HERDING BEHAVIOUR IN THE UNITED KINGDOM PENSION FUNDS. Abstract. The pension fund investment has a social importance in financial markets because

Transcription

1 HERDING BEHAVIOUR IN THE UNITED KINGDOM PENSION FUNDS Astrat. The pension fund investment has a soial importane in finanial markets eause represents an important fration of family savings. Therefore, the ehavior of pension fund managers may play an important role in market staility. This fat is partiularly relevant when managers tend to imitate eah others, eause phenomena suh as herding may appear and affet market effiieny. This paper studies the existene of herding in the UK equity pension funds with domesti and gloal investment voations. This analysis is arried out onsidering a less ommon methodology, the estimated ross-setional standard deviations of etas. Additionally, etas are estimated with state-spae models. We also examine the existene of herding towards the market and different style fators: size, ook-to-market and momentum. Our results provide evidene of herding towards the market and the style fators. With regard to style fators, this effet is higher towards the size fator, ut smaller towards the momentum fator. Keywords: herding, pension funds, state-spae models, United Kingdom 1

2 1. INTRODUCTION. Over reent years, the inreasing onern aout the future viaility of puli pensions has enhaned the investment in pension funds. The pension fund investment has a soial importane in finanial markets eause represents an important fration of family savings. Consequently, the ehavior of pension fund managers may affet market staility. This fat is partiularly relevant when managers tend to imitate eah others, appearing phenomena suh as herding. The herding phenomenon arises when investors deide to imitate the deisions of others partiipants in the market; that it is to say, they imitate market agents who are thought to e etter informed, rather than follow their own eliefs and information. It is generally aepted that herding an lead to a situation in whih market pries annot reflet all information; in this ase, the market eomes unstale and moves towards ineffiieny. For that reason, market regulators show an interest in reduing this type of phenomena. In this work we study the influene of pension fund managers on the existene of herding, eause as pension funds are managed professionally, managers are responsile for varying the omposition of pension fund portfolios, uying and selling diretly in the market. We analyze herding using oserved returns with state-spae models, as Christie and Huang (1995) and Hwang and Salmon (2004). We do not follow Lakonishok et al. (1992a) eause their measure presents several shortomings (Wylie, 2005; Walter and Weer, 2006; Bellando, 2012; or Frey et al., 2012) and needs detailed reords of individual trading ativities, whih are not availale in many ases. Additionally, we apply a less ommon methodology, ased on the ross-setional dispersion of market eta and oserving deviations from the equilirium expressed in CAPM pries. 2

3 Nonetheless, as this method suffers from some defiienies, as supposes stati market etas, we uild a time-varying distriution of the ross-setional dispersion of etas. Likewise, as etas do not take into aount outliers, we utilize the roust M-estimation to solve this prolem. Therefore, we study the existene of herding towards the market and several style fators (size, ook-to-market and momentum) in the UK equity pension funds with domesti and gloal investment voations. The rest of the paper is organized as follows. In the Setion 2 we undertake a literature review. Setion 3 presents the methodology. Setion 4 ompiles the data and the empirial results. Finally, the onlusions are drawn in Setion five. 2. LITERATURE REVIEW. Theoretial and empirial studies find a variety of auses for the herding phenomenon: imperfet information (Banerjee, 1992; Bikhhandani et al., 1992; Hirshleifer et al., 1994; Calvo and Mendoza, 2000; Avery and Zemsky, 1998; Chari and Kehoe, 2004; Gompers and Metrik, 2001; Pukett and Yan, 2007; Sahut et al., 2011), osts of reputation (Sharfstein and Stein, 1990; Trueman, 1994; Rajan, 1994; Maug and Naik, 1996), ompensation shemes (Roll, 1992; Brennan, 1993; Rajan, 1994; or Maug and Naik, 1996), and other fators suh as the degree of institutional partiipation, the spread of opinions, derivatives markets and their sophistiation, or uninformed investors (Patterson and Sharma, 2006; Demirer and Kutan, 2006; Henker et al., 2006; Pukett and Yan, 2007). Although these studies display several auses leading to herding ehavior, the study of this phenomenon in finanial markets has followed two lines of investigation. The first one analyzes the tendeny of individuals. Amongst them, we highlight the works of Lakonishok et al. (1992a), Grinlatt et al. (1995), Wermers (1999) and Uhida and Nakagawa (2007). 3

4 The seond trend fouses on market herding as a whole; that is to say, as a olletive ehavior of all partiipants uying or selling a ertain asset at the same time. The most representative studies within this line are those of Christie and Huang (1995), Chang et al. (2000), Hwang and Salmon (2004), Patterson and Sharma (2006) and Wang (2008). In this paper we fous on the seond approah, where studies display mixed evidene aout the existene of herding. Gleason et al. (2003) show asene of herding in European futures markets. However, Hwang and Salmon (2004) find herding in the Korean and Amerian markets. In addition, they learly oserve herding when markets are stale and investors are sure of the future market diretion. Finally, Hwang and Salmon onlude that finanial rises stimulate a return towards effiieny. Wang (2008) applies the state-spae model to several markets (developed and emerging) and onludes that herding in emerging markets is greater than in developed ones. On the other hand, Demirer et al. (2010) apply some models to the Taiwanese market and find strong evidene with the state spae model. Finally, Shapour et al. (2010) also disover suh evidene in the Tehran stok market, ut do not find evidene of herding when they study herding towards size and ook-to-market fators. With regard to studies of herding on pension funds, we oserve different analyses. Voronkova and Bohl (2005) do not detet an influene of Polish pension funds on the stok market. Jame (2011) examines the magnitude and effet of herding on pension fund pries in the United States. This author applies the measure proposed y Lakonishok, Shleifer and Vishny (1992) and onfirms that pension funds are involved in the development of herding. Given the small numer of studies that analyze this topi on pension funds and, as far as we are aware, there are not pension fund studies ased on state-spae methodology, this paper ontriutes to the finanial literature trying to fill this gap. 4

5 3. METHODOLOGY. We apply the methodology ased on the work of Christie and Huang (1995). Nonetheless, as this suffers from several prolems, we also fous on the work of Hwang and Salmon (2004), whih alulates herding using a single-fator model. In partiular, this method is ased on the market returns from the CAPM model and uses the etas dispersion of all market stoks. In this way, when herding exists, the ross-setional variane of the estimated etas will derease, and investors follow the onsensus of all market partiipants CAPM AND HERDING. Herding leads to mispriing, so rational deisions may e distured through the use of iased eliefs and expeted returns or risks. More speifially, in the CAPM model, herding produes iased etas and they deviate from equilirium. In order to oserve empirially how this phenomenon affets the etas, we take as starting point the CAPM model in equilirium: Where: r it and r E r ) = β E ( r ) (1) t ( it i t are the exess return of fund i and the exess market return over the risk-free asset during the period t, respetively; β i is the systemati risk measure; and Et (.) is the onditional expetation at time t in order to assess the fund i. Hwang and Salmon (2004) show etas do not hange over time in equilirium; whih means that the variation of etas an e interpreted as ehavioral anomalies, suh as herding. When there is herding in the market portfolio, the CAPM equilirium does not our, and oth eta and expeted return are iased. Therefore, instead of the equilirium shown in (1), Hwang and Salmon (2004) assume that the following relation is produed in presene of herding towards the market: 5

6 Et ( r E ( r t it ) = β ) i = β i - h ( β i -1) (2) Where: E r ) is the market s iased short run onditional expetation on the exess t ( it returns of fund i; β i is the market eta at time t in presene of herding; h is a latent herding parameter that hanges over time, less than one ( h 1) and onditional on market fundamentals. When h = 0, then β i = βi, and herding does not exist, produing the CAPM equilirium. However, when h = 1, then β = 1, so it is perfet herding towards the market i portfolio eause all funds move in the same diretion and magnitude as the market portfolio. In general, when the herding parameter ( h ) is etween zero and one ( < h < 1), a ertain degree of herding exists in the market, and it is determined y the 0 magnitude of the herding oeffiient. Considering the situation desried in the previous setion, the relationship etween the real and iased expeted exess fund returns and its eta an e explained. Therefore, for a fund with β i >1, then E r ( rit ) > Et ( r ), presenting herding towards the market, so E r ) moves towards E r ), and E r ) > E ( r ) > E ( r ) ; that is to say, t ( it t ( r ( it t it t investors follow the market more than they should in equilirium, and they ignore the equilirium relation, trying to math the individual asset returns with the market return As a result, the fund seems less risky than it should e, suggesting that β < β. i i On the other hand, for a fund with β < 1, it gives E r ) < E ( r ) and the fund i r ( it t presents herding towards the market when E r ) moves towards E r ) t ( it t ( eause E r ) < E ( r ) < E ( r ). Therefore, a fund seems riskier than it should e, suggesting r ( it t it t 6

7 that β > β. Finally, for a fund with a eta equal to one ( β = 1), the fund is neutral to i i i herding. Nonetheless, we an also oserve adverse herding, whih appears when high etas (larger than one) eome higher, and low etas (smaller than one) eome lower. This leads to a reversion in the long-term equilirium of β i, produing a systemati adjustment ak to the CAPM equilirium. In this ase, h <0; therefore, for a fund with β > 1, we oserve E r ) > E ( r ) > E ( r ) ; whilst a fund with β < 1 will produe the following situation: t ( it r it t E r ) < E ( r ) < E ( r ). t ( it r it t i i 3.2. HERDING MODELS. The herding of a market portfolio an e aptured with the parameter h of the expression (2); however, neither the eta nor the herding parameters are oserved. To solve this prolem, we use state-spae models whih allow us to extrat these parameters. Moreover, as we aim to measure herding in terms of the market as a whole, we assume equation (2) aptures all market assets, and we an alulate herding using all assets and not only one, eliminating the effets of the idiosynrati movements of individual etas. Sine the ross-setional mean of etas ( β i or β i ) is always one, Hwang and Salmon (2004) demonstrate: Std ( β i ) = E (( β i - h ( β i -1) 2 1) ) = E (( β i )(1- h 2-1) )(1- h ) = Std ( β i ) (3) Where: ( E C ) represents the ross-setional expetation; Std ( β i ) is the ross- 2 setional standard deviation of the eta in equilirium, and E (( β - h ( β -1) -1) ) is a diret funtion of the herding parameter. i i 7

8 In order to minimize the impat of the idiosynrati hanges in β i, a great numer of funds are used in the alulation of Std β ), so Std β ) will e stohasti in order to ( i oserve the movements in the equilirium eta. ( i Nonetheless, as it is expeted that the market as a whole does not hange signifiantly in the short-term, unless the struture of ompanies hanges suddenly, it is assumed that Std β ) does not exhiit any systemati movement, and the hanges of Std ( ) in the ( i β i short-term are due to the hanges in h ; that is to say, due to the presene of herding THE STATE-SPACE MODELS. In the previous setion we remark that the herding parameter is not oserved, so we apply state-spae models. These models an e estimated y using the Kalman filter. In order to extrat herding from model (3), we follow the proedure applied y Hwang and Salmon (2004). In first plae, taking logarithms of equation (3), we otain: i i Considering the assumptions arried out for Std β ), expression (4) is re-written: ( i log[ Std ( β )] = μ + υ (5) i m 2 Where: μ E[log[ Std ( β )]] and υ ~ iid(0, ), then: m = i σ mυ log[ Std ( β )] = μ + H + υ (6) i m log[ Std ( β )] = log[ Std ( β )] + log(1- h ) (4) Where: H log(1- h ). = Therefore, supposing herding ( H for example, assuming a mean zero AR(1), we otain model (7): ) evolves over time and follows a dynami proess; log[ Std ( β H = φ m H i )] = μ 1 + η m + H + υ (7) 8

9 2 Where: η ~ iid(0, ). σ mη As a result, we have a standard state-spae model, similar to those used in stohasti volatility modeling, whih are estimated using the Kalman filter. Furthermore, as we are interested in studying the existene of herding, we fous on the movements of the latent variale ( H ). 2 In addition, it should e oserved that when σ = 0, the model (7) eomes: mη log[ Std ( β )] = μ + υ (8) i m This means that herding does not exist; so H = 0 for all t. A signifiant value of σ 2 mη an e interpreted as herding existene, and a signifiant value of φ supports the autoregressive struture onsidered. One restrition is the herding proess ( H ) should e stationary, and as we do not expet herding towards the market portfolio to e an explosive proess, it requires: φ m HERDING CONSIDERING ADDITIONAL VARIABLES. We explain aove that Std ( ) β i hanges over time depending on the herding level in the market. However, it is interesting to study whether this ehavior, extrated from Std ( β i ), is roust in presene of variales that reflet the state of the market: degree of volatility, market returns, or variales that reflet maroeonomi fundamentals. Therefore, if the herding parameter eomes insignifiant when these variales are inluded, the hanges in Std ( ) ould e explained y hanges in the fundamentals rather β i than herding. In order to onsider the influene of market volatility and market return, Hwang and Salmon (2004) inlude them as independent variales in model (7), otaining model (9): 9

10 log[ Std ( βi )] = μm + H + m 1 logσ + m2r + υ (9) H + η = φmh 1 Where: at time t, respetively. log σ and r are the logarithm of the market volatility and the market return In a seond step, Hwang and Salmon (2004) inlude the fators of the Fama and Frenh model (1993) in model (9). Nevertheless, we also inlude the four fators of the Carhart (1997) model, onsidering the size (SMB), ook-to-market (HLM) and momentum (PR1YR) fators: log[ Std ( i )] µ m + H + m 1 logσ + m2r + m3smbt + m2hmlt + m3 β = PR1YR + υ H = φ H 1 + η (10) m Lastly, we add three maroeonomi variales in the model (9): dividend yield (DY), time spread (TS) and short-term interest rate (STIR), in order to onsider information variales representative of the eonomi yle: log[ ( βi )] = μm + H + m 1 logσ + m2r + m6dyt + m7tst + m8 Std STIR + υ t H = φ H 1 + η (11) m 3.5. GENERALIZED HERDING MEASUREMENT IN LINEAR FACTOR MODELS. In the previous setion we oserve herding an e measured in any fator, employing linear fator models. Therefore, supposing the exess returns of the fund i (r it ) follow this linear model: r it = α it K + β f + ε, k =1 ikt kt it i=1,,n y t=1,,t (12) Where: α it is an interept that hanges over time; β ikt are the oeffiients on fator k at time t; f kt is the realized value of fator k at time t, and ε it is mean zero with variane σ 2 ε. 10

11 The supersript on the etas indiates that the etas are iased under herding; therefore, the herding towards the fator k at time t an e aptured y (13): β β - h ( β - E [ β ]) (13) ikt = ikt kt ikt ikt Where: E [ β ikt ] is the ross-setional expeted eta for fator k at time t. In partiular, we ase our final analysis on two models: the CAPM model, olleted in expression (14), and the four-fator Carhart model, aptured y (15): r = α + β r + ε (14) it it i it r = α + β r + β r + β SMB + β HML + β PR1YR + ε (15) it it i i ist t iht Ht ipt Mt it With these etas we otain the estimated ross-setional standard deviation of the etas, and these are used in the state-spae model ROBUST ESTIMATE OF THE BETAS. Although the ordinary least squares (OLS) estimation is the most ommon tehnique to estimate etas, it has some drawaks. Firstly, it ehaves adly when errors are not from a normal i.i.d. distriution, partiularly when data is heavily-tailed, very frequent in return data. Furthermore, the existene of outliers may also influene the OLS eta, leading to a distorted perspetive on the relationship etween fund returns and index returns. In order to overome these disadvantages, and provide a etter fit, a roust estimation of eta should e implemented, as Martín and Simin (2002) indiate. One roust regression is the M-estimation method, whih may e implemented with the roust Huer tehnique. After estimating etas roustly, we otain the ross-setional standard deviation of the etas on the market portfolio as: ^ Std ( βˆ i ) = Nt i=1 ( ˆ ˆ ) β i N - β t i 2 (16) 11

12 Where: β ˆ i = 1 N t N t βˆ i=1 i, and N t is the numer of funds in the month t. and (11). Finally, we estimate the four state-spae models presented in the models (7), (9), (10) 4. DATA AND EMPIRICAL RESULTS DATA. The dataase was provided y Thomson Reuters. The data omprises the monthly returns otained y all private pension funds with domesti and gloal equity investment voations registered for sale in the United Kingdom. We possess 2440 pension funds with domesti equity voation and 1571 pension funds with gloal equity investment voation. The time period of analysis is from January 1999 to Septemer We require pension funds present data for at least 24 months to ensure the onsisteny of the analyses. In this way, our dataase is free of the so-alled survivorship ias. The market enhmark used are the MSCI-United Kingdom and MSCI-World indexes, given the domesti and gloal equity voations of the pension funds studied. The representative variales for the risk-free asset are the 1-month Lior rate for domesti equity funds and the 1-month Eurior rate for gloal equity pension funds. The three maroeonomi variales onsidered are onstruted as we desrie: Dividend yield 1 is the ratio etween the dividends paid out y the MSCI index (MSCI- World or MSCI-UK) in the previous twelve months and the urrent index prie. Time spread is the annualized differene etween the return on the British 10 year det 2 ond and the three-month Lior for domesti funds, or the annualized differene etween the EMU 10-year ond 3 and Eurior rate for the gloal funds. 1 For its alulation we apply the differene etween the monthly return otained y the orresponding MSCI Gross and the MSCI Prie; then we otain the total of the twelve previous values for a determined month. Information otained from MSCI: 12

13 Short-term interest rate is the 3-month Lior or the 3-month Eurior rates for domesti and gloal equity pension funds, respetively. In the investment style analysis we onsider the four fators of the Carhart model: exess market return, size (SMB), ook-to-market (HML) and momentum (PR1YR). We follow the instrutions y Fama and Frenh (1993) to uild the size and ook-tomarket fators. We use the monthly returns otained y the indies MSCI-UK and MSCI- World for the domesti and gloal pension funds, respetively, as we explain elow. In regard to the size fator (SMB t ), we uild the mimiking portfolio as the differene etween the portfolio made up of the MSCI small value prie, the MSCI small ore prie and MSCI small growth prie indies, and the portfolio made up of the MSCI large value prie, the MSCI large ore prie and the MSCI large growth prie indies. In relation with the ook-to-market fator (HML ), the mimiking portfolio is the differene etween the portfolio made up of the MSCI small value prie and MSCI large value prie indies, and the portfolio made up of the MSCI small growth prie and MSCI large growth prie indies. Finally, the one-year momentum fator (PR1YR ) has een approahed aording to the instrutions of Carhart (1997): the equal-weight average of indies with the highest 30% eleven-month returns, lagged one month, minus the equal-weight average of indies with the lowest 30% eleven-month returns, lagged one month. As a onsequene, we use monthly returns of the market indies representative of eah geographi universe studied: In the ase of the gloal pension funds, we use the 23 MSCI indies that omprise the MCSI-World index; orresponding to the following markets: Australia, Austria, Belgium, Canada, Denmark, Finland, Frane, Germany, Greee, Hong Kong, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the t t 2 Data otained from the Bank of England: 3 Data otained from the Bank of Spain: 13

14 United Kingdom and the United States. All of indies have een otained from the offiial MSCI wesite. In the ase of domesti funds, we selet the firms of the FTSE 100 index (the most signifiant referene index in the United Kingdom), omprising the 100 largest ompanies in the ountry, and representing approximately the 81% of the market. Tale 1 is divided into two panels and displays the desriptive statistis of the risk fators used for domesti and gloal pension funds, respetively. INSERT TABLE 1 The results of tale 1 reveal the exess market return is the fator with least return, on average, presenting negative values on oth panels. The minimum values are oserved in the exess market return of gloal pension funds and in the momentum fator of domesti funds. Moreover, the maximum values are in the ook-to-market and momentum fators of domesti funds and in the momentum fator of gloal pension funds. With respet to kurtosis, this is important in all fators (greater than three); indiating leptokurtosis. Furthermore, it is also remarkale the negative skewness on all fators, exept on the ook-to-market fator alulated for domesti pension funds EMPIRICAL RESULTS. In order to apply the herding models, we must first take several steps. In the first plae we estimate the etas of models (14) and (15), and then alulate the ross-setional deviations, as setion 3.6 desries. The main harateristis of the standard deviations of the estimated etas are refleted in tale 2. INSERT TABLE 2 This tale is divided into two panels (A and B), refleting the market etas alulated for domesti and gloal equity pension funds. Additionally, these panels differentiate etween 14

15 the market etas from the CAPM model and the etas from the four-fator Carhart model. All of them are estimated with the Huer roust tehnique. The first two olumns of oth panels show the ross-setional standard deviations of the market etas, whih are signifiantly different from zero in all ases. However, the market etas from the CAPM model present negative skewness, whilst the skewness is positive in the market etas from the four-fator model, whih is ommon in series with volatility. We also oserve a high kurtosis, revealing non-normality. These patterns are onfirmed with the Jarque-Bera test, whih rejets the null hypothesis of normality; therefore, the standard deviation of etas is not Gaussian. The orrelation etween the two market etas is high; susequently, if there is herding, this may reveal similar herding etween models. Respet to the ross-setional deviations of the etas for the SMB, HML and PR1YR fators, they also exhiit similar harateristis: non-normality, high kurtosis and negative skewness, although the HML etas of gloal funds have positive skewness RESULTS OF HERDING TOWARDS THE MARKET FACTOR. In this setion we estimate models (7), (9), (10) and (11) with the ross-setional deviations of the market etas [ Std ( ) ] from the CAPM model and from the four-fator β i model, estimated in the prior setion. The results of these models are displayed on tale 3. This tale is divided into two panels. Panel A shows the results for domesti equity funds and panel B for gloal equity pension funds. INSERT TABLE 3 We interpret the signifiane of the market variales inluded in the models (9), (10) and (11) as adjusting the mean level ( µ ) of log[ Std ( )] in the measurement equation not m β i herding ativity, so we examine the degree of herding given the state of the market. 15

16 Panel A shows the results of domesti equity pension funds. These results show evidene of quite persistent herding, as the φˆ m oeffiient is large and signifiant in the different models studied. Likewise, the standard deviations of η ( σ mη ) are signifiant, although this oeffiient is not signifiant in model (10). As a onsequene, given the level of market volatility and market return, the UK domesti equity pension funds lead, in general, to herding towards the market portfolio. Moreover, the oeffiients of model (9) show the term H is still signifiant when the two market variales (volatility and return) are inluded, suggesting hanges in the volatility of the sensitivity fator [ Std ( β i ) ] an e explained y herding, rather than y hanges in fundamentals. Therefore, the deviation of the etas dereases when market volatility rises, ut inreases with the level of market return, as the logarithm of the market volatility and the market return have signifiantly negative and positive oeffiients, respetively. As a result, when the market eomes riskier and is falling, Std ( ) dereases, while β i this deviation inreases when the market eomes less risky and rises. Therefore, a redution in the standard deviation, due to the herding proess, suggests that herd ehavior is signifiant and exists independently of a partiular state of the market. The model (10) inludes the SMB, HML and PR1YR fators as explanatory variales, ut their oeffiients are not signifiant; so this model does not supply additional information. The model (11) inludes three maroeonomi variales, ut none of them are signifiantly different to zero. Nonetheless, the herding is still persistent, eause the oeffiient φˆ m is still signifiant, refleting hanges in the etas deviations are explained y herding. 16

17 Panel B of tale 3 displays the results of gloal equity funds, presenting also persistent herding on the different models, although the oeffiients are higher than in panel A. Moreover, all standard deviation oeffiients of η ( σ mη ) are signifiant and all market variales are signifiant, eing negative the logarithm of market volatility and positive the market return, so the etas deviation dereases when the market volatility rises, ut inreases with the level of market return. With respet to model (10), the SMB, HML and PR1YR fators are not signifiant. Equally, in model (11), the maroeonomi variales are not signifiant. Therefore, herding is not influened y the size ompany, the relation etween ook equity and market equity, or the momentum strategy. However, herding varies with the model applied; speifially, we find more evidene of herding in the model with market variales for domesti funds ut, in the ase of gloal funds, the herding evidene is greater in the model with information variales. As onsequene, we oserve that the inlusion of additional variales is useful, ut does not provide additional information RESULTS OF HERDING TOWARDS SIZE, BOOK-TO-MARKET AND MOMENTUM FACTORS. To examine the existene of herding towards size, ook-to-market and momentum fators, we use the estimated etas of size ( Std ( β ) ), ook-to-market ( Std ( ) ) and ( β ipr 1YRt momentum ( Std ) ) fators of model (15), and repeat the prior analysis. Tale 4 displays the results of the herding towards the size fator. ist INSERT TABLE 4 β iht This tale is divided into two panels (A and B) and shows the results of domesti and gloal equity pension funds, respetively. We oserve the same ehavior in oth panels: existene of herding towards all fators, and even greater than in tale 3. Likewise, all standard deviations ( σ Sη ) are highly signifiant 17

18 and persistent. The market variales are signifiant: the volatility is negative and the return is positive; although, in the models (10) and (11) of the panel A, the return is signifiantly negative, whih means herding inreases when market return and market volatility derease. With regard to style fators (size, ook-to-market and momentum) and the maroeonomi variales, none of these variales is signifiant. The results of herding towards the ook-to-market fator are shown in tale 5, whih is divided into two panels, olleting the results of domesti (panel A) and gloal (panel B) pension funds. INSERT TABLE 5 We also notie the presene of herding towards the ook-to-market in oth panels, although the parameter on average). φˆ H is greater in domesti funds (0.95 in panel A and 0.7 in panel B, We notie the logarithm of market volatility and market return in model (10), for domesti funds, and in model (11), for gloal funds, present ontrary signs to prior results; that is to say, positive and negative, respetively. Nevertheless, these results are onsistent with previous studies, where herding arises most likely during market instaility; namely, periods of high volatility. Moreover, in model (11) of panel A and in models (9) and (10) of panel B, these oeffiients are oth positive, so herding arises when the market volatility and the market return inrease. Additionally, the style fators (size, ook-to-market and momentum) and the maroeonomi variales are not signifiant in oth panels. Finally, tale 6 presents the analysis of herding towards the momentum fator and is divided into two panels. Panel A shows the results of domesti pension funds and Panel B displays the results of gloal pension funds. INSERT TABLE 6 18

19 parameter average). Both panels show presene of herding towards the ook-to-market, although the φˆ H is greater in domesti pension funds (0.95 in panel A and 0.67 in panel B, on One more, style fators and maroeonomi variales are not signifiant in the different models. Moreover, the logarithm of market volatility and the market return present signifiant negative oeffiients in model (11) for domesti funds, indiating herding arises with the derease in the market volatility and market return. Additionally, in model (10) and model (9) this latter only for gloal funds-, these oeffiients are oth signifiantly positive. Therefore, it is lear the existene of herding, ut its relation with the market volatility and market return depends on the model applied and the pension fund studied. As a onsequene, we detet herding towards the three styles (size, ook-to-market and momentum), although with different intensity, eing the highest towards the size fator, and the lowest towards the momentum fator. 5. CONCLUSIONS. The herding arises when investors deide to imitate the oserved deisions of others, instead of following their own eliefs and information. This phenomenon an lead to a situation in whih market pries do not reflet all of the information, and the market moves towards ineffiieny. In this paper we analyze whether the managers ehavior of the UK equity pension funds with domesti and gloal equity voations arises herding. For this purpose, we apply a less ommon methodology, ased on oserved returns; instead of reords of individual trading ativities, whih are not availale in many ases. Speifially, we estimate the ross-setional standard deviations of etas. The estimation tehnique is also innovative, eause we apply state-spae models, using the Kalman filter. 19

20 Furthermore, in order to arry out roust eta estimations, we implement the roust M- estimation with the Huer estimator. We study the existene of herding towards different fators: market, size, ook-tomarket and momentum. Moreover, we apply different models to detet the existene and persistene of the phenomenon onsidering market variales, style fators and maroeonomi variales. The results otained are similar in all analyses. We find herding towards the market and the style fators, showing signifiant movements and persistene independently from and given market onditions. Nonetheless, this effet is smaller in the ase of herding towards the momentum fator, and higher towards the size fator. Additionally, maroeonomi and style variales do not affet herding. In onlusion, we prove the existene of UK pension fund herding, and the influene of pension fund managers on market effiieny. This finding may e primarily attriuted to the high market onentration in the pension fund industry (Voronkova and Bohl, 2005), eause in this senario, the imitation etween agents inreases and emphasizes herding. 20

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25 Tale 1. Properties of the risk fators. Panel A: UK pension funds with domesti equity investment voation Variale Average Standard deviation Minimum Maximum Kurtosis Skewness Market exess return SMB HML PR1YR Panel B: UK pension funds with gloal equity investment voation Variale Average Standard deviation Minimum Maximum Kurtosis Skewness Market exess return SMB HML PR1YR Tale 1 inludes the main statistis (average, standard deviation, minimum, maximum, kurtosis and skewness) for the four risk fators alulated to analyze eah type of pension fund: market exess return, size (SMB), ook-to-market (HML) and momentum (PR1YR). The tale is divided into two panels, panel A ollets the statistis of the fators used for the UK domesti equity pension funds, and panel B ollets the statistis of the fators for the UK gloal equity pension funds. 25

26 Tale 2. Properties of the ross-setional standard deviation of the estimated etas on eah type of pension fund. Panel A: Domesti equity pension funds CAPM model Market return eta (A) Market return eta (B) Four fator Carhart (1997) model Beta of Beta of SMB fator HML fator Beta of PR1YR fator Average Standard deviation Minimum Maximum Kurtosis Skewness Jarque-Bera test (p-value) (0.0000)*** (0.0000)*** (0.0000)*** (0.0000)*** (0.0000)*** Correlation A-B Panel B: Gloal equity pension funds CAPM model Market return eta (A) Market return eta (B) Four fator Carhart (1997) model Beta of Beta of SMB fator HML fator Beta of PR1YR fator Average Standard deviation Minimum Maximum Kurtosis Skewness Jarque-Bera test (p-value) (0.0000)*** (0.0000)*** (0.0000)*** (0.0000)*** (0.0000)*** Correlation A-B Tale 2 is divided into two panels (A and B), orresponding to the UK domesti and gloal equity pension funds, respetively. Eah panel inludes the main statistis (average, standard deviation, minimum, maximum, kurtosis, skewness and Jarque-Bera normality test) of the ross-setional standard deviation for the estimated market etas in the CAPM model, and for the etas of the Carhart model; speifially, market, size (SMB), ook-to-market (HML) and momentum (PR1YR) etas. *** Represents signifiane at 1% level 26

27 Tale 3: Estimates of the state-spae models for herding towards the market fator in the United Kingdom. Panel A. Herding in domesti equity pension funds. Model (7), alulated with the market return eta of the CAPM model Model (7), no exogenous variales Herding models with the market return eta of the four-fator Carhart (1997) model Model (10), Model (9), with the with the fators: exess fators: exess market market return, volatility, return and volatility SMB, HML and PR1YR Model (11), with the fators: exess market return, volatility, DY, TS and STIR µ (0.098)* (0.090)* (0.161) (0.106) (0.183) φm (0.000)*** (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ m υ (0.090)* (0.082)* (0.050)* (0.000)*** (0.000)*** σ m η (0.000)*** (0.000)*** (0.000)*** (0.125) (0.000)*** logσ (0.001)*** (0.127) (0.040)** r (0.069)* (0.090)* (0.054)* SMB (0.372) HML (0.135) PR1YR (0.267) DY (0.192) TS (0.101) STIR (0.325) 27

28 Panel B. Herding in gloal equity pension funds. Model (7), alulated with the market return eta of the CAPM model Model (7), no exogenous variales Herding models with the market return eta of the four fator Carhart (1997) model Model (10), Model (9), with the with the fators: exess fators: exess market market return, volatility, return and volatility SMB, HML and PR1YR Model (11), with the fators: exess market return, volatility, DY, TS and STIR µ (0.298) 0.964(0.912) (0.169) (0.179) (0.133) φm (0.000)*** (0.000)*** 0.908(0.000)*** 0.971(0.000)*** 0.998(0.000)*** σ m υ (0.000)*** (0.000)*** (0.079)* (0.09)* (0.046)** σ m η (0.000)*** (0.005)*** (0.000)*** (0.000)*** (0.000)*** logσ (0.000)*** (0.000)*** (0.05)** r (0.009)*** (0.000)*** (0.000)*** SMB (0.110) HML (0.280) PR1YR (0.219) DY (0.191) TS (0.219) STIR (0.172) Tale 3 displays the estimates of the state-spae models for herding towards the market fator in the UK pension funds with domesti equity investment voation (Panel A) and with gloal equity investment voation (Panel B) from January 1999 to Septemer Eah panel shows the results of the different estimated models. The first olumn exhiits model (7) results, alulated with the market return eta from the CAPM model. The seond, third, fourth and fifth olumns show the results of models (7), (9), (10) and (11), estimated with the market return eta from the four-fator Carhart (1997) model. SMB represents the size fator, HML is the ook-to-market fator, PR1YR is the momentum fator, DY is the dividend yield, TS is the time spread and STIR is the short term interest rate. *,**,*** represent signifiane at 10%, 5% and 1% level, respetively. 28

29 Tale 4: Estimates of the state-spae models for herding towards the size fator. Model (7), no exogenous variales Panel A. Herding in domesti equity pension funds. Herding models with the size eta of the four fator Carhart (1997) model Model (10), Model (9), with the with the fators: exess fators: exess market market return, volatility, return and volatility SMB, HML and PR1YR Model (11), with the fators: exess market return, volatility, DY, TS and STIR µ (0.100) (0.101) (0.112) (0.109) φ S (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ S ν (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ S η (0.000)*** (0.000)*** (0.000)*** (0.000)*** logσ (0.000)*** (0.000)*** (0.000)*** r (0.000)*** (0.430)* (0.107)* SMB (0.158) HML (0.197) PR1YR (0.136) DY (0.175) TS (0.139) STIR (0.173) Model (7), no exogenous variales Panel B. Herding in gloal equity pension funds. Herding models with the size eta of the four fator Carhart (1997) model Model (10), Model (9), with the with the fators: exess fators: exess market market return, volatility, return and volatility SMB, HML and PR1YR Model (11), with the fators: exess market return, volatility, DY, TS and STIR µ (0.115) (0.152) (0.150) (0.105) φ S (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ S ν (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ S η (0.000)*** (0.000)*** (0.000)*** (0.000)*** logσ (0.000)*** (0.000)*** (0.000)*** r (0.204) (0.000)*** (0.000)*** SMB (0.214) HML (0.216) PR1YR (0.198) DY (0.216) TS (0.110) STIR (0.108) Tale 4 displays the estimates of the state-spae models for herding towards the size fator in the UK pension funds with domesti equity voation (Panel A) and gloal equity voation (Panel B) from January 1999 to Septemer The models are alulated with the eta of the size fator from the four-fator Carhart (1997) model. The first, seond, third and fourth olumns show the results of models (7), (9), (10) and (11). SMB represents the size fator, HML is the ook-to-market fator, PR1YR is the momentum fator, DY is the dividend yield, TS is the time spread and STIR is the short term interest rate. *,**,*** represent signifiane at 10%, 5% and 1% level, respetively. 29

30 Tale 5: Estimates of the state-spae models for herding towards the ook-to-market fator. Panel A. Herding in domesti equity pension funds. Herding models with the ook-to-market eta of the four fator Carhart (1997) model Model (10), Model (11), with the Model (9), with the Model (7), with the fators: exess fators: exess market fators: exess market no exogenous market return, volatility, return, volatility, DY, TS return and volatility variales SMB, HML and PR1YR and STIR µ (0.125) (0.119) (0.127) (0.146) φ H (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ H ν (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ H η (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ log (0.000)*** (0.000)*** (0.000)*** r (0.120) (0.000)*** (0.000)*** SMB (0.210) HML (0.206) PR1YR (0.193) DY (0.402) TS (0.142) STIR (0.156) Panel B. Herding in gloal equity pension funds. Herding models with the ook-to-market eta of the four fator Carhart (1997) model Model (7), no exogenous Model (9), with the fators: exess market return and Model (10), with the fators: exess market return, volatility, Model (11), with the fators: exess market return, volatility, DY, TS µ variales volatility SMB, HML and PR1YR and STIR (0.108) (0.123) (0.142) (0.186) φ H (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ H ν (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ H η (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ log (0.000)*** (0.000)*** (0.000)*** r (0.089)* (0.120) (0.000)*** SMB (0.137) HML (0.140) PR1YR (0.159) DY (0.173) TS (0.142) STIR (0.157) Tale 5 displays the estimates of the state-spae models for herding towards the ook-to-market fator in the UK pension funds with domesti (Panel A) and gloal (Panel B) equity investment voations from January 1999 to Septemer 2010, alulated with the eta of the ook-to-market fator from the four-fator Carhart (1997) model. The first, seond, third and fourth olumns show the results of models (7), (9), (10) and (11). SMB represents the size fator, HML is the ook-to-market fator, PR1YR is the momentum fator, DY is the dividend yield, TS is the time spread and STIR is the short term interest rate. *,**,*** represent signifiane at 10%, 5% and 1% level, respetively. 30

31 Tale 6: Estimates of the state-spae models for herding towards the momentum fator. Panel A. Herding in pension funds with domesti equity voation. Model (7), no exogenous variales Herding models with the momentum eta of the four fator Carhart (1997) model Model (10), Model (9), with the with the fators: exess fators: exess market market return, volatility, return and volatility SMB, HML and PR1YR Model (11), with the fators: exess market return, volatility, DY, TS and STIR µ (0.264) (0.234) (0.465) (0.136) φ PR1YR (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ PR1 YRν (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ PR1 YRη σ (0.000)*** (0.000)*** (0.000)*** (0.000)*** log (0.000)*** (0.000)*** (0.000)*** r (0.000)*** (0.045)** (0.055)* SMB (0.132) HML (0.451) PR1YR (0.245) DY (0.115) TS (0.135) STIR (0.169) Panel B. Herding in pension funds with gloal equity voation. Herding models with the momentum eta of the four fator Carhart (1997) model Model (10), Model (9), with the with the fators: exess fators: exess market market return, volatility, return and volatility SMB, HML and PR1YR Model (7), no exogenous variales Model (11), with the fators: exess market return, volatility, DY, TS and STIR µ (0.123) (0.116) (0.146) (0.141) φ PR1YR (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ PR1 YRν (0.000)*** (0.000)*** (0.000)*** (0.000)*** σ PR1 YRη σ (0.000)*** (0.000)*** (0.000)*** (0.000)*** log (0.000)*** (0.000)*** (0.000)*** r (0.0990)* (0.100)* (0.102) SMB (0.115) HML (0.148) PR1YR (0.194) DY (0.164) TS (0.116) STIR (0.147) Tale 6 displays the estimates of the state-spae models for herding towards the momentum fator in the pension funds with domesti (Panel A) and gloal (Panel B) equity voations in the period from January 1999 to Septemer 2010; alulated with the eta of the momentum fator from the four fator Carhart (1997) model. The first, seond, third and fourth olumns show the results for the models (7), (9), (10) and (11). SMB represents the size fator, HML is the ook-to-market fator, PR1YR is the momentum fator, DY is the dividend yield, TS is the time spread and STIR is the short term interest rate. *,**,*** represent signifiane at 10%, 5% and 1% level, respetively. 31