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Redaktor Naczelny

Dr hab. Radosław Pastusiak, prof. nadzw. UŁ – Uniwersytet Łódzki

Zastępca Redaktora Naczelnego

Dr Monika Bolek – Uniwersytet Łódzki

Recenzenci:

Prof. dr hab. Krystyna Brzozowska – Uniwersytet Szczeciński

Dr hab. Iwona Dorota Czechowska, prof. nadzw. UŁ – Uniwersytet Łódzki

Dr hab. ElŜbieta Rychłowska Musiał, prof. nadzw. UŁ – Uniwersytet Ekonomiczny w Poznaniu

Dr hab. Sebastian Majewski, prof. nadzw. US – Uniwersytet Szczeciński

Dr hab. Tomasz Słoński – Uniwersytet Ekonomiczny we Wrocławiu

Prof. dr hab. Wacława Starzyńska – Uniwersytet Łódzki

Dr hab. Danuta Zawadzka, prof. nadzw. PK – Politechnika Koszalińska

Redaktorzy Tematyczni:

Finanse Publiczne: Dr hab. Beata Guziejewska, prof. nadzw. UŁ – Uniwersytet Łódzki

Finanse Przedsiębiorstwa: Dr hab. Danuta Zawadzka, prof. nadzw. PK – Politechnika Koszalińska

Ekonometria: Dr Adam Kucharski – Uniwersytet Łódzki

Statystyka: Dr Dariusz Parys – Uniwersytet Łódzki

Rynek Kapitałowy: Dr Monika Bolek – Uniwersytet Łódzki

Finanse Behawioralne: Dr ElŜbieta Kubińska – Uniwersytet Ekonomiczny w Krakowie

Sekretarz Redakcji: Mgr Małgorzata Jabłońska

Uniwersytet Łódzki, Wydział Ekonomiczno-Socjologiczny

Członek Redakcji – Mgr Jakub Koziński

skład, druk, dystrybucja: Uniwersytet Łódzki, Wydział Ekonomiczno-Socjologiczny

Redakcja techniczna, Mgr Monika Wolska-Bryl

skład i łamanie: Uniwersytet Łódzki, Wydział Ekonomiczno-Socjologiczny

ISSN: 2392-0726

Adres Redakcji: Zakład Finansów Korporacji, Uniwersytet Łódzki, ul. Rewolucji 1905 r. nr 39, 90–214 Łódź Telefon: +48 42 635 51 89

e-mail: jcmbf(at)uni.lodz.pl

www.jcmbf.uni.lodz.pl

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SPIS TREŚCI

Od Redakcji ………... 5

Krzysztof Borowski – Analysis of Selected Seasonality Effects in Market of

Frozen Concentrated Orange Juice (FCOJ) Future Contracts ……… 7

Karolina Wrzesińska – Kaizen – czynniki determinujące skuteczne wdroŜenie

w przedsiębiorstwach na całym świecie ………. 31

Katarzyna Kuta, Krzysztof Rudnicki – Activity-Based Costing jako metoda

usta-lania wyniku operacyjnego w słuŜbie zdrowia …….……….. 49

Anna Topolska, Karina Tomczyk – Szanse i zagroŜenia dla menedŜerów na

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JCMBF • www.jcmbf.uni.lodz.pl 5 Journal of Capital Market and Behavioral Finance • 2015, Vol. 1(1), p. 5–6 Radosław Pastusiak_{, Od Redakcji}

OD REDAKCJI

Journal of Capital Market and Behavioral Finance publikuje artykuły z

ob-szaru finansów przedsiębiorstwa oraz rynku kapitałowego, ze szczególnym uwzględnieniem zjawisk mających podłoŜe psychologiczne. Niniejszym chcemy przedstawić czytelnikom drugi numer czasopisma, który jest poświęcony wyko-rzystaniu rachunkowości zarządczej celem zwiększenia efektywności funkcjo-nowania biznesu, zawiera rozwaŜania o strukturze kapitału w świetle ostatnich trendów światowych, a takŜe analizuje zjawiska sezonowości na rynku kontrak-tów futures na sok pomarańczowy.

Rynek kontraktów pochodnych jest rosnącym co do wolumenu segmentem handlu rynku kapitałowego. Kontrakty futures na mroŜony sok pomarańczowy są niszowym instrumentem, którego znaczenie doceniają przede wszystkim in-westorzy spekulacyjni, firmy spoŜywcze chcące zabezpieczyć się przed waha-niami cen półproduktu, a takŜe producenci soków owocowych. Znaczenie sezo-nowości w kształtowaniu cen produktów jest zjawiskiem dobrze znanym, tym bardziej warto poświecić uwagę kształtowaniu się cen kontraktu futures na po-niekąd sezonowy produkt oraz implikacjach z tym związanych dla inwestorów.

Strategia zarządzania Kaizen Costing, to właściwie filozofia, która jest wpi-sana w japońską kulturę korporacyjną. Pozwala ona na swoiste zjednoczenie pracownika z przedsiębiorstwem oraz wyeksponowanie myślenia, mającego za zadanie niwelowanie deficytów organizacyjnych, skutkujących błędami, a tym samym zwiększonymi kosztami działania. Artykuł prezentowany w numerze ma za zadanie pokazać, czy Kaizen da się zaimplementować wszędzie na świecie, czy są potrzebne specjalne do tego warunki.

Metoda ABC transferu kosztów pośrednich na końcowy produkt jest znana od ponad 30 lat. Wykorzystanie tej metody w kolejnych sektorach jest uwarun-kowane liczbą procesów jakie da się skutecznie opisać kosztami. SłuŜba zdrowia jest działem gdzie kontrola kosztów ma duŜe znaczenie ogólnospołeczne, więc kaŜde działania mające na celu lepszą kontrolę kosztów stanowią na pewno war-tość dodaną dla wszystkich.

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JCMBF • www.jcmbf.uni.lodz.pl 6

Journal of Capital Market and Behavioral Finance • 2015, Vol. 1(1), p. 5–6 Radosław Pastusiak_{, Od Redakcji}

W artykule poświęconym zagroŜeniom w transakcjach fuzji i przejęć dla menedŜerów, autorzy starają się wyeksponować rolę zarządzających w przedsię-biorstwie, a szczególnie w procesie fuzji i przejęcia. MenedŜerowie pełnią nie tylko znaczącą rolę w transakcji wykupu menadŜerskiego MBO, ale takŜe pod-czas zarządzania procesem fuzji lub przejęcia. Ich zaangaŜowanie ma duŜe zna-czenie, a wiara w powodzenie transakcji dodatkowo wpływa pozytywnie na jej zamknięcie. MenedŜerowie są najwaŜniejszymi pracownikami przedsiębiorstwa, ich znaczenie dla transakcji fuzji jest kluczowe.

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JCMBF • www.jcmbf.uni.lodz.pl 7 Journal of Capital Market and Behavioral Finance • 2015, Vol. 1(1), p. 7–30

Krzysztof Borowski, Analysis of Selected Seasonality Effects…

ANALYSIS OF SELECTED SEASONALITY

EFFECTS IN MARKET OF

FROZEN CONCENTRATED ORANGE JUICE

(FCOJ) FUTURE CONTRACTS

Krzysztof Borowski*

Abstract Likely to the equity market, the problem of anomalies in the commodities

market is becoming an interesting phenomenon, particularly in the segment of the agricultural market. This paper tests the hypothesis of monthly, daily, the day-of-the week, the first and the second half of monthly effects on the market of Frozen Concentrated Orange Juice (FCOJ) futures, quoted in the period from 28.02.1967 to 31.03.2015. Calculations presented in this paper indicate the absence of the day-of-the-week effect and the existence of monthly effect: in February and June with the use of the average monthly rates of return and in February, June and December, when the daily average rates of return were implemented. The seasonal effects were also observed in the case of testing the statistical hypothesis for averaged rates of returns for different days of the month (2nd, 21st, 23th and 31st), as well as for the daily average rates of return in the first and in the second half of a month.

Key words market efficiency, commodity market, FCOJ, calendar effects, market anomalies.

INTRODUCTION

According to Efficient Market Hypothesis (EMH), introduced by Fama [1970] the security prices fully reflect all available information. This theory has been subjected to many analysis and has become a main source of disagreement between academics and practitioners. The latter tends to reject the EMH while the academics support it. Current definitions of EMH differ from that formulated by Fama [1970]. According to them, the efficiency of markets prevents

* Warsaw School of Economics (Institute of Banking and Business Insurance). ACCEPTED: 31st

October 2015 PUBLISHED: 20th

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Journal of Capital Market and Behavioral Finance • 2015, Vol. 1(1), p. 7–30 Krzysztof Borowski, Analysis of Selected Seasonality Effects …

systematic beating of the market, usually in a form of above-average risk--adjusted returns. Because of the fact, that stock market anomalies breach the EMH, they are the subject to many empirical research.

The problem of the financial markets efficiency, especially of equity markets, has become a main topic of number of scientific works, which has led to a sizable set of publications examining this issue. In many empirical work dedicated to the time series analysis of rates of return and stock prices, statistically significant effects of both types were found, i.e. calendar effects and effects associated with the size of companies. These effects are called „anomalies”, because their existence testifies against market efficiency. Discussion of the most common anomalies in the capital markets can be found, among others, in Simson [1988] or Latif et al. [2011].

One of the most common calendar anomalies observed on the financial markets are:

A) Day-of-the-week effect – different distributions of expected rates of return can be observed for different days of the week [Keim and Stambaugh, 1984]. Strong evidence of the day-of-the-week effect has been found by many academics in major markets, Gibbon and Hess [1981]. The day-of-the-week effect in the US market was also presented, among others, in the works of: Jaffe et al. [1989], French [1980], Lakonishok and Maberly [1990]. The evidence for UK market was examined by: Theobald and Price [1984], Jaffe and Westerfield [1985], Board and Sutcliffe [1988], Agrawal and Tandon [1994], Peiro [1994], Mills and Coutts [1995], Dubois and Louvet [1996], Coutts and Hayes [1999]. Peiro [1994], Agrawal and Tandon [1994], Dubois and Louvet [1996] and Kramer [1996] provided evidence of negative Monday and Tuesday returns for Frankfurt exchange. In works of Solnik and Bousquet [1990], Agarwal and Tandon [1994], there was found an evidence of negative Tuesday rates of return in Paris market, while Condoyanni et al. [1987] and Peiro [1994] demonstrated negative Monday and Tuesday rates or return on the same market and Barone [1990] in Milan. Research regarding rates of return on other market was performed in works of Kato et al. [1990], and also by Sutheebanjard and Premchaiswadi [2010]. On the Polish market, findings regarding the day-of-the--week effect were conducted among others by: Tarczyński [1997], Piontek [2000], Buczek [2005: 51–55], Szyszka [2007: 141–146], Ślepaczuk [2006], Witkowska and Kompa [2007], Sojda [2008], Grotowski [2008], Borowski [2013], as well as by Fiszeder and KoŜuchowska [2013].

B) Monthly effect – achieving by portfolio replicating the specified stock index, different returns in each month. The most popular monthly effect is called „January effect”, i.e. the tendency to observe higher average rate of return of stock market indices in the first month of the year. For the first time, this effect was observed by Keim [1983], who noted that the average rate of return on

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stocks with small capitalization is the highest in January. In case of large and mid-capitalization companies the effect was not so perceptible. Although January was the best single month in UK, the period from December to April consisted of months, which on average produced positive returns [Rozeff and Kinney 1976, Corhay et al. 1988]. Bernstein [1991], taking into consideration the behavior of the US equity market in the period from 1940 to 1989, observed the interdependence between rates of returns in each month. Modern researches, e.g. Gu [2003] and Schwert [2002] prove that in the last two decades of the twentieth century, phenomenon of the month-of-the-year effect was much weaker. This fact would suggest that the discovery and dissemination of the monthly effect in world financial literature contributed to the increase of market efficiency.

C) Other seasonal effects – in the financial literature, the following calendar effects can be found:

The weekend effect – Cross [1973] found that markets tend to raise on Fridays and fall on Mondays. His findings generated a flood of research [Lakonishok and Levi 1982; Jaffe and Westerfield 1985; Condoyanni et al. 1987; Connolly 1991; Abraham and Ikenberry 1994]. In the literature two ways of computing weekend rates of return are implemented. In the first approach, Friday close and Monday open prices are used, while in the second example Friday close and Monday close prices are employed.

The holiday effects – markets before holidays or other trading breaks tend to rise. In the US there is a number of studies looking at this issue, e.g., Fields [1934], Ariel [1987 and 1990], Lakonishok and Smith [1988] and Cadsby and Ratner [1992].

Within-the-month effect – positive rates of returns only occur in the first half of the month [Ariel 1987; Kim and Park 1994].

Turn-of-the month effect – average rate of return calculated for the last day of the month and for three days of the next month, was higher than the average rate of return calculated for the month, for which the rate of return of only one session, was taken. Lakonishok and Smidt [1988] found that the four days at the turn-of-the-month averaged a cumulative rate of increase of 0,473% versus 0,0612% for and average four days. The average monthly increase was 0,349%, i.e., the DJIA went down during non-turn-of-the-month period.

Commodity market is one of the segments of the financial market, characterized by high heterogeneity of assets compared to the stock or bond markets [Johnson and Soenen 1997]. It is often perceived as a separate asset class, which in turn leads to low correlation of commodity market rates of return in comparison to the returns on the stock or bonds markets. The consequence of this fact is the possibility of constructing more diversified investment portfolio compared to a portfolio solely consisting of shares or bonds. Another factor in

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favor of investing in the commodity market is the ability to protect the investment portfolio from the negative effects of inflation. This type of investor preferences in building an investment portfolio are clearly visible in the period of increased inflation [Gorska and Krawiec 2013]. Another factor encouraging investors to carry out investments in the commodity market can be a threat of currency devaluation or the outbreak of armed conflict.

In the world literature, in contrast to the stock market, relatively little attention has been dedicated to the occurrence of the seasonality effects on the agricultural commodity market. This fact was one of the reasons encouraging the author to undertake empirical studies.

The aim of this article is to examine the prevalence of selected seasonality effects on the markets of Frozen Concentrated Orange Juice (FCOJ). Analysis of the seasonality effects will apply to monthly returns (average monthly returns and average daily returns in each of analyzed months), to returns over various days of the week, over various days of a month, and as well as to average daily

rates of return in the first (days from the 1st to the 15th) and in the second half of

month (from 16th to the end of the month). Statistical tests were conducted for

FCOJ futures on the basis of Bloomberg prices for the period from 28.02.1967 to 31.03.2015. The prices for FCOJ futures are expressed in USD per pound – the trading unit of each FCOJ future is equal to 15 000 pounds. FCOJ futures have traded in New York since 1966, first on the New York Cotton Exchange, and letter on the successor New York Board of Trade and now on Intercontinental Exchange (ICE Futures U.S.).

1. LITERATURE REVIEW

In the scientific literature a statement can be found that the stock market is somehow predestined to record number of anomalies, whereas the foreign exchange is the most effective of all the markets [Froot and Thaler 1990]. It is worth noting that the number of scientific papers dedicated to commodity market efficiency is lower than those relating to the stock market. Numerous research has examined the price efficiency of agricultural markets. However, many of the studies differ with respect to the analyzed commodity, the covered time period and implemented method of analysis, and the type of data employed in the research [Garcia et al. 1988].

Tests of price market efficiency in a weak form were conducted among others by Bigman et al. [1983], Kofi [1972], Leath and Garcia [1983], Springs [1981] and Tomek and Gray [1970]. All of these studies focused on the following agricultural commodities: wheat, corn, soybeans [Bigman et al. 1983], wheat, corn, soybeans, cocoa, coffee [Kofi 1972], corn [Leath and Garcia

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1983], corn [Springs 1981], corn, soybeans and potatoes [Tomek and Gray 1970]. In turn, test of price market efficiency in a semi-strong form were performed by Canarella and Pollard [1985], Just and Rausser [1975], Rausser and Carter [1983] and regarded markets of: wheat, corn, soybeans, soybean oil (the two first papers) and markets of soybean and soybean oil (the third paper).

The price inefficiency of some agriculture commodity markets was proved by [Garcia et al. 1988]:

a)Bigman et al. [1983] – wheat, corn and soybeans,

b)Bigman and Goldfarb [1985] – wheat, corn, soybeans,

c)Brinegar [1970] – wheat, corn, rye,

d)Helms et al. [1984] – soybeans, soybean oil,

e)Hunt [1974] – wool,

f) Martel and Helms [1978] – wheat, corn, oats, soybeans, soybean oil,

g)Stevenson and Bear [1970] – cottonseed oil and soybeans.

There are, however, works proving thesis of the effectiveness of selected commodity market segments:

a)Labys and Granger [1970] – corn, oat, rye, wheat, lard,

b)Larson [1960] – corn.

The third group of scientific works prove thesis of the mixed nature of the effectiveness of different types of commodity markets:

a)Cargil and Rausser [1972] – corn, oat, rye, soybeans, wheat,

b)Cargil and Rausser [1975] – corn, oat, rye, soybeans, wheat,

c)Gordon [1985] – wheat, corn, rough rice, soybeans, cotton, orange juice,

soybean oil,

d)Labys and Granger [1970] – cottonseed oil, corn, cocoa, lard, soybeans,

soybean oil, cotton, rye, oat, wheat, rubber,

e)Martel and Phillippatos [1974] – wheat and soybeans,

f) Smidt [1965] – rye and soybeans.

On the basis of above mentioned research, one may formulate the hypothesis that the markets were relatively efficient prior to 1973. Due to the increasing turbulence in the 1970s, the market inefficiency was observed in the period from 1973 to 1979. The period from 1979 to 1987 was hypothesized to be more efficient than the period from 1973 through 1979 [Garcia et al. 1988]. Fortenberry and Zapata [1993] evaluated the relationship of the North Carolina corn and soybean markets with respect to CBOT – no strong evidence was found to reject the efficiency hypothesis. Aulton et al. [1997] investigated the efficiency of agricultural commodities in UK markets. They found wheat market as efficient. Sabuhoro and Lare [1997] demonstrated with the use of cocoa and coffee futures prices, that there was no evidence to reject the null hypothesis concerning the effectiveness of both markets. Result indicated by Mckenzie and Holt [1998], on the basis of future and spot prices of some

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agricultural commodities in the period of 1966–1995, proved that corn and soybean futures markets are both efficient and unbiased in the long-run, but short-run inefficiencies were found to exist in each market.

Wang and Ke [2005] studied wheat and soybean futures markets in China. The results suggest that future market of wheat was inefficient, which might be caused by overspeculation and government intervention on this market. Lokare [2007] found an evidence concerning sugar and cotton markets in India, but Sahoo and Kumar [2009] concluded that the commodity futures markets of soybean oil was efficient in the same country. Ali and Gupta [2011] examined the efficiency of the futures markets of twelve agricultural commodities quoted at NCDEX with the use of Johansen’s cointegration analysis. They proved that there was a long-term relationship between futures and spot prices for all of the selected commodities except wheat and rice. Sehgal et al. [2012], during the analysis of ten agricultural prices in the period of June 2003–March 2011 quoted on NCDEX, observed that all commodity markets were efficient except one (turmeric).

Zunino et al. [2011] applied information theory methods to the commodity markets and ranked them finding that silver, copper and cotton were the most efficient commodities in the analyzed period. Kim et al. [2011b] with the use of the random matrix theory and network analysis found that stock and commodity markets were well decoupled except oil and gold, showing signs of inefficiency. The analysis of Korean agricultural market with the application of detrended fluctuation analysis proved its inefficiency [Kim et al. 2011a]. Lee et al. [2013] found that returns in October for corn, April for soybeans and August for wheat futures dominate returns of other months.

Kristoufek and Vosvrda [2013] introduced the Efficiency Index to rank the commodity according to their efficiency. Authors analyzing daily futures prices of 25 commodities, registered the strongest anti-persistence concerning cocoa, oats and orange juice. There were sugar, copper, palladium and platinum among commodities with a signs of persistence. On the other hand, cotton and natural gas were classified as the closest to the efficient market value. With the use of Efficiency Index, calculated for all of analyzed commodities, the most efficient of the commodities turned out to be heating oil, followed by WTI crude oil. Cotton, wheat and coffee came after these with the smaller level of efficiency. Kellard et al. [1999] analyzed the efficiency of several commodities traded in different markets, including soybeans on the CBOT, finding a long-run equilibrium relationship but a short-run inefficiency for most of the markets.

In summary, there has not been consensus about the efficiency of agricultural commodities. One reason for the heterogeneous results are the different test setups and the second a single-market perspective [Otto 2011].

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According to Roll [1984], who with the use of frozen concentrated orange juice futures quoted in the period of October 1975–December 1981, a total of 1 564 trading sessions, proved that it was possible to predict freezing temperatures in Florida better than the US national weather service could do. Roll [1988] proved that in the orange futures market there was a large amount of inexplicable price volatility, but weather could explain only a small fraction of the observed variability in futures prices. To the same conclusion came Ross [2005: 52]. Hirshleifer [2001] states that little part of stock prices or orange juice price variability can be explained by relevant public news. His observation was confirmed by Daniel et al. [2002]. Seasonality effects on the market of FCOJ were examined also by Malic and Ronald [1987].

2. DATA AND METHODS

The adapted methodology can be divided into two parts:

a)testing the null hypothesis regarding equality of variances of rates of

return in two populations,

b)testing the null hypothesis regarding equality of averages rates of return

in two populations.

2.1. Testing the null hypothesis regarding equality of variances of rates of return in two populations

The null and alternative hypothesis can be formulated as follows:

_: _: (1) where:

– variance of rates of return in the first population,

– variance of rates of return in the second population.

As the last part of the calculation will be carried out using the F-statistics (so called Fisher-Snadecor statistics) for equality of variances of two population

rates of return, where

, with the condition that:

and the degrees

of freedom are equal:

– for variance in the numerator of F,

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If F-test (computed for α=0,05) is lower than F-statistics, e.g. the ratio F-test to F-statistics is lower than 1, there is no reason to reject the null hypothesis.

2.2. Testing the null hypothesis regarding equality of average rats of returns in two populations

According to the adopted methodology, the survey covers two populations of returns, characterized by normal distributions. On the basis of two

independent populations of rate of returns, which sizes are equal n1 and n2,

respectively, the hypotheses H0 and H1 should be tested with the use of statistics z

[Osinska 2006: 43–44]: (2) where:

– average rate of return in the first population,

– average rate of return in the second population.

The Formula 2 can be used in the case of normally distributed populations, when the populations variances are unknown but assumed equal. The number of

degrees of freedom is equal to: 1 2.

When the populations variances are unequal, the number of degrees should be modified according to the following formula [Defusco et al. 2001: 335]:

2 _⁄ _⁄ (3)

In the case of two populations, both with equal or unequal variances,

the null hypothesis H0 and alternative hypothesis H1 regarding equality of rates

of return in two populations, can be formulated as follows:

: # #

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In particular:

1.For the analysis of the monthly rates of return, if is the monthly

average rate of return in month X (the first population), then is the monthly

average rate of return in all other months, except month X (the second population).

2.For the analysis of the daily rates of return, if is the daily average rate

of return in month X (the first population), then is the daily average rate of

return in all other months, except month X (the second population).

3.For the analysis of the daily rates of return for individual days of

the week, if  is the daily average rate of return on day Y (the first population),

then  is the daily average rate of return in all other days, except day Y

(the second population).

4.For the analysis of the rates of return for individual days of month, if is

the daily average rate of return on day Y (the first population), then is

the daily average rate of return in all other days, except day Y (the second population).

5.For the analysis within-the-month effect, if is the average rate of return

in the first half of the analyzed months (days from the 1st to the 15th – the first

population), then is the average rate of return in the second half (days from

16th to the end of the analyzed month – the second population).

In all analyzed cases, the p-values will be calculated with the assumption that the populations variances are unknown, but:

1.population variances are assumed equal – p-value(1),

2.population variances are assumed unequal – p-value(2).

In the case, when there is no reason to reject the null hypothesis about equality of variances of two observed returns, the p-value(1) should be compared with the critical value 0,05; otherwise the p-value(2) will be used. If the p-value (p-value(1) or p-value(2)) is less than or equal to 0,05; then the

hypothesis H0 is rejected in favor of the hypothesis H1. Otherwise, there is no

reason to reject hypothesis H0. In the part 3 of the article, the p-value listed in

the tables are equal to p-value(1) or p-value(2) depending on the result of testing the null hypothesis, concerning the equality of variance in the two populations of rates of returns.

3. ANALYSIS OF RESULTS

3.1. The analysis of the monthly effect

The prices of FCOJ futures in the period from 28.02.1967 to 31.03.2015 are presented in Figure 1.

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Figure 1. The daily FCOJ futures prices in USD in the period from 28.02.1967 to 31.03.2015

Source: own calculations

The monthly average rates of return of FCOJ futures are visible in Table 1. The highest monthly rate of return equal to 4,86% was observed in January, and the lowest one (–2,15%) in February. The monthly average rates of return, higher than 2% were registered 4 times, e.g. in January (4,86%), March (2,48%), May (2,85%), and October (2,33%). The monthly average rates of return lower than minus 1% occurred 3 times in analyzed period: in February (–2,15%), June (–1,85%) and December (–1,86%).

Table 1. The number and percentage of positive and negative monthly returns on the markets of FCOJ futures in the analyzed period

January February March April May June July August September October November December Monthly average rate of return in % 4,8573 –2,1522 2,4776 –0,7292 2,8528 –1,8514 1,5703 0,5346 -0,3072 2,3318 0,6991 –1,8602 Number of positive returns 26 22 29 18 31 20 28 25 25 25 26 14 Number of negative returns 22 26 19 30 17 28 20 22 23 23 22 34 Percentage of months with positive rates of return 54,2% 45,8% 60,4% 37,5% 64,6% 41,7% 58,3% 53,2% 52,1% 52,1% 54,2% 29,2% Percentage of months with negative rates of return 45,83% 54,17% 39,58% 62,50% 35,42% 58,33% 41,67% 46,81% 47,92% 47,92% 45,83% 70,83%

Source: own calculations.

The number and percentage of positive and negative monthly returns on the agricultural commodity market for each month, is presented in Table 1 and on the Figure 2. In the analyzed period, the positive monthly returns, were the most frequently observed in May – in 64,58% of all observations. The second and the third months, in which the positive returns were most frequent were: March

0 50 100 150 200 250 2 -1 -1 9 6 7 2 -1 -1 9 6 9 2 -1 -1 9 7 1 2 -1 -1 9 7 3 2 -1 -1 9 7 5 2 -1 -1 9 7 7 2 -1 -1 9 7 9 2 -1 -1 9 8 1 2 -1 -1 9 8 3 2 -1 -1 9 8 5 2 -1 -1 9 8 7 2 -1 -1 9 8 9 2 -1 -1 9 9 1 2 -1 -1 9 9 3 2 -1 -1 9 9 5 2 -1 -1 9 9 7 2 -1 -1 9 9 9 2 -1 -2 0 0 1 2 -1 -2 0 0 3 2 -1 -2 0 0 5 2 -1 -2 0 0 7 2 -1 -2 0 0 9 2 -1 -2 0 1 1 2 -1 -2 0 1 3 2 -1 -2 0 1 5

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(60,42%) and July (58,33%). In turn, the months with the highest percentage of negative monthly returns resulted to be: December (70,83%), April (62,50%) and June (58,33%).

Figure 2. The percentage of monthly positive and negative returns in each month Source: own calculations.

The outcome obtained in the process of testing statistical hypotheses for the monthly returns on market of FCOJ futures, are presented in Table 2.

Table 2. The results of testing the null hypothesis for the monthly returns for prices of FCOJ futures

January February March April May June July August September October November December Average r1 in % 4,8573 –2,1522 2,4776 -0,7292 2,8528 –1,8514 1,5703 0,534 –0,3072 2,3318 0,6991 –1,8602 Average r2 in % 0,3238 0,9622 0,5405 0,8326 0,5063 0,9348 0,6232 0,7171 0,7942 0,5538 0,7025 0,9356 n1 48 48 49 48 48 48 48 48 48 48 48 48 n2 527 527 526 527 527 527 527 527 527 527 527 527 Variance (n1) 0,0291 0,0055 0,0075 0,0028 0,0086 0,0056 0,0062 0,0057 0,0065 0,0160 0,0094 0,0132 Variance (n2) 0,0082 0,0105 0,0103 0,0108 0,0102 0,0105 0,0105 0,0105 0,0104 0,0096 0,0102 0,0098 Statistic z 1,8170 –2,6832 1,4636 –1,7691 1,6683 –2,3767 0,7749 –0,1534 –0,8853 0,9488 –0,0023 –1,6313 p-value(1) –variance equality 0,0697 0,0075 0,1438 0,0774 0,0958 0,0178 0,4387 0,8782 0,3764 0,3431 0,9982 0,1034 If p-value(1) less than 0,05 TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE p-value(2) – variance inequality 0,0755 0,0093 0,1487 0,0805 0,1008 0,0205 0,4414 0,8786 0,3795 0,3472 0,9982 0,1089 If p-value(2) less than 0,05 TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE F statistics 3,5437 1,8976 1,3843 3,9042 1,1933 1,8549 1,6845 1,8368 1,6128 1,6713 1,0807 1,3509 F-Test 1,3861 1,4739 1,4739 1,4739 1,4739 1,4739 1,4739 1,4803 1,4739 1,3861 1,4739 1,3861 Equality of variance hypothesis verification FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE TRUE

54,17% 45,83% 60,42% 37,50% 64,58% 41,67% 58,33% 53,19% _52,08% _52,08% 54,17% 29,17% 45,83% 54,17% 39,58% 62,50% 35,42% 58,33% 41,67% 46,81% 47,92% 47,92% _45,83% 70,83% 20,00% 30,00% 40,00% 50,00% 60,00% 70,00% 80,00%

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The results permit to draw the following conclusions:

1.There was no reason to reject the null hypothesis regarding equality of

variances of monthly rates of return in two populations in the following month: March, May, November and December. In all other months the variances in two group of populations were different (for α=0,05). For March, May and December the p-value(1), and for all remaining months the p-value(2), are valid.

2.In the process of testing the equality of monthly rates of return in two

group of populations, the null hypothesis was rejected in favor of the alternative hypothesis for the following month: February and June. This fact indicates the occurrence of the effect of the month on the analyzed market. The February p-value(2) was slightly lower than 0,01 (0,0093), what can be interpreted as a stronger monthly effect in comparison to June, for which the p-value(2) reached the level of 0,0205. Regarding all of the remaining months, the null hypothesis was not rejected, which indicates that month of the year effect did not occur. It is worth to mention that p-value(2) calculated for monthly rates of return in January was equal to 0,0755, which was the third lowest p-value(2) among all calculated.

3.2. The analysis of the day-of-the-week effect

Average rates of return for each day of the week on the market of FCOJ futures are shown in the Table 3. In the same table the results of testing statistical hypotheses are presented for the daily rates of returns for different days of the week during analyzed period.

Table 3. The results of testing the null hypothesis for the day-of-the week rates of return

Monday Tuesday Wednesday Thursday Friday

Average r1 in % 0,0024 –0,0587 0,0211 0,0492 –0,0654 Average r2 in % –0,0134 0,0024 –0,0180 –0,0247 0,0029 n1 2417 2418 2360 2312 2239 n2 9329 9328 9386 9434 9507 Variance (n1) 0,00043 0,00032 0,00040 0,00040 0,00060 Variance (n2) 0,00043 0,00046 0,00043 0,00043 0,00039 Statistic z 0,3359 –1,4402 0,8381 1,5837 –1,2258 p-value(1) 0,7369 0,1498 0,4020 0,1133 0,2203

If p-value(1) less than 0,05 TRUE TRUE TRUE TRUE TRUE

df(2) 3772,87 4395,10 3739,14 3658,21 2946,79

p-value(2) 0,7370 0,1499 0,4020 0,1134 0,2204

If p-value(2) less than 0,05 TRUE TRUE TRUE TRUE TRUE

F statistics 1,0047 1,4358 1,0747 1,0975 1,5672

F-Test 1,0551 1,0551 1,0556 1,0561 1,0556

Equality of variance hypothesis verification TRUE FALSE FALSE FALSE FALSE

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The highest average daily rate of return for FCOJ futures was observed on Thursdays (0,0492%), and the lowest on Fridays (–0,0654%). The second highest and the second lowest average daily rate of return were registered on Wednesdays (0,0211%) and on Tuesdays (–0,0587%), respectively.

The results of testing null hypothesis permit to draw the following conclusion.

variances of daily rates of return in two populations: on Monday sessions (first population) and on all other days of the week (second population). In all other cases, the variances in two group of populations were different (for α=0,05).

2.For all analyzed daily rates of return, there was no reason to reject

the null hypothesis regarding equality of two average rates of return. The lowest p-value(2) equal 0,1134 was calculated for rates of return on Thursday sessions. In turn, the highest p-value(1) equal 0,7369 was computed for Monday sessions. Information regarding number and frequency of positive and negative rates of return, computed for each day of the week, are included in Table 4.

Table 4. The number and percentage of positive and negative daily rates of returns

Number of positive returns 1254 1217 1237 1198 1126

Number of negative returns 1163 1201 1123 1114 1113

Percentage of sessions with

positive rates of return 51,88% 50,33% 52,42% 51,82% 50,29% Percentage of sessions with

negative rates of return 48,12% 49,67% 47,58% 48,18% 49,71%

Figure 3. The frequency of positive and negative daily returns over various days of the week for FCOJ futures prices

The FCOJ futures market experienced positive daily returns mostly on Wednesdays (52,42%), followed by 51,88% on Mondays and by 51,82% on Thursdays. The negative daily rates of return were reported more often on Fridays (49,71%) and Tuesdays (49,67%) – see Figure 3.

51,88% 50,33% 52,42% 51,82% 50,29% 48,12% 49,67% 47,58% 48,18% 49,71% 44,00% 46,00% 48,00% 50,00% 52,00% 54,00%

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3.3. The analysis of the daily rates of return in different months

Analysis of the average daily rates of return of FCOJ futures, calculated for each of the analyzed months, as well as the result of testing the null hypothesis, are shown in the Table 5.

Table 5. The average daily rates of return on the market of FCOJ futures and results of testing the null hypothesis for the average daily rates of return in each month

January February March April May June July August September October November December Average r1 in % 0,1375 –0,1517 0,0765 –0,0559 0,1009 –0,1174 0,0423 –0,0055 –0,0543 0,0482 –0,0221 –0,1431 Average r2 in % –0,0238 0,0014 –0,0189 –0,0063 –0,0206 –0,0005 –0,0152 –0,0109 –0,0066 –0,0160 –0,0094 –0,0104 n1 973 910 1047 976 983 1001 972 1030 944 1027 913 971 n2 10774 10837 10700 10771 10764 10746 10775 10717 10803 10720 10834 10776 Variance (n1) 0,0008 0,0003 0,0003 0,0003 0,0003 0,0003 0,0004 0,0003 0,0004 0,0005 0,0007 0,0004 Variane (n2) 0,0004 0,0004 0,0004 0,0004 0,0004 0,0004 0,0004 0,0004 0,0004 0,0004 0,0004 0,0004 Statistic z 1,7177 –2,4258 1,5727 –0,8935 1,9485 –2,0919 0,8588 0,0876 –0,6673 0,8941 –0,1402 –1,9838 p-value(1) 0,0859 0,0153 0,1158 0,3716 0,0514 0,0365 0,3905 0,9302 0,5046 0,3713 0,8885 0,0473 If p-value(1) less

than 0,05 TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE Degree of freedom

df(2) 1058,21 1124,36 1320,99 1295,95 1222,71 1324,16 1170,50 1293,64 1107,70 1202,64 1003,28 1169,61

p-value(2) 0,0861 0,0154 0,1160 0,3717 0,0516 0,0366 0,3906 0,9302 0,5047 0,3715 0,8885 0,0475 If p-value(2) less

than 0,05 TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE F statistics 2,1025 1,3355 1,2682 1,6944 1,2699 1,6250 1,0846 1,2641 1,0456 1,1613 1,7419 1,0875 F-Test 1,0795 1,0854 1,0798 1,0825 1,0822 1,0815 1,0827 1,0804 1,0806 1,0775 1,0818 1,0827 Equality of variance

hypothesis verification

FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE

The highest average daily rate of return for FCOJ futures was observed in January (0,1375%), and the lowest in February (–0,1517%). The second highest and the second lowest average daily rate of return were registered in May (0,1009%) and in December (–0,1431%), respectively.

The results obtained during testing the null hypothesis permit to formulate the following conclusions:

1.The null hypothesis regarding equality of variances of daily rates of

return in two populations was rejected in all analyzed cases.

2.The null hypothesis regarding equality of average rates of return in two

populations, was rejected in favor of the alternative hypothesis for the following months: February, June and December. This fact indicates the occurrence of the month effect on the analyzed market.

3.The results obtained for daily average rates of return in February and in

June are in line with the results received in the analysis executed for monthly effects (paragraph 3.1). The December p-value(2) was slightly lower than the critical value (0,05) and equal to 0,0475, what can be interpreted as a weak

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inefficiency effect in comparison to the other two months, for which the p-value(2) mounted to 0,0154 (February) and 0,0366 (June).

4.For all other analyzed months (e.g. January, March, April, May, July,

August, September, October and November) there was no reason to reject the null hypothesis referred to equality of average returns in two group of populations.

Information regarding number and frequency of positive and negative rates of return, computed for each month, are included in Table 6.

Table 6. The number and percentage of positive and negative daily rates of returns in each of analyzed months

January February March April May June July August September October Nowember December Number of positive returns 519 427 528 499 527 489 504 524 511 540 505 459 Number of negative returns 454 483 519 477 456 512 468 506 433 487 408 512 Percentage of sessions with positive rates of return 53,34% 46,92% 50,43% 51,13% 53,61% 48,85% 51,85% 50,87% 54,13% 52,58% 55,31% 47,27% Percentage of sessions with negative rates of return 46,66% 53,08% 49,57% 48,87% 46,39% 51,15% 48,15% 49,13% 45,87% 47,42% 44,69% 52,73%

Figure 4. Percentage of positive and negative daily rates of returns in each of analyzed months Source: own calculations.

On the FCOJ futures market, the frequency of positive daily returns, higher than 50% was observed in nine months, and was the highest in November (55,31%), and then in September (54,13%) and in May (53,61%) – see Figure 4. The negative daily rates of return were reported more often in February (53,08%), December (52,73%) and June (51,15%), so in these months, for which the tested null hypothesis regarding equality of average rates of return in two populations, was rejected.

53,34% 46,92% 50,43% 51,13% 53,61% 48,85% 51,85% 50,87% 54,13% 52,58% 55,31% 47,27% 46,66% 53,08% 49,57% 48,87% 46,39% 51,15% 48,15% 49,13% 45,87% 47,42% 44,69% 52,73% 40,00% 42,00% 44,00% 46,00% 48,00% 50,00% 52,00% 54,00% 56,00% 58,00%

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3.4. The analysis of the average daily rates of return in different days of month

Analysis of the average daily rates of return of FCOJ futures, calculated for each day of the analyzed months, as well as the result of testing the null hypothesis, are shown in the Table 7. The positive average daily rates of return were observed in 14 out of all 31 days of month, e.g. in 45,16% cases.

The highest positive value equal 0,2550% was registered in the 2nd, and

the lowest (–0,2354%) in the last (31st) day of each analyzed months.

The results obtained during testing the null hypothesis allow to formulate the following conclusions:

variances of daily rates of return in two populations for the following days of

month: the 8th and the 16th. In all other cases, the variances in two group of

populations were different (for α=0,05).

2.The null hypothesis regarding equality of the daily average rates of return

in two populations, was rejected in favor of the alternative hypothesis for

the following days of month: 2nd, 21st, 23th and 31st. The p-value(2) calculated

for daily rates of return on the session falling on the 31st day of the month, was

equal 0,0440, e.g. slightly lower than the critical value (0,05). For all other analyzed days of the month there was no reason to reject the null hypothesis.

The frequency of positive average daily returns, higher than 50% was observed during 19 days of each month (61,29% of all sessions in each month),

and was the highest on the 2nd day of each month (61,68%), and then on the 1st

(56,09%) and on the 4th (55,68%) – see Table 8 and Figure 5. The lowest

frequency of positive average daily returns were reported on the 9th (45,01%) and 31st (46,30%) day of each month.

Figure 5. Percentage of positive average daily rates of returns for each of analyzed days of the month Source: own calculations

45, 01% 46, 30% 47, 09% 47, 47% 47, 69% 48, 47% 48, 81% 48, 85% 48, 87% 48, 88% 49, 00% 49, 74% 50, 50% 50, 77% 50, 90% 50, 90% 51, 25% 52, 08% 52, 26% 52, 27% 52, 69% 52, 75% 52, 85% 53, 08% 53, 32% 53, 45% 53, 89% 54, 20% 55, 68% 56, 09% 61, 68% 40,00% 45,00% 50,00% 55,00% 60,00% 65,00% 9 31 23 27 18 16 26 15 14 10 25 28 11 6 17 7 30 29 12 24 22 13 3 8 5 20 21 19 4 1 2

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Table 7. The average daily rates of return on the market of FCOJ futures and results of testing the null hypothesis for the average daily rates of return for each day of month

Day of the month 1 2 3 4 5 6 7 8 9 10 Average r1 in % 0,1315 0,2550 0,1000 0,1279 0,1738 –0,0171 –0,0477 0,0777 –0,0596 –0,1838 Average r2 in % –0,0145 –0,0190 –0,0139 –0,0144 –0,0162 –0,0099 –0,0088 –0,0132 –0,0084 –0,0040 n1 353 381 386 352 377 388 387 390 391 401 n2 11362 11334 11329 11363 11338 11327 11328 11325 11324 11314 Variance (n1) 0,00032 0,00029 0,00027 0,00033 0,00035 0,00031 0,00025 0,00043 0,00062 0,00056 Variane (n2) 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 0,00042 0,00042 Statistic z 1,5074 3,0447 1,3309 1,4425 1,9372 –0,0789 –0,4673 0,8496 –0,4010 –1,5010 p-value(1) 0,1317 0,0023 0,1833 0,1492 0,0528 0,9371 0,6403 0,3956 0,6884 0,1334 If p-value(1) less than 0,05 TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE Degree of freedom

df(2) 383,30 419,45 429,60 381,05 408,51 426,02 433,52 417,05 409,44 422,69

p-value(2) 0,1325 0,0025 0,1839 0,1500 0,0534 0,9372 0,6405 0,3960 0,6886 0,1341 If p-value(2) less than 0,05 TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE F statistics 1,3537 1,4661 1,6150 1,3064 1,2324 1,3981 1,7112 1,0092 1,4807 1,3276 F-Test 1,13924 1,13365 1,13272 1,13946 1,13441 1,13235 1,13254 1,12320 1,12304 1,12152 Equality of variance hypothesis verification FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE Day of the month 11 12 13 14 15 16 17 18 19 20 Average r1 (%) –0,1998 0,1805 –0,1150 0,0405 0,0347 –0,0480 –0,2127 –0,2239 0,0691 0,1357 Average r2 (%) –0,0035 –0,0168 –0,0064 –0,0119 –0,0117 –0,0088 –0,0031 –0,0028 –0,0129 –0,0152 n1 398 398 400 397 391 392 391 390 393 391 n2 11317 11317 11315 11318 11324 11323 11324 11325 11322 11324 Variance (n1) 0,00075 0,00074 0,00051 0,00052 0,00048 0,00040 0,00080 0,00081 0,00065 0,00039 Variane (n2) 0,00042 0,00042 0,00042 0,00042 0,00043 0,00043 0,00041 0,00041 0,00042 0,00043 Statistic z –1,4151 1,4309 –0,9514 0,4531 0,4123 –0,3799 –1,4488 –1,5206 0,6297 1,4806 p-value(1) 0,1571 0,1525 0,3414 0,6505 0,6801 0,7040 0,1474 0,1284 0,5289 0,1387 If p-value(1) less than 0,05 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE Degree of freedom

df(2) 413,62 413,84 424,07 420,23 415,24 421,48 405,02 403,83 410,73 421,13

p-value(2) 0,1578 0,1532 0,3419 0,6507 0,6803 0,7042 0,1482 0,1292 0,5292 0,1395 If p-value(2) less than 0,05 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE F statistics 1,8088 1,7845 1,1919 1,2156 1,1302 1,0673 1,9419 1,9585 1,5558 1,0957 F-Test 1,12197 1,12197 1,12167 1,12212 1,12304 1,13163 1,12304 1,12320 1,12273 1,13181 Equality of variance hypothesis verification FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE Day of the month 21 22 23 24 25 26 27 28 29 30 31 Average r1 (%) 0,2133 –0,0020 –0,1904 0,0395 –0,0013 –0,1306 –0,1563 –0,0770 –0,0926 0,0394 –0,2354 Average r2 (%) –0,0177 –0,0104 –0,0038 –0,0118 –0,0104 –0,0061 –0,0053 –0,0079 –0,0075 –0,0117 –0,0059 n1 386 391 395 375 351 377 375 380 361 361 216 n2 11329 11324 11320 11340 11364 11338 11340 11335 11354 11354 11499 Variance (n1) 0,00034 0,00026 0,00027 0,00030 0,00024 0,00035 0,00035 0,00024 0,00030 0,00031 0,00027 Variane (n2) 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 0,00043 Statistic z 2,4224 0,1000 –2,1835 0,5604 0,1068 –1,2716 –1,5246 –0,8497 –0,9204 0,5411 –2,0249 p-value(1) 0,0154 0,9203 0,0290 0,5752 0,9150 0,2036 0,1274 0,3955 0,3574 0,5884 0,0429 If p-value(1) less than 0,05 FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE Degree of freedom

df(2) 420,31 437,30 439,80 411,45 390,60 408,66 405,71 428,02 395,31 393,74 229,15

p-value(2) 0,0158 0,9204 0,0295 0,5755 0,9150 0,2043 0,1281 0,3959 0,3579 0,5887 0,0440 If p-value(2) less than 0,05 FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE F statistics 1,2775 1,6685 1,5831 1,4369 1,7791 1,2381 1,2146 1,8307 1,4617 1,3962 1,5965 F-Test 1,13272 1,13181 1,13109 1,13479 1,13967 1,13441 1,13479 1,13384 1,13757 1,13757 1,18247 Equality of variance hypothesis verification FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

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Table 8. The number and percentage of positive and negative daily average rates of returns for each of analyzed days of the month

Day of the month 1 2 3 4 5 6 7 8 9 10

Number of positive returns 198 235 204 196 201 197 197 207 176 196

Number of negative returns 155 146 182 156 176 191 190 183 215 205

Percentage of sessions with positive rates of return 56,09% 61,68% 52,85% 55,68% 53,32% 50,77% 50,90% 53,08% 45,01% 48,88%

Percentage of sessions with negative rates of return 43,91% 38,32% 47,15% 44,32% 46,68% 49,23% 49,10% 46,92% 54,99% 51,12%

Day of the month 11 12 13 14 15 16 17 18 19 20

Number of positive returns 201 208 211 194 191 190 199 186 213 209

Number of negative returns 197 190 189 203 200 202 192 204 180 182

Percentage of sessions with positive rates of return 50,50% 52,26% 52,75% 48,87% 48,85% 48,47% 50,90% 47,69% 54,20% 53,45%

Percentage of sessions with negative rates of return 49,50% 47,74% 47,25% 51,13% 51,15% 51,53% 49,10% 52,31% 45,80% 46,55%

Day of the month 21 22 23 24 25 26 27 28 29 30 31 Number of positive returns 208 206 186 196 172 184 178 189 188 185 100 Number of negative returns 178 185 209 179 179 193 197 191 173 176 116 Percentage of sessions with positive rates of return 53,89% 52,69% 47,09% 52,27% 49,00% 48,81% 47,47% 49,74% 52,08% 51,25% 46,30% Percentage of sessions with negative rates of return 46,11% 47,31% 52,91% 47,73% 51,00% 51,19% 52,53% 50,26% 47,92% 48,75% 53,70%

3.5. The analysis of the average daily rates of return in the first and the second half of month

Analysis of the average daily rates of return of FCOJ futures, calculated for the first and the second half of a month, as well as the result of testing the null hypothesis, are shown in the Table 9.

Table 9. The average daily rates of return on the market of FCOJ futures and results of testing the null hypothesis for the average daily rates of return for the first and second half of a month

Average r1 in % – average rate of return in the first half (1–15) of a month 0,0306 Average r2 in % – average rate of return in the second half (16–31) of a month –0,0499

n1 5790 n2 5925 Variance (n1) 0,00045 Variance (n2) 0,00040 Statistic z 2,1048 p-value(1) 0,0353

If p-value(1) less than 0,05 FALSE

Degree of freedom df(2) 11630,04

p-value(2) 0,0353

If p-value(2) less than 0,05 FALSE

F statistics 1,1332

F-Test 1,0439

Equality of variance hypothesis verification FALSE

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The average daily rate of return in the first and the second half of a month was equal 0,0306% and –0,0499%, respectively. The null hypothesis, regarding equality of variances of daily rates of return in two populations, was rejected. The null hypothesis referring to the equality of average rates of return in two populations, was rejected in favor of the alternative hypothesis – it means that the daily average rates of return in the first half differ from the daily average rates of return in the second half of a month (for α=0,05). The p-value(2) calculated in the process of testing the null hypothesis was lower than the critical value (0,05) and mounted to 0,0353.

Table 10. The number and percentage of positive and negative daily average rates of returns in the first and the second half of a month

Number of positive rates of return in the first half of a month 3012 Number of negative rates of return in the first half of a month 2778 Number of positive rates of return in the second half of a month 2990 Number of negative rates of return in the second half of a month 2936 Percentage of sessions with positive rates of return in the first half of a month 52,02% Percentage of sessions with negative rates of return in the first half of a month 47,98% Percentage of sessions with positive rates of return in the second half of a month 50,46% Percentage of sessions with negative rates of return in the second half of a month 49,54%

The frequency of positive average daily returns in the first half was equal 52,02%, whilst in the second half was a little bit lower – 50,56% (see table 10). Both, in the first and the second half, the frequency of positive daily rates of return was higher than the frequency of daily negative rates of return.

CONCLUSION

In recent years, there has been observed an increased interest in the commodity market, including agricultural commodities, from both institutional and individual investors. Investment strategies implemented in the commodity market by its participants, heavily resemble those of the stock and currency markets. However it should be mentioned that particular characteristics are assigned to the agricultural commodity market such as stock level or marginal unit cost. It is also important to note that, despite the physical diversity, this asset class is often characterized by a high degree of price correlation.

The aim of this study was to determine the prevalence of selected effects of seasonality on the market of FCOJ futures. Analysis of the effects of seasonality included an examination of monthly returns, daily returns over various days of

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the week, average daily rates of return in different days of a month and average daily rates of return in the first and the second half of a month. The main limitation of this research is the assumption of normal distribution of return rates of analyzed commodities as well as the use of price data gained from Bloomberg data source.

Calculations presented in this paper indicate the absence of the day-of-the--week effect and the existence of monthly effect: in February and June with the use of the average monthly rates of return and in February, June and December, when the daily average rates of return were implemented. The seasonal effects were also observed in case of testing the statistical hypothesis for daily averaged rates of returns for different days of the month

(2nd, 21st, 23th and 31st), as well as for the daily average rates of return in the first

and in the second half of a month.

Further research on the occurrence of calendar anomalies in the agricultural market should include the following assets: oat, rye, barley and rubber.

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