Feedback Trading and Predictability of Stock Returns in Germany,

Transcription

1 Kiel Insiue for World Economics Duesernbrooker Weg Kiel (Germany) Kiel Working Paper No Feedback Trading and Predicabiliy of Sock Reurns in Germany, by Chrisian Pierdzioch May 2004 The responsibiliy for he conens of he working papers ress wih he auhor, no he Insiue. Since working papers are of a preliminary naure, i may be useful o conac he auhor of a paricular working paper abou resuls or caveas before referring o, or quoing, a paper. Any commens on working papers should be sen direcly o he auhor.

2 Feedback Trading and Predicabiliy of Sock Reurns in Germany, Chrisian Pierdzioch Kiel Insiue for World Economics, Duesernbrooker Weg 120, Kiel, Germany Absrac I use a ime-varying parameer model in order o sudy he predicabiliy of monhly real sock reurns in Germany over he period I find ha he exen o which reurns were predicable underwen significan changes over ime. Specifically, predicabiliy of reurns, as measured by heir firs-order auocorrelaion coefficien, was posiive mos of he ime. I ended o be significan during exended periods of sock marke decline, bu no during periods of sock marke increase. I argue ha his imepaern of predicabiliy of reurns is consisen wih feedback effecs of fuures rading on he spo marke. Keywords: Sock marke; Reurn Predicabiliy; Germany JEL classificaion: G14, N24 Address: Kiel Insiue for World Economics Duesernbrooker Weg Kiel Germany Telephone: Telefax: c.pierdzioch@ifw.uni-kiel.de Homepage: hp:// saff/pierdzio.hm Acknowledgemens: I hank Claudia Buch, Kai Carsensen, Jörg Döpke, Paul Kramer, Serkan Yener, Andrea Scherler, and Georg Sadmann for helpful commens. The usual disclaimer applies.

3 1 1. Inroducion An imporan foundaion of modern finance heory is he Efficien Marke Hypohesis. This hypohesis ress on he assumpion ha he informaion se used by agens o form heir raional forecass of fuure expeced reurns conains all he informaion relevan for he pricing of financial securiies. According o he so-called weak form of he Efficien Marke Hypohesis, a financial marke is called weakly efficien if his se of informaion incorporaes all he informaion already embedded in pas reurns (Fama 1970, 1991). Hence, in a weakly efficien financial marke, reurns are no predicable in he sense ha i is no possible o forecas reurns in a paricular monh by using reurns observed in a previous monh. Given he key imporance of he Efficien Markes Hypohesis for modern finance heory, predicabiliy of reurns has always been an imporan research opic in he empirical finance lieraure. Mos auhors who have conribued o his lieraure have used daa for modern sock markes o sudy predicabiliy of reurns. I complemen hese sudies by analyzing he predicabiliy of monhly real reurns in he German sock marke during he period A number of compeing explanaions for predicabiliy of reurns have been developed in he noise rader lieraure. Noise raders are agens who behave irraionally in he sense ha heir invesmen decisions are no enirely deermined by economic fundamenals. If a sufficienly large proporion of all raders acing in a sock marke behave as noise raders, hen sock prices can, a leas emporarily, deviae from economic fundamenals (DeLong e al. 1990). This deviaion of sock prices from economic fundamenals can imply auocorrelaion and, hence, predicabiliy of reurns. Specifically, predicabiliy of reurns can arise if noise raders follow so called feedback rading sraegies (Culer e al. 1990). Posiive feedback rading involves buying socks when prices have risen and selling socks when prices have fallen. Negaive feedback rading, in conras, requires jus he opposie: buying socks when prices have fallen and selling socks when prices have risen. Posiive feedback rading should resul in negaive 1 For sudies of he efficiency of he pre-world War I German sock marke, see also DeLong and Bech (1992) and Wezel (1996).

4 2 auocorrelaion of reurns because i gives rise o a shor-run overreacion of sock marke prices o, e.g., news abou dividends. Negaive feedback rading, in conras, should resul in posiive auocorrelaion of reurns. I sudy wheher feedback rading played an imporan role for sock marke flucuaions in Germany before World War I. In order o answer his quesion, I esimaed a regression model wih ime-varying parameers. I used a model wih ime-varying parameers because he repors of hen-conemporary commenaors of he German sock marke in he nineeenh cenury sugges ha feedback rading did influence sock marke flucuaions, bu ha his influence changed over ime. I found ha, for mos of he ime, he predicabiliy of reurns in Germany before World War I, as measured by he firs-order auocorrelaion coefficien, was posiive. This posiive auocorrelaion of reurns is consisen wih empirical resuls ha, beginning wih Cowles and Jones (1937), have been repored in numerous conribuions o he empirical finance lieraure. However, he ime-series properies of auocorrelaion of reurns in he German sock marke before World War I differ from hose of many oher markes insofar as auocorrelaion ended o be significan during exended periods of sock price decreases, bu no during periods of sock price increases. This resul suggess ha negaive feedback rading played an imporan role for he dynamics of reurns during periods of sock marke decreases, and ha is effec on reurns was less significan during periods of sock marke increases. This is an ineresing resul because he empirical evidence available for modern sock markes indicaes ha posiive feedback rading ends o be an imporan driving force of predicabiliy of reurns when sock markes are declining (Senana and Whadwani 1992; Koumos 1997). Hence, here is a remarkable difference beween he resuls I obained for he pre-world War I German sock marke and he resuls available for wenieh cenury sock markes. This difference gives rise o he quesion wheher he ime-varying predicabiliy of reurns in nineeenh cenury Germany was caused by feedback rading, or wheher I should explore one of he oher explanaions for reurn predicabiliy ha have been pu forward in he finance lieraure. Therefore, I sudy in deail he sources of predicabiliy of reurns in he German sock marke

5 3 before World War I. The resuls of his sudy sugges ha feedback rading is he mos promising candidae for explaining boh he magniude and he ime-paern of predicabiliy of reurns I found in my empirical analysis. Wha was he source of feedback rading in he German sock marke before World War I? In order o answer his quesion I compared he narraive evidence repored by hen-conemporary economiss wih my esimaion resuls. This comparison revealed ha he paern of auocorrelaion of reurns I found in he daa could reflec feedback effecs of fuures rading on he spo marke. Given he quaniaive imporance of fuures rading before World War I, his is a view ha was also held by many hen-conemporary economiss. 2 Specifically, many henconemporary economiss argued ha rading in he fuures marke could give rise o wha we oday call negaive feedback rading. They also argued ha feedback effecs of rading in he fuures marke on spo marke dynamics were paricularly srong in exended periods of sock marke decline. This argumen was based on he inuiion ha in periods of sock marke decline hose invesors who were mainly acive in he fuures marke sold socks shor. Hence, hese invesors were engaged in fuures rading on declining sock prices. This rading implied a negaive feedback rading sraegy in he spo marke because, while sock prices coninued declining, he invesors in he fuures marke sared o cover heir open shor posiions (or o carry hem forward o he nex monh). This required purchasing socks in he spo marke (Deckungskäufe). In such a siuaion, even a shorage of shocks (Sückemangel) could arise if oher raders like, for example, banks, long-erm invesors, or uninformed invesors were no willing o sell heir socks. As a resul, he downward pressure on sock prices was eased. In consequence, i ook longer for 2 Significan feedback effecs of fuures rading on spo marke dynamics could arise because fuures conracs played a very imporan role for sock rading in nineeenh cenury Germany. For example, Gömmel (1992) has esimaed ha in 1880 approximaely 60% of all ransacions on he Berlin sock exchange, he mos imporan marke place for sock rading in Germany before World War I, involved fuures conracs on socks.

6 4 sock prices o decline, and he auocorrelaion of reurns became significanly posiive. 3 While his sabilizing propery of fuures rading was in general acknowledged in he economics lieraure, i did no remain undispued. In fac, his dispue was one imporan elemen in he debae on he German Securiies Exchange Law (Deusches Börsengesez) which was enered ino force in Among oher hings, his law resriced fuures rading in he socks of mining and indusrial companies. 5 Many economiss including Desenberg (1904) and Wermer (1904) argued ha his resricion of fuures rading brough abou an increase in sock marke volailiy because he purchases by raders in he fuures marke could no longer exer heir sabilizing effec on sock prices in periods of sock marke downurns. Advocaes of fuures rading argued ha because he fuures marke was larger and more liquid han he spo marke, i guaraneed less volaile sock prices (see, e.g., Cohn 1895, pages 71-72). 6 Oher economiss were more skepical in his regard. For example, Prion (1910) argued ha he sabilizing role of fuures rading had been oversaed by oher researchers. 7 He acknowledged ha, in heory, sock price decreases would 3 In periods of increasing sock prices, rading in he fuures marke required aking long posiions in socks, no shor posiions. Thus, rading in he fuures marke on an increase in sock prices could no give rise o a shorage of socks, and his made, according o Prion (1910, page 88), fuures rading on increasing sock prices less difficul and risky han fuures rading on decreasing sock prices. 4 Concerns ha rading in he fuures marke could desabilize he spo marke led o he formaion of a Sock Exchange Commission (Börsenenqueekommission) in 1882/1893. The hearings of his commission formed he basis for he German Securiies Exchange Law of However, agens developed business pracices ha allowed hem o circumven he resricions of he German Sock Exchange Law of Thus, de faco, a fuures marke for hese socks exised even afer See, e.g., Prion (1910, page 160) for a discussion of his. See also Wezel (1996) for a quaniaive sudy of he impac of he German Sock Exchange Law of 1896 on he German sock marke. Wezel has repored ha he volume of fuures rading decreased afer This was also he posiion of he represenaives of German banks. See Cenralverband des deuschen Bank- und Bankiersgewerbes (1903, page 26). 7 A similar posiion was aken by Bachmann (1898). See he book review by Spiehoff (1900). See also Prion (1930), who also provides a useful discussion of echnical

7 5 rigger sabilizing purchases by raders in he fuures marke (page 90). However, based on visual inspecion of ime-series of sock prices, he argued ha fuures rading made sock prices more volaile. 8 He also argued ha i, on average, resuled in larger deviaions of sock prices from heir respecive fundamenal values (innerer Wer). Prion concluded ha, whenever a period of declining sock prices began, Deckungskäufe implied by shor selling in he fuures marke did no, or did so only afer a delay, dampen he downward pressure on sock prices. 9 I argue ha my empirical evidence does no lend suppor o he argumen ha fuures rading ypically did no unfold a sabilizing effec in exended periods of declining sock prices. I organize he remainder of his paper as follows. In Secion 2, I describe he heoreical and he empirical model I used o sudy he predicabiliy of reurns. In Secion 3, I describe he daa I used in my empirical analysis. In Secion 4, I presen my esimaion resuls. I also discuss wheher predicabiliy of reurns refleced he feedback effecs of fuures rading or wheher i was caused by oher facors like, e.g., a ime-varying risk premium. Furhermore, I discuss wheher my esimaion resuls are in line wih he repors of hen-conemporary commenaors on he German sock marke. In Secion 5, I offer some concluding remarks. deails of fuures and spo marke rading of socks on he Berlin sock exchange. Prion (1910, pages ) and Wezel (1996, pages ) have provided useful summaries of sudies of hen-conemporary economiss on he impac of he German Sock Exchange Law of 1896 on he link beween fuures rading and spo marke developmens. 8 For quaniaive evidence ha he resricions on fuures rading codified in he German Sock Exchange Law resuled in a decrease in sock marke volailiy, see Wezel (1996). 9 Zieh man die Erfahrungen der früheren Zei zu Rae, so is keine Behaupung gewager als die, dass die Baissespekulaion in kriischen Zeien große Kurssprünge verhindere. [If one akes he hisorical experience ino accoun, one canno say ha bearish speculaion prevens large jumps of sock prices during criical imes.] (Prion 1910, page 181). See also his commens on he role of fuures speculaion for he impac of he Russian-Japanese war of 1904 on European sock exchanges: Die in der Theorie so belieben Deckungskäufe, die die Kursschwankungen mildern sollen, bleiben in der Praxis in solchen Momenen aus, und an ihre Selle reen neue Abgaben, um die Baissespekulaion möglichs lohnend zu machen. [The Deckungskäufe, ha have been so popular in heoreical sudies and ha are supposed o smooh ou sock price flucuaions do no ake place in pracice in such siuaions [e.g., during wars]; raher addiional sales of sock prices ake place in order o make selling shor as profiable as possible.] (page 194).

8 6 2. Modeling Predicabiliy of Reurns This secion comes in wo pars. In he firs par, I briefly describe he heoreical model I used o analyze he implicaions of feedback rading for he predicabiliy of reurns (Secion 2.1). In he second par, I describe he empirical model I esimaed o analyze he possibly ime-varying predicabiliy of reurns (Secion 2.2). 2.1 Theoreical Model The heoreical model builds on Shiller (1984) and Senana and Whadwani (1992). Their models res on he assumpion ha wo differen groups of raders populae a sock marke. The firs group of agens is called smar money raders because heir demand for socks is governed by risk-reurn consideraions: Q = α ) / µ, (1) 1, ( E 1R where Q 1, denoes he proporion of smar money raders in he marke, α denoes he reurn a which he demand for socks by smar money raders is zero, and is he risk-premium for holding socks. I assume ha boh α and µ may change over ime. If only smar money raders were acive in he sock marke hen µ Q 1, = 1 and socks were priced according o Meron s (1980) Capial Asse Pricing Model. The second group of agens is feedback raders. Their demand for socks can be described by means of he following equaion: Q γ, (2) 2, = R 1 where denoes he proporion of feedback raders in he marke. If γ >, Q 2, 0 hen feedback raders adhere o a posiive feedback rading sraegy, i.e., hey buy (sell) socks when he prices of socks have risen (fallen). If, in conras, γ < 0, feedback raders follow a negaive feedback rading sraegy, i.e,. hey buy (sell) socks when he prices of socks have fallen (risen). I allow for changes over ime in he parameer γ in order o accoun for changes in he influence of feedback raders who follow a posiive or negaive feedback rading sraegy.

9 7 Upon invoking he assumpion of raional expecaions, R = E 1 R + ε, and he condiion for sock marke equilibrium, Q 1, + Q2, = following difference equaion wih ime-varying coefficiens: 1, one obains he R = β, + β1, R ε, (3) where denoes a sochasic disurbance erm and β = α + and ε 0, µ β 1, = γ µ. Equaion (3) shows ha changes in he parameer ha capures he predicabiliy of reurns, β 1,, can resul from changes in he parameer ha reflecs he influence of feedback raders, γ, and changes in he risk premium for holding socks, µ. Hence, an imporan quesion is wheher changes in he parameer β 1, are caused by changes in he predicabiliy of reurns or changes in he risk premium. I will address his quesion in Secion 4.3 below Empirical Model In order o esimae Equaion (3), I used a ime-varying parameer model ha is similar o he models ha Zalewska-Miura and Hall (1999) and Rockinger and Urga (2000, 2001) have recenly developed. The ime-varying parameer model I esimaed has he following form: 2 R β + u, u ~ i. i. d. N(0, σ ), (4) = 0, + β1, R 1 u 2 β, v ~ i. i. d. N(0, σ ) (5) m, = β m, 1 + v m, m, m, v where m = {0,1}. Equaion (4) is he empirical counerpar of Equaion (3). 11 I sipulaes ha sock marke reurns are equal o a ime-varying inercep, β 0,, plus a ime-varying slope coefficien, β 1,, imes lagged reurns plus a sochasic 10 Because boh he inercep coefficien and slope coefficien in Equaion (3) are funcions of he risk premium, i is reasonable o ask wheher one should assume in he empirical model in Secion 2.2 ha hese coefficiens are correlaed. The answer o his quesion depends on wheher he risk premium changes over ime. 11 I used he Kalman-filer approach o esimae he model in Equaions (4) (5). Harvey (1992) and Kim and Nelson (2000) provide deailed descripions of he Kalman-filer approach. I used Gauss 3.6 o implemen he Kalman-filer approach, and I acknowledge use of compuer programs described in Kim and Nelson (2000).

10 8 disurbance erm. Equaion (5) implies ha he ime-varying inercep and slope coefficiens follow random-walk processes. Hence, he only source of variaion in β 0, and β 1, is due o he variance of he respecive sochasic disurbance erms, v 0, and. The sochasic disurbance erms, u and, are assumed o be v 1, v m, independenly normally disribued and are uncorrelaed wih each oher ( E(u ) = 0). 12 v m, 3 Daa In order o sudy he predicabiliy of reurns, I used he monhly nominal sock marke index compiled by Donner (1934). Donner s daa sar in 1870:1 and end in 1913:12. In order o obain a real sock marke index, I used he monhly cosof-living daa used by Gielen (1994, Chaper 8). The real sock marke index I analyzed is idenical o he index also analyzed by DeLong and Bech (1992) in heir sudy of excess volailiy of he German sock marke before World War I. 13 A deailed descripion of he daa can be found in heir paper. Inser Figure 1 abou here. In order o ge he ball rolling, Panel A of Figure 1 graphs he real sock marke index for he German sock marke for he period 1880:1 1913:12. The figure begins in 1880 because, in my empirical analysis in Secion 4, I will drop he 1870s from he sample. One reason for his is ha Donner s index only covers a relaively small number of companies in he early 1870s. 14 Anoher reason is ha excepional bubble-like phenomena were characerisic of he German sock 12 I also esimaed a version of he model in which he error erm in he reurn equaion is condiionally heeroskedasic, bu he esimaion resuls urned ou o be very similar o he esimaion resuls I will repor in Secion 4.1 below. 13 The only difference beween heir daa and my daa is ha DeLong and Bech analyzed yearly daa. 14 The number of companies in Donner s index increased over ime. The index covered seven companies in 1870, 13 companies in 1876, 51 companies in 1890, and 69 companies in Fur more deails, see Donner (1934, page 96).

11 9 marke in he early 1870s. 15 Ye anoher reason is ha, a saisical poin of view, beginning in 1870 he ieraions required ha I esimae my empirical model, bu neglecing he 1870s when evaluaing he log-likelihood funcion of he model minimizes he effec of he saring values of he models parameers on he esimaion resuls. I should be noed, hough, ha he esimaion resuls do no change much when one les he sample period begin in, for example, 1876, as DeLong and Bech (1992) did. Inser Table 1 abou here. Table 1 offers summary saisics of coninuously compounded real reurns. 16 The mean of reurns is almos zero, he skewness of he uncondiional reurns disribuion is slighly negaive, and he uncondiional reurns disribuion is lepokuric, i.e., is kurosis exceeds ha of he normal disribuion. Thus, he uncondiional reurns disribuion has fa ails. There is also evidence for a significanly posiive firs-order auocorrelaion coefficien. The auocorrelaion coefficiens of orders larger han one are almos zero and are saisically no significan. There is also some evidence for auocorrelaion in he squared reurns. However, because I used monhly daa, i is no surprising ha he evidence for auocorrelaion in squared reurns is no overwhelmingly srong. All in all, Table 1 highlighs ha he summary saisics of real reurns in nineeenh cenury Germany closely resemble he summary saisics and sylized facs of oher hisorical and modern financial marke daa (Lux and Marchesi 2000; Goezmann 1993; Harrison 1998). 15 See Henning (1996) for a deailed descripion of his crisis of he early 1870s (he socalled Gründerkrise). 16 Summary saisics of nominal and excess reurns (i.e., reurns minus a risk-free ineres rae (Privadiskon; see Donner 1934)) are similar and are, herefore, no repored.

12 10 4. Resuls In order o discuss my esimaion resuls, I proceed in hree seps. In a firs sep, I describe he resuls of esimaing he ime-varying parameer model described in Secion 2.2 (Secion 4.1). In a second sep, I inerpre my esimaion resuls in he ligh of a hen-conemporary repor of sock marke developmens in nineeenh cenury Germany (Secion 4.2). I will argue ha my esimaion resuls are consisen wih he argumen ha he predicabiliy of reurns in he German sock marke before World War I refleced he influence of fuures rading on he spo marke. In a hird sep, I discuss wheher he evidence for predicabiliy of sock reurns could be due o facors oher han feedback effecs of fuures marke (Secion 4.3). 4.1 Descripion of Esimaion Resuls Table 2 summarizes my esimaion resuls. Esimaion resuls sugges ha he variance, 2 σ 1, u, of he disurbance erm in he equaion ha governs flucuaions in he slope coefficien, β 1,, is saisically significanly differen from zero. Because his coefficien capures he degree of firs-order auocorrelaion in sock reurns, his resul indicaes ha he predicabiliy of sock reurns was no consan over ime. 17 The resuls given in Table 2 also indicae ha he variance, σ 2 0, u, of he disurbance erm in he equaion ha governs flucuaions in he inercep, β 0,, of he reurns equaion is saisically insignifican. Thus, here is no evidence ha he inercep changed over ime. I will come back o his evidence on he inercep of he esimaed reurns equaion in Secion 4.2 below. Inser Table 2 abou here. 17 Because he sampling disribuion of he parameers is nonsandard, care mus be aken when conducing ess for significance. See Harvey (1989, page 236). If he poin esimae of a parameer is zero, hen he corresponding coefficien is a consan, and convenional saisical heory can be used o conduc ess for significance. If he poin esimae of a parameer is nonzero, hen he corresponding coefficien varies and is significance can be graphically analyzed (see Figure 1). β i, β i,

13 11 I is ineresing o sudy he ime pah of he coefficien β 1,. Specifically, i is ineresing o sudy when his coefficien was saisically significan, and wheher he significance of his coefficien is sysemaically linked o developmens in he sock marke. Given he discussion of feedback rading in Secion 2.1, i is also ineresing o sudy wheher he coefficien of he ime. β 1, was posiive or negaive for mos As shown in Panel B of Figure 1, he coefficien β 1, was posiive for mos of he ime. 18 A major excepion in his regard is he period During his period, he coefficien β 1, was negaive. Ineresingly, during his period, a run-up of he sock marke index began. Using he heoreical model oulined in Secion 2.1, I conclude ha he negaive auocorrelaion of reurns during his period could indicae ha posiive feedback rading may have conribued o he run-up of he sock marke index ha began in 1887/1888. Inser Figure 1 abou here. I is also eviden from Panel B ha, as he sock marke index converged on is (local) maximum during he years 1889/1890, he sign of he coefficien β 1, changed significanly from negaive o posiive. 19 The coefficien β 1, became significanly posiive afer he sock marke index had already reached is peak in 18 When using he Kalman-filer approach, one can eiher use he filered or he smoohed esimaes of he models coefficiens o measure predicabiliy of reurns. The difference beween he wo lies in he informaion se one uses (Kim and Nelson 2000). Filered esimaes are based on informaion available up o period. Smoohed esimaes are based on all available informaion in he enire sample. I repor filered esimaes because, in any given period, a sock marke paricipan can only use informaion up o ime for making inferences abou ime-varying predicabiliy of reurns. 19 This significan change in he coefficien was confirmed by he resuls of a Chow es, recursively esimaed over he sample period. The es resul indicaed significan insabiliy of he slope coefficien in a regression of reurns on lagged reurns in he firs half of This resul also obained when criical values were adjused o accoun for he fac ha he exac period of he break was unknown.

14 12 early Thereafer, a period of ime of significan posiive auocorrelaion in sock reurns began. This period of ime coninued while he sock marke index was declining from early 1890 unil lae 1891, and only ended when he sock marke index approached a rough in From 1892 o 1900, he coefficien β 1, remained posiive, and i was more or less consan and insignifican. Thus, in line wih he heoreical model oulined in Secion 2.1, i is possible ha posiive feedback rading may have conribued o he auocorrelaion and, hus, he predicabiliy of sock reurns during he years 1890/1891, and ha he exen of posiive feedback rading was less significan from 1892 on. 20 In 1900/1901, he coefficien β 1, increased when he large and subsanial rise of sock prices ha had begun in 1894 ended. As in 1890/1891, he coefficien β 1, remained significanly posiive during he enire period during which he sock marke index declined. From his i follows ha, as in 1890/1891, negaive feedback rading may have conribued o he predicabiliy of reurns during he downswing of he sock marke index in 1900/1901. This period of significan posiive auocorrelaion of reurns ended in 1902/1903 only afer sock prices had begun increasing again. Thereafer, he coefficien was more or less consan. β 1, remained posiive, and i I is also ineresing o noe ha a smaller change in he coefficien β 1, occurred in lae During ha ime, a downswing of he sock marke index ha began in 1905 came o an end. 4.2 Fuures Trading and Reurn Predicabiliy: A Case Sudy In order o undersand he economics behind he resuls described in Secion 4.1, i is useful o compare my esimaion resuls wih he repors of sock marke 20 Wezel (1996) has repored ha he German Sock Exchange Law of 1896 had no effec on he informaional efficiency of he German sock marke. To his end, he has consruced a monhly sock marke index for he period I is ineresing o noe ha he esimaes of reurn predicabiliy implied by my ime-varying parameer model also show ha reurns were hardly predicable during his period.

15 13 developmens documened by hen-conemporary commenaors on he German sock marke. The book by Prion (1910) is paricularly useful in his regard. Prion described he developmens of he German sock marke beween 1888 and 1896 in deail. 21 Here, I will use his repor o sudy he economics behind my esimaion resuls. In doing his, I will focus on he period because, as evidenced by Figure 1, his period seems o be paricularly ineresing for sudying predicabiliy and, hus, auocorrelaion of reurns. This period winessed exended phases of negaive (1888/1889) and posiive (1890/1891) auocorrelaion of reurns. Thus, he period can provide imporan insighs ino o wheher feedback rading was an imporan source of auocorrelaion in reurns. Inser Figure 2 abou here. Figure 2 shows he real sock marke index, he esimaed ime-varying firsorder auocorrelaion of reurns, and a number of economic and poliical evens repored by Prion (1910). In he firs monhs of 1888, he sock marke index and he auocorrelaion of reurns began increasing. During hese monhs, he auocorrelaion of sock reurns was negaive. A ha ime, business cycle prospecs were favorable and here was much liquidiy in he marke. Also, because of favorable credi marke condiions, i was relaively easy for bullish fuures raders o finance heir rading aciviies. According o Prion s repors, in June 1888, he upswing of he sock marke gave rise o band-wagon effecs and herding which implied ha he upswing gained momenum. In Sepember 1888, his upswing came o a emporary sop because he financial press and one of he German Grossbanken (large banks), he Deusche Bank, publicly saed ha he increase in he sock marke was excessive. These saemens, however, had only emporary effecs on he sock marke, and a he end of 1888 he sock marke index began rising again. The auocorrelaion of reurns began increasing during he second half of Maybe one reason for his is ha he firs monhs of 1889 were 21 See also he repors of he Älesen der Kaufmannschaf von Berlin ( ).

16 14 characerized by discussions abou wheher business cycle prospecs would say favorable. Also, according o Prion, raders sared unwinding heir bullish posiions. I is, herefore, no surprising ha in spring 1889 massive srikes in he mining indusry in he Ruhrgebie and in Oberschlesien exered a dampening effec on he sock marke. In hese monhs, i was no so clear wheher invesors would remain bullish, or wheher he decline in sock prices indicaed he beginning of an exended bearish phase. The bearish phase, however, did no las long because agens again sared purchasing socks. As a consequence of hese purchases, raders in he fuures marke who had buil up bearish posiions also purchased socks. The resul was a furher rise of he sock marke index in summer In December 1889, money-marke condiions became igher, making i more difficul o rade in he fuures marke. Also, uncerainy characerized sock marke developmens because professional raders were expecing a decrease of sock prices. As Prion repored, he large majoriy of oher sock marke paricipans, in conras, hoped for a furher increase in sock prices. These hopes for furher increases in sock prices, however, did no maerialize. The end of 1889 marked he beginning of a long phase of declining sock prices. I also marked he beginning of an exended period of significan posiive auocorrelaion of sock reurns. A he beginning of 1890, raders massively unwound heir bullish posiions, and his exered a depressive effec on he sock marke because he large majoriy of sock marke paricipans were no willing o buy socks. The ensuing decline in sock prices came o a emporary hal in February 1890 only because, as Prion repored, he Deusche Bank inervened by purchasing socks in an aemp o sabilize he marke. 22 Hence, he Deusche Bank conduced a leaning agains he wind policy, i.e., a ype of negaive feedback-rading policy. Is inervenion purchases were followed in Augus 1890 by purchases of raders in he fuures 22 For a sudy of he role of he German Grossbanken for he sock marke in Germany before World War I, see DeLong and Bech (1992).

17 15 marke o cover here bearish posiions. As can be seen in Figure 2, he resul of hese purchases was a emporary increase in sock prices. Prion furher repored ha i was characerisic for he sock marke siuaion in 1891 was ha many raders had wihdrawn from he marke and ha, as a consequence, he sock marke was mainly populaed by professional raders. These raders were engaged in massive fuures rading on declining sock prices. This fuures rading involved shor sales of socks. While sock prices coninued declining, he raders in he fuures marke sough o cover heir shor posiions by purchasing socks in he spo marke. Prion (page 139) repored ha hese purchases were an imporan deerminan of sock prices in I conclude ha he behavior of raders in he fuures marke helps explaining why, as shown in Figure 2, he year 1891 did no winess a full-fledged sock marke crash. Raher, sock prices declined over many monhs. I also conclude ha, because i may have given rise o a kind of negaive feedback rading, he behavior of raders in he fuures marke can be used o explain why he imevarying parameer model deecs a significanly posiive auocorrelaion of reurns in Oher Explanaions for Predicabiliy of Reurns Before jumping o definiive conclusions wih regard o he link beween shor sales in he fuures marke, feedback rading in he spo marke, and reurn predicabiliy, i is worh sudying wheher explanaions oher han feedback rading may accoun for he magniude of and ime-paern in he predicabiliy and, hus, auocorrelaion of reurns described in Secion For example, i could be he case ha a ime-varying risk premium helps explain auocorrelaion of reurns (for a discussion, see Culer e al. 1991). Ye anoher explanaion has been pu forward by Lo and MacKinlay (1990) who have examined nonsynchronous rading as a source of auocorrelaion of reurns. 24 Moreover, 23 No all of he resuls are repored, bu are available from he auhor upon reques. 24 I mus also be aken ino accoun ha using monhly averages of daily or weekly prices of he socks inroduces posiive firs-order auocorrelaion ino reurns even if sock prices are a purely random sequence. See Working (1960) and Cowles (1960). I

18 16 Mech (1993) has found ha ransacion coss could help explain auocorrelaion of reurns. Finally, i is ineresing o sudy o wha exen my resuls are influenced by seasonal anomalies like, for example, monh-of-he-year effecs (Choudhry 2001) Time-Varying Risk Premium A naural quesion ha arises is wheher posiive auocorrelaion of reurns is due o feedback rading, or wheher a ime-varying risk premium may have caused posiive auocorrelaion of reurns. In order o sudy his quesion, I plo in Panel C of Figure 1 he condiional variance of he forecas error of prediced reurns implied by my ime-varying parameer model. Furher, I plo in Panel D he coefficien β 0,. Panel C illusraes ha he condiional variance of he forecas error increased during some, bu no all, of he periods of ime during which he coefficien was significanly posiive and reurns were, hus, predicable. For example, he condiional variance of he forecas error increased when he predicabiliy of sock reurns became significan in 1890 and in The quesion, herefore, is wheher i is likely ha he predicabiliy of sock reurns was merely due o changes in he premium paid for holding risky socks. To examine his quesion, i is useful o reurn o he heoreical analysis in Secion 3.1. Tha analysis has shown ha he poenially ime-varying risk premium should show up in boh he inercep and he slope coefficien of he ime-varying parameer model: β = α + and β = γ. Thus, if changes 0, µ 1, µ β 1, in he risk premium help explain changes in he slope coefficien, β 1,, changes in he risk premium should also help explain changes in he inercep coefficien, β 0,. Panel D shows ha he inercep coefficien,, is no significanly differen from zero and hardly changes over ime, even in hose monhs in which β 0, is no enirely clear o his reader wheher Donner (1934) acually used averages of weekly or even daily daa o consruc his index, hough he following quoe suggess ha he did no: Die Berechnung beginn mi dem Jahr 1870 und is für das Kurniveau und den Akienmark monalich durchgeführ. [Compuaions sar in he year 1870 and are performed on a monhly basis for he level of sock prices and for he sock marke.] (Donner 1934, page 96).

19 17 he condiional variance of he forecas error increased. This suggess ha i is unlikely ha a ime-varying risk premium was he main source of reurn predicabiliy in he German sock marke before World War I Nonsynchronous rading The magniude of he firs-order auocorrelaion coefficien in Panel B of Figure 1 suggess ha i is unlikely ha nonsynchronous rading can accoun for he predicabiliy of reurns. This follows from he heoreical resuls repored by Lo and MacKinlay (1990). They have derived he asympoic auocorrelaion of he reurns of a well-diversified porfolio ha consiss of a large number of socks. Each sock in he porfolio is no raded in any given period of ime wih a cerain probabiliy. A comparison of my empirical resuls shown in Figure 1 wih he heoreical resuls derived by Lo and MacKinlay suggess ha he firs-order auocorrelaion coefficien implied by my ime-varying parameer model is way oo large o be caused by nonsynchronous rading. Thus, I conclude ha i is no very likely ha non-synchronous rading was he main source of auocorrelaion and, hus, predicabiliy of monhly reurns in he German sock marke before World War I. This conclusion is furher corroboraed by he fac ha Donner s (1934) sock marke index comprises a sample of Germany s larges companies. Furhermore, for he years 1892/1893, Gömmel (1992) has esimaed he average daily urnover on he Berlin sock exchange, he mos imporan sock exchange in Germany 25 Anoher possibiliy is ha changes in he risk premium affec boh he slope and he inercep of he regression equaion, bu he laer does no change because changes in are negaively correlaed wih changes in α. In order o check his possibiliy, I µ esimaed a GARCH-in-mean model as in Senana and Whadwani (1992). In heir model, he coefficiens in he reurn equaion are defined as = α α and β1, = γµ, where µ is given by he condiional variance of reurns and he coefficien γ is assumed o be a linear funcion of he condiional variance of reurns: β 0, 0 + 1µ γ = η + 0 η1µ. The esimaion resuls for his GARCH-in-mean model did no provide evidence for a GARCH-in-mean effec. Furhermore, aside from he coefficiens in he GARCH equaion, he only significan coefficien urned ou o be he coefficien η (wih he expeced posiive sign). 0

20 18 before World War I, o be approximaely 163 million Marks. 26 Of course, imevariaion in paricipaion in sock rading mus cerainly be aken ino accoun. 27 However, Gömmel s esimae suggess ha i is unlikely ha he predicabiliy of monhly reurns during exended phases of a declining sock marke was mainly due o nonsynchronous rading Transacion Coss I used a model developed by Mech (1993) in order o sudy he effecs of ransacion coss on reurn predicabiliy. 28 Mech s model is based on he insigh ha if ransacion coss are an imporan source of predicabiliy of reurns, hen sock prices should adjus rapidly o new informaion in periods when price changes are large relaive o ransacion coss. Based on his insigh, he has developed a parial-adjusmen model for sock prices. The main assumpion on which his model is buil is ha, in each period, observed sock prices adjus parially o he ime-varying bes esimae of sock prices. An immediae consequence of his assumpion is ha observed reurns are a weighed-average of lagged observed reurns and he rue reurns of he bes esimae of sock prices. The weighing facor is a funcion of he coefficien ha describes he parialadjusmen of reurns. This coefficien can change over ime. Specifically, Mech has assumed ha i is a funcion of he magniude of absolue observed reurns: The larger absolue observed reurns are, he less imporan should be ransacion coss, he faser sock prices should adjus, and, as a resul, he larger he 26 Gömmel has deduced his esimaes from he oal amoun of ax revenues paid for sock marke ransacion in Berlin. If 60% of all ransacions involved fuures conracs, hen, assuming 300 rading days per year and a yearly ransacion volume of 49 billions Marks, he daily volume of spo ransacions was on average 65 million Marsk and he ransacions volume of fuures conracs was on average 98 million Marks (Gömmel 1992, page ). 27 See Secion 4.2. For a sudy of changes in he urnover on German sock exchanges in he nineeenh cenury, see also Wezel (1996, pages ). 28 Taking ino accoun he possibiliy ha predicabiliy of reurns could be linked o ransacion coss is ineresing because sock marke ransacions were axed in pre- World War I Germany. Ineresingly, he main purpose of axing sock marke ransacions was o raise ax revenues ha could be used for financing miliary spending, no o hrow a spammer in he works of capial markes. See Warschauer (1905) for a discussion.

21 19 adjusmen coefficien should be. A larger adjusmen coefficien, in urn, implies a faser and more complee adjusmen of sock prices o new informaion, implying ha predicabiliy of reurns should become insignifican. Esimaion of Mech s (1993) model requires he definiion of a bes esimae of he value of Donner s sock index. The choice of an insrumen for his bes esimae is no an easy ask. Mech has used a large firm porfolio as an insrumen in his analysis. This reflecs his assumpion ha ransacion coss should be smaller for large firms han for small firms. Unforunaely, Donner s daa se does no cover separae daa for small and large firms. Raher, Donner s daa se only comprises daa for an index of he larges German companies. 29 I, herefore, dropped he value of he bes esimae of he index from Mech s regression equaion and, hus, esimaed a simplified version of his model. 30 As an alernaive, I used he reurns on he U.K. or he U.S. sock marke index as an insrumen for he reurns on he bes esimae of Donner s index. 31 In all esimaed specificaions of Mech s model, esimaion resuls showed no evidence of a reurn-dependen adjusmen coefficien. The coefficiens were eiher insignifican or had he wrong signs. Hence, i is unlikely ha ransacion coss were a main source of he predicabiliy of reurns documened in Figure Monh-of-he-Year Effecs Choudhry (2001) has found significan monh-of-he-year effecs in German sock marke reurns during he pre-world War I period. Hence, in order o assess he robusness of my resuls, I ook monh-of-he-year effecs ino accoun in my empirical analysis. In a firs sep, I regressed real reurns on welve monhly dummies. The esimaion resuls of his regression confirmed Choudhry s resul of significan monh-of-he-year effecs. In a second sep, I saved he residuals from 29 Noe ha his implies ha, if one buys he argumen ha ransacion coss should be small for large firms, hen ransacion coss should play a minor role for he predicabiliy of reurns on Donner s index. 30 In his simplified model, I regressed reurns on a consan, lagged reurns, and lagged reurns muliplied by a dummy variable which was posiive whenever absolue reurns were larger han he median of absolue reurns. 31 I downloaded he daa from he NBER Macroeconomic Hisory inerne page. For simpliciy, I used nominal reurns.

22 20 his regression and used hem o reesimae my ime-varying parameer model. Esimaion resuls urned ou o be very similar o he resuls summarized in Figure 1. In paricular, he conclusions regarding he magniude, sign, and significance of he coefficien effecs ino consideraion. β 1, were no affeced by aking monh-of-he-year 5. Concluding Remarks The empirical resuls documened in his paper sugges ha he German sock marke before World War I provides an ineresing case sudy o he effec of feedback effecs from fuures rading on auocorrelaion and, hus, he predicabiliy of reurns. Three main resuls emerge from my empirical resuls. Firs, he firs-order auocorrelaion coefficien was posiive mos of he ime, albei is significance changed over ime. Second, auocorrelaion of reurns ended o be significan during exended periods of a declining sock marke. Third, he ime-paern of auocorrelaion can be explained in erms of poenial feedback effecs of fuures rading on spo marke dynamics. This resul is ineresing in iself because i sheds new ligh on an old debae among economiss in Germany a cenury ago. Bu, hopefully, he insighs provided by he resuls I repored in his paper will also conribue o he debae on he causes and consequences of he financial globalizaion ha we see in our modern imes. This debae focuses, for example, on he coss and benefis of high inernaional capial mobiliy. Furher, i focuses on wheher financial derivaives are he beas of modern finance ha desabilize financial markes, wheher financial ransacions should be resriced, and wheher a Tobin ax should be implemened. Sudying he debae ha ook place in Germany in he nineeenh cenury reveals ha many of hese quesions were already on he poliical agenda more han a cenury ago. Of course, he erminology used by economiss and poliicians a ha ime was differen from he erminology we use oday. Bu his does no imply ha i is no worhwhile sudying wha we can learn from he argumens used by economiss and researchers in pre-world-war-i-germany, and from hisory iself.

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