Applying Markowitz portfolio theory to measure the systematic risk in agriculture

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1 Applyng Markowtz portfolo theory to measure the systematc rsk n agrculture Marán Tóth 1, Ivan Holúbek 2, Roman Serenčéš 3 1, 2,3 Slovak Unversty of Agrculture n Ntra Faculty of Economcs and management, Department of Fnance 1,2, Department of Economc Polcy 3 Treda A. Hlnku 2 Ntra, Slovak republc e-mal 1,2,3 : maran.toth@unag.sk, van.holubek@unag.sk, roman.serences@unag.sk Abstract Markowtz portfolo theory s the basc theory n Fnance for portfolo dversfcaton. Based on ths theory market rsk can be assessed. The paper uses the alternatve Markowtz portfolo theory approach, by replacng the stock return wth return on equty (ROE), to estmate the rsk and proftablty of unquoted agrcultural farms. The development of rsk and return of Slovak farms s estmated n the perod of years , usng the 5-years movng average. The portfolos are created for two types of producton: crop farms and anmal farms. The results show that from the pont of producton orentaton, the crop farms record hgher return and also hgher rsk n comparson to the anmal farms. The development of rsk and return reflects the structural changes n Slovak agrculture, whch has been contnually changng n the way of ncreasng the share of crop orented farms. Key words: Agrculture, Markowtz portfolo theory, producton orentaton, return, rsk JEL Classfcaton: Q32, Q38 Introducton After 1989, Slovak agrcultural sector was transformed from centrally planned economy to the market economy. Fundamentally, ths process was based on prvatzaton, the transformaton of co-operatves, whch meant co-op owned assets were dvded nto ndvdual property shares and then allotted to co-op members and other elgble persons, and the renstatement of former owners (Blaas, 2000). Before 1989, Slovak agrculture conssted of cooperatves only and state farms wth large acreage, wthout exstence of prvate companes. Snce that tme the number of prvate companes (Jont Stock Company (JSC.), Lmted Lablty Company (Ltd.)) has been gradually ncreasng, because ths type of legal form s consdered to be more effectve. (Pokrvčák et al, 2005). Durng ths perod agrcultural producton decreased and n ths way adapted to a domestc demand nfluenced by the lower purchasng power of populaton and by changes that occurred n the structure of consumpton and n consumer behavour of the populaton. Snce the year 1995 the level of producton has stablsed. Accesson to European Unon (EU) became the most sgnfcant factor nfluencng agrcultural polcy. The year 2004, when we adopted Common agrcultural polcy and farmers receved ther frst drect payments, became a next mlestone n the development of Slovak agrculture. Snce that tme the expectatons led more proftable, growng, more effcent and compettve agrcultural sector, that would also contrbute to the economc growth of other sectors of the economy of Slovaka. However, new poltcal regulatons, quotas, requrements and sngle payment system led to the number of substantal changes that have been ultmately mpactng economc development n ths sector and prortes of farmers. In the years 2003, 2007 and 2009 agrcultural producton, and n partcular crop producton, was affected by extraordnarly dry weather, whch nfluenced total agrcultural producton and the economc stuaton of farms. Not only the legal structure has been changng, but also the crop producton has been year to year on the ncrease (except of year 2009), whle the anmal producton has been n general decreasng. Therefore, we decded to examne the changng 985

2 structure of Slovak agrculture wth the focused on rskness and proftablty of Slovak farms, accordng to ther legal form and producton orentaton. Rsk generally refers to devaton of the evaluated ndcator, and the level depends on the volatlty over a certan perod. Rsk n agrculture has been a matter of worldwde concern snce 1933, when the concept of rsk analyss had been ntroduced (Hardaker et al, 2004). Agrculture s a sector facng partcularly large rsks, resultng manly from natural factors outsde the control of farmers. The resultng varatons n farm output, combned wth a relatvely low prce responsveness of supply and demand, also cause agrcultural markets to be rather volatle (Tangermann, 2011). The sources of rsks, that are relevant n agrculture have dfferent characterstcs, and can be classfed n very dfferent ways (Hurne et al, 2000; Holzman and Jorgensen, 2001). Sources of rsk of Slovak agrculture nclude bologcal nature of producton, dependency on clmatc condtons, seasonalty, anmal and plant health, prces nstablty, polcy regulatons, and range of macroeconomc factors (Serenčéš et al, 2010). There have been several approaches to measure agrcultural rsk resultng from dfferent focus of authors. Some of them are focused on agrcultural rsk of ndvdual farms, others took nto account the whole aggregate level (El Benn and Fnger, 2013; Špčka and Vlhelm, 2013, Just and Pope, 2003). Because farms can be thought of as assets wthn an overall portfolo, agrcultural producers also pad attenton to the concept of dversfcaton and portfolo theory. In the Markowtz portfolo theory, total rsk s standardly measured by the meanvarance model and standard devaton of stock return (Markowtz, 1952). But, not all busnesses provde the ablty to rase ther captal n the form of stocks. These busnesses represent unquoted companes, to whch the majorty of agrcultural companes belong. The stocks, consdered n the orgnal model, represent the equty securtes, and the return on stock reflects smply the return on equty nvested nto the busness. Therefore, t mght be assumed that to be able to measure the rsk of unquoted companes, the devaton of return on equty could be consdered, as well. In order to focus on other than securty market the alternatve of Markowtz theory approach, the Smple ndex model, was created (Sharpe, 1963). In SIM the nput varables used n analyss are the accountng fundamentals of companes. SIM approach was appled n the number of studes, such as usage of gross and net returns (Gempesaw et al, 1988), farm equty returns (Bagnsk and Wahlen, 2003), book to market ratos (Fama and French 1995) or cash flow varablty (Cohen et al, 2009; Da, 2009). It empowers our assumpton to measure the market rsk of unquoted farms, usng the return on equty rato ROE. The rsk analyss of agrculture, usng the Markowtz approach or Sngle ndex model, has been appled to a number of studes, however many of them dd not have aggregate character. They manly focused on the certan part of agrculture producton, for example, Peterson and Leuthold (1987) used the portfolo approach to examne the cattle feedng problem, Sanchrco et al (2005) use portfolo theory to develop optmal management of fsheres, Gempesaw et al. (1988) appled the model to Delaware farm sector market portfolo or n more recent study Lbbn et al (2004) appled the Markowtz portfolo model drectly to a seres of New Mexco farms. Many other studes could be mentoned, because the range of applcatons s really wde. Smlarly, we decded to focus our study on examnng market rsk and return of Slovak agrculture sector and ts development over the tme. All the farms operatng n Slovaka were ncluded nto several portfolos, accordng to the legal form (cooperatves/companes) and producton orentaton (crop/anmal). The man objectve of the paper s to estmate the development of market rsk and return of Slovak unquoted agrcultural farms over the perod , usng volatlty of ROE. Ths paper s the extenson of our prevous study (Tóth et al, 2014). 986

3 Materal and Methods The data used for the analyss are from the database of Mnstry of Agrculture and Rural Development of the Slovak Republc, over the perod For our analyss, data were selected accordng to the producton orentaton to the subset of crop farms and anmal farms. The selectng crteron for producton orentaton was the percentage share of revenues from crop producton, or revenues from anmal producton from the overall revenues from own products and servces. When the farm generated more than 50% of revenues from crop producton, t was determned to be crop farm. Analogcally, the selecton was done for anmal farms. To avod the deteroraton of results and trend n data, the 5-years movng averages were used. It dvded our overall observed tme horzon nto 10 perods ( , , , , , , , , , ). Moreover, from the dataset the followng farms were excluded: farms that started or qutted durng each observed 5 year perod, farms wth negatve equty (labltes exceedng total assets) and farms wth return on equty (ROE) exceedng +/- 100% (average proft or loss exceeds equty) over the observed perod. The number of farms used for calculaton n each 5-year perod are descrbed n the table 1. The modfed Markowtz portfolo theory approach was used to estmates the total rsk of fve portfolos consstng of all agrcultural farms, captal companes, cooperatves, crop farm and anmal farms. We assumed that the return of the nvestor s based on the proft of the company and the equty nvested. Therefore, we consdered return on equty ROE (Eq. 1) to be equvalent to the return on stocks, generally used n the case of quoted companes. Measurng volatlty of return n the Markowtz portfolo theory s based on the average return over the observed perod for each nvestment. We calculated the average return on equty EROE (Eq. 2) for each ndvdual farm. Earnngs After Taxes ROE Sharesholders Equty (1) EROE ROE d t 1 (2) Where ROE s return on equty of farm, d s a weght of ROE over the observed perod (5 years, d = 0.20), t s number of years n observed perod,, j are ndvdual farms. The ndvdual rsk of each farm (σ ) s calculated usng the standard devaton. t 1 2 ( ROE EROE ) d (3) Where σ s standard devaton of the ndvdual return on equty (ndvdual farm rsk), ROE s ndvdual return on equty, EROE s average ndvdual return on equty. The portfolo rsk (σ p ) s determned by three varables: weght of the ndvdual nvestment n portfolo (w),standard devaton of the ndvdual nvestment - ndvdual rsk (σ), and covarance, relaton between the ROE and ROEj (σj). To take nto account market portfolo of all agrculture farms, the weght w of each farm s determned by farm market share, whch s the share of the farm` s equty on the total equty of all farms.the covarance represents the 987

4 relatonshp between returns on equty of farms (Eq 4) and Σ covarance matrx (Eq. 5). The portfolo rsk s then measured accordng to eq. 6 1 ( ROE EROE )( ROE EROE ) (4) j n n 1 j j = [ σ 11 σ 12 σ 13 σ 1k σ 21 σ 22 σ 23 σ 2k σ 31 σ 32 σ 33 σ 3k σ k1 σ k2 σ k3 σ kk ] (5) p n n 2 2 n w 1 1 j1 w w j j (6) Where w s an ndvdual weght of -farm (farm`s equty) n a portfolo (total equty of all farms) and n s number of farms. The expected return on equty of portfolo s estmated by the multplcaton of k x 1 vector of ndvdual weghts of portfolo (w) and k x 1 vector of correspondng ndvdual expected returns on equty (the sum of multplcaton of each farm s expected ROE and ts share n the market portfolo). EROE p n EROE w 1 (7) Where EROEp s expected portfolo return on equty and EROE s the average return on equty of ndvdual farm. Results and Dscusson The frst part of the paper focuses on the changng structure of Slovak agrculture, from the pont of the use of utlzed agrcultural land and legal forms n agrculture. The structural changes result from the economc stuaton of farms, ther proftablty and rsk. In the second part of the paper the rsk and return of Slovak farms s estmated, wth the more detaled vew on legal forms and producton orentaton of farms. Structure of Slovak Agrculture The busness structure of agrcultural prmary sector conssts of wde range of busness enttes, whch number, use of cultvated area and sze has been constantly changng. In the year 2014 the total number of farms was , whch together operated on ha of utlzed agrcultural area (UAA). It represents only 52% of known owners of agrcultural land, consstng of 43.5% ndvduals, 4.5% frms and 4% state-owned land. The rest of the agrcultural land of unknown owners s temporally admnstrated by the Slovak Land Fund (SPF) and the users of the land pay a rent. From the pont of the sze of the farm (the utlzed agrcultural area sze), s structure of farms n Slovaka dfferent compared to the EU average. It results from the hstorcal development of agrculture n former Czechoslovaka before Nowadays, the majorty of UAA (74.64% n 2014) s cultvated by large farms wth over 500 hectares, whle the UAA per farm n the EU s much lower. Therefore, also measures mplemented through CAP result dfferent 988

5 n Slovaka. The dvson of the farms and ther percentage share on the total utlzed agrcultural area s shown n Table1. Table 1. UAA per farm as a percentage of total area Years Category of the Utlzed Agrcultural Area 0-5 ha 5-10 ha ha ha ha ha over 500 ha ,01 1,04 4,23 2,97 7,04 8,21 75, ,04 1,09 4,52 3,1 7,07 8,55 74,64 Source: Data of the Agrcultural Payng Agency of Slovaka (2015). Snce 1989 the former socalst cooperatves and state-owned companes have been transformed nto prvate busness companes and co-partner cooperatves. The number of ndependent farmers n the prmary sector ncreased n the frst years of the transformaton and then stablsed. Structural changes, whch had been carred out n Slovak agrculture have led to a decrease of the share of cooperatves on the total number of farms, and to an ncrease n the number of busness companes. In the year 2014 were recorded 2082 prvate companes (1968 Ltd. and 119 JSC.), and only 566 cooperatves. In comparson to the year 2010 the share of cooperatves decreased by 2.25%, share of jont-stock companes ncreased by 9.17%, and share of Ltd. ncreased by 50.23%. Moreover, we can observe the rregular nature of Slovak agrculture, where a mnorty of farms (14.98 %) owns the vast majorty (80.23 %) of the agrcultural land (Table 2). In absolute terms, 2653 agrcultural holdngs farmed 1,4 mllon hectares of agrcultural land n Ths phenomenon was also observed n the Czech Republc, although n Slovaka t was more promnent. Ths dstrbuton of land, wth many small farms sharng a low percentage of agrcultural land and a few large holdngs farmng the vast majorty of the UAA, explans the very hgh average area per holdng regstered n Slovaka. Large farms generally rent the land and therefore sgnfcantly nfluence the rent and land prce. Accordng to the Eurostat, n Slovaka 89% of the land n 2007 was rented (n 2005, 96%). Unfortunately, the stuaton has not been changng n recent years. For example n the year 2007 only 11,2% of farms owned 81% of agrcultural land, and n 2010 year 12.5% of farms owned 80.38% of agrcultural land. Table 2. Sze structure of Slovak farms Legal form Number of farms Index UAA Change (%) 989 Land (ha) Land per farm Share on all farms (%) Jont stock company ,17% 13272, ,21 0,67 Cooperatve ,25% , ,94 3,2 Small famly farm ,48% ,14 5,45 55,26 Ltd ,23% ,45 349,3 11,11 Farmers ,70% ,73 60,22 28,5 Other ,59% 12,383 n.a. 0,97 Total ,11% ,05 n.a. 100

6 Source: Data of the Agrcultural Payng Agency of Slovaka (2015). The structural changes can be also explaned by the results of the economc development of farms n recent years. Therefore, n the second part of the paper the proftablty and rskness of farms have been estmated. Rsk and return of Slovak farms For the rsk assessment were used all agrcultural farms operatng at least 5 consecutve years, that ncludes 785 farms each year on average. All the farms are dvded based on ther producton orentaton (crop and anmal farms). From the structure of samples n each perod s obvous, that the number of cooperatves s contnually decreasng, whle the amount of companes s on the ncrease. The same trend can be seen n the case of producton orentaton, wth the ncreasng amount of crop farms and decreasng anmal farms (Tab.1). It means that the structure of the Slovak agrculture has been gradually changng n favour of companes (JSC, Ltd) focusng on crop producton. The portfolo return s measured by ndvdual ROE and the weght of each farm n each portfolo. Generally s clamed that the hgher the return, the better for the nvestor. We can conclude that overall proftablty n the Slovak agrcultural sector s at the low level. From the comparson of crop and anmal farms s obvous that the dfferences of return n ndvdual perod are small. Producton s very closely related, and therefore ther development trends are smlar as well. However, the return of crop farms n each perod s postve, whle the anmal farms are sufferng loss. The excepton s the perod 5 ( ). It s subjected to the before crss year 2008, when not only the agrcultural producton was very favourable, but also the prces of agrcultural commodtes reached ther maxmum. Fgure 1. Return of portfolos of crop farms and anmal farms Source: own processng Rsk of portfolos was estmated usng portfolo theory approach, wth the measured volatlty of ROE. Ths offers an aggregate vew on rsk of all farms. By addng all farms exstng over the observed perods n the approprate weght to a portfolo, we smulated the stuaton what rsk nvestor would face by buyng all the farms n agrculture for the prce equal to ther total equty. We can see (Fg.2) the results n each perod. The rsk of all farms vared between 1 to 3.61% of ROE. In the case of crop and anmal farms the dfference n rsk s more vsble. It results from the producton character and the fact that crop producton s more dependent on the clmate and the amount of ranfall receved durng the croppng season (Hurley, 2010, 990

7 Hardaker et al, 2004). The anmal producton s consdered to be long-run and therefore more stable n comparson to crop plantng usually wth 1-year producton cycle. Fgure 2. Rsk of portfolos of crop farms and anmal farms Source: own processng In all cases there s a sgnfcant change n rskness between perod 5 and 6. It s reasoned by the devaton n the year 2009, when the majorty of farms generated loss. Not only the 2009 was the crss year, what pushed the prces of agrcultural commodtes down, but also the clmate condtons were unfavourable and the producton suffered by drought. These facts caused the ncreased volatlty of returns and producton. Fgure 3. Return vs. rsk: crop farms, anmal farms Source: own processng The relatonshp between rsk and return for each portfolo (Fg.3.) s mportant for nvestors. In the theory, the hgher return requres hgher rsk. In the stuaton of equal rsks the nvestment wth hgher return should be preferred and conversely, when returns are equal nvestor should prefer lower rsk. Ths statement leads us to concluson, that the agrculture producers should prefer the crop producton orentaton. 991

8 Concluson Farmers faced varety of rsks that orgnate from dfferent sources. These rsks are very rarely completely ndependent from each other, partcularly when measured n terms of ther mpact on the ncome varablty. Concern on ncreasng farm ncome volatlty n the EU has nduced wde range of research n ths area. Only a few studes pad attenton to the ssue of rsk n agrculture n Slovaka, therefore we decded to focus our research on ths area. The rsk n the European agrculture s decreased by Common Agrculture Polcy n form of subsdes and regulatons. The dffculty to measure the rsk of agrculture companes results from ther unquoted character. The majorty of farms n agrculture are unquoted, meanng to assess the market value for return and rsk calculaton has to rely on fnancal statements. One of the negatves s that these statements are used for tax purposes, and therefore can be adjusted n sense of tax. In the frst part, the paper s focused on the structure of Slovak agrculture. From the pont of the utlzed agrcultural area sze, structure of farms n Slovaka s dfferent when compared to the EU average. The majorty of UAA (74.64% n 2014) s cultvated by large farms wth over 500 hectares, whle the UAA per farm n the EU s much lower. Structural changes, whch had been carred out n Slovak agrculture have led to a decrease of the share of cooperatves n the total number of farms, and to an ncrease n the number of busness companes. In the Slovak agrculture the specfc phenomenon s observed, where a mnorty of farms (14.98 %) owns the vast majorty (80.23 %) of the agrcultural land. Ths dstrbuton of land, wth many small farms sharng a low percentage of agrcultural land and a few large holdngs farmng the vast majorty of the UAA, explans the very hgh average area per holdng regstered n Slovaka. Large farms generally rent the land and therefore sgnfcantly nfluence the rent and land prce. Moreover, ths stuaton has not been changng n recent years. The structural changes can be also explaned by the development of proftablty and rskness of farms n recent years. In the second part, the paper focuses on the estmaton of the development of rsk and return of Slovak unquoted agrcultural farms over the perod For the measurement s used the alternatve Markowtz portfolo theory approach, where the return of stocks s replaced by the volatlty of ROE. Not only all exstng farms n ten 5-years perods were examned, we focused specfcally on two producton orentatons (crop and anmal farms). It can be concluded that from the pont of producton orentaton, the crop farms record hgher return, and also hgher rsk n comparson wth the anmal farms. It agrees wth the general opnon that the crop producton s rsker than the anmal producton, because of the dependence on clmate and producton cycle. Smlarly, there has been a gradual ncrease of the amount of crop orented farms and decrease of the anmal farms. One of the reasons for ths development s the CAP sngle payments system. We expect that n the future the structure of Slovak agrculture wll change n the way of ncreasng percentage share of crop orented prvate companes. Acknowledgement Ths paper was created wthn the VEGA project 1/0790/14 Transmsson mechansm of CAP nstruments and ther mpact on the fnancal stuaton of farms and VEGA project 1/0912/14 The Common Agrcultural Polcy and the mpact on the fnancal stuaton of farms n Slovak Republc. References [1] Bagnsk S. P., Wahlen J. M. (2003): Resdual Income Rsk, Intrnsc Values, and Share Prces. The Accountng Revew, 78:

9 [2] Blaas G. (2000): Agrcultural reform n Slovaka: Changng Insttutons and structure. In Internatonal workshop: The new structure of the Rural Economy of Post-communst Countres, Lomnce nad Luznc. [3] Cohen R. B., Polk C., Vuolteenaho T. (2009): The prce s (almost) rght. Journal of Fnance, 64: [4] Da Z. (2009): Cash flow, consumpton rsk, and cross-secton of stock returns. Journal of Fnance, 64: [5] El Benn N., Fnger R. (2013): Gross revenue rsk n Swss dary farmng. Journal of Dary Scence, 96: [6] Fama E. F., French K.F. (1995): Sze and book-to-market factors n earnngs and returns. Journal of Fnance, 50: [7] Gempesaw C. M., Tambe A. M., Nayga R. M., Toensmeyer U. C. (1988): The Sngle Index Market Model n Agrculture. Northeast Journal of Agrcultural and Resource Economcs, 17: [8] Hardaker J., Hurne R., Anderson J., Len G. (2004): Copng wth rsk n agrculture. CABI Publshng, ISBN [9] Holzman R., Jorgensen S. (2001): Socal Rsk management: A New conceptual framework for socal protecton, and beyond. Internatonal Tax and Publc Fnance, 8: [10] Hurne R., Meuwssen M., Hardaker B., Anderson J. (2000): Rsk and rsk management n agrculture: an overvew and emprcal results. Internatonal Journal of Rsk Assessment and Management, 1: [11] Hurley T. M. (2010): A revew of agrcultural producton rsk n the developng world. Unversty of Mnnesota, Mnnesota. [12] Just R. E., Pope R. D. (2003): Agrcultural rsk analyss: adequacy of models, data, and ssues. Amercan Journal of Agrcultural Economcs, 85: [13] Lbbn J. D., Kohler J. D., Hawkes J. M. (2004): Does Modern Portfolo Theory Apply to Agrcultural Land Ownershp? Concepts for Farmers and Farm Managers. Journal of the Amercan Socety of Farm managers and Rural Apprasers, 67: [14] Markowtz H. M. (1952): Portfolo Selecton. Journal of Fnance, 7: [15] Peterson P. E., Luethold R. M. (1987): A portfolo approach to optmal hedgng for a commercal cattle feedlot. Journal of Futures Markets, 7: [16] Pokrvčák J., Serenčéš R., Kuzma F. (2005): Slovak agrculture and Slovak agrcultural polcy. Acta agrara et slvestra, 44: [17] Sanchrco J. N., Smth M. D., Lpton D. W. (2005): Ecosystem Portfolos: A Fnance-Based Approach to Ecosystem Management. Proceedngs of the Conference AERE Workshop 2005: Natural Resources at Rsk, Jackson Hole, 33. [18] Serenčéš P., Serenčéš R., Tóth M., Černa Z., Rábek, T. (2010): Fnance v poľnohospodárstve (Fnance n Agrculture). SPU, Ntra, ISBN [19] Sharpe W. F. (1963): A Smplfed Model for Portfolo Analyss. Management Scence, 9: [20] Špčka J., Vlhelm V. (2013): Determnanty rzkového prostředí zemědělských podnků v České republce. (Determnants of rsk envronment of farms n the Czech republc). Acta Oeconomca Pragensa, 21: [21] Tangermann S. (2011): Rsk management n Agrculture and the Future of the EU s Common Agrcultural Polcy. ICTSD, Issue Paper, 34. [22] Tóth M., Lančarč D., Pterková A. and Savov R. (2014): Systematc rsk n Agrculture: A case of Slovaka. Agrs on-lne Papers n Economcs and Informatcs, 6: * Onlne full-text paper avalablty: do: 993

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