The Predictive Content of Futures Prices in Iran Gold Coin Market

Transcription

1 American Inernaional Journal of Conemporary Research Vol. 7, No. 3, Sepember 017 The Predicive Conen of Fuures Prices in Iran Gold Coin Marke Ali Khabiri PhD in Financial Managemen Faculy of Managemen, Universiy of Tehran Nasr Bridge, Tehran, Iran. Absrac The presen paper sudies gold coin fuures marke in Iran in erms of hree conceps ha deermine how well fuures markes may perform heir price discovery funcion. Firs, he maringale hypohesis is esed. The resuls from linear models show ha curren changes in fuures prices canno be prediced by pas changes in fuures prices. However, when nonlineariies are accouned for, we obain evidence ha rejec he maringale hypohesis. The second issue is he unbiased expecaions hypohesis. The findings show ha fuures prices are unbiased esimaors of erminaion cash prices in he normal marke condiion. Bu when spo prices fall or rise sharply, fuures raders demand risk premia alhough he one-for-one relaionship beween fuures prices and erminaion spo prices sill holds. Finally, power of he basis o predic subsequen changes in spo prices is examined. The resuls indicae ha he basis fails unbiasedness ess when cash marke eners bearish or bullish erriory. Keywords: Maringale, coinegraion, unbiasedness, linear and nonlinear dependence 1. Inroducion The weak-form marke efficiency implies ha prices follow a random walk and ha curren changes in prices should no be predicable by hisorical sequence of price changes (Samuelson, 1965). Assuming ha marke paricipans are risk neural and heir expecaions are raional, he financial heory also suggess ha he k-periodahead fuures price a ime T k and he realized spo price a ime T should be coinegraed wih a coinegraing vecor (1, -1), i.e., hey should move ogeher one for one in he long run (Hsieh and Kulailaka, 198). Furhermore, given ha fuures prices and spo prices are nonsaionary, he Granger Represenaion Theorem (Granger, 1986) implies ha he basis migh predic subsequen changes in spo prices. A large number of sudies have esed he predicive conen of fuures prices in advanced economies. The resuls are ofen mixed due o using differen mehodologies and sample periods. For insance, Chow (1998) documens ha fuures prices are unbiased esimaors of fuure spo prices in gold, plainum, silver and palladium markes. In conras, Chinn and Coibion (014) find evidence ha fuures prices and erminaion spo prices of precious and base meals are coinegraed bu no wih a coinegraing vecor (1, -1). Gold coins are popular in Iran as hey are purchased for invesmen purposes and used as gifs. Each of hese coins has a fineness of 90 percen, equivalen o 1.6 karas, and has an acual gold weigh of roy ounces. The Iran Mercanile Exchange (IME) launched gold coin fuures conracs in November 008. The gold coin fuures marke has rapidly grown in recen years such ha he conrac is currenly one of he mos raded financial insrumens in Iran. The presen sudy aims o conduc an empirical analysis of gold coin fuures marke by combining linear and nonlinear mehods. The res of his research paper is organized as follows. Secion briefly reviews heoreical argumens and explains daa and mehodology. Secion 3 presens empirical resuls and heir inerpreaions. Finally, Secion 4 sums up all discussions and makes a conclusion.. Daa and Mehodology.1. Maringale Hypohesis The weak-form efficiency in financial markes requires ha curren prices reflec all informaion conained in hisorical sequence of prices. In oher words, fuures prices should follow a random walk. The random walk is an example of he maringale process ha saes ha expecaion of he nex value in a sequence is equal o he presen observed value given knowledge of all prior observed values (Samuelson, 1965): 49

2 ISSN X (Prin), 16-14X (Online) Cener for Promoing Ideas, USA 50 E ( F 1, T ) F, T According o Fujihara and Mougoue (1997), he maringale hypohesis implies ha raders who rely on pas changes in fuures prices o predic curren changes in fuures prices should no expec o receive risk-adjused excess reurn, on average. Therefore, a ypical es of he maringale hypohesis is carried ou using he following model: r m 0 ir i i1 where r is he log reurn on daily fuures prices of gold coin and m denoes he lag order. Daily fuures prices are obained from he neares-o-expiraion fuures conracs over he period from Ocober 011 o March 017. If he maringale hypohesis holds, all regression coefficiens should joinly be equal o zero and error erms should no be serially correlaed. Above regression model is esimaed using hree differen mehods, namely, he ordinary leas squares (OLS), he Generalized Auoregressive Condiional Heeroskedasiciy (GARCH) and he quanile regression. The leas squares mehod capures condiional mean relaionship beween he variables. The oher wo mehods accoun for nonlineariies and asymmeries. As argued by Brock, Hsieh and LeBaron (1991), analysis of nonlinear dynamics may provide a useful descripion of movemens in asse prices. Given ha asse prices, including fuures prices, may display condiional heeroskedasiciy, we use he GARCH (p,q) which is inroduced by Bollerslev (1986) in order o model condiional variance of residuals in equaion (): where i and u ~ N 0, p q iui i1 j1 u j are called persisence parameers. The GARCH (p,q) process is saionary if he sum of persisence parameers is less han uniy. The quanile regression aims o esimae he relaionship beween dependen variable and all regressors a eiher median or oher quaniles of response variable. The quanile regression, developed by Basse and Koenker (1978), minimizes he sum of absolue deviaions, and hence i is also called he mehod of leas absolue deviaions (LAD): n n ˆ argmin Yi X i (1 ) Yi X i (4) i{i:yi X i } i{i:yi X i } where lies wihin he range from 0 o 1 and i is condiional quanile of dependen variable such ha: 1 Q( ) FY ( ) inf y : FY ( y) (5) The main advanage of he leas absolue deviaions compared o he ordinary leas squares is ha he former gives equal emphasis o all observaions, whereas he laer gives more weigh o larger residuals. Hence, he quanile regression is robus in he sense ha i is resisan o ouliers in daa. Also, i allows us o see how esimaes of parameers in equaion () may change in differen quaniles of dependen variable. Lower quaniles of reurn series represen he bear marke and upper quaniles consiue he bull marke. Also, he median of reurn series conains he normal marke condiion... Unbiased Expecaions Hypohesis Under join assumpions of risk neuraliy and raional expecaions, expeced reurns o speculaive aciviy in an efficien marke should be zero. I implies ha, in a forward or fuures marke, he curren price of an asse for delivery a conrac expiraion should be he unbiased predicor of fuure spo price. According o Crowder and Hamed (1993), he fuure spo price of an asse in a paricular conrac is he cash price on he las rading day of he conrac. Each fuures conrac is open for a relaively large period of ime and daily fuures prices reflec marke expecaions abou erminaion spo price given all publicly available informaion. Among many daily fuures prices, only one of hem should be seleced and mached wih erminaion spo price for a paricular conrac. j j (1) () (3)

3 American Inernaional Journal of Conemporary Research Vol. 7, No. 3, Sepember 017 This selecion depends on forecas horizon ha is under examinaion. In his sudy, he predicive conen of gold coin fuures prices is esed using forecas horizons of 5, 10, 15, 0, 5, 30, 35 and 40 days. Thus, fuures prices for a paricular conrac are picked ou by working backwards 5, 10, 15, 0, 5, 30, 35 and 40 days from conrac erminaion dae. Longer forecas horizons are no esed because Hansen and Hodrick (1980) argue ha if he previous conrac is sill being raded when maching spo and fuures prices for he nex conrac, wrong inferences migh be made due o informaional overlap. In oher words, when maching spo and fuures prices for a paricular conrac, i should be ensured ha he conrac under consideraion is he neares-o-expiraion conrac among all open conracs wih he same underlying asse. The firs gold coin fuures conrac ha was raded in he IME had a delivery monh of January 009. In his sudy, sample daa aken o es he unbiased expecaions hypohesis comprises all gold coin fuures conracs whose expiraion daes were wihin he period from November 009 o March 017. Fama (1991) argues ha o es wheher prices properly reflec informaion, we need a model ha depics he meaning of properly. According o Chow (1998), he convenional approach o examine he unbiasedness hypohesis requires esablishing presence of coinegraion beween fuures prices and erminaion spo prices, and hen esing wheher fuures price a a specific forecas horizon is he unbiased esimaor of spo price ha is realized a conrac erminaion dae. Hence, a coinegraing regression is specified as follows: s f (6) T T 1 k T where s T is he naural logarihm of realized spo price a he las rading day of he conrac and ft k is he naural logarihm of fuures price a a specific forecas horizon denoed by k. As saed earlier, his regression model is run for muliple forecas horizons. Similar o he es of maringale hypohesis, equaion (6) is esimaed using OLS, GARCH and LAD mehods in order o accoun for linear and nonlinear dependence beween erminaion spo prices and fuures prices a each forecas horizon. Given ha fuures prices and erminaion spo prices have a uni roo, error erms of he coinegraing regression should be inegraed of order zero o ensure ha fuures prices and erminaion cash prices have a coinegraing relaionship ha implies he long-run equilibrium. Therefore, he Augmened Dickey-Fuller (ADF) es is used o perform uni roo ess on residuals of he coinegraing regression. Having esablished exisence of coinegraion, join resricions ( 1 0 and 1 ) and single resricion ( 1) are esed. If join resricions are rejeced bu single resricion is no rejeced, i indicaes ha erminaion spo price is equal o fuures price plus a risk premium. This siuaion does no give evidence agains raional expecaions because he posulaed one-for-one relaionship beween fuures prices and erminaion spo prices sill holds in he long-run equilibrium..3. Predicive Conen of he Basis The Granger Represenaion Theorem (Granger, 1986) saes if random variables X and Y are I(1) bu here exiss a linear combinaion of hem in he form of Y bx ha is I(0), an error correcion represenaion of hese coinegraed variables could be specified as follows: Y 1 X 3Y 1 bx 1 (7) where he erm ( Y 1 bx 1) is he 1-period lag of linear combinaion of X and Y. The linear combinaion of X and Y is called coinegraing relaionship and i represens he long-run equilibrium in he form of Y bx where coefficien b denoes coinegraing parameer. The coefficien 3 in above equaion is called adjusmen coefficien and i measures how variable Y adjuss o error in he previous period. The error correcion model explains shor-run changes in variable Y by shor-run changes in variable X and he error correcion erm which measures lagged deviaions of variable Y from he long-run equilibrium. Above error correcion specificaion is applied o gold coin fuures marke in order o es wheher he basis conains all relevan informaion o predic subsequen changes in spo prices. Hence, he following model is specified (Newbold, Kellard, Rayner and Ennew, 1999): s s ( f s ) (8) T T k 1 T k T k T where he erm ( ft k st k ) is he basis a a paricular forecas horizon denoed by k. In his model, he basis represens he coinegraing relaionship beween fuures prices and spo prices and he coinegraing parameer is se equal o uniy due o he unbiasedness hypohesis. As saed earlier, his regression model is run for muliple forecas horizons. Similar o he es of unbiasedness hypohesis, equaion (8) is esimaed by OLS, GARCH and 51

4 ISSN X (Prin), 16-14X (Online) Cener for Promoing Ideas, USA LAD mehods. If he basis is he unbiased predicor of subsequen changes in spo prices, join resricions ( 1 0 and 1) should hold in equaion (8). 3. Resuls and Inerpreaions 3.1. Maringale Hypohesis Table I repors OLS and GARCH resuls for he maringale hypohesis. The lag lengh of 6 for equaion () was seleced by iniially seing m equal o 10 and hen removing lags ha were insignifican a 10 percen. The leas squares resuls show ha, on average, join resricions on inercep and slope coefficiens canno be rejeced and ha regression residuals have no auocorrelaion up o order 30. However, he ARCH-LM es and he Q-Saisics of squared residuals find significan evidence for heeroskedasiciy in OLS residuals of equaion (). This finding moivaes he GARCH mehod o modeling ime-varying volailiy. The lag lengh of (1,1) for he GARCH model was sufficien o remove he ARCH effecs in regression residuals. The GARCH resuls show ha when heeroskedasiciy is accouned for, he Chi-squared Saisic for null hypohesis of join resricions on regression parameers is highly significan. Alhough here is no auocorrelaion in GARCH (1,1) residuals, rejecion of join resricions implies ha changes in gold coin fuures prices do no follow he maringale process. Besides, failure o rejec null hypohesis ha persisence parameers in he GARCH (1,1) sum up o uniy, 1, means ha volailiy shocks persis over ime. Table I OLS and GARCH Resuls for Maringale Hypohesis Regression Coefficiens OLS GARCH (1,1) (0.0004) (0.0001) (0.0419) (0.0191) (0.0516) (0.0191) (0.037) (0.0190) (0.0483) (0.0185) (0.036) (0.0174) (0.0378) (0.0168) (0.0000) (0.096) (0.0199) Esimaion Mehod ARCH Effecs in Residuals OLS GARCH (1,1) Hypohesis Tes of Join Resricions on Regression Chi-squared Saisics Coefficiens OLS GARCH (1,1) (7) ** (1) Ljung-Box Q-Saisics for Lag Order Serial Correlaion in Residuals OLS GARCH (1,1) ** Figures in parenheses are sandard errors; (7) H0 : i 0 for i 0,1,,..., 6 ; (1) is he es saisic for H 0 : 1; * Denoes saisically significan a 5% level; and 5

5 American Inernaional Journal of Conemporary Research Vol. 7, No. 3, Sepember 017 The GARCH and LAD mehods capure nonlinear dynamics. The GARCH resuls confirmed exisence of imevarying volailiy in he maringale process of changes in daily fuures prices. Table II repors resuls of esimaing equaion () in hree differen quaniles, namely, median, 15 h percenile and 85 h percenile. The median represens he normal marke condiion, whereas lower and upper ails consiue he bear marke and he bull marke, respecively. The lag lengh a each quanile was seleced by iniially seing m equal o 10 and hen removing lags ha were insignifican a 10 percen. The LAD resuls indicae exisence of nonlinear dynamics in he sense ha esimaes of regression parameers and inferences abou he maringale hypohesis vary among quaniles. In he normal marke condiion, findings show ha gold coin fuures marke has weak-form efficiency because join resricions on regression parameers canno be rejeced and residuals have no serial correlaion a leas up o order 10. This evidence is in line wih OLS resuls shown in Table I. Therefore, esimaes of equaion () in condiional mean and condiional median reveal ha he maringale hypohesis holds. Table II LAD Resuls for Maringale Hypohesis Regression Coefficiens Lower Tail Median Upper Tail (0.0005) (0.000) (0.0007) (0.0470) (0.0456) (0.051) (0.0496) (0.044) (0.0671) (0.0461) (0.0459) (0.0464) Chi-squared Saisics Hypohesis Tes of Join Resricions on Regression Coefficiens Lower Tail Median Upper Tail (3) ** (6) ** Lag Order Ljung-Box Q-Saisics for Serial Correlaion in Residuals Lower Tail Median Upper Tail * * * * * ** ** * ** * ** ** ** ** Lower ail is he 15 h percenile; Upper ail is he 85 h percenile; Figures in parenheses are sandard errors; (.) is he es saisic for H0 : i 0 for i 0,1,,..., p ; Denoes saisically significan a 5% level; and In conras, he siuaion is differen in ails of he disribuion. In boh bear marke and bull marke, he Chisquared Saisic becomes significan and join resricions on regression coefficiens are rejeced. Also, resuls deec serial correlaion in residuals since he Q-Saisics are highly significan. I means ha when gold coin fuures marke eners bearish or bullish erriory, raders migh be able o predic curren changes in fuures prices using hisorical daa. 53

6 ISSN X (Prin), 16-14X (Online) Cener for Promoing Ideas, USA Alhough gold coin fuures marke shows some elemens of weak-form efficiency in he normal marke condiion, pas changes in fuures prices could be used o forecas curren changes in fuures prices as he marke eners exreme condiions. In oher words, when fuures marke volailiy increases, hisorical sequence of price changes migh predic curren changes in prices. Thus, he maringale hypohesis does no hold in boh ails. 3.. Unbiased Expecaions Hypohesis Table III shows ha boh fuures and cash prices are nonsaionary because null hypohesis of uni roo canno be rejeced. Table IV repors OLS resuls of he coinegraing regression. The ADF es reveals ha residuals have no uni roo. I implies ha fuures prices and erminaion spo prices are coinegraed a all forecas horizons. The hypohesis es of join resricions on parameers of he coinegraing regression shows ha, apar from forecas horizons of 10, 15 and 0 days, fuures prices are unbiased esimaors of erminaion spo prices. The single resricion on he slope coefficien is rejeced a forecas horizons of 10, 15 and 0 days. Therefore, leas squares resuls show ha fuures prices, in 5 ou of 8 forecas horizons under examinaion, correcly predic erminaion cash prices, on average. The GARCH was no used o model condiional heeroskedasiciy since no ARCH effecs were found in error erms. Table III Resuls for Uni Roo Forecas horizon (days) Fuures Price ADF Uni Roo Tes Terminaion Spo Price ADF ADF sands for Augmened Dickey-Fuller; * Denoes saisically significan a 5% level; and Table IV OLS Resuls for Unbiased Expecaions Hypohesis Forecas Horizon (days) Coinegraion Unbiasedness ADF () (1) ** ** * * ** ** ** ** 9.9 ** ** ** ** ** ** ADF sands for Augmened Dickey-Fuller; () H 0 and 1 ; (1) 0 : 1 is he es saisic for H 0 : 1; * Denoes saisically significan a 5% level; and 54

7 American Inernaional Journal of Conemporary Research Vol. 7, No. 3, Sepember 017 Table V shows null hypohesis of nonsaionary residuals is rejeced a 1 percen significance level for all forecas horizons. I means ha fuures prices and erminaion spo prices are coinegraed a all forecas horizons in he median and in boh ails. In he normal marke condiion, represened by he median, he unbiasedness hypohesis is rejeced a forecas horizons of 10, 15 and 5 days. The join resricions on parameers of he coinegraing regression canno be rejeced a oher forecas horizons. The LAD resuls in he case of median are similar o OLS resuls. However, resuls of unbiasedness ess are differen in lower and upper ails because join resricions are rejeced a mos forecas horizons. For example, join resricions are rejeced bu single resricions are no rejeced when spo marke eners bearish erriory. I means ha inercep coefficien of he coinegraing regression is significan when cash marke is bearish. The significance of inercep coefficien in lower ail implies ha fuures raders expec risk premia when spo prices are falling sharply. However, since he single resricion on he slope coefficien canno be rejeced, i is inferred ha here exiss a long-run one-for-one relaionship beween fuures prices and erminaion spo prices a all forecas horizons even when spo marke is bearish. The resuls are similar a forecas horizons of 5, 10, 5, 35 and 40 days in upper ail. The risk premium is insignifican in mean and median bu i is significanly larger han zero in boh ails. So, i is concluded ha when spo prices become more volaile, fuures raders ofen expec risk premia bu he one-for-one relaionship beween fuures prices and erminaion spo prices usually holds in he long run. This evidence also implies ha gold coin is considered as a safe-haven asse in he normal marke condiion, and hence has no sysemaic risk. Bu when spo prices fall or rise sharply, a posiive risk premium should compensae fuures raders for he sysemaic risk of gold coin. Table V LAD Resuls for Unbiased Expecaions Hypohesis Forecas Horizon (days) Lower Tail Coinegraion Unbiasedness ADF () (1) ** ** ** * ** ** ** ** ** ** ** ** ** ** ** * Median Coinegraion Unbiasedness Forecas Horizon (days) ADF () (1) ** ** * * ** ** ** ** ** * * ** ** ** Upper Tail Coinegraion Unbiasedness Forecas Horizon (days) ADF () (1) ** ** ** * ** * 5.83 * ** ** ** ** ** 1.53 ** ** ** Lower ail is he 15 h percenile; Upper ail is he 85 h percenile; ADF sands for Augmened Dickey-Fuller; () is he es saisic for H 0 and 1 ; 0 : 1 (1) is he es saisic for H 0 : 1; * Denoes saisically significan a 5% level; and 55

8 ISSN X (Prin), 16-14X (Online) Cener for Promoing Ideas, USA Predicive Conen of he Basis Table VI repors OLS and GARCH resuls for equaion (8). In erms of condiional mean dependence, he basis is he unbiased esimaor of subsequen changes in spo prices a all forecas horizons excep 15- and 5-day horizons. The OLS residuals have ARCH effecs a forecas horizons of 15 and 30 days only. The lag lengh of (1,1) for he GARCH model was sufficien o remove he ARCH effecs in error erms. The GARCH resuls show ha when heeroskedasiciy is modeled, he Chi-squared Saisic for null hypohesis of join resricions on regression parameers becomes insignifican a 15-day forecas horizon. Therefore, he basis seems o be he unbiased esimaor of subsequen changes in spo prices a all forecas horizons excep 5-day horizon. Also, failure o rejec null hypohesis ha persisence parameers in he GARCH (1,1) sum up o uniy provides evidence for persisen ime-varying volailiy. Table VI OLS and GARCH Resuls for Predicive Conen of he Basis Forecas Horizon (days) OLS GARCH (p,q) () ARCH Effecs (p,q) () (1) ARCH Effecs * (1,1) ** (1,1) () is he es saisic for H 0 : 1 0 and 1; (1) is he es saisic for H 0 : 1; Denoes saisically significan a 5% level; and The LAD resuls for equaion (8) are shown in Table VII. The resuls in he case of median are similar o hose of leas squares. In conras, evidence shows ha he basis fails o provide unbiased predicions of subsequen changes in spo prices in bear and bull markes. In oher words, he basis does no seem o have significan predicive conen when cash prices fall or rise sharply. Table VII LAD Resuls for Predicive Conen of he Basis Forecas Horizon (days) Lower Tail Median Upper Tail () () () ** ** ** * ** ** * ** ** * ** * ** Lower ail is he 15 h percenile; Upper ail is he 85 h percenile; () H 0 : 1 0 and 1 ; Denoes saisically significan a 5% level; and 56

9 American Inernaional Journal of Conemporary Research Vol. 7, No. 3, Sepember Conclusion The objecive of he presen paper was o es maringale, coinegraion and unbiasedness hypoheses in Iran gold coin marke using linear and nonlinear mehods. The resuls from analysis of nonlinear dynamics imply ha changes in daily fuures prices are forecasable by pas sequence of changes in fuures prices in bear and bull markes even hough linear models show ha he maringale hypohesis holds. Also, when condiional heeroskedasiciy is accouned for, we obain evidence ha rejecs he maringale hypohesis. The resuls of esimaing he coinegraing regression in condiional mean and condiional median reveal ha fuures prices are unbiased esimaors of erminaion spo prices a mos forecas horizons. I is concluded ha in he normal marke condiion, fuures prices and erminaion spo prices are ofen coinegraed wih a coinegraing vecor (1, -1). Bu when cash marke eners bearish or bullish erriory, fuures raders demand risk premia alhough he one-for-one relaionship beween fuures prices and erminaion spo prices sill holds in he long run. Overall, i seems ha gold coin fuures marke has so far provided relaively fair esimaes of fuure cash prices. Also, evidence shows ha he basis fails unbiasedness ess when cash marke eners bearish or bullish erriory. References Basse, G., and R. Koenker, 1978, Regression Quaniles, Economerica 46(1): Brock, W. A., Hsieh, D., and LeBaron, B., 1991, Nonlinear Dynamics, Chaos, and Insabiliy, Cambridge, MA: MIT Press. Bollerslev, T., 1986, Generalized Auoregressive Condiional Heeroskedasiciy, Journal of Economerics 31(3): Chinn, M., and O. Coibion, 014, The Predicive Conen of Commodiy Fuures, Journal of Fuures Markes 34 (7): Chow, Y., 1998, Regime Swiching and Coinegraion Tess of he Efficiency of Fuures Markes, Journal of Fuures Markes 18 (8): Crowder, W. J., and A. Hamed, 1993, A Coinegraion Tes for Oil Fuures Marke Efficiency, Journal of Fuures Markes 13(8): Fama, E. F., 1991, Efficien Capial Markes: II, Journal of Finance 46(5): Fujihara, R.A., and M. Mougoue, 1997, Linear Dependence, Nonlinear Dependence and Peroleum Fuures Marke Efficiency, Journal of Fuures Markes 17(1): Granger, C. W. J., 1986, Developmens in he Sudy of Coinegraed Economic Variables, Oxford Bullein of Economics and Saisics 48(3): Hansen, L.P., and Hodrick, R.J., 1980, Forward Exchange Raes as Opimal Predicors of Fuure Spo Raes: An Economeric Analysis, Journal of Poliical Economy 88 (5): Hsieh, D., and Kulailaka, N., 198, Raional Expecaions and Risk Premia in Forward Markes: Primary Meals a he London Meal Exchange, Journal of Finance 37(5): Newbold, P., Kellard, N., Rayner, T. and C. Ennew, 1999, The Relaive Efficiency of Commodiy Fuures Markes, Journal of Fuures Markes 19(4): Samuelson, P. A., 1965, Proof ha Properly Anicipaed Prices Move Randomly, Indusrial Managemen Review 6: