The Fundamental Equation in Tourism Finance

Transcription

1 J. Risk Financial Manag. 205, 8, ; doi:0.3390/jrfm Commenary OPEN ACCESS Journal of Risk and Financial Managemen ISSN The Fundamenal Equaion in Tourism Finance Michael McAleer,2,3,4, * Deparmen of Quaniaive Finance, Naional Tsing Hua Universiy, Hsinchu 3003, Taiwan Economeric Insiue, Erasmus School of Economics, Erasmus Universiy Roerdam, Roerdam 3000 DR, The Neherlands Tinbergen Insiue, Amserdam and Roerdam, The Neherlands Deparmen of Quaniaive Economics, Compluense Universiy of Madrid, Spain * Auhor o whom correspondence should be addressed; michael.mcaleer@gmail.com; Tel.: (ex ). Received: 5 December 205 / Acceped: 2 December 205 / Published: 22 December 205 Absrac: The purpose of he paper is o presen he fundamenal equaion in ourism finance ha connecs ourism research o empirical finance and financial economerics. The energy indusry, which includes, oil, gas and bio-energy fuels, ogeher wih he ourism indusry, are wo of he mos imporan indusries in he world oday in erms of employmen and generaing income. The primary purpose in aracing domesic and inernaional ouriss o a counry, region or ciy is o maximize ourism expendiure. The paper will concenrae on daily ourism expendiure, regardless of wheher such daa migh be readily available. If such daa are no available, a pracical mehod is presened o calculae he appropriae daa. Keywords: ourism research; ourism finance; growh in ourism; reurns on ourism; volailiy; fundamenal equaion; empirical finance; financial economerics. JEL Classificaion: C22; C32; C58; G32

2 J. Risk Financial Manag. 205, Inroducion The purpose of he paper is o presen he fundamenal equaion in ourism finance ha connecs ourism research o empirical finance and financial economerics. In addiion o he energy indusry, which includes, oil, gas and bio-energy fuels, ourism is one of he mos imporan indusries in he world oday in erms of generaing employmen and income. The primary purpose in aracing domesic and inernaional ouriss o a counry, region or ciy is o maximize ourism expendiure. In his sense, ourism is a commodiy ha provides income and income growh. This associaion is he primary reason for ourism adverising and promoional expendiures ha are inended o arac ouriss from a source counry, region or ciy. The growh in income is essenially idenical o he reurns on financial asses, such as socks, bonds and any associaed financial derivaives. This parallel inerpreaion, which leads o reurns and associaed measures of financial risk, will be developed in he following secion. There has been subsanial research in empirical finance and financial economerics o analyze he high frequency reurns financial asses, ha is, reurns on a weekly, daily, or hourly basis, and ulrahigh frequency ick daa ha measures prices, reurns and associaed financial risk on a minue, second or nano-second basis. Such analysis has no generally been he case in ourism research, one reason being he lack of ulra-high frequency daa. Twelve papers ha have addressed he modelling of ourism demand and he associaed volailiy (or uncerainy) include Chan, Lim and McAleer [], Chang, Hsu and McAleer [2], Chang e al. [3], Chang, Lim and McAleer [4], Divino and McAleer [5,6], Hoi, McAleer and Shareef [7,8], McAleer and Shareef [9,0,], and Medeiros e al. [2]. These papers have analyzed ourism demand and he associaed risk in leading journals such as Journal of Economerics, Tourism Managemen, Tourism Economics, Inernaional Journal of Tourism Research, Inernaional Journal of Tourism Sciences, Norh American Journal of Economics and Finance, Environmenal Modelling and Sofware, and Mahemaics and Compuers in Simulaion. However, none of hese ineresing papers has sough o presen ourism research in he same conex as empirical finance and financial economerics, or analyzed he fundamenal equaion in ourism finance ha connecs ourism research o empirical finance and financial economerics. This lack of an obvious connecion misses ou on he overlap of ourism research wih ourism finance, which herefore neglecs he porabiliy of he mehods and echniques ha are widely used in empirical finance and financial economerics. The paper concenraes on daily ourism expendiure, regardless of wheher such daa migh be readily available. If such daa are no available, a pracical mehod is presened o calculae he appropriae daa. One paper ha has analysed daily ourism expendiure daa and risk is Medeiros e al. [2], who used neural nework regression wih condiional volailiy for ulra-high frequency air passenger arrivals o Mallorca in he Balearic Islands, Spain. Chang, Hsu and McAleer [2] analyzed he impac of China on he daily closing prices of ourism sock prices, reurns and volailiy in he Taiwan ourism indusry, bu hey did no examine ouris expendiures or oal ourism. I is fair o say ha high frequency daa have ypically no been analyzed widely in ourism research, which may well be a srong reason for he connecion beween ourism finance and ourism research no having been advocaed. This paper seeks o emphasize he connecion beween he wo

3 J. Risk Financial Manag. 205, 8 37 opical areas of research o enable porabiliy of research mehods and echniques across he wo research areas. The remainder of he paper is as follows. Secion 2 presens he fundamenal equaion, Secion 3 develops a pracical mehod o make he fundamenal equaion operaional, and Secion 4 provides some concluding commens. 2. Fundamenal Equaion Consider he equaion ha relaes oal daily ourism expendiure, y, o he oal number of ouriss, x, and he average daily expendiure by ouriss, z : y x z () As here is lile evidence o sugges ha he average daily expendiure by ouriss, z, changes on a daily basis, z can be replaced by a consan, c, so ha Equaion () can be replaced by he following: I follows from Equaion (2) ha: y c (2) x y c x (3) where is he firs difference operaor, namely A A A. for a variable A, such ha y is he change in oal daily ourism expendiure, and x measures he ne daily ouris arrivals, namely he oal number of daily ouris arrivals minus daily ouris deparures. Using he lagged version of Equaion (2) o divide he lef-hand side of Equaion (3) by y and he righ-hand side of Equaion (3) by c x, leads o: / y x / x y (4) which, in urn, leads o he following Proposiion regarding he fundamenal equaion in ourism finance: Proposiion: Equaion (4) gives he fundamenal equaion in ourism finance, and relaes he growh in oal daily ourism expendiure, or alernaively he daily reurns on oal ourism, y / y, o he ne daily ouris arrivals divided by he previous day s oal number of ouriss, x / x. The variable ha can be observed on a daily basis in he fundamenal Equaion (4) is x, which is he change in he ne daily ouris arrivals. The primary purpose of ourism auhoriies in he public and privae secors is o achieve high daily reurns on oal ourism, which can be accomplished by increasing x, ha is, encouraging high ne daily ourism. As x migh no be available, he following secion provides a mehod for calculaing he variable o make he fundamenal equaion operaional.

4 J. Risk Financial Manag. 205, Operaional Mehod The daily reurns on oal ourism, y / y, are no observable, and similarly for daily oal ourism, whereas ne daily ourism, x, can be obained from appropriae daa sources. As monhly, quarerly or annual ourism are ypically available from sandard governmen daa sources and ourism auhoriies, assuming a uniform rae of ourism arrivals, which may accommodae seasonal facors, x can be obained as he average number of daily ouriss, denoed x. Rewriing Equaion (4) as he following: / y x / x y (5) ensures ha x / x can be used o measure y / y, namely he growh in oal daily ourism expendiure, or equivalenly he daily reurns on he oal number of ouriss, based on observable daa. As y / y is he mos widely used measure of financial reurns in invesmen finance, wih associaed volailiy o capure financial risk, i can be modelled as: r E r I ) ( (6) where r measures financial reurns, and I capures he informaion se ha is available a he end of he previous day in order o predic r and is associaed volailiy, which is a measure of financial risk. Numerous alernaive measures of volailiy, such as hisorical, implied, expeced, realized (such as range, namely, he highes minus he lowes daily price), opimal realized, condiional, and sochasic, are available o esimae he volailiy associaed wih financial reurns. In erms of ourism research and ourism finance, he daily reurns on he oal number of ouriss is he financial variable based on inerpreing he oal number of ouriss as a ourism sock index (see, for example, McAleer [3] for a comprehensive analysis of he alernaive ypes of mehods ha can be used o esimae financial volailiy for boh univariae and mulivariae processes). Mulivariae mehods can be used o measure spillovers across alernaive sources of ourism, such as from differen counries, regions or ciies. Spillovers can be calculaed in many differen ways, mos of which are incorrec. A recen guide o calculaing spillovers correcly across differen financial markes, has been developed by Chang e al. [4], where hree new definiions of volailiy and covolailiy spillovers are given, namely full volailiy spillovers, parial volailiy spillovers, and covolailiy spillovers. The models and mehods can easily be adaped o differen ouris markes in ourism finance. 4. Concluding Commens The energy indusry, which includes, oil, gas and bio-energy fuels, ogeher wih he ourism indusry, are wo of he mos imporan indusries in he world oday in erms of employmen and generaing income. The primary purpose in aracing domesic and inernaional ouriss o a counry, region or ciy is o maximize ourism expendiure. The purpose of he paper was o presen he fundamenal equaion in ourism finance ha connecs ourism research o empirical finance and financial economerics. I is fair o say ha high frequency daa have no been analyzed widely in ourism research, which may well be a srong reason for he

5 J. Risk Financial Manag. 205, connecion beween ourism finance and ourism research no ye having been advocaed. This paper emphasized he connecion beween he wo opical areas of research o enable porabiliy of a wide range of research mehods and echniques across he wo research areas. The paper concenraed on daily ourism expendiure, regardless of wheher such daa migh be readily available. If such daa are no available, a pracical mehod was presened o calculae he appropriae daa in order o calculae he growh in oal daily ourism expendiure, or equivalenly he daily reurns on he oal number of ouriss. The mehods can easily be adaped o differen high frequency daa periods, such as monhly, weekly, daily, hourly, and ulra-high frequency minue, second and nano-second daa measuremens. The connecion beween daily reurns on oal ourism and he associaed volailiy o capure financial risk was also discussed. Acknowledgemen The auhor is mos graeful o Chialin Chang and Teo Jasic for insighful discussions. For financial suppor, he auhor wishes o hank he Ausralian Research Council and he Naional Science Council of Taiwan. Conflics of Ineres The auhors declare no conflic of ineres. References. Chan, F.; Lim, C.; McAleer, M. Modelling mulivariae inernaional ourism demand and volailiy. Touri. Manag. 2005, 26, Chang, C.-L.; Hsu, H.-K.; McAleer, M. The impac of China on sock reurns and volailiy in he Taiwan ourism indusry. Norh Am. J. Econ. Financ. 204, 29, Chang, C.-L.; Khamkaew, T.; McAleer, M.; Tansucha, R. Inerdependence of inernaional ourism demand and volailiy in leading ASEAN desinaions. Touri. Econ. 20, 7, Chang, C.-L.; Lim, C.; McAleer, M. Modelling he volailiy in shor and long haul Japanese ouris arrivals o New Zealand and Taiwan. In. J. Touri. Sci. 202, 2, Divino, J.A.; McAleer, M. Modelling susainable inernaional ourism demand o he Brazilian Amazon. Environ. Model. Sofw. 2009, 24, Divino, J.A.; McAleer, M. Modelling and forecasing daily inernaional mass ourism o Peru. Touri. Manag. 200, 3, Hoi, S.; McAleer, M.; Shareef, R. Modelling counry risk and uncerainy in small island ourism economies. Touri. Econ. 2005,, Hoi, S.; McAleer, M.; Shareef, R. Modelling inernaional ourism and counry risk spillovers for Cyprus and Mala. Touri. Manag. 2007, 28, McAleer, M.; Shareef, R. Modelling inernaional ourism demand and volailiy in small island ourism economies. In. J. Touri. Res. 2005, 7, McAleer, M. Shareef, R. Modelling he uncerainy in inernaional ouris arrivals o he Maldives, Touri. Manag. 2007, 28,

6 J. Risk Financial Manag. 205, McAleer, M.; Shareef, R. Modelling inernaional ourism demand and uncerainy in Maldives and Seychelles: A porfolio approach. Mah. Compu. Simul. 2008, 78, Medeiros, M.; McAleer, M.; Sloje, D.; Ramos, V.; Rey-Maquieira, J. An alernaive approach o esimaing demand: Neural nework regression wih condiional volailiy for high frequency air passenger arrivals. J. Econom. 2008, 47, McAleer, M. Auomaed inference and learning in modeling financial volailiy. Econom. Theory 2005, 2, Chang, C.-L.; Li, Y.-Y.; McAleer, M. Volailiy spillovers beween energy and agriculural markes: A criical appraisal of heory and pracice, Discussion Paper 5-077/III; Tinbergen Insiue: Amserdam and Roerdam, The Neherlands, by he auhor; licensee MDPI, Basel, Swizerland. This aricle is an open access aricle disribued under he erms and condiions of he Creaive Commons Aribuion license (hp://creaivecommons.org/licenses/by/4.0/).