           0.06           0.07          -0.00
                         (1.48)         (1.53)        (-0.07)
[[beta].sub.IA]           0.11           0.12 (*)      -0.01
                         (1.62)         (1.83)        (-0.35)
[[beta].sub.ARI]          0.28 (**)     -0.69 (***)     0.97 (**)
                         (8.81)       (-21.78)        (61.14)
Adj. [R.sup.2]            0.89           0.93           0.97

                        Panel A. Four-Factor Model
Variable                            [??]
                          Long           Short           L-S

E([r.sup.e.sub.gross])   10.18            7.35           2.82
[[alpha].sub.gross]       2.96 (**)      -2.83           5.80 (***)
                         (2.59)         (-1.60)         (2.94)
[[beta].sub.mkt]          0.88 (***)      1.04 (***)    -0.16 (***)
                        (25.03)         (19.17)        (-2.65)
[[beta].sub.IA]           0.17 (***)      0.26 (***)    -0.09
                         (3.64)          (3.62)        (-1.13)
[[beta].sub.IA]          -0.10            0.48 (***)    -0.58 (***)
                        (-1.51)          (4.56)        (-4.97)
[[beta].sub.ROE]          0.10 (*)       -0.06           0.16
                         (1.71)         (-0.68)         (1.61)
N                         0.87            0.78           0.18
Adj. [R.sup.2]            0.68            0.41           0.27
[r.sup.e.sub.net]         9.09           -8.57           0.52
[[alpha].sub.net]         2.28 (**)       0.23           2.50
                         (2.18)          (0.14)         (1.44)
TO                       40.4            39.5           39.9
T costs                   0.27            0.30           0.58

                            Panel B. Controlling for the Ex
                            Post Profitability Strategy
[[alpha].sub.gross]       3.73 (***)     -1.76           5.49 (***)
                         (3.54)         (-1.17)         (3.24)
[[beta].sub.MKT]          0.87 (***)      0.97 (***)    -0.11 (*)
                        (24.15)         (19.01)        (-1.83)
[[beta].sub.ME]           0.16 (***)      0.28 (***)    -0.12
                         (3.38)          (4.15)        (-1.58)
[[beta].sub.IA]          -0.11            0.42 (***)    -0.53 (***)
                        (-1.61)          (4.26)        (-4.77)
[[beta].sub.[PI]]         0.03           -0.34 (***)     0.37 (***)
                         (0.57)         (-4.62)         (4.45)
Adj. [R.sup.2]            0.87            0.81           0.27

                          Panel C. Controlling for the AR] Strategy
[[alpha].sub.gross]       3.13 (***)     -0.34           3.46 (***)
                         (3.06)         (-0.28)         (2.86)
[[beta].sub.mkt]          0.88 (***)      0.99 (***)    -0.11 (***)
                        (26.15)         (25.17)        (-2.77)
[[beta].sub.ME]           0.19 (***)      0.14 (**)      0.06
                         (4.11)          (2.47)         (1.03)
[[beta].sub.IA]          -0.07            0.31 (***)    -0.38 (***)
                        (-1.09)          (3.91)        (-4.78)
[[beta].sub.ARI]          0.14 (***)     -0.56 (***)     0.70 (***)
                         (3.04)        (-10.67)        (13.09)
Adj. [R.sup.2]            0.87            0.88           0.63

                          Panel A. Four-Factor Model
Variable                          [??]
                          Long            Short            L-S

E([r.sup.e.sub.gross])    11.21            8.07           3.14
[[alpha].sub.gross]        2.90 (***)      0.64           2.26
                          (2.60)          (0.38)         (1.21)
[[beta].sub.mkt]           0.95 (***)      1.03 (***)    -0.08
                         (27.83)         (20.27)        (-1.44)
[[beta].sub.IA]            0.10 (***)      0.17 (***)    -0.07
                          (2.23)          (2.49)        (-0.88)
[[beta].sub.IA]           -0.15 (***)      0.38 (***)    -0.53 (***)
                         (-2.27)          (3.81)        (-4.73)
[[beta].sub.ROE]           0.23 (***)     -0.34 (***)     0.57 (***)
                          (4.14)         (-4.11)         (6.10)
N                          0.89            0.82           0.33
Adj. [R.sup.2]             0.72            0.44           0.29
[r.sup.e.sub.net]         10.47           -9.22           1.25
[[alpha].sub.net]          2.64 (***)      0.00           0.76
                          (2.66)                         (0.46)
TO                        28.1            39.9           34.0
T costs                    0.19            0.29           0.47

                              Panel B. Controlling for the Ex
                              Post Profitability Strategy
[[alpha].sub.gross]        3.36 (***)      0.91           2.45 (**)
                          (3.50)          (0.74)         (2.13)
[[beta].sub.MKT]           0.95 (***)      1.01 (***)    -0.06
                         (30.29)         (25.01)        (-1.56)
[[beta].sub.ME]            0.09 (**)       0.18 (***)    -0.09 (*)
                          (2.12)          (3.29)        (-1.77)
[[beta].sub.IA]           -0.04            0.12          -0.16 (**)
                         (-0.55)          (1.47)        (-2.03)
[[beta].sub.[PI]]          0.25 (***)     -0.50 (***)     0.75 (***)
                          (6.31)        (-10.05)        (16.03)
Adj. [R.sup.2]             0.90            0.88           0.70

                           Panel C. Controlling for the AR] Strategy
[[alpha].sub.gross]        3.05 (***)      1.82 (*)       1.24 (*)
                          (3.30)          (1.78)         (1.97)
[[beta].sub.mkt]           0.95 (***)      0.99 (***)    -0.04 (*)
                         (31.65)         (29.90)        (-1.95)
[[beta].sub.ME]            0.11 (***)      0.14 (***)    -0.03
                          (2.66)          (3.01)        (-0.97)
[[beta].sub.IA]           -0.01            0.06          -0.07
                         (-0.22)          (0.80)        (-1.63)
[[beta].sub.ARI]           0.28 (***)     -0.62 (***)     0.91 (***)
                          (7.37)        (-14.62)        (34.66)
Adj. [R.sup.2]             0.91            0.92           0.91

(***) Significant at the 0.01 level.
(**) Significant at the 0.05 level.
(*) Significant at the 0.10 level.
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Author:Detzel, Andrew; Schaberl, Philipp; Strauss, Jack
Publication:Financial Management
Date:Jun 22, 2019
Words:17276
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