Habit persistence, consumption based asset pricing, .Habit persistence, consumption based asset pricing,

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  • Habit persistence, consumption based asset pricing,and time-varying expected returns

    Stig Vinther MllerDepartment of Business Studies

    Aarhus School of Business, University of Aarhus

    September 2008

  • Table of contents

    Acknowledgements

    Summary

    Dansk resum (Danish summary)

    Chapter 1: An iterated GMM procedure for estimating the Campbell-Cochranehabit formation model, with an application to Danish stock and bond returns

    Chapter 2: Habit persistence: Explaining cross-sectional variation in returns andtime-varying expected returns

    Chapter 3: Habit formation, surplus consumption and return predictability: Inter-national evidence

    Chapter 4: Consumption growth and time-varying expected stock returns

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  • AcknowledgementsFirst and foremost, I would like to express my sincere gratitude to my thesis advisor

    Tom Engsted for providing guidance and numerous insightful comments and suggestionsthroughout my Ph.D. studies. Two of the chapters in this thesis are co-authored withTom Engsted, and I am grateful for having had the opportunity to work with him. Ialso thank Stuart Hyde who I worked with in the spring of 2007, while I was visitingManchester Business School on a Marie Curie Fellowship.

    During my Ph.D. studies, I enjoyed very much the friendly atmosphere at the De-partment of Business Studies, and I thank my colleagues for generating a pleasant andmotivating research environment. I also thank the Department of Business Studies forgenerous nancial support that gave me the opportunity to attend several courses, work-shops and conferences.

    I would also like to take this opportunity to thank the members of the assessmentcommittee Bjrn Hansson, Jesper Rangvid, and Esben Hg (chairman) for theiruseful and insightful suggestions.

    Last, but not least, a special thank you to my girlfriend Carina for your invaluablemoral support and much needed patience during the entire process of writing this thesis.

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  • SummaryWithin the consumption based asset pricing framework, the habit persistence model of

    Campbell and Cochrane (1999) model has become one of the leading models in explainingasset pricing behavior. Campbell and Cochrane show that their model explains a numberof stylized facts on the US stock market, including pro-cyclical stock prices, time-varyingcounter-cyclical expected returns on stocks, and it has the ability to explain the equitypremium puzzle without facing a risk-free rate puzzle. Campbell and Cochrane andsubsequent applications of their model only rely on calibration and simulation exercisesand do not engage in formal econometric estimation and testing of the model. Given thefact that the Campbell-Cochrane model seems to work so well in several dimensions, itis also of great relevance to estimate and test the model econometrically.

    In the rst chapter "An iterated GMM procedure for estimating the Campbell-Cochranehabit formation model, with an application to Danish stock and bond returns" (joint workwith Tom Engsted), we perform formal econometric estimation and testing of the modelusing Danish stock and bond returns. To our knowledge, there have been no formaleconometric studies of the Campbell-Cochrane model on data from other countries thanthe US. Our paper is the rst attempt to ll this gap. Denmark is interesting becausehistorically over a long period of time the average return on Danish stocks has not beennearly as high as in the US and most other countries, and at the same time the returnon Danish bonds has been somewhat higher than in other countries, see e.g. Engstedand Tanggaard (1999), Engsted (2002), and Dimson et al. (2002). Thus, the Danishequity premium is not nearly as high as in most other countries, and might not even beregarded a puzzle. The results we obtain using our GMM procedure on Danish assetmarket returns do not in general support the conclusions from the US studies. Althoughthere is some evidence of time-varying counter-cyclical risk aversion in recent years, theCampbell-Cochrane model does not produce lower pricing errors or more plausible para-meter values than the benchmark CRRA model.1

    The second chapter "Habit persistence: Explaining cross-sectional variation in re-turns and time-varying expected returns" estimates and tests the Campbell-Cochranemodel along both cross-sectional and time-series dimensions of the US stock market.The model is estimated in a cross-sectional setting using the 25 Fama and French valueand size portfolios, which has not been tried previously, cf. Cochrane (2007). The cross-sectional estimation documents that the model is able to explain the size premium, butfails to explain the value premium. Besides cross-sectional variation in returns, I examinewhether the model is able to account for variation in expected returns over time. Con-sistently with the model, I nd that low surplus consumption ratios in recession timespredict high future stock returns. Thus, the model captures time-varying counter-cyclicalexpected returns on stocks.2

    In the third chapter "Habit formation, surplus consumption and return predictability:International evidence" (joint work with Tom Engsted and Stuart Hyde), we present

    1The paper is forthcoming in the International Journal of Finance and Economics.2The paper has been invited for third resubmission to the Journal of Empirical Finance.

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  • further international evidence on the relative performance of the Campbell-Cochranemodel and the benchmark CRRA model. There seems to be quite large cross-countrydierences in the ability of the Campbell-Cochrane model to explain stock and bondreturn movements over time, but for the majority of the countries in our sample, themodel gets empirical support in a variety of dierent dimensions. The model generatescounter-cyclical time-varying relative risk aversion, and in contrast to the benchmarkCRRA model, the Campbell-Cochrane model has the important ability to escape therisk-free rate puzzle. Moreover, we nd that the surplus consumption ratio is a strongpredictive variable of future stock and bond returns. Since a common limitation toexisting predictive variables is that they only contain information about either futurestock returns or future bond returns, the ability of the surplus consumption ratio tocapture predictive patterns in both stock and bond markets is particularly interesting.

    The fourth chapter "Consumption growth and time-varying expected returns" exam-ines the ability of the consumption growth rate to predict future stock returns. Previousstudies show that the consumption growth rate has no predictive power for future stockreturns. However, I nd that the consumption growth rate based upon fourth quarterdata is a strong predictive variable of future stock returns. The fourth quarter con-sumption growth rate explains a substantial amount of the variation in 1-year aheadstock returns and is a better predictive variable than traditional benchmark predictivevariables such as the price-dividend ratio [Campbell and Shiller (1988) and Fama andFrench (1988, 1989)] and performs marginally better than new predictive variables suchas the consumption-wealth ratio [Lettau and Ludvigson (2001)] in predicting future stockreturns. Interestingly, when the consumption growth rate is measured based upon otherquarters, the predictive power breaks down. This striking evidence is consistent with theinsight of Jagannathan and Wang (2007) that investors tend to review their consumptionand investments plans during the end of each calendar year, and at possibly random timesin between. Importantly, the fourth quarter consumption growth rate is an almost i.i.d.process, which eliminates potential concerns about nding spurious evidence of returnpredictability, cf. Stambaugh (1999).3

    3The paper is published in Finance Research Letters, 2008 volume 5, pages 129-136.

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  • Dansk resum (Danish summary)Indenfor det forbrugsbaserede asset pricing framework er Campbell og Cochranes

    (1999) habit persistence model blevet en af de frende modeller i at forklare prisfastst-telsen p aktiver. Campbell og Cochrane viser, at deres model forklarer en rkke stilis-erede facts p det amerikanske aktiemarked inklusiv pro-cykliske aktiekurser, tidsvari-erende kontra-cykliske forventede afkast p aktier, og modellen har evnen til at forklareequity premium puzzlet uden at blive konfronteret med et risk-free rate puzzle. Camp-bell og Cochrane og efterflgende applikationer af deres model beror udelukkende pkalibrering og simulering og anvender ikke formel konometrisk estimering og testningaf modellen. Givet det faktum, at Campbell-Cochrane modellen synes at fungere sgodt i ere dimensioner, er det ogs af vsentlig relevans at estimere og teste modellenkonometrisk.

    I det frste kapitel "An iterated GMM procedure for estimating the Campbell-Cochranehabit formation model, with an application to Danish stock and bond returns" (flles ar-bejde med Tom Engsted) foretager vi formel konometrisk estimering og testning af mod-ellen ved brug af danske aktie- og obligationsafkast. Ud fra vores kendskab har der ikkevret formelle konometriske studier af Campbell-Cochrane modellen p data fra andrelande end USA. Vores artikel er det frste forsg p at udfylde dette hul i litteraturen.Danmark er interessant, fordi historisk set over en lang tidsperiode har det gennemsnitligeafkast p danske aktier ikke vret nrt s hjt som i USA og de este andre lande, ogsamtidigt har afkastet p danske obligationer vret noget hjere end i andre lande, seeksempelvis Engsted and Tanggaard (1999), Engsted (2002), og Dimson mf. (2002).Dermed er den danske risikoprmie ikke nr s hj som i de este andre lande og ansesmuligvis ikke engang for vrende et puzzle. De resultater vi opnr med vores GMM pro-cedure anvendt p danske aktie- og obligationsafkast sttter gen