Empirical studies on stock return predictability

Transcription

1 Empirical studies on stock return predictability A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Humanities 2015 Jingya Wang Manchester Business School

2 Contents Abstract 8 Declaration 9 Copyright statement 10 Acknowledgements 11 1 Introduction Motivation Thesis structure References 17 2 Literature review Introduction Predicting stock market returns Conventional studies on predictability The predictor candidates related to the commodity market Research methodologies Predicting stock returns out-of-sample The consumption capital asset pricing model (CCAPM) Modifications to the standard CCAPM References 39 3 Predicting consumption growth and stock market returns Introduction The model

3 3.2.1 Forecasting expected consumption growth Making the adjustment Data Empirical findings Forecasting consumption growth Forecasting excess returns Conclusion References 71 4 Consumption risk and conditional consumption CAPM Introduction The models The standard consumption CAPM Conditional consumption CAPM The scaled consumption CAPM with the ultimate consumption risk Conditioning variable The methodology The Fama and MacBeth (1973) procedure Data Empirical findings Forecasting consumption growth The investigation of predictability from cay and cay adj Testing the consumption CAPM Conclusion References 96 5 Analyzing the short-term predictability of the stock market Introduction Methodology The univariate predictive regression The PLS methodology Data Empirical findings Forecasting monthly excess returns from commodity returns 139 3

4 5.4.2 Forecasting the stock market returns at three-month horizon Forecasting market returns at six-month and twelve-month horizons Forecasts from other predictors Robustness checks Forecasting industry returns from commodities Conclusion References Conclusion Summary of empirical findings Limitations and extensions References 167 This thesis contains 47,211 words including title page, tables and footnotes. 4

5 List of Figures 3.1 Aggregate and disaggregate consumption growth rates Contributions of each commodity returns to predictability

6 List of Tables 3.1 Descriptive statistics Predicting consumption growth Predicting i=1 ρi w c t+i Predicting excess returns in-sample Predicting excess returns out-of-sample Predictive regression of excess returns on the adjustment Predicting consumption growth Predicting excess returns Tests of unscaled CCAPM Tests of conditional CCAPM(z t = E[ c t:t+4 ]) Correlation matrix Tests of two-factor model (z t = E[ c t:t+4 ]) (z t, c t+s+1 ) Tests of two-factor model (z t = E[ c t:t+4 ]) ( c t+s+1, z t c t+s+1 ) Tests of two-factor model (z t = E[ c t:t+4 ]) (z t, z t c t+s+1 ) Tests of conditional CCAPM (z t = cay t ) Correlation matrix Tests of two-factor model (z t = cay t ) (z t, c t+s+1 ) Tests of two-factor model (z t = cay t ) (z t, z t c t+s+1 ) Tests of two-factor model (z t = cay t ) ( c t+s+1, z t c t+s+1 ) Tests of conditional CCAPM(z t = cay adj,t ) Correlation matrix Tests of two-factor model (z t = cay adj,t ) (z t, c t+s+1 ) Tests of two-factor model (z t = cay adj,t ) ( c t+s+1, z t c t+s+1 ) Tests of two-factor model (z t = cay adj,t ) (z t,z t c t+s+1 ) Conditional CCAPM including ultimate consumption risk factor Monthly forecast from commodity returns

7 5.2 Monthly forecast from commodity returns Three-month forecast from commodity returns Six-month forecast from commodity returns Twelve-month forecast from commodity returns Prediction results from individual commodity returns Prediction results from alternative predictors Robustness check with control variables Forecasting monthly industry returns from commodity returns

8 The University of Manchester Jingya Wang Doctor of Philosophy (PhD) Empirical studies of stock return predictability September 2015 Abstract This thesis includes three essays on topics related to the predictability of market returns. I investigate i) the predictability of market returns from an adjustedversion of cay ratio (cay adj ), ii) the explanatory power of a conditional version of the consumption-capm which uses predictor variables to scale the pricing kernel, and iii) whether information about future market returns can be extracted from a large set of commodity data. The first essay studies the predictive ability of cay adj. In Campbell and Mankiw (1989), the consumption-wealth ratio is represented as a linear function of expected market returns and consumption growth. Lettau and Ludvigson (2001) build their study on Campbell and Mankiw (1989) and estimate the ratio cay as a proxy for the consumption-wealth ratio, assuming that the fluctuation in expected consumption growth is constant. I argue that the variation in expected consumption growth should be taken into consideration and propose adjusting the cay ratio by the estimates of expected consumption growth. After making the adjustment, I find that the predictabilities of market returns, particularly at annual, bi-annual, and tri-annual horizons, are greatly improved. The significant predictive ability of cay adj still holds in out-of-sample forecasts. The second essay examines the performance of a conditional version of the consumption-capm, where conditioning variables are used to scale the pricing kernel. I find that incorporating the conditioning information into the standard consumption-capm greatly improves the performance in asset pricing tests, particularly when using cay adj as the conditioning variable. Moreover, the performance of conditional consumption-capm is as good as the ultimate consumption risk model (Parker and Julliard, 2005) which measures the consumption risk over several quarters. Further tests show that the factors of conditional consumption- CAPM drive out the consumption risk measured over several quarters. The third essay evaluates the ability of lagged commodity returns to forecast market returns. In order to exploit the predictive information from a relatively large amount of commodity returns, I apply the partial-least-squares (PLS) method pioneered by Kelly and Pruitt (2013). I find that the commodity returns measured over previous twelve months show strong predictive power in monthly and three-month forecasts, in-sample and out-of-sample. The findings are robust to controlling for risk factors such as momentum, Fama-French three factors and industry returns previously identified to be significant predictors of market returns (Hong, Torous and Valkanov, 2007). 8

9 Declaration I, Jingya Wang, declare that no portion of the work referred to in the thesis has been submitted in support of application for another degree or qualification of this or any other university or other institute of learning. 9

10 Copyright statement i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright ) and s/he has given The University of Manchester the right to use such Copyright for any administrative, promotional, educational and/or teaching purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the regulations of the John Rylands University Library of Manchester. Details of these regulations may be obtained from the Librarian. This page must form part of any such copies made. iii. The ownership of any patents, designs, trade marks and all other intellectual property rights except for the Copyright (the Intellectual Property ) and any reproductions of copyright works, for example graphs and tables ( Reproductions ), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and exploitation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available from the Head of School of Manchester Business School (or the Vice-President) and the Dean of the Faculty of Humanities. 10

11 Acknowledgements I would like to thank my supervisors, Doctor Alex Taylor and Professor Stuart Hyde, for their support, advice, and valuable experience over the four-year study in Manchester Business School. I am greatly indebted to Doctor Alex Taylor who supervises my research and excites my interest in predictability study. I am deeply grateful for his patience, encouragement and constructive suggestions on this thesis. I am very thankful to Professor Stuart Hyde for his response to my PhD application in summer Without the response, I would have no opportunity to write this thesis. I would like to thank my PhD committee members Professor Ian Garrett, Dr Kevin Aretz, Dr Alex Kostakis for their valuable comments during my annual and semi-annual reviews. I would also like to express my grateful thanks to my colleague Liu Liu for very instructive conversations and valuable research experience. Special thanks to Doctor Hugh Gong and his family for their invaluable help and understanding during my study in U.K. The four-year study life would be extremely stressful and boring without them. Finally, I would like to express my heartfelt thanks to my parents who always support me and my maternal grandparents for their warmest care and encouragement. Their unconditional love makes me keep the momentum going during my PhD study. Last but not least, my special and sincere thanks go to my fiancé for his unconditional support, full respect and understanding. I also would like to extend my thanks to the parents of my fiancé for their support during my study. 11

12 Chapter 1 Introduction 1.1 Motivation Establishing whether expected market returns are time-varying has attracted a substantial literature and many variables have been identified as predictors of aggregate market returns. predictability literature. 1 variables. My thesis is concerned with two strands of the The first strand concerns the search for new predictor Both chapters 3 and 5 offer ways to construct predictor variables that are new to the literature. Chapter 3 develops an adjusted cay ratio that accounts for variation in expected consumption growth in order to improve cay s ability to predict returns; chapter 5 extracts information from the cross-section of commodity prices using the partial-least-square (PLS) approach to predict market returns. The second strand of the predictability literature uses predictor variables in tests of conditional asset pricing models. 2 Chapter 4 analyzes a conditional version of the consumption-capm using predictor variables to scale the pricing kernel. Financial valuation ratios, such as the dividend-price (dp) ratio, book-tomarket (bm) ratio, earnings-price (ep) ratio, have played an important role in establishing the predictability of market returns over relatively long horizons. However, the evidence can be criticized on a number of fronts including concerns 1 Early studies such as Keim and Stambaugh (1986), Fama and French (1988, 1989), Campbell (1987) observe significant results of market return predictability. Welch and Goyal (2008) conduct a review of a number of well-known predictors. 2 Kelly and Pruitt (2013) estimate a compositive predictor from disaggregate book-to-market (bm) ratios by employing the PLS method and find improved predictability of market returns. 12

13 over data mining due to the search over a large number of potential predictors (e.g., Foster, Smith, and Whaley, 1997), econometric issues due to the high persistence of the financial ratios (e.g., Stambaugh, 1999), and the poor out-ofsample performance in predictability tests which gauges the success of a trader attempting to implement the predictability model in real-time (e.g., Welch and Goyal, 2008; Brennan and Xia, 2005). One ratio variable that has attracted considerable attention is Lettau and Ludvigson (2001a) s empirical version of the consumption-wealth ratio (cay). This predictor variable can be motivated from the present-value identity described in Campbell and Mankiw (1989) who shows that the consumption-wealth ratio is a function of both expected market returns and expected consumption growth. Accordingly, Lettau and Ludvigson (2001a) argue that the consumption-wealth ratio has the potential for forecasting market returns, assuming the expected consumption growth is constant or varies little. They estimate the ratio (cay) from the cointegrating regression between aggregate consumption, asset holdings and labor income. The cay ratio shows strong ability to forecast market returns (Lettau and Ludvigson, 2001a), however, the evidence appears weaker in the recent study (Bianchi et al., 2014) which uses an updated sample. In the first study I raise the possibility that the predictive ability of cay may be underestimated if expected consumption growth varies substantially over time, thereby contaminating cay, and reducing its ability to predict market returns. Currently, direct evidence for predictable variation in consumption growth rates is weak. However, the success of models such as ultimate consumption risk (Parker and Julliard, 2005) suggests that consumption growth, rather than remaining constant, varies in a predictable way. Therefore, in the first essay, I propose adjusting the cay ratio to take into account time-varying expected consumption growth which I model using past disaggregate consumption growth rates. In this way, the predictive ability of cay ought to be improved and in chapter 3, I present evidence that this is the case for intermediate horizon forecasts. In order to implement such an adjusted cay ratio, I need to construct a good predictor of consumption growth. I firstly decompose aggregate consumption into spending on durable, nondurable goods and services and assess the predictability of consumption growth by past disaggregate consumption growth rates. Using these disaggregate quantities as predictor variables is motivated by Kelly and 13

14 Pruitt (2013) who find improved predictability of market returns from the compositive predictor extracted from portfolio-level bm ratios. I find that the growth rates of disaggregate consumption measured over last four quarters show superior performance to benchmarks, such as the consumption growth rate measured over last four quarters, the cay ratio, in forecasting consumption growth at the annual horizon. Furthermore, by adding the expected consumption growth at the annual horizon to the cay ratio, I obtain an adjusted cay ratio (cay adj ) and use it as the predictor of market returns. I show that cay adj outperforms cay and greatly improves the predictabilities of market returns at annual, bi-annual and tri-annual horizons. The superior performance of cay adj holds out-of-sample. Moreover, I show that the improved predictability is purely from the cay adj ratio rather than the adjustment term itself. This essay contributes to the literature in two aspects. First, it helps establish the predictability of consumption growth. The existing literature generally considers consumption growth to be unpredictable and there is a lack of good predictors. My findings show that consumption growth is predictable using the components of aggregate consumption, and suggest that the consumption growth rate varies over time. Second, I provide evidence on the predictability of market returns over the intermediate horizon. My results indicate that using the new forecasts of consumption growth can improve the ability of the consumption-wealth ratio to predict returns. Predictor variables are often used in tests of conditional asset pricing models, and in chapter 4, I consider a conditional version of the consumption-capm. In the standard consumption-capm, the expected returns are determined by risk exposure, as measured by the contemporaneous covariance of consumption growth with stock returns. However, empirical evidence supporting this model is very weak (e.g., Hansen and Singleton, 1983; Breeden et al., 1989; Cochrane, 1996) and considerable effort has been made in the literature to improve the model performance. Lettau and Ludvigson (2001b) propose a multi-factor model by incorporating conditioning information, and the model shows better performance that is roughly comparable to the performance of Fama-French three-factor model. Parker and Julliard (2005) propose replacing the consumption risk factor in the standard consumption-capm by the covariance of stock returns with consumption growth measured over following several quarters, which is named as ultimate consumption risk, and find significant evidence that the model explains variations 14

15 in expected returns over Fama-French 25 portfolios substantially. If the work by Lettau and Ludvigson (2001b) and Parker and Julliard (2005) are combined together, the performance of the model may be improved. The second essay in my thesis follows this logic and examines performance of the consumption-capm scaled by conditioning variables which are the expected consumption growth, the cay ratio and the cay adj ratio. Since measuring the consumption growth over following several quarters captures the expectation of future growth rate, I use the expected consumption growth as a conditioning variable. The ratio cay, as is shown in Lettau and Ludvigson (2001b), substantially improves the explanatory power of the consumption-capm for Fama-French 25 portfolios, however, recent study (Bianchi, Lettau, and Ludvigson, 2014) finds that the ratio cay estimated on updated data appears to have weaker predictive power. Therefore, I re-examine the performance of the model scaled by the newly estimated cay. Moreover, since the construction of the cay adj ratio removes the contamination from variations in expected consumption growth, which makes the cay adj ratio have the potential for higher predictability, for this reason, I use the cay adj ratio as another conditioning variable. I find evidence that the model scaled by either cay or cay adj explains as much as the model with ultimate consumption risk of cross-sectional variations in expected returns. I observe that the risk factors of scaled model, using the cay adj ratio as the conditioning variable, drive out the ultimate consumption risk factor. This study stresses the importance of incorporating conditioning information into the consumption-capm and contributes to the selection of appropriate conditioning variables. In general, most predictors in the literature are aggregate market quantities such as the dp ratio and other financial ratios. Researchers, such as Sousa (2010), Kelly and Pruitt (2013), 3 have started to pay attention to disaggregate quantities, aiming to utilize predictive information contained in the cross-section (e.g., Ludvigson and Ng, 2007). In chapter 5, I examine whether it is possible to extract information about future market returns from the commodity market. Previous studies have looked at commodities on an individual basis which makes it difficult to assess statistical significance and to estimate the total amount of 3 Kelly and Pruitt (2013) achieve success in forecasting market returns by using predictive information contained in the cross-section of bm ratios for portfolios. The study relies on the partial-least-squares (PLS) methodology which aims to extract relevant information from a large number of potential predictors. The PLS approach is able to filter out irrelevant information from large information sets, and this technique has been utilized in many subsequent studies (e.g., Qiao, 2013; Liu et al. (2014); Fuentes, Poncela, and Rodríguez (2015)). 15

16 predictive information contained in commodities. In the third essay, I apply the PLS, the method proposed by Kelly and Pruitt (2013, 2015), to a large group of commodities, aiming to find significant evidence of improved predictability. I show that the commodity returns measured over last twelve months have the strongest power in forecasting monthly and three-month market returns. And I show that the identified predictability is largely driven by predictive information from soybean oil, Chicago yellow corn and West Texas intermediate oil. The superior performance also exists in out-of-sample forecasts. The results are robust to controlling for the momentum factor, Fama-French three factor, and the industry returns that are significant predictors of market returns (Hong, Torous, and Valkanov, 2007), suggesting that the commodity returns represent different determinants of expected market returns. The essay contributes to the literature from the following two aspects. First, it provides evidence that, similar to lagged industry returns (Hong, Torous, and Valkanov (2007)), the information from lagged commodity returns can lead the stock market. While Jacobsen, Marshall, and Visaltanachoti (2009) show that commodity returns that are measured at different horizons have strong predictive power, I use the PLS technique to conduct the study in a systematic way and clarify the horizon over which a collection of commodity returns show the strongest predictive power. Second, the results provide further evidence that predictive information is often contained in the cross-section of disaggregate quantities. 1.2 Thesis structure The thesis is organized following guidance on alternative format theses accepted by the University of Manchester. According to the guidance, chapters in the thesis are written in a format suitable for publication in peer-reviewed journals. The empirical chapters included in this thesis are structured around three essays representing the original contribution to asset pricing studies. The equations, footnotes, tables, figures and appendices are numbered from the beginning of each chapter. However, page numbers, titles and subtitles have a sequential order throughout the thesis. The thesis is arranged as follows. Chapter 2 reviews literature on predictability of stock market returns and consumption-capm. Chapter 3 investigates whether an adjusted-cay ratio shows better performance than standard cay in 16

17 the forecast of market returns. Chapter 4 examines whether the performance of consumption-capm is improved by incorporating conditioning information. Chapter 5 explores whether the predictability of market returns is improved by predictive information extracted from disaggregate commodity returns. Chapter 6 concludes. In chapters 3-5 I use the third person (we, our) instead of the first person (I, my), as these empirical chapters are in the form of working, or submitted, papers co-authored with my supervisors. 17

18 References Bianchi, F., Lettau, M., Ludvigson, S. C., A markov-switching cay. mimeo. Breeden, D. T., Gibbons, M. R., Litzenberger, R. H., Empirical test of the consumption-oriented capm. Journal of Finance 44 (2), Brennan, M. J., Xia, Y., tay s as good as cay. Finance Research Letters 2, Campbell, J. Y., Stock returns and the term structure. Journal of Financial Economics 18 (2), Campbell, J. Y., Mankiw, N. G., Consumption, income and interest rates: reinterpreting the time series evidence. NBER Macroeconomics Annual 4, Cochrane, J. H., A cross-sectional test of an investment-based asset pricing model. Journal of Political Economy 104 (3), Fama, E. F., French, K. R., Dividend yields and expected stock returns. Journal of Financial Economics 22, Fama, E. F., French, K. R., Business conditions and expected returns on stock and bonds. Journal of Financial Economics 25 (1), Foster, F. D., Smith, T., Whaley, R. E., Assessing goodness-of-fit of asset pricing models: the distribution of the maximal r 2. Journal of Finance 52 (2), Fuentes, J., Poncela, P., Rodríguez, J., Sparse partial least squares in time series for macroeconomic forecasting. Journal of Applied Econometrics 30,

19 Hansen, L. P., Singleton, K. J., Stochastic consumption, risk aversion, and the temporal behavior of asset returns. Journal of Political Economy 91 (2), Hong, H., Torous, W., Valkanov, R., Do industries lead stock markets? Journal of Financial Economics 83, Jacobsen, B., Marshall, B., Visaltanachoti, N., May Return predictability revisited. FMA Asian Conference. Keim, D. B., Stambaugh, R. F., Predicting returns in the stock and bond markets. Journal of Financial Economics 17 (2), Kelly, B., Pruitt, S., Market expectations in the cross-section of present values. Journal of Finance 68 (5), Kelly, B., Pruitt, S., The three-pass regression filter: A new approach to forecasting using many predictors. Journal of Econometrics 186, Lettau, M., Ludvigson, S., 2001a. Consumption, aggregate wealth and expected stock returns. Journal of Finance 56 (3), Lettau, M., Ludvigson, S., 2001b. Resurrecting the (c)capm: a cross-sectional test when risk premia are time-varying. Journal of Political Economy 109 (6), Liu, Q., Tao, L., Wu, W., Yu, J., Short- and long-run business conditions and expected returns. Working paper (May). URL ssrn Ludvigson, S. C., Ng, S., The empirical risk-return relation: a factor analysis approach. Journal of Financial Economics 83, Parker, J. A., Julliard, C., Consumption risk and the cross section of expected returns. Journal of Political Economy 113 (1), Qiao, X., Cross-sectional evidence in consumption mismeasurement. Working paper (August). URL ssrn

20 Sousa, R. M., Consumption, (dis)aggregate wealth, and asset returns. Journal of Empirical Finance 17, Stambaugh, R. F., Predictive regressions. Journal of Financial Economics 54, Welch, I., Goyal, A., A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies 21,

21 Chapter 2 Literature review 2.1 Introduction In asset pricing studies, researchers find an enormous amount of predictors having the ability to explain patterns of asset returns. In general, these factors may be sorted into two groups: i) variables that forecast variations in investment opportunities, for instance, the dp ratio, the dy ratio (e.g., Rozeff, 1984; Fama and French, 1988; Hodrick, 1992, Campbell and Viceira, 2002), the interest rate (Campbell, 1987), the bm ratio (Kothari and Shanken, 1997; Pontiff and Schall, 1998); ii) variables that directly measure status of the economy, for instance, the labor income (Jagannanthan and Wang, 1996), the investment growth (Cochrane, 1996). The principal objective of this thesis is to study i) the predictability of market returns (in excess of the short-term risk-free rate); ii) the ability of consumption risk in explaining variations in average returns across assets conditional on the information set. Accordingly, this chapter reviews literature from the two strands, first, studies on the predictability of the market returns; second, investigations of the consumption-capm (CCAPM), in particular the conditional CCAPM. 21

22 2.2 Predicting stock market returns Over the past 25 years, researchers have widely accepted that the stock returns are predictable. 1 2 Starting from the definition of stock price, Campbell and Shiller (1988) derive the present-value identity and show that variations in expected returns may be driven by either discount rate shocks or cash flow shocks, or both. In particular, the dp ratio is represented as a linear function of expected future market returns and dividend growth. A drop in stock price, for example, leading to an increase in dp ratio, must be driven by either higher market return expectations or lower forecasts of dividend growth, or both. Empirically, dp ratio shows limited ability in dividend growth forecasts which implies that discount rate shocks may be the main force driving stock price movements. 3 However, recent studies have started to pay attention to the potential effect of cash flow shocks. For example, Garrett and Priestley (2012) find empirical evidence that the expected dividend growth is highly predictable when using a variable, which is estimated from the cointegrating relationship between dividends, earnings and prices, as the predictor. Moreover, they show that the cash flow beta help explain size effect of stock returns which suggests that cash flow shocks also contribute to stock price fluctuations. 4 Indeed, researchers find that some other variables having strong predictive 1 Some researchers provide empirical evidence criticizing the identified predictability of market returns. For example, Stambaugh (1999) points out that the significance of predictive coefficients may be over-estimated when using highly persistent variables as predictors. Welch and Goyal (2008) re-examine the predictive performance of existing good predictors on recent data ( ) and find that most predictors fail to show significant predictive performance out-of-sample. Nevertheless, Campbell and Thompson (2008) provide evidence that the poor out-of-sample performance can be greatly improved when imposing restrictions to the sign of predictive coefficients. 2 Related work include Keim and Stambaugh (1986), Campbell and Shiller (1988), Fama and French (1989),Cochrane (1999), Lettau and Ludvigson (2001a) and so on. 3 There is a considerable amount of studies indicating the smoothing expected dividend growth. Related studies, including Campbell (1991), Cochrane (2008), show that the dp ratio has limited predictive power for dividend growth. Lacerda and Santa-Clara (2010) propose taking variations in expected dividend growth into consideration and using the expectation of dividend growth as the adjustment to standard dp ratio. Although using the history of dividend growth as predictor, they argue that there is potential of improving predictive ability of the adjusted-dp ratio as long as strong predictors can be found. This argument implies that the forecast of dividend growth remains to be a challenge in empirical studies. 4 Related work, including Lacerda and Santa-Clara (2010), Binsbergen and Koijen (2010) and Golež (2014), propose modifying the standard dp ratio by considering variations in expected dividend growth, also implies that the failure to consider variations in expected dividend growth may underestimate predictability of market returns. 22

23 power for market returns may be regarded as following the same logic. For example, Vuolteenaho (2002) propose an accounting-based present-value identity by using earnings over book equity (ROE) as cash flow and show that the bm ratio performs well in explaining variations in asset returns. Lettau and Ludvigson (2001a) build the work on the present-value identity proposed by Campbell and Mankiw (1989), estimate the consumption-wealth ratio (cay) from cointegrating relationship between aggregate consumption, asset holdings and labor income and find that cay has strong predictive power for intermediate horizon market returns. In Campbell and Mankiw (1989) s identity, as is shown in Lettau and Ludvigson (2001a), the aggregate consumption may be regarded as the dividend paid by aggregate wealth. As such, the estimated cay ratio is somewhat similar to the dp ratio Conventional studies on predictability Among the identified predictors, the valuation ratios, perhaps the most celebrated, signal the time-varying investment opportunities in future returns, showing strong predictive power in forecasting market returns over the long-run (e.g., Jegadeesh, 1991; Cochrane, 2005, pp ). These ratios include the dividendprice (dp) ratio, the dividend-yield (dy) ratio (e.g., Rozeff, 1984; Fama and French, 1988; Hodrick, 1992; Campbell and Viceira, 2002; Campbell and Yogo, 2006; Lewellen, 2004; Menzly and Veronesi, 2004), the book-to-market (bm) ratio (Kothari and Shanken (1997); Pontiff and Schall (1998)), the earnings-dividend (ed) ratio (e.g., Campbell and Shiller, 1988, 1998; Lamont, 1998), the priceearnings (pe) ratio (e.g., Cole, Helwege, and Laster, 1996; Campbell and Shiller (1998); Lander, Orphanides, and Douvogiannis, 1997; Pu, 2000), and so on. Empirical studies show that these predictors have a common feature that almost all of them are highly persistent. 5 Therefore, the predictive ability, as measured by R 2, tends to rise as forecast horizon increases. For instance, Fama and French (1988) show that, at the one-year forecast horizon, the dp ratios explains a relatively small amount (15%) of variations in expected market returns, however, at the five-year horizon, the fraction dramatically rises to 60%. Lewellen (2004) examines the autocorrelation coefficient of various valuation ratios over the period 5 Lewellen (2004), Ferson, Sarkissian, and Simin (2003) show that the first-order autocorrelation coefficients of financial ratios, at monthly frequency, such as the bm ratio, the dividend-yield (dy) ratio, the ep ratio reach 0.97 or even higher. 23

24 , the empirical results show that the dy ratio, the bm ratio and the ep ratio are highly persistent with the coefficient around 0.99 on the monthly basis. Lettau and Ludvigson (2001a) compare the predictive ability of the consumptionwealth ratio (cay), the dp ratio, the de ratio and the detrended short-term interest rate in forecasting excess market returns at horizons from quarterly to six years, and show that, at the six-year horizon, the predictability is largely contributed by the dp and de ratios. Kelly and Pruitt (2013) show that, base on a recent sample , the aggregate bm ratio only forecasts 0.71% of variations in future monthly market returns, however, at the one-year horizon, approximately 8.83% of expected market returns is predicted by the bm ratio. They observe similar findings in the forecasts from the dp ratio, the de ratio, the ep ratio and the net equity expansion ratio (ntis). Moreover, researchers link the stock market with other markets, such as the bond market and the exchange market. They find empirical evidence that the variables observed from these markets also show great predictive ability. For instance, the spread of long- and short-term bond yields (e.g., Campbell, 1987; Asness, 2003; Hodrick, 1992), the Treasury-bill rate (e.g.,fama and French, 1989; Chen, Roll, and Ross, 1986), the lagged value of changes in U.S. dollar exchange rate (e.g., Amihud, 1994; Bartov and Bohnar, 1994), the currency appreciation (e.g Obben, Pech, and Shakur, 2007) all show significant predictive impact on the stock market returns. Making modifications to predictors Some researchers argue that some predictors (e.g., the dp ratio) are noisy proxies for the expected returns and propose making modifications to improve the predictive ability by removing components unrelated to expected returns. For instance, according to the present-value relationship proposed in Campbell and Shiller (1988), the dp ratio is a linear function of both expected market returns and expected dividend growth, therefore, the variation in dp ratio may not be a clean estimate of expected returns. Fama and French (1988) observe that the dp ratio is a noisy proxy for expected returns given that the expected dividend growth is time-varying. Motivated by these considerations, Lacerda and Santa- Clara (2010) propose adjusting the dp ratio by taking account of the expected dividend growth which is estimated from a 10-year moving average value of dividend growth and provide evidence of the annual predictability is substantially 24

25 improved. Our chapter on adjusting the ratio cay is motivated by analogous arguments. Other studies, such as Binsbergen and Koijen (2010) consider the variations in expected dividend growth and employ a latent variable approach to extract the expected dividend growth and market returns from historical data; Golež (2014) estimates the expected dividend growth from variables related to the derivative market and finds improved predictability from the adjusted dp ratio; Rytchkov (2012) observes significant predictive impact of an adjusted dp ratio by applying the Kalman Filter to historical data to obtain a proxy for the expected dividend growth, are in line with? and show that there is space to improve predictability by altering existing predictors. Another example of modifying the existing predictor is Sousa (2010) which estimates a corrected version of the consumption-wealth ratio (cay) according to the cointegrating relationship between aggregate consumption, labor income and disaggregate wealth, and finds stronger ability to forecast stock market returns. The consumption-wealth ratio Apart from the highly persistent predictors, researchers find a handful of variables showing strong predictive power in forecasting market returns at the businesscycle frequency (Cochrane, 2005, p.390). For example, the variance risk premium, defined as the difference between the conditional variance of future returns and the realized variance, exhibits significant and strong predictive impact in the quarterly forecast (Bollerslev, Tauchen, and Zhou, 2009). The inflation (inf l) rate shows some predictive power (Campbell and Vuolteenaho, 2004) and is negatively related to the stock market returns (Fama, 1981). However, in recent studies, the predictive ability of inf l tends to vanish in monthly and annual forecast (Kelly and Pruitt, 2013). The ratio cay, which is estimated by Lettau and Ludvigson (2001a), has been well-known for the remarkable predictive performance in medium-horizon forecasts. 6 Building on the present-value relationship implied in Campbell and Mankiw (1989), Lettau and Ludvigson (2001a) show that the consumption-wealth ratio may be represented as a function of expected market returns and consumption growth. They argue that, regarding the expected consumption growth as constant, changes in consumption-wealth ratio are purely owing to variations in 6 Lettau and Ludvigson (2001a) report the first-order autocorrelation coefficient of cay is

26 expected market returns. Following this logic, the consumption-wealth ratio may be an appropriate predictor of the market returns. In empirical studies, Lettau and Ludvigson estimate the consumption-wealth ratio (cay) from the cointegrating relationship between aggregate consumption, asset holdings and labor income, and find statistical evidence that cay outperforms conventional valuation ratios in forecasting market returns at horizons up to one year. However, researchers cast doubt on the ability of cay in forecasting stock market returns out-of-sample. Brennan and Xia (2005) argue that the predictive ability of cay identified in insample forecast is purely due to the fact that the cointegrating coefficients of asset holdings and labor income are estimated from the entire sample, this means the estimation of cay suffers from look-ahead bias. The cay ratio estimated period by period almost loses the predictive power. Similar findings are also obtained by Welch and Goyal (2008). Moreover, the recent study by Bianchi, Lettau, and Ludvigson (2014) finds that the extent of persistence of cay ratio has increased over recent years, this makes the ratio a highly persistent variable and almost loses the strong predictive power in the quarterly prediction. 7 To solve this problem, they propose a markov-switching cay ratio by adjusting the unusual shifts and show that the markov-switching cay works as well as the original cay. Other paper related to cay include Julliard (2007) who emphasizes the importance of the labor income risk, which is measured as the expected returns of future income growth rate, in predicting quarterly market returns by testing the predictive power of the labor income risk jointly with cay. Sousa (2010) shows the limitation of ignoring the composition of aggregate wealth. By re-estimating the cay ratio from the cointegrating relationship between consumption, financial wealth, housing wealth and labor income, he finds that the modified cay ratio has stronger predictive power for quarterly market returns. In addition, due to the strong predictive ability, cay is also applied in tests of conditional version of the CAPM and the CCAPM (e.g., Lettau and Ludvigson, 2001b; Gao and Huang, 2008; Li and Zhong, 2005), the improved performance of these asset pricing models potentially shows that the cay ratio represents the time-varying investment opportunity in future. 7 Bianchi, Lettau, and Ludvigson (2014) show that, in quarterly forecast, the R 2 delivered by the predictive regression approximates to 2% based on a sample period of 1952 Q Q3 whereas the R 2 reported in Lettau and Ludvigson (2001a) reaches 9% based on a sample period of 1952 Q Q3. 26

27 Forecasting the consumption growth In general, the empirical findings on forecasting the consumption growth are mixed. On the one hand, the consumption growth is regarded as unpredictable or close to unpredictable. For example, Hall (1978) tests the permanent income hypothesis (PIH) which implies that the consumption growth follows a randomwalk by regressing the consumption growth on lagged values of consumption and income, the empirical findings suggest that these predictors fail to show significant predictive impact, and therefore, the consumption growth is believed to be unpredictable. Campbell (2003) points out that the consumption growth is poorly forecast by past consumption growth or stock market returns. Argyropoulos and Tzavalis (2015) test the term structure model on real consumption growth and provide evidence that is consistent with the PIH. Lettau and Ludvigson (2001a) find little evidence that the consumption growth is predicted by cay. Nevertheless, on the other hand, researchers argue that there is lack of evidence showing the consumption growth follows a random-walk or is unpredictable. Campbell and Mankiw (1989) argue that, some investors behave following the PIH that would only change consumption spending when the permanent income (expected income) varies whereas other investors would adjust the spending intertemporally according to changes in interest rate. This stands in contrast to the implication of PIH that the consumption growth follows a random-walk. However, there are few variables in existing literature have been identified as strong predictors of the consumption growth. Early studies show that the term structure exhibits significant predictive impact on consumption growth (e.g., Harvey, 1988; Estrella and Hardouvelis, 1991) whereas the identified predictive ability no longer exists in recent years (e.g., Argyropoulos and Tzavalis, 2015). The work by Parker and Julliard (2005) provides indirect evidence that the consumption varies in a predictable way. Possible reasons could be: i) error in consumption measurement; ii) high costs of adjustment; iii) the limitation of investors capacity for making use of all the available information. Accordingly, they define a different measure of risk, the ultimate consumption risk, as the covariance of asset returns with the consumption growth cumulated over following several quarters rather than the contemporaneous covariance, is similar to Dimson or Scholes-Williams betas. The model with the ultimate consumption risk shows greater ability in pricing the Fama-French 25 portfolios formed on size and bookto-market. The success indirectly supports the proposal that the consumption is 27

28 predictable. Moreover, some researchers focus on examining the predictive ability of surveybased indicators for future consumption growth, though the empirical evidence appears to be ambiguous. One possible reason is that different questions associated with the same concept may get different, or even contradictory, answers (see, for example, Ludvigson, 2004). Therefore, survey-based indicators may not be able to accurately represent consumers sentiment about current economy state (see, for example, Vosen and Schmidt, 2011). On the one hand, some researchers achieve success by using survey-based indicators to forecast future consumption growth. For instance, Bram and Ludvigson (1998) measure consumer confidence by two indices constructed on consumer attitudes surveys, the University of Michigan s Index of Consumer Sentiment and the Conference Board s Consumer Confidence Index, and find evidence that consumer confidence has some ability in explaining variations in expected consumption growth. In particular, the performance of the latter index is superior to the performance of the former index. 8 The following work by Ludvigson (2004) confirms the in-sample predictive ability of consumer confidence by using a longer testable sample, 1968Q1-2002Q4, however, the findings suggest that there is minor difference in the predictive performance of these two indices. Ludvigson argues that this may be due to the difference in testable sample: Bram and Ludvigson s sample ends in the third quarter of Moreover, the work seeks to understand the driving force of the predictive ability of consumer confidence, though not successful. Recent work by Dees and Brinca (2013) re-examines the predictive performance of consumer confidence using data from U.S. market and Euro area and privides empirical evidence confirming the predictive ability of consumer confidence. However, the in-sample predictive regression shows that the identified predictive ability appears to vanish when including fundamental indicators such as the past growth rates of wealth, stock returns, interest rates, unemployment rates and real oil prices. Interestingly, the out-of-sample analysis shows that consumer confidence performs well when the consumer confidence is highly volatile. Souleles (2004) focuses on household-level data of the University of Michigan s Index of Consumer Sentiment and provides statistical evidence that indicators of consumer sentiment do contain predictive information for consumption growth. Nevertheless, on the 8 Bram and Ludvigson (1998) conclude that the performance of specific index may be different without further explanations and leave this questions for future research. 28

29 other hand, some studies, including Croushore (2005) finds poor out-of-sample performance when using either of these two indices as the predictor; Vosen and Schmidt (2011) investigate the predictive performance of a search query-based data series obtained from Google Trends and find that this new variable outperforms the aforementioned two survey-based indices in-sample and out-of-sample, fail to observe good performance of survey-based predictors The predictor candidates related to the commodity market The commodity risk factor Despite the fact that researchers find extensive predictors of the market returns, few studies have been conducted to investigate variables related to the commodity market. Most of the previous studies focus on investigating the contemporaneous correlation between stock returns and commodity risk factors (e.g., Brooks et al., 2014; Baker and Routledge, 2015). In addition, the empirical evidence provided by these studies are primarily based on oil. Chen, Roll, and Ross (1986) examine the performance of asset pricing models including a number of macroeconomic variables and the price changes of an oil index which is regarded as a key risk factor. Hamilton (1983) focuses on the U.S. market and shows that variations in oil supply and changes in the oil price signal recessions after the World War II. Jones and Kaul (1996) provide international evidence stressing the key effect of oil price changes on economy. 9 Until recent years, the size of the literature on commodity risk tends to increase. Brooks et al. (2014) show that the commodity risk factor should matter for variations in expected returns as the consume of commodities is closely related to industrial production and households daily life. Boons, de Roon, and Szymanowska (2012) also point out that the manufacturers would hedge against the commodity price risk by investing in the futures market. Moreover, the researchers, no longer limit their studies to the oil product, investigate a wide range of commodities. Focus on the futures market, Brooks et al. (2014) evaluate the relationship between the commodity risk and cross-sectional asset returns, other studies including Baker and Routledge (2012), Hong and Yogo (2012), Bakshi, 9 Similar findings are also presented in recent work, such as Nandha and Faff (2008), Park and Ratti (2008). 29