Prospective book-to-market ratio and expected stock returns

Size: px
Start display at page:

Download "Prospective book-to-market ratio and expected stock returns"

Transcription

1 Prospective book-to-market ratio and expected stock returns Kewei Hou Yan Xu Yuzhao Zhang Feb 2016 We propose a novel stock return predictor, the prospective book-to-market, as the present value of expected future demeaned book-to-market ratios. We find that the aggregate prospective book-to-market ratio can significantly predict stock market return, with adjusted R-squared between 5.0% and 5.8% out-of-sample. In addition, a high-minus-low investment strategy based on prospective book-to-market ratio generates significant monthly alpha ranging from 13.4 to 20.8 basis points across various factor models, and the return spread is also shown to be non-redundant as an alternative value factor in pricing cross-section of stock returns. Fisher College of Business, The Ohio State University, 2100 Neil Avenue, Columbus, OH 43210, USA; phone: ; fax: ; hou.28@osu.edu. Faculty of Business and Economics, University of Hong Kong; Pokfulam Road, Hong Kong; phone: ; fax: ; yanxuj@hku.hk. Rutgers Business School, Rutgers, The State University of New Jersey, Newark, NJ 07102, USA; Phone: ; fax: ; yzhang@business.rutgers.edu

2 Prospective book-to-market ratio and expected stock returns We propose a novel stock return predictor, the prospective book-to-market, as the present value of expected future demeaned book-to-market ratios. We find that the aggregate prospective book-to-market ratio can significantly predict stock market return, with adjusted R-squared between 5.0% and 5.8% out-of-sample. In addition, a high-minus-low investment strategy based on prospective book-to-market ratio generates significant monthly alpha ranging from 13.4 to 20.8 basis points across various factor models, and the return spread is also shown to be non-redundant as an alternative value factor in pricing cross-section of stock returns. 2

3 1 Introduction In this paper, we propose a new stock return predictor, through decomposing the book-to-market ratio into permanent and transitory components. Our decomposition relates the present value of demeaned stock return to the temporary component of the book-to-market ratio, the present value of demeaned book-to-market, and the present value of demeaned return on equity. When expected return moves with each or all of these three terms, future stock return can be predictable when the investor observes new information about book-to-market ratio. Specifically, we focus on the prospective book-to-market, 1, defined as the expected sum of all future book-to-market around its long run trend. When the expected sum of future book-to-market is above its long run trend, it signals that either the expected return is above its long run trend, or the market value is temporarily underpriced than the book value and is expected to rise in the future. Indeed, we find that the prospective book-to-market is particularly useful in predicting next period returns. Empirically, we model the prospective book-to-market by assuming a simple autoregressive form of book-to-market ratio then estimate its infinite sum while taking into consideration of the historical average. Similar to?, which utilize the difference of persistence in state variables to better predict stock returns, in our setup the superior predictive power of the prospective bookto-market depend on the persistence of book-to-market ratio and its current level relative to the long run trend. Our data include returns and book-to-market on three different levels: market, industry portfolios, and cross-section of individual firms. In out-of-sample tests, we use only the currently available information to ensure there is no look-ahead bias. There are two parameters to estimate: for the long run trend, we simply use the historical sample average to proxy for it. The estimation of autoregressive coefficient of book-to-market ratio deserves further elaboration. For both market and industry portfolios, we rely on simple autoregression as the measure for the persistence. Other than the OLS, we also conduct robust regression to minimize the effect of outliers in the return predictability tests. 2 1 The naming of this term is analogous to?, although in a different setting. 2 In the meantime, we are aware that we will suffer the well-known? bias that occurs when a sample size is small especially at the early stage of out-of-sample period. This bias constitutes another difficulty: that our point 1

4 We find that our prospective book-to-market ratio is a significant return predictor at the market, industry, individual stock level. At the market level, the prospective book-to-market ratio produces out of sample adjusted R-squared between 5.0% and 5.8%, in contrast to the conclusion of? that market returns can not reliably be predicted out of sample. Moreover, as shown in?, these out-of-sample R-squared implies substantial economic gains for the investor. In industry level time series tests, we show that the prospective book-to-market ratio predicts 48 industry portfolio returns. Moreover, using a zero cost long-short strategy, industry prospective book-to-market ratio is shown to generate a significant monthly spread of 2.3% 2.4% in riskadjusted returns across industries, but the original book-to-market ratio fails to do so, consistent with?. At the individual firm level, as firm by firm estimation of the persistence in book-to-market ratios is very imprecise with shorter sample period, we use a straightforward pooling OLS regression at industry level then assign to individual stocks within that industry. Interestingly, we observe a lot of cross-industry difference in the persistence parameter, which creates additional degrees of heterogeneity in book-to-market ratios when we sort firms into portfolios to develop a highly profitable investment strategy. To demonstrate the forecasting power of our new predictor, we long (short) firms when the expected sum of future book-to-market ratio is higher (lower) than its historical average, after controlling for firm size. This strategy generates significant monthly alphas ranging from 13.4 to 20.8 basis points, over models with q-factors, Fama-French 3 factors, 3 factors augmented with momentum factor, Fama-French 5 factors, and 5 factors augmented with momentum factor. We provide time series spanning tests by regressing the returns of the standard HML factor and the alternative annually formed HML factor with updated price information on our prospective book-to-market factor. We find that these two versions of HML factors are spanned by our prospective factor, but not the other way around. Finally, we contribute to the debate whether HML is a redundant factor in the existing factor models. Although these two annually formed HML factors are indeed redundant in the Fama-French 5 factor model, the prospective factor is estimates will be imprecise in the early sample period, thereby contaminating the return predictability results. We thus also employ other econometric tools to address such bias, for example, the recursive mean least squares. 2

5 not redundant and can be useful in pricing cross-section of stock returns. Methodologically, we extend the model in? and decompose the book-to-market into transitory and permanent components. In deriving the transitory component of the book-to-market, our model implies the stock return predictability of a multiple period sum of expected book-to-market ratio, which we term as prospective book-to-market ratio. This is a similar construct as the prospective interest rate differentials in? excess returns. and?, which has been shown to predict currency Finally, our work also contributes to the literature on the value premium in the cross-section of stock returns. In particular, recent studies have focused on decomposing the book-to-market ratio and examine each components return predictive power. For example,? demonstrate that most of the return predictability of book-to-market comes from the within-industry component.? and? also examine the components of the book-to-market ratio.? propose the use of priced component of book-to-market which outperforms the raw value of book-to-market. In contrast, we study the transitory component of book-to-market ratio as a starting point to improve the predictive power of the raw value of book-to-market. The paper is organized as follows. In section 2, we detail our present-value model and present the permanent-temporary components decomposition. In section 3, we introduce the data. We then report estimation of model parameters, present predictive regressions of expected returns and compare out-of-sample portfolio performance. We also explore various variations of our proposed predictor and conduct robustness checks. Section 4 concludes. 2 Model We start from the definition of stock return P t+1 P t ( 1 + D ) t+1 = R t+1 P t+1 where P t, D t, R t denote the stock price, dividend, and returns separately. case letters to denote the logarithm of these variables. 3 We use the lower Let δ t be the log dividend-price ratio

6 δ t = ln (1 + exp (dp t )), and if we take log on both sides p t+1 p t + δ t+1 = r t+1 taking expectations at time t and iterating forward we have E t p t+1 p t + E t δ t+1 = E t r t+1 E t p t+2 E t p t+1 + E t δ t+2 = E t r t+2... E t p t+j E t p t+j 1 + E t δ t+j = E t r t+j summing up we have k k E t p t+j p t + E t δ t+j = E t r t+j j=1 j=1 We then write the expected return E t r t+1 as the sum of risk premium µ t and risk free rate i t, and we specify the dynamics of the risk free rate, risk premium and log dividend-price ratio as i t ī = φ (i t 1 ī) + error µ t µ = γ (µ t 1 µ) + error δ t δ = β ( δ t 1 δ ) + error that is, we assume these three variables all follow simple first order autoregressive processes, with AR(1) coefficients φ, γ, and β, and their long run trend ī, µ, and δ separately. Just like?,?, and?, by so doing, we abstract away from specifying a utility function and deriving the dynamics for expected returns. It is also worth noting that a different modeling approach may impose cross-equations restrictions on these AR(1) coefficients (?,?,?), while we only require estimation of β in this paper. Besides, our method does not necessarily require these restrictions as our methodology does not rely on Campbell and Shiller s approximate identity on log dividend-price. 4

7 We then let τ = µ + ī δ, k, thus we have lim E tp t+j p t jτ + j [ E t δt+j δ ] = j=1 E t (µ t+j µ) + E t [i t+j ī] (1) j=1 j=1 The modeling methodology follows?, which focuses on the sum of deviations of expected future interest rate from its long run trend.? develop an empirical proxy for this prospective interest rate and show it predicts currency return, beyond the conventional carry trade. According to the? decomposition, lim j E t p t+j jτ can be seen as the permanent component of the stock price p P t. After we eliminate the permanent components of stock price, both sides of the equation are stationary. Note that on appearance, this equation is just another identity expressing the temporary component of book-to-market as present value of return and cash-flow. This model thus is reminiscent of the well-known Campbell and Shiller s approximate identity relating log dividend-price to present value of return and cash-flow, and Vuolteenaho s approximate identity relating bookto-market to present value of return and cash-flow (?,?). However, they differ conceptually. Our decomposition is on an unobservable term, namely, the transitory component of book-to-market, and our equation holds as an identity instead of approximation. Also, as put in?,? s (1991) return decomposition is related to the Beveridge-Nelson (1981) decomposition in the time-series literature, such that cash-flow news corresponds to the shock to the random-walk component of the log stock price and expected-return news to the shock to the stationary component of the log stock price. Our decomposition does not have this implication necessarily, and we use it to only motivate the present-value identity, so we refrain from modeling the dynamics of book-to-market in our empirical work. We then simplify the permanent-transitory components decomposition as p P t p t + β δ t δ 1 β = µ t µ 1 γ + i t ī 1 φ (2) Next, we apply the same approach to the log book equity b t = log (B t ). Define the log 5

8 dividend-book equity as ψ t = ln (1 + exp (db t )), then we also have b P t b t + β ψ t ψ 1 β = g t ḡ 1 ξ + i t ī 1 φ (3) where the expected excess returns on equity g t also follows a simple first order autoregressive process, with AR(1) coefficient ξ and long run trend ḡ: g t = E t [roe t+1 ] i t ; and g t ḡ = ξ (g t 1 ḡ) + e t Now define the book-to-market ratio as θ t log (BE t /ME t ) = b t p t Then if we subtract 3 from 2 ( θ P t ) [ψ t θ ψ t β 1 β δ t δ ] µ t µ = 1 β 1 γ g t ḡ 1 ξ Next, we conduct the loglinearization (?) and we also exploit the same assumption as? such that in the steady state, the historical dividend-price and dividend-book equity are equivalent: ρ = 1/ [ 1 + D P ] [ D ] = 1/ 1 + B Then we obtain for both the log dividend-price ratio and log dividend-book equity ratio δ t = ln (1 + exp (dp t )) (1 ρ) ( dp t dp ) + κ t ψ t = ln (1 + exp (db t )) (1 ρ) ( db t db ) + κ t We emphasize that we follow the convention in this literature and assume the historical dividendprice and dividend-book equity are known to the investor, in contrast to? which estimate the 6

9 sample mean at each time t. Then it follows ( θt θ P t ) µ t µ 1 γ g ( t ḡ θt θ ) (1 ρ)β 1 ξ 1 β This equation decomposes the temporary component of the book-to-market ratio into three parts, namely, the infinite sum of three terms: future demeaned expected return, expected demeaned return on equity, and demeaned log book-to-market ratio. Thus if the book-to-market is temporarily high, it may be that investors expect a persisting above average future discount rate, or a persisting below average future cash-flow. If there is no time variation of cash-flow and discount rate, then the current change of book-to-market reflects purely the time variation of book-to-market in the future. Now if we write the equation as µ t µ 1 γ ( ( θ t θt P ) g t ḡ θt θ ) + + (1 ρ)β 1 ξ 1 β If investor expects no time variation of cash-flow, and book-to-market ratio is independent to its own history, then return can be predicted in the conventional regression where the lagged bookto-market is the predictor. However, investor updates the belief every time when she received new information about the cash-flow or/and book-to-market ratio, thus all the future cash-flow or/and book-to-market will be expected to fluctuate around their own average. Therefore, instead of running the conventional predictive regression, we find from this equation that the three variables on the RHS, could separately or jointly predict future returns. We label the variable π = (1 ρ) β(θt θ) 1 β as the prospective book-to-market and this is the novel predictor we develop in this paper. By taking into consideration of the persistence and long run trend of book-to-market ratio, the prospective book-to-market ratio is much more volatile than the original book-to-market. In our analysis we focus our attention on the prospective book-to-market, and we treat the AR(1) coefficient γ of return process as constant, thus it plays no role in the time series predictive regression. Even abstracting away from its estimation, we still achieve superior performance in return predictability. Also, we do not make attempts on the temporary component of the book- 7

10 to-market ratio, as the estimation of which requires more time series modeling and defeats our purpose of develop a parsimonious new return predictor. Finally, we also leave the term involving returns on equity in a separate research. 3 3 Data and empirical results 3.1 Predicting market returns We use three sets of data for the empirical analysis. We first apply the methodology to the aggregate market book-to-market ratio and examine the predictive power of the prospective bookto-market. For the aggregate market data, we rely on those from?, available on Amit Goyal s website. The book value is from Value Line and Dow Jones. The annual book-to-market ratio is the ratio of book value at the end of the previous year to market value at the end of the current year, for the Dow Jones Industrial Average. It starts from 1921 and market return starts from Both samples end in Parameter estimation To construct the prospective book-to-market, we start with using the sample historical mean as a proxy for long run trend, and the sample first order autoregression coefficient as a proxy for persistence of the log book-to-market ratios. In order to facilitate a fair comparison with the benchmark log book-to-market ratio, these parameters are (re)estimated every year only using data available at the time of estimation. This estimation requires some history of log book-to-market ratio to initialize. Specifically, we use the first 10 observations to obtain the initial estimates of the moving average and persistence. Each year after, we add one more observation to the data and reestimate the parameters and eventually we obtain the time-series of the estimated parameters. 4 Table 1 3 In a companion paper, we propose a slightly different empirical approach to better suit the much weaker persistence of return on equity, and show this framework also allows the prospective ROE to predict returns. In fact, we introduce a much larger array of accounting variables to improve their return predictive power, for U.S. equity market and international markets, all within the same framework. 4 Our main results do not depend on the choice of the beginning year in the estimation. 8

11 Panel A presents the summary statistics of the historical mean and persistence parameters. The sample mean of the moving average is 0.531, slightly higher than the full sample average ( shown in Panel B). The average persistence is 0.772, confirming that the log book-to-market ratio is a slow moving random variable. Finally, the literature has set the parameter ρ to be 0.96 per year as in? and?. We follow this custom and treat this parameter as a constant, therefore actually the value of it will not affect our empirical work. Our baseline prospective book-to-market is constructed as follows, π = β(θ θ) 1 β, in which the persistence (β) parameter is the simple OLS estimate. Both the historical mean and persistence parameters are updated each year. We emphasize that each observation is constructed using only available information at the point in time and there is no look-ahead bias in obtaining the π variable. Our main results are based on π and we will also examine alternative specifications in the robustness check section. Table 1 about here. Table 1 Panel B presents the summary statistics of the market excess returns, log book-tomarket ratios, and prospective log book-to-market ratios. Market excess returns and log bookto-market ratios have been extensively studied in the literature and therefore we focus on our main predictor, prospective log book-to-market ratio. We note that the mean of the prospective book-to-market is slightly smaller in magnitude than the original variable ( vs ) and the standard deviation of prospective book-to-market ratio (14.728) is much larger than that of the original variable (0.496). The seemingly amplified variability is due to the fact that the prospective book-to-market can be large especially when β approaches one. For example, the maximum of π is as large as (in 1933), and the minimum value is To ensure that our results are not driven by the particularly large positive outlier, we also conduct robust regression which uses an iteratively re-weighted least squares algorithm, the estimates of which are less sensitive to outliers in the data as compared with the OLS estimates. Furthermore, the 9

12 prospective book-to-market ratio is not nearly as persistent as the original variable, which is also expected because the prospective variable removes the persistence of the original book-tomarket ratio. Panel C shows the pairwise correlations among market excess returns, log book-tomarket ratios, and prospective log book-to-market ratios. The correlation between the original and prospective book-to-market ratios is 0.510, suggesting that the two variables are different and yet still share common information Predictive regressions Our main goal in this paper is to compare the predictive power of the prospective ratio with that of the original variable. We first examine the predictability on the market risk premium in a time-series setting and the results are reported in Table 2. Table 2 about here. Panel A presents the full sample in-sample (IS) predictive regression results. Note that insample refers to the regression being conducted using the full sample and there is no look-ahead bias in our prospective variable. We first show that the original book-to-market ratio marginally predicts the market risk premium, with a moderate t-statistics of More importantly, when we turn to regression with π as predictor, the coefficient for π is and highly significant with a t-statistic of 5.86 and adjusted R 2 of 8%. The economic significance is also impressive and a one standard deviation shock in π predicts a positive 5.89% (computed as ) excess return the following year. Many known return predictors fail in the post oil-shock sample (?). Accordingly, we examine the performance of predictors from 1975 to 2013 in Panel B. As suggested, the log book-to-market itself completely loses its predictive power for market returns during this period (t = 0.59 and R 2 = 0.01). On the contrary, the coefficient of prospective book-to-market, proxied by π, 5 Because our sample period covers the most recent financial crisis period, this result is generally consistent with, albeit different from, those in? and? 10

13 remains very significant. The point estimate, 0.008, is about twice as large as that in the full sample and is statistically significant with t-statistics 2.71 and adjusted R 2 9%. As discussed above, to minimize the effect of outliers, we winsorize the 1933 observation (Panel C) by replacing with the next largest value and this procedure reduces the statistical significance of π, with t-statistics 2.60 and adjusted R 2 3%. To further control for outliers, we also winsorize 5% of the π variables and the results are in Panel D. The slope coefficient, 0.008, is significant with a t-statistic of It s worth noting that in both winsorized samples, the log book-to-market ratio itself turns insignificant at 10% level in each winsorized samples.? cautions that in-sample predictability often fails to translate into out-of-sample (OOS) predictability. To address this issue, we examine the out-of-sample predictive powers in Table 3 and the metrics we use are adjusted R 2, RMSE, and MSE-F, as advocated by?. 6 Table 3 about here. Panel A presents the out-of-sample predictive test results using the first 15 observations 7 to initialize the regression (also known as the burn-in period). As documented in the extant literature, the original book-to-market ratio shows negative values in all 3 metrics we examine, suggesting that the original book-to-market fails to outperform a simple historical moving average estimate. In contrast, the prospective book-to-market ratio (π) exhibits strong out-of-sample performance in all 3 measures we use. The adjusted out-of-sample R 2 is 4.3% with a p-value of 0.01, significantly outperforming the naïve model using simple moving average. The extant literature also finds that the commonly used predictors perform even worse in the modern sample starting only from To investigate whether our proposed predictor also suffers from this reduced predictive power in the most recent period, we perform the out-of-sample test using the first 45 6 We reproduce the formulas for these measures in the appendix, which are all statistics examining the relative performance of a predictor against the historical mean. 7 Because we use another 10 observations to start estimating the prospective book-to-market ratio, the first 25 observations are not used to evaluate the model performance. Our results are not sensitive to the choice of the out-of-sample period. 11

14 observations to initialize the estimate and the results are in Panel B. Because we use another 10 observations to start estimating the prospective ratio, this specification effectively only tests the predictive power in the post oil-shock period. We find that the raw book-to-market ratio entirely loses its predictive power in this out-of-sample test, with p-values equal to In sharp contrast, the prospective book-to-market ratio still generates a significant R 2 at 5.0% with a p-value of 2%. Collectively, the results in Tables 2 and 3 demonstrate the strong predictive power of our prospective ratio both in- and out-of-sample and in different sample periods Robustness We have shown strong return predictability using empirical proxies for the long run trend and persistence in the model. To further investigate the robustness of the preceding results, we examine several other alternative constructs 8. As the prospective book-to-market relies critically on the estimate of the β, the time variation of prospective book-to-market will also be sensitive to outliers in the raw book-to-market ratio. Therefore we also consider the iteratively re-weighted least squares (?). The new estimate (β RLS ) is generated from an iteratively re-weighted least squares algorithm, which gives lower weight to points that don t fit well. Specifically, the weights at each iteration are calculated by applying the bi-square function to the residuals from the previous iteration. The RLS estimates are known to be less sensitive to outliers in the data as compared with the OLS estimates. With this alternative measure of persistence, we construct π = β RLS(θ θ) 1 β RLS Table 1 Panel A also presents the summary statistics of the alternative measure (β RLS ). In general, β RLS is similar with β and the linear correlation between the alternative π measure and π is (Table 1 Panel C). Panel A of Table 2 establishes the full sample predictive power of this alternative measures, with t-statistics 5.41 and adjusted R 2 8%. Panels B presents the 8 We are more concerned with the large value of π due to estimate uncertainty of β. Another concern is that β has downward bias in estimation especially when the sample size is small. We alternatively try the recursive mean least squares to address this issue, for market level, industry portfolios, and cross-section of stock returns. The results are similar and we don t report them to save space. Adjusting estimate of β upward of course may increase of the time variation of the π. 12

15 post oil-shock sample and Panels C and D examine two winsorized samples. In the post oil-shock sample and winsorized samples, π are all statistically significant, with t-statistics 3.08, 2.81, and 2.13 respectively. Interestingly, the point estimates of π are almost identical at across all 4 Panels. This is because the measure is more robust to outliers by construction. The significance of π remains the same when we examine the OOS performance in Table 3. The OOS R 2 is 4.1% in the full sample and 5.8% in the post oil-shock sample, with p-values 0.01 and 0.02, respectively. As the OLS AR(1) coefficient is potentially sensitive to outliers, it is not surprising to see that this alternative measure sometimes outperforms our baseline prospective book-to-market ratio, which corroborates our main findings. 3.2 Predicting industry portfolio returns In this section we turn to industry level stock returns.? finds that book-to-market ratio not only predicts returns at the market level, industry book-to-market ratios also predict industry portfolio returns in a time-series setting. Based on the strong predictability of our prospective ratio at the aggregate level, we investigate whether the prospective book-to-market ratios at industry level can also predict industry returns. Our industry classification, returns data, industry book values, and industry market values are all from Ken French s data library. We compute end-of-year industry book-to-market ratios by dividing book value at the end of the previous year to market value at the end of the current year. The sample period for industry portfolio data are from 1926 to 2013 and we use the 48 industry portfolios Parameter estimation We use the Fama-French 48 industry portfolios as test assets and estimate the moving average and persistence parameters for each industry using the same method as that used for the market book-to-market ratios. Table 4 presents the summary statistics of industry excess returns and industry log book-to-market ratios of each industry. 9 Results on 12 and 38 industry portfolios are reported in the appendix. 13

16 Table 4 about here. There are ample variations in excess returns and book-to-market across industries. For example. the highest average excess return is 20% per year (Aircraft ind Business Supplies) and the lowest is 9% (Utilities, Communication, Retail, and a few other industries). The Transportation industry registers the highest log book-to-market ratio (0.34) and Pharmaceutical Products lowest (-1.27). The AR(1) coefficients of excess returns are mostly negative for all industries and those of log book-to-market are all very high. Table 5 about here. Table 5 presents the summary statistics of the estimated parameters of each industry. Naturally, the industries with the highest bm and industries with the most persistent bm do not necessarily coincide with each other. For instance, the bm of Coal industry is the most persistent (average β is 0.895) and that of Apparel industry is the least persistent (average β is 0.530). Table 6 about here. This finding would lead to different patterns of heterogeneities between bm and π. Table 6 presents the summary statistics of π of each industry. The Coal industry shows the most negative π at and Automobiles and Trucks shows the highest π at Table 7 about here. Table 7 further shows the cross-industry average of summary statistics after we pool all the industry estimates. Panel A presents those of the estimated parameters. Similar to the market level estimates from the last section, the sample mean of the average persistence of 48 industry portfolios is 0.719, suggesting that the log book-to-market ratios are also persistent at industry level. Panel B shows the summary statistics of industry returns, industry book-to-market ratios, 14

17 and industry prospective book-to-market ratios (π). Comparing with the original book-to-market ratios, the prospective book-to-market ratios display a higher volatility (2.606 vs ) and a lower persistence (0.755 vs ). Both features are consistent with how we construct the variables, as discussed in the previous section. Panel C presents the correlations among the variables of interest. At industry level, the correlation between the original and prospective book-to-market ratios is quite high, Predictive regressions and industry portfolio sorts We next examine whether the prospective book-to-market ratios help predict industry portfolio returns. Table 8 presents the in-sample predictive regressions of annual 48 industry returns 10 on lagged industry bm, π, and π. All time-series predictive regressions are adjusted for Newey-West correction with 3 lags. For the sake of brevity, we only display the coefficient and t-statistics of the predictor and the adjusted R 2 of the predictive regression. Table 8 about here. For the original bm, 16 coefficients out of 48 industries are significant with p-values less than 5% and the average adjusted R 2 is 1.59%. For prospective book-to-market ratio π, 17 coefficients out of 48 industries are significant with p-values less than 5% and the average adjusted R 2 is 1.50%. For the alternative prospective book-to-market ratio π, 15 coefficients out of 48 industries are significant with p-values less than 5% and the average adjusted R 2 is 1.39%. Overall, the 3 predictors show similar predictive power in sample. Table 9 about here. To examine the out-of-sample predictive power of our variables, Tables 9 and 10 present the OOS results at industry level For robustness, we also present results of these tests for 12 industry portfolios and 38 industry portfolios in the Appendix. 11 We use the first 15 observations to initialize the estimate 15

18 Table 10 about here. To directly compare with out-of-sample results of the aggregate market, we apply the same time-series out-of-sample methods to every industry and count the number of industries with a p-value of adjusted R 2 measure less than 5% and 10% 12. Using the original book-to-market ratio, 8 R 2 s out of 48 industries show a p-value lower than 5%. The 8 industries are Healthcare, Textiles, Construction, Aircraft, Petroleum and Natural Gas, Personal Services, Real Estate and Other. The prospective book-to-market ratio significantly predicts 7 industries OOS, including Healthcare, Construction, Aircraft, Petroleum and Natural Gas, Real Estate, Trading, and Other. Although we do not perform a formal tests, both 7 and 8 exceed the number of portfolios that would have been expected to be significant just by chance. The numbers of portfolio OOS R 2 s that are significant at the 10% level are 10 (Fabricated Products and Transportation, in addition to the 8 listed above) and 9 (Fabricated Products and Utilities, in addition to the 7 listed above), respectively for the original and prospective ratios. We also examine the alternative measure π and its OOS results are shown in Table 11. For π, the number of industry portfolio OOS R 2 s that are significant at 5% and 10% level are 5 and 7, respectively. Overall, the original and 2 prospective book-to-market ratios demonstrate similar predictive power in the out-of-sample tests. Table 11 about here. The industry portfolios naturally provides us with a cross-section to increase the power of our test. To test whether the book-to-market and prospective book-to-market ratios predict returns across industries, we sort 48 industries into 5 quintiles every year end, based on the available bookto-market ratio. The high and low quintiles each includes 10 industry portfolios and we examine mean returns of the 5 quintiles, as well as the zero-cost High-minus-Low industry portfolios in Table 12 Panel A. Table 12 about here. 12 Using p-values of the other two metrics yield identical results. 16

19 Industry portfolio excess returns are increasing with both bm and π. And both strategies generate cross-industry return spreads of 3.7% per year. The risk-adjusted returns, however, show a different pattern. Panel B shows the α augmented by the Fama-French 3-factor model. The High-minus-Low α for the book-to-market ratio is 0.5% per year with a t-statistics of 0.63, whereas that for the prospective book-to-market ratio is significant at 2.3% per year with a t- statistics of For robustness,we also examine the portfolios formed by the alternative measure, π. The mean return spread is 3.8% with t-statistics 3.64 and α is 2.4% with t-statistics The results are quantitatively similar with those generated by π. Therefore, industry prospective book-to-market ratio generates a significant spread in risk-adjusted returns across industries, but the original book-to-market ratio fails to do so, consistent with the findings in? Robustness Similar to the robustness check for the aggregate market, we perform robustness checks for industry portfolios using the industry level π, which are similarly constructed as those for the market. Table 8 Panel A presents the in-sample SUR results and π show similarly significant predictive power for industry portfolio returns. The t-statistics for π is 7.64 and system R 2 is 8%. Panels B and C presents the industry portfolio sorting results and the methodology used remains the same. We focus on the mean returns and 3-factor α of the zero-cost portfolios sorted by π. The mean return spread is 3.8% with t-statistics 3.64 and α is 2.4% with t-statistics The results are similar with those generated by π. The OOS results are shown in Table 11 and also comparable with the OOS results of π. 3.3 Cross-section of returns The evidence in the stock market and industry portfolios has indicated the superior predictive power of the prospective book-to-market ratio in the next period return over that of the raw log book-to-market value. In this section we turn to the cross-section of individual stocks and examine whether the predictability can translate into profitable investment strategies. 17

20 We take stock returns from CRSP and accounting data from Compustat. Our sample starts with all common shares (share code 10 or 11) traded on NYSE, Amex, and Nasdaq. For these firms, we calculate the book value of equity (shareholder equity, plus balance sheet deferred taxes, plus balance sheet investment tax credits, minus preferred stock) at the end of June. We set missing values of balance sheet deferred taxes and investment tax credit equal to zero. To calculate the value of preferred stock, we set it equal to the redemption value if available, or else the liquidation value, or the carrying value. Our main sample of individual firms starts from July 1959 and ends in December 2013, including stock returns, firms SIC codes and accounting information Parameter estimation As stated earlier, unlike industry portfolios data, our CRSP-Compustat data begin from We still conduct all our tests in the out-of-sample (OOS) period to avoid any look-ahead bias. Yet, estimating the first order autocorrelation coefficient and long run trend becomes a more acute problem in the cross-section of individual stocks as we have a panel with a large dimension of cross-section but a small dimension of time series. To overcome this difficulty, we pool the individual firms into groups and focus our attention on estimating the parameters from the group then assign the group values to individual firms. To be consistent with our industry portfolio results, we assume all firms within the same industry share the same AR(1) coefficient and long run trend. At the end of this section, we also report the results that are based mainly on estimation of individual firms AR(1) and long run trend, and only supplemented by their group counterparts when individual estimations based on short history become highly unreliable. This alternative produces very similar results. Our out-of-sample period starts from 1962:07 up to 2013:12. At the beginning of July 1962, we pool the firms according to their industry SIC codes at that time. Then we estimate a pooling OLS on this panel to generate a first estimate of β using the log book-to-market values between 1959 and We take each firms past book-to-market ratios then simply estimate a value weighted average as the long run trend θ. Again, for every year afterwards, we expand our estimation 18

21 window to generate a new set of estimates. Based on these estimates we calculate the value of prospective book-to-market ratio then assign to each firms within that industry 13. Table 13 about here. Table 13 reports the estimates and standard deviations of ˆβ and θ for each of the 48 industries during the sample period. There are large variations across different industries. For example, the Smoke industry has an AR(1) coefficient of 0.966, as the largest estimate compared to other industries. The Health industry on the other hand has the smallest estimate of only. The smoke industry generates a very stable estimate with the standard deviation of only, while the other industry contains the most volatile estimate with a very large standard deviation of Across all the firms, the average firm s β is estimated to be 0.820, which is lower than average of market or industry estimates. Turning to the estimate of long run trend, we find that the smoke industry again has the largest estimate of 0.605, while the drugs industry has the smallest estimate of The health industry s estimate has largest standard deviation of 0.420, while the smallest standard deviation comes from paper industry, only On average, the long run trend of US firms is Prospective factor We examine whether the return predictability of prospective book-to-market can be detected from profitable portfolio performances. Our key variable is still π = β[θ t θ]/[1 β]. The raw book-to-market ratio is known to produce the value anomaly. In addition,? show that two alternative ways of constructing book-to-market portfolios, using the June-end market value and using current month market value in calculating the book-to-market ratio, can produce significant alpha above and beyond that of the raw book-to-market ratio portfolio. Our aim in this section 13 We have also tried a firm individual fixed effect regression, two way fixed effect regression, or random effect regression (GLS) and obtain similar results in the next section. We have also tried equally weighted past book-tomarket ratios within industry as long run trend and obtain similar results in the next section 19

22 is then to contrast our proposed prospective book-to-market ratio portfolio against the standard book-to-market ratio along with these two alternatives. Following? and?, we construct the prospective factor using six value-weighted portfolios formed on size and prospective book-to-market ratio. At the end of June of year t, stocks are assigned to two size-sorted portfolios with median NYSE market equity as breakpoint. We valueweight these portfolios then refresh every June. The prospective factor s high-minus-low return is the average return on the two portfolios with the highest prospective book-to-market ratios minus the average return on the two portfolios with the lowest prospective book-to-market ratios. Table 14 about here. Panel A of Table 14 reports the basic portfolio characteristics of this prospective book-tomarket ratio factor. We present the mean, std dev, max, min, and Sharpe ratio. During our sample period, the prospective book-to-market factor has mean return of 36.3 basis point per month, with annualized Sharpe ratio of Panel B of Table 14 reports the time series regression results of prospective book-to-market factor on various factor asset pricing models. We consider the following risk factors: the q-factors MKT, ME, IA and ROE as in?, Fama-French three factors MKT, SMB, and HML as in?, the three factors augmented with momentum factor (UMD), and Fama-French five factors MKT, SMB, HML, RMW, and CMA as in?. The t-statistics are based on 6 lags Newey-West standard errors and reported in parentheses. Except that the q-factors are available from 1967:01, all the factors start from 1963:07. We find that the αs for all the regressions are significantly different from zero. Among all the model, the q-factors leave the largest alpha with 20.8 basis points per month (t=2.09), while the FF five factors leave the smallest alpha with 13.4 basis points per month (t=1.88). Generally, we find that the prospective factor is weakly related to the market portfolio negatively and related to the size factor, strongly related to investment positively and related to profitability strongly, and weakly related to RMW negatively and related to CMA positively. 20

23 In Table 15, we run additional time-series regressions and test whether our proposed prospective HML factor adds value in the presence of the competing versions of HML: the standard version using the ME at Dec 31 of year t ME which we denote as HML A,L following?, the annually updated version using the ME at June 30 of year t+1 (HML A,C ) following?, along with other conventional factors. These two versions are constructed similarly in that they both use the annual observation of ME in calculating the book-to-market ratio. Since HML does not belong to q-factors, we only examine the FF 3-factor model, the 3-factor augmented with UMD, the FF 5- factor model, and 5-factor model augmented with UMD. Each time, we replace the standard HML factor with our prospective factor. Besides, we specifically examine whether the two competing versions can be spanned by the prospective HML factor. Table 15 about here. Panel A presents results with the standard HML factor as the dependent variable, where the π HML is our prospective factor. Apparently, all the models show that standard HML is spanned by π HML with an insignificant alpha, ranging from to (t-stat from 1.63 to 1.19). It is worth noting that almost all of the alphas are negative, except when UMD is added to the 3-factor model. When we start from the simple regression, HML A,L is about times π HML. When we add more factors, it seems that MKT and SMB do not capture the return of HML A,C other than the π HML. Consistent with?, HML A,L is an inefficient way to load momentum into a portfolio. Particularly, in the presence of π HML, HML A,C is negatively correlated with UMD, and positively with CMA. Panel B presents results with the HML A,C factor as the dependent variable. Again, all the models show that HML A,C is spanned by π HML with an insignificant alpha, ranging from to (t-stat from 1.12 to 0.97). This time, almost all of the alphas are positive, except in the case of 5 factor model. Compared to the results in panel A, it is consistent that HML A,L is a somewhat inferior portfolio to HMl A,C. When we start from the simple regression, HML A,C is about times π HML. When we add more factors, again MKT and SMB do not capture return of the HML A,C. Further, UMD does not load significantly. 21

24 Finally, we consider the debate whether HML is a redundant factor in the presence of other factors.? find HML can be completely described by other four factors resulting in an insignificant alpha, thus concluding HML is a redundant factor in measuring abnormal returns.? conduct similar regressions and find that HML A,L alpaha still does not survive the time series regressions even after incorporating the UMD factor. They further show that the monthly updated bookto-market ratio, HML M,C, does generate significant alpha due to the heavy negative loading on momentum. Therefore, after showing prospective HML is not spanned by HML A,L or HML A,C but rather spans these two factors, in the presence of other factors, our next goal is to examine whether prospective HML can be useful in asset pricing models. Table?? about here. In panel A of Table??, we focus on the q-factors, while the dependent variables are four different versions of HML. The first model replicates the results from Table 15 that π HML has a significant alpha of The next three models show that q-factors do explain the standard HML, consistent with?, and the HML A,C. Finally, consistent with?, HML A,C also has a significant alpha of In panel B, we move on to the FF 5-factors without HML. The result shows that all versions of HML are highly positively related with CMA, and does not produce significant alpha. A closer look indicates that our π HML does produce the largest alpha of with the most largest t-value among all. Finally, following?, we add the momentum factor to the above model. The result shows that the π HML, along with the HML M,C, generates significant alpha of (t=1.99). It is interesting to note that π HML is the least loaded on CMA with the regression coefficient of (t=7.84), compared to especially that of for HML A,C, and the least loaded on UMD with a regression coefficient of (t= 2.38), compared to especially that of for HML M,C. Overall, these regression results suggest that our prospective HML is not as redundant as the monthly updated version of HML. However, the latter version is refreshed every month (thus heavily loading on UMD), while our prospective HML still relies on the Dec 31 year t value of ME and refreshed only annually. 22

25 4 Conclusion We model the transitory components of book-to-market ratio as sum of the present value of three demeaned terms: stock return, return on equity, and book-to-market. We propose an empirical proxy of the last term, the prospective book-to-market, as a novel stock return predictor. This new variable is more volatile than book-to-market, and requires the estimates of long run trend and persistence. Our data include market, industry portfolios, and cross-section of individual firms. We find that the prospective book-to-market can significantly predict market return with adjusted R- squared between 4.1% and 6.1% out-of-sample, can generate cross industry risk adjusted monthly return spread of 1.6%, and a cross sectional high-minus-low strategy on it generates significant monthly alpha ranging from 13.4 to 20.8 basis points across various workhorse factor models. As the prospective book-to-market factor spans instead of being spanned by the standard HML factor, it is also useful as an alternative value factor in factor models. 23

26 References Asness, C. S., R. B. Porter, and R. L. Stevens (2000). Predicting stock returns using industryrelative firm characteristics. Available at SSRN: Beveridge, S. and C. R. Nelson (1981). A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle. Journal of Monetary Economics 7 (2), Campbell, J. Y. (1991). A variance decomposition for stock returns. Economic Journal 101 (405), Campbell, J. Y. and R. J. Shiller (1988). Stock prices, earnings, and expected dividends. The Journal of Finance 43 (3), pp Campbell, J. Y. and R. J. Shiller (1991). Yield spreads and interest rate movements: A bird s eye view. The Review of Economic Studies 58 (3), pp Campbell, J. Y. and S. B. Thompson (2008). Predicting excess stock returns out of sample: Can anything beat the historical average? The Review of Financial Studies 21 (4), pp. Cochrane, J. H. (1992). Explaining the variance of price-dividend ratios. The Review of Financial Studies 5 (2), pp Cochrane, J. H. (2008). The dog that did not bark: A defense of return predictability. The Review of Financial Studies 21 (4), pp Cochrane, J. H. (2011). Presidential address: Discount rates. The Journal of Finance 66 (4), pp Cohen, R. B., P. A. Gompers, and T. Vuolteenaho (2002). Who underreacts to cash-flow news? evidence from trading between individuals and institutions. Journal of Financial Economics 66 (2-3), Daniel, K. and S. Titman (2006). Market reactions to tangible and intangible information. The Journal of Finance 61 (4), pp Engel, C. (2011). The real exchange rate, real interest rates, and the risk premium. University of Wisconsin, working paper. 24

Premium Timing with Valuation Ratios

Premium Timing with Valuation Ratios RESEARCH Premium Timing with Valuation Ratios March 2016 Wei Dai, PhD Research The predictability of expected stock returns is an old topic and an important one. While investors may increase expected returns

More information

Statistical Understanding. of the Fama-French Factor model. Chua Yan Ru

Statistical Understanding. of the Fama-French Factor model. Chua Yan Ru i Statistical Understanding of the Fama-French Factor model Chua Yan Ru NATIONAL UNIVERSITY OF SINGAPORE 2012 ii Statistical Understanding of the Fama-French Factor model Chua Yan Ru (B.Sc National University

More information

Revisiting Idiosyncratic Volatility and Stock Returns. Fatma Sonmez 1

Revisiting Idiosyncratic Volatility and Stock Returns. Fatma Sonmez 1 Revisiting Idiosyncratic Volatility and Stock Returns Fatma Sonmez 1 Abstract This paper s aim is to revisit the relation between idiosyncratic volatility and future stock returns. There are three key

More information

A Lottery Demand-Based Explanation of the Beta Anomaly. Online Appendix

A Lottery Demand-Based Explanation of the Beta Anomaly. Online Appendix A Lottery Demand-Based Explanation of the Beta Anomaly Online Appendix Section I provides details of the calculation of the variables used in the paper. Section II examines the robustness of the beta anomaly.

More information

Return Reversals, Idiosyncratic Risk and Expected Returns

Return Reversals, Idiosyncratic Risk and Expected Returns Return Reversals, Idiosyncratic Risk and Expected Returns Wei Huang, Qianqiu Liu, S.Ghon Rhee and Liang Zhang Shidler College of Business University of Hawaii at Manoa 2404 Maile Way Honolulu, Hawaii,

More information

Addendum. Multifactor models and their consistency with the ICAPM

Addendum. Multifactor models and their consistency with the ICAPM Addendum Multifactor models and their consistency with the ICAPM Paulo Maio 1 Pedro Santa-Clara This version: February 01 1 Hanken School of Economics. E-mail: paulofmaio@gmail.com. Nova School of Business

More information

Volatility Appendix. B.1 Firm-Specific Uncertainty and Aggregate Volatility

Volatility Appendix. B.1 Firm-Specific Uncertainty and Aggregate Volatility B Volatility Appendix The aggregate volatility risk explanation of the turnover effect relies on three empirical facts. First, the explanation assumes that firm-specific uncertainty comoves with aggregate

More information

Smart Beta #

Smart Beta # Smart Beta This information is provided for registered investment advisors and institutional investors and is not intended for public use. Dimensional Fund Advisors LP is an investment advisor registered

More information

Economics of Behavioral Finance. Lecture 3

Economics of Behavioral Finance. Lecture 3 Economics of Behavioral Finance Lecture 3 Security Market Line CAPM predicts a linear relationship between a stock s Beta and its excess return. E[r i ] r f = β i E r m r f Practically, testing CAPM empirically

More information

Applied Macro Finance

Applied Macro Finance Master in Money and Finance Goethe University Frankfurt Week 2: Factor models and the cross-section of stock returns Fall 2012/2013 Please note the disclaimer on the last page Announcements Next week (30

More information

Online Appendix to. The Value of Crowdsourced Earnings Forecasts

Online Appendix to. The Value of Crowdsourced Earnings Forecasts Online Appendix to The Value of Crowdsourced Earnings Forecasts This online appendix tabulates and discusses the results of robustness checks and supplementary analyses mentioned in the paper. A1. Estimating

More information

Liquidity skewness premium

Liquidity skewness premium Liquidity skewness premium Giho Jeong, Jangkoo Kang, and Kyung Yoon Kwon * Abstract Risk-averse investors may dislike decrease of liquidity rather than increase of liquidity, and thus there can be asymmetric

More information

An analysis of momentum and contrarian strategies using an optimal orthogonal portfolio approach

An analysis of momentum and contrarian strategies using an optimal orthogonal portfolio approach An analysis of momentum and contrarian strategies using an optimal orthogonal portfolio approach Hossein Asgharian and Björn Hansson Department of Economics, Lund University Box 7082 S-22007 Lund, Sweden

More information

A Note on Predicting Returns with Financial Ratios

A Note on Predicting Returns with Financial Ratios A Note on Predicting Returns with Financial Ratios Amit Goyal Goizueta Business School Emory University Ivo Welch Yale School of Management Yale Economics Department NBER December 16, 2003 Abstract This

More information

Persistence in Mutual Fund Performance: Analysis of Holdings Returns

Persistence in Mutual Fund Performance: Analysis of Holdings Returns Persistence in Mutual Fund Performance: Analysis of Holdings Returns Samuel Kruger * June 2007 Abstract: Do mutual funds that performed well in the past select stocks that perform well in the future? I

More information

Interpreting the Value Effect Through the Q-theory: An Empirical Investigation 1

Interpreting the Value Effect Through the Q-theory: An Empirical Investigation 1 Interpreting the Value Effect Through the Q-theory: An Empirical Investigation 1 Yuhang Xing Rice University This version: July 25, 2006 1 I thank Andrew Ang, Geert Bekaert, John Donaldson, and Maria Vassalou

More information

University of California Berkeley

University of California Berkeley University of California Berkeley A Comment on The Cross-Section of Volatility and Expected Returns : The Statistical Significance of FVIX is Driven by a Single Outlier Robert M. Anderson Stephen W. Bianchi

More information

An Online Appendix of Technical Trading: A Trend Factor

An Online Appendix of Technical Trading: A Trend Factor An Online Appendix of Technical Trading: A Trend Factor In this online appendix, we provide a comparative static analysis of the theoretical model as well as further robustness checks on the trend factor.

More information

Online Appendix to Bond Return Predictability: Economic Value and Links to the Macroeconomy. Pairwise Tests of Equality of Forecasting Performance

Online Appendix to Bond Return Predictability: Economic Value and Links to the Macroeconomy. Pairwise Tests of Equality of Forecasting Performance Online Appendix to Bond Return Predictability: Economic Value and Links to the Macroeconomy This online appendix is divided into four sections. In section A we perform pairwise tests aiming at disentangling

More information

Exploiting Factor Autocorrelation to Improve Risk Adjusted Returns

Exploiting Factor Autocorrelation to Improve Risk Adjusted Returns Exploiting Factor Autocorrelation to Improve Risk Adjusted Returns Kevin Oversby 22 February 2014 ABSTRACT The Fama-French three factor model is ubiquitous in modern finance. Returns are modeled as a linear

More information

Optimal Debt-to-Equity Ratios and Stock Returns

Optimal Debt-to-Equity Ratios and Stock Returns Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 5-2014 Optimal Debt-to-Equity Ratios and Stock Returns Courtney D. Winn Utah State University Follow this

More information

Can Hedge Funds Time the Market?

Can Hedge Funds Time the Market? International Review of Finance, 2017 Can Hedge Funds Time the Market? MICHAEL W. BRANDT,FEDERICO NUCERA AND GIORGIO VALENTE Duke University, The Fuqua School of Business, Durham, NC LUISS Guido Carli

More information

Decimalization and Illiquidity Premiums: An Extended Analysis

Decimalization and Illiquidity Premiums: An Extended Analysis Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 5-2015 Decimalization and Illiquidity Premiums: An Extended Analysis Seth E. Williams Utah State University

More information

Online Appendix for Overpriced Winners

Online Appendix for Overpriced Winners Online Appendix for Overpriced Winners A Model: Who Gains and Who Loses When Divergence-of-Opinion is Resolved? In the baseline model, the pessimist s gain or loss is equal to her shorting demand times

More information

Predictability of aggregate and firm-level returns

Predictability of aggregate and firm-level returns Predictability of aggregate and firm-level returns Namho Kang Nov 07, 2012 Abstract Recent studies find that the aggregate implied cost of capital (ICC) can predict market returns. This paper shows, however,

More information

Style Timing with Insiders

Style Timing with Insiders Volume 66 Number 4 2010 CFA Institute Style Timing with Insiders Heather S. Knewtson, Richard W. Sias, and David A. Whidbee Aggregate demand by insiders predicts time-series variation in the value premium.

More information

Predictive Regressions: A Present-Value Approach (van Binsbe. (van Binsbergen and Koijen, 2009)

Predictive Regressions: A Present-Value Approach (van Binsbe. (van Binsbergen and Koijen, 2009) Predictive Regressions: A Present-Value Approach (van Binsbergen and Koijen, 2009) October 5th, 2009 Overview Key ingredients: Results: Draw inference from the Campbell and Shiller (1988) present value

More information

Does Transparency Increase Takeover Vulnerability?

Does Transparency Increase Takeover Vulnerability? Does Transparency Increase Takeover Vulnerability? Finance Working Paper N 570/2018 July 2018 Lifeng Gu University of Hong Kong Dirk Hackbarth Boston University, CEPR and ECGI Lifeng Gu and Dirk Hackbarth

More information

Portfolio strategies based on stock

Portfolio strategies based on stock ERIK HJALMARSSON is a professor at Queen Mary, University of London, School of Economics and Finance in London, UK. e.hjalmarsson@qmul.ac.uk Portfolio Diversification Across Characteristics ERIK HJALMARSSON

More information

Market timing with aggregate accruals

Market timing with aggregate accruals Original Article Market timing with aggregate accruals Received (in revised form): 22nd September 2008 Qiang Kang is Assistant Professor of Finance at the University of Miami. His research interests focus

More information

Indian Institute of Management Calcutta. Working Paper Series. WPS No. 797 March Implied Volatility and Predictability of GARCH Models

Indian Institute of Management Calcutta. Working Paper Series. WPS No. 797 March Implied Volatility and Predictability of GARCH Models Indian Institute of Management Calcutta Working Paper Series WPS No. 797 March 2017 Implied Volatility and Predictability of GARCH Models Vivek Rajvanshi Assistant Professor, Indian Institute of Management

More information

Portfolio performance and environmental risk

Portfolio performance and environmental risk Portfolio performance and environmental risk Rickard Olsson 1 Umeå School of Business Umeå University SE-90187, Sweden Email: rickard.olsson@usbe.umu.se Sustainable Investment Research Platform Working

More information

Common Risk Factors in the Cross-Section of Corporate Bond Returns

Common Risk Factors in the Cross-Section of Corporate Bond Returns Common Risk Factors in the Cross-Section of Corporate Bond Returns Online Appendix Section A.1 discusses the results from orthogonalized risk characteristics. Section A.2 reports the results for the downside

More information

The Tangible Risk of Intangible Capital. Abstract

The Tangible Risk of Intangible Capital. Abstract The Tangible Risk of Intangible Capital Nan Li Shanghai Jiao Tong University Weiqi Zhang University of Muenster, Finance Center Muenster Yanzhao Jiang Shanghai Jiao Tong University Abstract With the rise

More information

Predicting Inflation without Predictive Regressions

Predicting Inflation without Predictive Regressions Predicting Inflation without Predictive Regressions Liuren Wu Baruch College, City University of New York Joint work with Jian Hua 6th Annual Conference of the Society for Financial Econometrics June 12-14,

More information

MUTUAL FUND PERFORMANCE ANALYSIS PRE AND POST FINANCIAL CRISIS OF 2008

MUTUAL FUND PERFORMANCE ANALYSIS PRE AND POST FINANCIAL CRISIS OF 2008 MUTUAL FUND PERFORMANCE ANALYSIS PRE AND POST FINANCIAL CRISIS OF 2008 by Asadov, Elvin Bachelor of Science in International Economics, Management and Finance, 2015 and Dinger, Tim Bachelor of Business

More information

Internet Appendix for: Cyclical Dispersion in Expected Defaults

Internet Appendix for: Cyclical Dispersion in Expected Defaults Internet Appendix for: Cyclical Dispersion in Expected Defaults March, 2018 Contents 1 1 Robustness Tests The results presented in the main text are robust to the definition of debt repayments, and the

More information

It is well known that equity returns are

It is well known that equity returns are DING LIU is an SVP and senior quantitative analyst at AllianceBernstein in New York, NY. ding.liu@bernstein.com Pure Quintile Portfolios DING LIU It is well known that equity returns are driven to a large

More information

This paper investigates whether realized and implied volatilities of individual stocks can predict the crosssectional

This paper investigates whether realized and implied volatilities of individual stocks can predict the crosssectional MANAGEMENT SCIENCE Vol. 55, No. 11, November 2009, pp. 1797 1812 issn 0025-1909 eissn 1526-5501 09 5511 1797 informs doi 10.1287/mnsc.1090.1063 2009 INFORMS Volatility Spreads and Expected Stock Returns

More information

Pricing and Mispricing in the Cross-Section

Pricing and Mispricing in the Cross-Section Pricing and Mispricing in the Cross-Section D. Craig Nichols Whitman School of Management Syracuse University James M. Wahlen Kelley School of Business Indiana University Matthew M. Wieland Kelley School

More information

Economic Review. Wenting Jiao * and Jean-Jacques Lilti

Economic Review. Wenting Jiao * and Jean-Jacques Lilti Jiao and Lilti China Finance and Economic Review (2017) 5:7 DOI 10.1186/s40589-017-0051-5 China Finance and Economic Review RESEARCH Open Access Whether profitability and investment factors have additional

More information

Lecture 5. Predictability. Traditional Views of Market Efficiency ( )

Lecture 5. Predictability. Traditional Views of Market Efficiency ( ) Lecture 5 Predictability Traditional Views of Market Efficiency (1960-1970) CAPM is a good measure of risk Returns are close to unpredictable (a) Stock, bond and foreign exchange changes are not predictable

More information

Long-run Consumption Risks in Assets Returns: Evidence from Economic Divisions

Long-run Consumption Risks in Assets Returns: Evidence from Economic Divisions Long-run Consumption Risks in Assets Returns: Evidence from Economic Divisions Abdulrahman Alharbi 1 Abdullah Noman 2 Abstract: Bansal et al (2009) paper focus on measuring risk in consumption especially

More information

Fama-French in China: Size and Value Factors in Chinese Stock Returns

Fama-French in China: Size and Value Factors in Chinese Stock Returns Fama-French in China: Size and Value Factors in Chinese Stock Returns November 26, 2016 Abstract We investigate the size and value factors in the cross-section of returns for the Chinese stock market.

More information

Internet Appendix for: Cyclical Dispersion in Expected Defaults

Internet Appendix for: Cyclical Dispersion in Expected Defaults Internet Appendix for: Cyclical Dispersion in Expected Defaults João F. Gomes Marco Grotteria Jessica Wachter August, 2017 Contents 1 Robustness Tests 2 1.1 Multivariable Forecasting of Macroeconomic Quantities............

More information

We follow Agarwal, Driscoll, and Laibson (2012; henceforth, ADL) to estimate the optimal, (X2)

We follow Agarwal, Driscoll, and Laibson (2012; henceforth, ADL) to estimate the optimal, (X2) Online appendix: Optimal refinancing rate We follow Agarwal, Driscoll, and Laibson (2012; henceforth, ADL) to estimate the optimal refinance rate or, equivalently, the optimal refi rate differential. In

More information

Deviations from Optimal Corporate Cash Holdings and the Valuation from a Shareholder s Perspective

Deviations from Optimal Corporate Cash Holdings and the Valuation from a Shareholder s Perspective Deviations from Optimal Corporate Cash Holdings and the Valuation from a Shareholder s Perspective Zhenxu Tong * University of Exeter Abstract The tradeoff theory of corporate cash holdings predicts that

More information

The Role of Credit Ratings in the. Dynamic Tradeoff Model. Viktoriya Staneva*

The Role of Credit Ratings in the. Dynamic Tradeoff Model. Viktoriya Staneva* The Role of Credit Ratings in the Dynamic Tradeoff Model Viktoriya Staneva* This study examines what costs and benefits of debt are most important to the determination of the optimal capital structure.

More information

Problem Set 6. I did this with figure; bar3(reshape(mean(rx),5,5) );ylabel( size ); xlabel( value ); mean mo return %

Problem Set 6. I did this with figure; bar3(reshape(mean(rx),5,5) );ylabel( size ); xlabel( value ); mean mo return % Business 35905 John H. Cochrane Problem Set 6 We re going to replicate and extend Fama and French s basic results, using earlier and extended data. Get the 25 Fama French portfolios and factors from the

More information

R&D and Stock Returns: Is There a Spill-Over Effect?

R&D and Stock Returns: Is There a Spill-Over Effect? R&D and Stock Returns: Is There a Spill-Over Effect? Yi Jiang Department of Finance, California State University, Fullerton SGMH 5160, Fullerton, CA 92831 (657)278-4363 yjiang@fullerton.edu Yiming Qian

More information

The Effect of Financial Constraints, Investment Policy and Product Market Competition on the Value of Cash Holdings

The Effect of Financial Constraints, Investment Policy and Product Market Competition on the Value of Cash Holdings The Effect of Financial Constraints, Investment Policy and Product Market Competition on the Value of Cash Holdings Abstract This paper empirically investigates the value shareholders place on excess cash

More information

Concentration and Stock Returns: Australian Evidence

Concentration and Stock Returns: Australian Evidence 2010 International Conference on Economics, Business and Management IPEDR vol.2 (2011) (2011) IAC S IT Press, Manila, Philippines Concentration and Stock Returns: Australian Evidence Katja Ignatieva Faculty

More information

What Drives Anomaly Returns?

What Drives Anomaly Returns? What Drives Anomaly Returns? Lars A. Lochstoer and Paul C. Tetlock UCLA and Columbia Q Group, April 2017 New factors contradict classic asset pricing theories E.g.: value, size, pro tability, issuance,

More information

Risk-managed 52-week high industry momentum, momentum crashes, and hedging macroeconomic risk

Risk-managed 52-week high industry momentum, momentum crashes, and hedging macroeconomic risk Risk-managed 52-week high industry momentum, momentum crashes, and hedging macroeconomic risk Klaus Grobys¹ This draft: January 23, 2017 Abstract This is the first study that investigates the profitability

More information

Using Pitman Closeness to Compare Stock Return Models

Using Pitman Closeness to Compare Stock Return Models International Journal of Business and Social Science Vol. 5, No. 9(1); August 2014 Using Pitman Closeness to Compare Stock Return s Victoria Javine Department of Economics, Finance, & Legal Studies University

More information

Internet Appendix to Leverage Constraints and Asset Prices: Insights from Mutual Fund Risk Taking

Internet Appendix to Leverage Constraints and Asset Prices: Insights from Mutual Fund Risk Taking Internet Appendix to Leverage Constraints and Asset Prices: Insights from Mutual Fund Risk Taking In this Internet Appendix, we provide further discussion and additional empirical results to evaluate robustness

More information

Accruals, cash flows, and operating profitability in the. cross section of stock returns

Accruals, cash flows, and operating profitability in the. cross section of stock returns Accruals, cash flows, and operating profitability in the cross section of stock returns Ray Ball 1, Joseph Gerakos 1, Juhani T. Linnainmaa 1,2 and Valeri Nikolaev 1 1 University of Chicago Booth School

More information

Underreaction, Trading Volume, and Momentum Profits in Taiwan Stock Market

Underreaction, Trading Volume, and Momentum Profits in Taiwan Stock Market Underreaction, Trading Volume, and Momentum Profits in Taiwan Stock Market Mei-Chen Lin * Abstract This paper uses a very short period to reexamine the momentum effect in Taiwan stock market, focusing

More information

The Value Premium and the January Effect

The Value Premium and the January Effect The Value Premium and the January Effect Julia Chou, Praveen Kumar Das * Current Version: January 2010 * Chou is from College of Business Administration, Florida International University, Miami, FL 33199;

More information

Does the Fama and French Five- Factor Model Work Well in Japan?*

Does the Fama and French Five- Factor Model Work Well in Japan?* International Review of Finance, 2017 18:1, 2018: pp. 137 146 DOI:10.1111/irfi.12126 Does the Fama and French Five- Factor Model Work Well in Japan?* KEIICHI KUBOTA AND HITOSHI TAKEHARA Graduate School

More information

Risk-Adjusted Capital Allocation and Misallocation

Risk-Adjusted Capital Allocation and Misallocation Risk-Adjusted Capital Allocation and Misallocation Joel M. David Lukas Schmid David Zeke USC Duke & CEPR USC Summer 2018 1 / 18 Introduction In an ideal world, all capital should be deployed to its most

More information

Is Information Risk Priced for NASDAQ-listed Stocks?

Is Information Risk Priced for NASDAQ-listed Stocks? Is Information Risk Priced for NASDAQ-listed Stocks? Kathleen P. Fuller School of Business Administration University of Mississippi kfuller@bus.olemiss.edu Bonnie F. Van Ness School of Business Administration

More information

Regression Discontinuity and. the Price Effects of Stock Market Indexing

Regression Discontinuity and. the Price Effects of Stock Market Indexing Regression Discontinuity and the Price Effects of Stock Market Indexing Internet Appendix Yen-Cheng Chang Harrison Hong Inessa Liskovich In this Appendix we show results which were left out of the paper

More information

GDP, Share Prices, and Share Returns: Australian and New Zealand Evidence

GDP, Share Prices, and Share Returns: Australian and New Zealand Evidence Journal of Money, Investment and Banking ISSN 1450-288X Issue 5 (2008) EuroJournals Publishing, Inc. 2008 http://www.eurojournals.com/finance.htm GDP, Share Prices, and Share Returns: Australian and New

More information

Combining State-Dependent Forecasts of Equity Risk Premium

Combining State-Dependent Forecasts of Equity Risk Premium Combining State-Dependent Forecasts of Equity Risk Premium Daniel de Almeida, Ana-Maria Fuertes and Luiz Koodi Hotta Universidad Carlos III de Madrid September 15, 216 Almeida, Fuertes and Hotta (UC3M)

More information

Robustness Checks for Idiosyncratic Volatility, Growth Options, and the Cross-Section of Returns

Robustness Checks for Idiosyncratic Volatility, Growth Options, and the Cross-Section of Returns Robustness Checks for Idiosyncratic Volatility, Growth Options, and the Cross-Section of Returns Alexander Barinov Terry College of Business University of Georgia This version: July 2011 Abstract This

More information

On the economic significance of stock return predictability: Evidence from macroeconomic state variables

On the economic significance of stock return predictability: Evidence from macroeconomic state variables On the economic significance of stock return predictability: Evidence from macroeconomic state variables Huacheng Zhang * University of Arizona This draft: 8/31/2012 First draft: 2/28/2012 Abstract We

More information

Implied Volatility v/s Realized Volatility: A Forecasting Dimension

Implied Volatility v/s Realized Volatility: A Forecasting Dimension 4 Implied Volatility v/s Realized Volatility: A Forecasting Dimension 4.1 Introduction Modelling and predicting financial market volatility has played an important role for market participants as it enables

More information

Overseas unspanned factors and domestic bond returns

Overseas unspanned factors and domestic bond returns Overseas unspanned factors and domestic bond returns Andrew Meldrum Bank of England Marek Raczko Bank of England 9 October 2015 Peter Spencer University of York PRELIMINARY AND INCOMPLETE Abstract Using

More information

Appendix. In this Appendix, we present the construction of variables, data source, and some empirical procedures.

Appendix. In this Appendix, we present the construction of variables, data source, and some empirical procedures. Appendix In this Appendix, we present the construction of variables, data source, and some empirical procedures. A.1. Variable Definition and Data Source Variable B/M CAPX/A Cash/A Cash flow volatility

More information

Dissecting Anomalies. Eugene F. Fama and Kenneth R. French. Abstract

Dissecting Anomalies. Eugene F. Fama and Kenneth R. French. Abstract First draft: February 2006 This draft: June 2006 Please do not quote or circulate Dissecting Anomalies Eugene F. Fama and Kenneth R. French Abstract Previous work finds that net stock issues, accruals,

More information

Are Firms in Boring Industries Worth Less?

Are Firms in Boring Industries Worth Less? Are Firms in Boring Industries Worth Less? Jia Chen, Kewei Hou, and René M. Stulz* January 2015 Abstract Using theories from the behavioral finance literature to predict that investors are attracted to

More information

Market Reactions to Tangible and Intangible Information Revisited

Market Reactions to Tangible and Intangible Information Revisited Critical Finance Review, 2016, 5: 135 163 Market Reactions to Tangible and Intangible Information Revisited Joseph Gerakos Juhani T. Linnainmaa 1 University of Chicago Booth School of Business, USA, joseph.gerakos@chicagobooth.edu

More information

Alternative Benchmarks for Evaluating Mutual Fund Performance

Alternative Benchmarks for Evaluating Mutual Fund Performance 2010 V38 1: pp. 121 154 DOI: 10.1111/j.1540-6229.2009.00253.x REAL ESTATE ECONOMICS Alternative Benchmarks for Evaluating Mutual Fund Performance Jay C. Hartzell, Tobias Mühlhofer and Sheridan D. Titman

More information

Further Test on Stock Liquidity Risk With a Relative Measure

Further Test on Stock Liquidity Risk With a Relative Measure International Journal of Education and Research Vol. 1 No. 3 March 2013 Further Test on Stock Liquidity Risk With a Relative Measure David Oima* David Sande** Benjamin Ombok*** Abstract Negative relationship

More information

Some Features of the Three- and Four- -factor Models for the Selected Portfolios of the Stocks Listed on the Warsaw Stock Exchange,

Some Features of the Three- and Four- -factor Models for the Selected Portfolios of the Stocks Listed on the Warsaw Stock Exchange, Some Features of the Three- and Four- -factor Models for the Selected Portfolios of the Stocks Listed on the Warsaw Stock Exchange, 2003 2007 Wojciech Grabowski, Konrad Rotuski, Department of Banking and

More information

Post-Earnings-Announcement Drift: The Role of Revenue Surprises and Earnings Persistence

Post-Earnings-Announcement Drift: The Role of Revenue Surprises and Earnings Persistence Post-Earnings-Announcement Drift: The Role of Revenue Surprises and Earnings Persistence Joshua Livnat Department of Accounting Stern School of Business Administration New York University 311 Tisch Hall

More information

Liquidity and IPO performance in the last decade

Liquidity and IPO performance in the last decade Liquidity and IPO performance in the last decade Saurav Roychoudhury Associate Professor School of Management and Leadership Capital University Abstract It is well documented by that if long run IPO underperformance

More information

The bottom-up beta of momentum

The bottom-up beta of momentum The bottom-up beta of momentum Pedro Barroso First version: September 2012 This version: November 2014 Abstract A direct measure of the cyclicality of momentum at a given point in time, its bottom-up beta

More information

What Does Risk-Neutral Skewness Tell Us About Future Stock Returns? Supplementary Online Appendix

What Does Risk-Neutral Skewness Tell Us About Future Stock Returns? Supplementary Online Appendix What Does Risk-Neutral Skewness Tell Us About Future Stock Returns? Supplementary Online Appendix 1 Tercile Portfolios The main body of the paper presents results from quintile RNS-sorted portfolios. Here,

More information

Aggregation, Capital Heterogeneity, and the Investment CAPM

Aggregation, Capital Heterogeneity, and the Investment CAPM Aggregation, Capital Heterogeneity, and the Investment CAPM Andrei S. Gonçalves 1 Chen Xue 2 Lu Zhang 3 1 UNC 2 University of Cincinnati 3 Ohio State and NBER PBCSF November 21, 218 Introduction Theme

More information

Equity risk factors and the Intertemporal CAPM

Equity risk factors and the Intertemporal CAPM Equity risk factors and the Intertemporal CAPM Ilan Cooper 1 Paulo Maio 2 This version: February 2015 3 1 Norwegian Business School (BI), Department of Financial Economics. E-mail: ilan.cooper@bi.no Hanken

More information

Online Appendix. Revisiting the Effect of Household Size on Consumption Over the Life-Cycle. Not intended for publication.

Online Appendix. Revisiting the Effect of Household Size on Consumption Over the Life-Cycle. Not intended for publication. Online Appendix Revisiting the Effect of Household Size on Consumption Over the Life-Cycle Not intended for publication Alexander Bick Arizona State University Sekyu Choi Universitat Autònoma de Barcelona,

More information

Unpublished Appendices to Market Reactions to Tangible and Intangible Information. Market Reactions to Different Types of Information

Unpublished Appendices to Market Reactions to Tangible and Intangible Information. Market Reactions to Different Types of Information Unpublished Appendices to Market Reactions to Tangible and Intangible Information. This document contains the unpublished appendices for Daniel and Titman (006), Market Reactions to Tangible and Intangible

More information

The cross section of expected stock returns

The cross section of expected stock returns The cross section of expected stock returns Jonathan Lewellen Dartmouth College and NBER This version: March 2013 First draft: October 2010 Tel: 603-646-8650; email: jon.lewellen@dartmouth.edu. I am grateful

More information

Predictability of Interest Rates and Interest-Rate Portfolios

Predictability of Interest Rates and Interest-Rate Portfolios Predictability of Interest Rates and Interest-Rate Portfolios Liuren Wu Zicklin School of Business, Baruch College Joint work with Turan Bali and Massoud Heidari July 7, 2007 The Bank of Canada - Rotman

More information

The predictive power of investment and accruals

The predictive power of investment and accruals The predictive power of investment and accruals Jonathan Lewellen Dartmouth College and NBER jon.lewellen@dartmouth.edu Robert J. Resutek Dartmouth College robert.j.resutek@dartmouth.edu This version:

More information

Tax-Loss Carry Forwards and Returns

Tax-Loss Carry Forwards and Returns Tax-Loss Carry Forwards and Returns Jack Favilukis Ron Giammarino Jose Pizarro December 29, 2015 Financial support from the Social Science and Research Council of Canada (SSHRC) is gratefully acknowledged.

More information

Great Company, Great Investment Revisited. Gary Smith. Fletcher Jones Professor. Department of Economics. Pomona College. 425 N.

Great Company, Great Investment Revisited. Gary Smith. Fletcher Jones Professor. Department of Economics. Pomona College. 425 N. !1 Great Company, Great Investment Revisited Gary Smith Fletcher Jones Professor Department of Economics Pomona College 425 N. College Avenue Claremont CA 91711 gsmith@pomona.edu !2 Great Company, Great

More information

Core CFO and Future Performance. Abstract

Core CFO and Future Performance. Abstract Core CFO and Future Performance Rodrigo S. Verdi Sloan School of Management Massachusetts Institute of Technology 50 Memorial Drive E52-403A Cambridge, MA 02142 rverdi@mit.edu Abstract This paper investigates

More information

Income Inequality and Stock Pricing in the U.S. Market

Income Inequality and Stock Pricing in the U.S. Market Lawrence University Lux Lawrence University Honors Projects 5-29-2013 Income Inequality and Stock Pricing in the U.S. Market Minh T. Nguyen Lawrence University, mnguyenlu27@gmail.com Follow this and additional

More information

The Common Factor in Idiosyncratic Volatility:

The Common Factor in Idiosyncratic Volatility: The Common Factor in Idiosyncratic Volatility: Quantitative Asset Pricing Implications Bryan Kelly University of Chicago Booth School of Business (with Bernard Herskovic, Hanno Lustig, and Stijn Van Nieuwerburgh)

More information

FE670 Algorithmic Trading Strategies. Stevens Institute of Technology

FE670 Algorithmic Trading Strategies. Stevens Institute of Technology FE670 Algorithmic Trading Strategies Lecture 4. Cross-Sectional Models and Trading Strategies Steve Yang Stevens Institute of Technology 09/26/2013 Outline 1 Cross-Sectional Methods for Evaluation of Factor

More information

Online Appendix to. The Structure of Information Release and the Factor Structure of Returns

Online Appendix to. The Structure of Information Release and the Factor Structure of Returns Online Appendix to The Structure of Information Release and the Factor Structure of Returns Thomas Gilbert, Christopher Hrdlicka, Avraham Kamara 1 February 2017 In this online appendix, we present supplementary

More information

Price, Earnings, and Revenue Momentum Strategies

Price, Earnings, and Revenue Momentum Strategies Price, Earnings, and Revenue Momentum Strategies Hong-Yi Chen Rutgers University, USA Sheng-Syan Chen National Taiwan University, Taiwan Chin-Wen Hsin Yuan Ze University, Taiwan Cheng-Few Lee Rutgers University,

More information

The Free Cash Flow and Corporate Returns

The Free Cash Flow and Corporate Returns Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 12-2018 The Free Cash Flow and Corporate Returns Sen Na Utah State University Follow this and additional

More information

Bayesian Dynamic Linear Models for Strategic Asset Allocation

Bayesian Dynamic Linear Models for Strategic Asset Allocation Bayesian Dynamic Linear Models for Strategic Asset Allocation Jared Fisher Carlos Carvalho, The University of Texas Davide Pettenuzzo, Brandeis University April 18, 2016 Fisher (UT) Bayesian Risk Prediction

More information

Hedging inflation by selecting stock industries

Hedging inflation by selecting stock industries Hedging inflation by selecting stock industries Author: D. van Antwerpen Student number: 288660 Supervisor: Dr. L.A.P. Swinkels Finish date: May 2010 I. Introduction With the recession at it s end last

More information

Geographic Diffusion of Information and Stock Returns

Geographic Diffusion of Information and Stock Returns Geographic Diffusion of Information and Stock Returns Jawad M. Addoum * University of Miami Alok Kumar University of Miami Kelvin Law Tilburg University February 12, 2014 ABSTRACT This study shows that

More information

Adjusting for earnings volatility in earnings forecast models

Adjusting for earnings volatility in earnings forecast models Uppsala University Department of Business Studies Spring 14 Bachelor thesis Supervisor: Joachim Landström Authors: Sandy Samour & Fabian Söderdahl Adjusting for earnings volatility in earnings forecast

More information