Volatility of rates of return on the example of wheat futures. Sławomir Juszczyk. Rafał Balina

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1 Overcomig the Crisis: Ecoomic ad Fiacial Developmets i Asia ad Europe Edited by Štefa Bojec, Josef C. Brada, ad Masaaki Kuboiwa Volatility of rates of retur o the example of wheat futures Sławomir Juszczyk Warsaw Uiversity of Life Scieces SGGW, Faculty of Ecoomic Scieces Rafał Balia Warsaw Uiversity of Life Scieces SGGW, Faculty of Ecoomic Scieces Abstract: This article presets chose examples of aomalies i the distributio of rates of retur o the capital markets i the world, based o a review of literature. Moreover, the authors has show that i the case of wheat futures listed o the FOREX market are also aomalies i the distributio of rates of retur. It was oted that the rate of retur ad the coefficiet of variatio for a give asset i the last four hours of the day of tradig are sigificatly higher tha i the early hours JEL Classificatio: G14, G13 Keywords: capital market, aomalies, wheat futures Itroductio The thesis of the capital market efficiecy eve i its weak form states that the study of historical rates of retur should ot provide useful iformatio for effectively predictig the rates of retur i the future (Coe A. 1999). However i literature oe ca fid umerous examples which are i coflict with this thesis. The basis o which ca be predict rates of retur are so-called aomalies or caledar effects. These pheomea costitute exceptios to the iformatioal efficiecy of capital markets. Aomalies i the distributio of rate of retur may be depedet o the time of the trasactio - the so-called temporary ad seasoal aomalies, the delayed ivestors reactio for market or over-reactig o icomig iformatio. Aomaly are ay kid of deviatio from the typical or average values of rate of retur. Therefore, ay deviatio of the repeated subject of the days, moth, hour, i which they ca be cosidered as a maifestatio of the capital market iefficiecies. A example of "caledar effect" is "the effect of moth of the year," also called "Jauary effect". This research carried out by may researchers, amog others Fam E. (1991), Hauge RA, Lakoishok J. (1988); Dimisio E. (1988), Gluteki MN, NB Gluteki (1983), Reigaum M.R. (1983). They lead to the coclusio that the rate of retur o stocks listed o U.S. ad Europea stock markets i Jauary are geerally sigificatly higher tha i the remaiig moths. This allows to use this relatioship to predict future rates of retur i Jauary. Aother example, which is icosistet with the hypothesis of efficiet capital market i a weak form are researches carried out by the RA Ariel'a (1987) i which Ariel poited to the sigificat differece betwee the decay rates of retur i a moth. He oted that the cumulative icrease o the US capital market was caught i the first moths, which also is the basis for cosideratio of the expected rate of retur o ivestmet i equities. Namely, it allows the use of this relatioship for speculative ivestmet decisios. 11

2 Aother example, which allows to predict the directio of chages i the stock market, based o historical data is the so-called "day of the week effect," which assumes that the differeces betwee the rates of retur o each day are differet. I umerous studies have show that the average Moday returs i the U.S. market are much lower tha average rates of retur i the remaiig days of the week (Frech K.R. 1980; D.K. Keim, Stambaugh R.F. 1985; Rogalski R.J. 1984; Smirlock M., Starks L. 1986). Aother example of the aomalies i the distributio of rates of retur is so-called "the effect o hours." I literature we ca fid may examples of study about relatio betwee rates of retur depedig of a hour, or quarter of a hour (Smirlock M., Starks L L. Harris, 1986). These studies show that the rate of retur o i each tradig hours are differet ad i may cases repetitive, which ca be used successfully i practice. Give the cited examples of "caledar effects" should be oted that all studies are coducted o the basis of data from stock exchages. Give the literary achievemets of issues should be oted that i priciple there are o studies of the aomalies o the futures market for agricultural commodities. Purpose ad test methods The mai objective of this paper is to demostrate the existece of sigificat differeces i the volatility of wheat listed o the FOREX market durig the hours of 04:35PM - 07:35PM compared to the quotatio from 01:35AM - 12:35PM hours, as a aomaly i the futures market for agricultural products. The results are based o real data about closig price of wheat futures cotracts for each hour from 27 Jauary 2010 to 26 Jauary Selectio of the study period was deliberated ad was iteded to cover a full year to take ito accout factors related to seasoality of agricultural market. For future cosideratio author formula for rate of retur expressed as a quotiet of the differece betwee the closig price i a give time ad the closig price i the first hour of tradig ad the closig price of the asset i the first hour of tradig. Moreover, the coefficiet of variatio was used as a measure of rate volatility durig the cosidered period. Results of research Study period iclude periods i which followed a icrease, decrease ad cosolidatio quotes. Aalyzig the quotes of wheat futures o a hourly arragemet may be otice a patter. Namely, listig the hours 4:30PM 7:35PM had sigificatly higher quotatio tha it have place i the hours before the 12:35PM - a graphical presetatio of the above observatios show Figure 2. 12

3 Figure 2 Fluctuatios of price of wheat futures o a hourly arragemet I order to cofirm the observed depedece later was used followig formula for rate of retur for log positio of wheat futures: Pt P0 Rt = P0 where: R t - the rate of retur i a give time, P t - closig price at the time, P 0 - the closig price i the first hour of tradig. Rates of retur i idividual hours is relate to daily chages. This assumptio illustrate how will chage the rate of retur depedig o the time to maitai a market positio. The rates of retur calculated by the above formula show Figure 3. Aalyzig Figure 3 should be emphasized that the rate of retur durig hours from 1:35AM to 12:35PM are relatively stable ad raged from -2.9% to 5.44%. Figure 3 Rate of retur of wheat futures [%] Their level should be cosidered as relatively low obtaied yields because after takig ito accout trasactio spared ot allow to obtai extraordiary results that a ivestor would be reach. Durig hours betwee the hours of 04:35PM ad 07:35PM rate of retur had sigificatly higher values tha the rates of retur obtaied i the hours of 01:35AM ad 12:35PM. Namely, these chages raged from -9.98% to 8.61%. From the perspective of a ivestor opeig positios i the first hour of tradig wheat futures o a give day ad keep it util the afteroo that same day gave the opportuity to gai a higher rate of retur because the rage of variability i the rate of retur was much higher tha i the morig. I order to idicate differeces i volatility betwee periods was used the coefficiet of variatio as a statistical measure to determie the scope of chages allowig tradig wheat 13

4 futures i periods. For the calculatio was used formula: (Sobczyk M., 2006, p. 46; Witkowska D., 1999, p. 90): i = 1 ( x V = x where: V - coefficiet of variatio, - umber of observatios, x i - value of the i-th observatio, i x 2 ) xi i= x = 1 The object of research were divided ito two groups accordig to the previously observed decay rates of retur. The first group cosisted of observatios from the period betwee the hours of 01:35AM ad 12:35PM, the secod group cosisted of observatios from 04:35PM to 07:35PM hours. For the each group was calculated the coefficiet of variatio. The obtaied results show Figure 4. Figure 4 Coefficiets of variatio i each group The study showed that the coefficiet of variatio calculated for the first group was i the case of 234 days of observatio higher tha i the secod group. For the other 19 cases calculated the coefficiet of variatio was lower tha i the first group. This meas that the variability betwee the hours of 01:35AM ad 12:35PM was lower tha that betwee 04:35PM ad 07:35PM i 92.5% of cases. The coefficiet of variatio i the first tradig period raged from 0.2 to 5.7% ad i the secod period raged from 0.1 to 14.7%. Clearly demostrates the sigificat differeces betwee the extet of variatio betwee the quotatios of wheat futures i hours betwee 01:35AM - 12:35PM ad quotatios from 04:35PM to 07:35PM. It should be oted that the biggest chages i the wheat futures prices took place durig the period form 04:35PM to 07:35PM. Coclusios O the basis of the aalysis it was oted that i the case of wheat futures prices they are reach their highest level of variatio betwee the hours of 04:35PM ad 07:35PM each day, which has a decisive ifluece o the daily rate of retur. I additio, rates of retur from takig positio before 12:35PM ad keep it secod tradig period gave sigificatly better 14

5 results tha closig it before 04:35PM. This pheomeo ca be cosidered as a example of aomalies of futures market for agricultural products. Also result of author s research ca be used to predict price movemets of wheat futures. Research coducted for the purposes of this article, due to sigificat differeces i specificatios ad hours tradig of futures market o agricultural products caot be trasferred to other markets. Refereces Ariel R.A Mothly Effect i Stock Returs. Joural of Fiacial Ecoomics. March. Dimisio E Stock Market Aomalies. Cambridge Uiversity Press. Cambridge. Fama E Efficiet Capital Markets II. Joural of Fiace. No. 5. December. Frech K.R Stock Returs for the Weeked Effect i Stock Returs. Joural of Fiace. Jue. Gluteki M.N., Gluteki N.B Stock Market Seasoality: Iteratioal Evidece. Joural of Fiacial Ecoomics. No 12. Hauge R.A., Lakoishok J The Icredible Jauary Effect. Dow Joes-Irwi, Homewood. Harris L A Trasactio Data Study of Weekly ad Itradaily Patters i Stock Returs. Joural of Fiase. Jue. Keim D.K., Stambaugh R.F A Further Ivestigatio of the Weeked Effect i Stock Returs. Joural of Fiace. Jue. Reigam M.R The Aomalous Stock Market Behavior of Small Firms i Jauary. Joural of Fiacial Ecoomics. Jue. Rogalski R.J New Fidigs Regardig Day-of-the-Week Returs over Tradig ad No-tradig Periods. Joural of Fiace. December. Smirlock M., Starks L Day-of-the-Week ad Itraday Effects i Stock Returs Joural of Fiacial Ecoomics. September. Sobczyk M Statystyka aspekty praktycze i teoretycze. Wydawictwo Uiwersytetu Marii Curie-Skłodowskiej. Lubli. Szyszka A Efektywość ryku kapitałowego a aomalie w rozkładzie stóp zwrotu w czasie. Nasz Ryek Kapitałowy. No 12. Witkowska D Metody statystycze w zarządzaiu. Wydawictwo Wydziału Orgaizacji i Zarządzaia Politechiki Łódzkiej. Łódź. 15