Asset Pricing and Option Trading for Harvesting Rights to Renewable Resources

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1 Asse Prcng and Opon radng or Harvesng Rghs o Reneable Resources Eyjólur Guðmundsson, Lecurer, Faculy o Fsheres udes, Unversy a Akureyr, Iceland and James L. Anderson, Proessor, Deparmen o Envronmenal and Naural Resource Economcs, Unversy o Rhode Island, Kngson, RI UA Absrac: hs paper dscusses he use o opons as a ool o rereve valuable normaon on he value and level o rsk assocaed h onng a share n a sock o reneable resource. he objecve s o sho ho heory on opons radng can be used o oban normaon on he perceved rsk o he resource, and o dscuss ho hs marke normaon can be used o enhance he economc perormance o he managemen rameork n place. Keyords: Reneable resources, sheres managemen, opons, opons radng, harvesng rghs, Is.. Inroducon he commons o he orld nclude reneable resources, such as aer, oress, sheres, land, ec. he ragedy o open access o he commons s all oo ell knon, here he common uure o he resource ends o decmae he resource n queson (Hardn, 968). he general rend n hsory has been one o prvazaon o common resources aer he resource has been over-harvesed as common propery (evenson, 99). In he las o decades, he rend has been he same or sheres resources, here more and more sheres are conrolled hrough ndvdual quoa and oher rghs-based sysems (see Wlen, 985; Hannesson, 99; Arnason, 995; qures, e al., 995; and Graon, e al., 996). Prvazaon o sheres resources has, n mos cases, led o enhanced economc perormance o he shery. Fsheres o Ne Zealand, Iceland, and he halbu shery n he U are all examples on ho prvazaon has mproved economc ecency o hose sheres (see Hannesson, 996, Runolsson, 996, Runolsson, 999, Homans and Wlen, 997). Wh he prvazaon o common resources, markes or onershp, or harvesng rghs, emerge. hose markes should generae valuable normaon or he resource manager. Fnancal and commody markes have developed rapdly over he pas cenury, despe he ac ha markes are ar rom perec. hese markes use uures conracs exensvely, and recenly varous orms o opons. hese markes provde valuable normaon o parcpans n he spo markes or he underlyng asses. he mos mporan role o markes or opons s no o be a prce dscovery mechansm bu raher: Provde valuable normaon abou he volaly and hence he rsk o he underlyng spo asse (Chance, 998). he objecve o hs paper s o sho ho opons radng can be used o oban normaon on he perceved rsk o a reneable resource, such as a sh sock. We also dscuss ho hs marke normaon can be used o enhance he economc perormance o he managemen rameork. We sar by reveng heorecal ork on prces o harvesng rghs o reneable resources, and gve an overve o classc nance heory on he asse prcng models. We hen go on o descrbe ho opons markes could be used as a prce ormaon marke or harvesng rghs o reneable resources. We hen dscuss ho hese ools could be used o nclude addonal normaon or he managemen process n order o enhance exsng managemen rameork.. Background he aseul means o unlmed harvesng o sh socks has probably been knon or a long me. Overharvesng o some sor has occurred, and ndeed as a reason or exploraon o ne shng grounds n he Mddle Ages. In Japan, coasal ocean resources ere allocaed o specc user groups as early as he 7 h

2 cenury (Yamamoo, 995). he economc problem o open access sheres as rs ormalzed by Warmng n 9 and Andersen (983). More amous s he ork o Gordon (954) and co (955). Inally, he economc dscplne suggesed ha lmed enry be used n order o reduce he eor n he shery (Copes, 986). he dea o allocang onershp o a share n he oal alloable cach rom an sh sock, o ndvduals, ere se orh by Chrsy (973), and ormalzed by Moloney and Pearse (979) and Clark (98). hs early ork ocused on shong ha ndvdual ranserable quoas (Is) are a susanable and ecen orm o managng sheres resources. As I sysems have been mplemened n sheres around he orld, he research ocus s shng oards ecency, equy, eecveness, and prce ormaon or onershp rghs n I sheres. Arnason (99) shoed ha under ndvdual ranserable share quoa sysem (I) mnmum normaon as needed oban socally opmum managemen n sheres, all he resource manager had o as o maxmze he spo value o he quoa shares. Arnason named hs approach he Mnmum Inormaon Managemen ysem, or MIM, or shor. he MIM sysem assumes ha he resource manager ans o nd a me pah o shng eor ha maxmzes presen value o ndusry pros, subjec o bologcal and echnologcal consrans, under a sysem o Indvdual ranserable hare uoas (I). he objecve uncon s: Maxmze or all { D },{ } subjec o : D x x D ³ F( x) or all ( p D C( D, x)) e here { D } sands or pah o ndvdual rms quoa shares or rm, {} s he opmal pah o he oal alloable cach (he allocaed quoa), F(x) s he groh uncon or he sock, p s prce (assumed consan), r s dscoun rae, and s number o rms. Prce and dscoun raes are assumed o represen rue socal shado prces. he ndvdual rm s assumed o maxmze s pros accordng o: r d D { z} D ³ Maxmze ( p subjec o : z D C( D, x) r s z) e here all varables are he same as n equaon () excep hs me he changes (z) n quoa held by each rm s mulpled by he prce each rms sells or buys quoa shares, and quoa holdngs becomes he conrol varable. Usng Hamlonan ormulaon or dynamc opmzaon and applyng Ponragyn's maxmum prncples, Arnason proves ha under he gven assumpons, maxmzng he prce or quoa, s, s he same as he rm maxmzed her ndvdual ne pros, or: Maxmze s( ) œ {} Maxmze { } ³ * * r [( p CE ( q, X ( x(),{ })))) q ] e Hence, he quoa auhory only needs o monor quoa prces and adjus allocaed quoas,, such ha he marke prce or quoas s maxmzed. hs resul s based on several crcal assumpons. Among hese are ha he expecaons o he shng rms are he bes avalable predcor o uure condons n he shery, and ha he resource ren and pros are equvalen, or: * * * * ( p C E ( q, x)) q p q C( q, x)) E q and equaon (4) mus hold or all and. Anoher crcal assumpon s ha socal and prvae dscoun raes are he same. Generally speakng, socal and prvae dscoun raes are no assumed o be he same, and some economss have argued ha socal dscoun rae should be close o zero (olo, 99). hese assumpons are resrcve and make praccal use o he MIM sysem dcul. qures and Krkley (996), Mahasson (997), and Lndner (99) have shon ha n he ace o ranson, or under nonequlbrum condons, quoa prces may no relec he rue shado value o he resource. As an example, e can magne ha dscoun raes are hgh. hs means ha uure revenues accoun or an ncreasngly smaller par o he asse's ne dscouned value. Le's say ha under hose crcumsances, he resource manager has been observng he quoa marke or a hle, and decdes o ncrease he alloable harves n order o ncrease he overall value o he share n he resource. he resource manager s unsure o he eec he ncrease n harves ll have on he uure susanably o he resource. he marke value d d

3 o he asse mgh ncrease, sgnalng o he resource manager ha hs decson as good. Hoever, hs ncrease n value may come h ncreased uncerany abou he uure sae o he resource. he value o hs uncerany s ncluded n he prce o he asse, and, hereore, s no possble or he resource manager o acually observe he ncrease n uncerany. He mgh be headed don he rong pah hou arnng. hs s here he resource manager ll make use o observng he opons marke or harvesng rghs o he reneable resource. 3. Fnance heory We dene ne ncome as he derence beeen prce, P, and economc coss, c: NI P c he value o each share s he dscouned uure ne ncome rom holdng ha asse. In sandard nancal heory he value o an asse n a deermnsc orld s: P NI ( r) Exensve varaons o hs ormula have been used n he nancal leraure, bu he basc noon s alays he same. Nohng s orh more han ll pay back o he oner. I s mporan o noe ha deren dscoun raes ll value he same asse n deren ays. Hence, he prvae dscoun rae s hgher han he socal opmum dscoun rae, he prvae secor ll value he asse less han s socally opmal. One mgh argue ha socks n a corporaon raded on he sock marke bear many smlares o a share n a reneable resource socks. Frs o all, one holds a share n he company, hch value mgh ncrease or decrease due o acons o he managemen eam, jus as resource manager can ncrease he sock o a resource hrough good managemen pracces. econd, hs share s expeced o yeld some dvdend and/or groh over a perod o me. In he same manner, he share n he resource s expeced o yeld some ne ncome and/or groh. Major acors ha aec he prce o an asse are rsk and uncerany. Generally speakng, nvesors are rsk averse and are llng o rade an asse h hgh rsk or an asse bearng loer rsk, boh asses pay he same dvdend. hs, o course, excludes all non-moneary arbues o he specc resource n queson. By holdng shares n many socks, he overall rsk o he collecon o socks (porolo) can be reduced. hs s he basc noon behnd he Capal Asse Prcng Model (CAPM) developed n he 96s and 97s (or overve on CAPM see Copeland, 99). he basc ormula o he CAPM model s: ~ ~ P ) cov(, ~ ) ( ) e O Pe r E r m m r P here O r var( r ) here P s he spo prce or he asse, P ~ e s he expeced value o he asse, r m s he expeced rae o reurn, and r s he rsk ree rae o reurn (dscoun rae). he CAPM model akes no accoun he relave rsk o he asse compared o he overall porolo o nvesmen. An overve o he basc asse prce heory shos ha he asse prce has o basc componens; he dscouned value o he ne ncome sream and he value o he rsk assocaed h he asse. In order o exrac he pure value o he rsk, one mus urn o heory on nancal dervaves. 3. Opons Opons have been used or a long me as a ay o allevae rsk among radng parners. Opons are a conrac ha gves he holder he rgh o buy, or sell, a specc asse a a gven prce and me n he uure. In 973, ormal radng exchange n opon conracs as esablshed by he Chcago Board o rade. hs as an ndependen exchange, named he Chcago Board Opons Exchange. hs marke became hghly successul rom he begnnng, and s currenly he larges opons exchange marke n he orld. o, ha s he value o an opon? Ho much s someone llng o pay or he rgh o do somehng? hs queson s complex. he are many acors ha ener he decson process, and some o hem, such as perceved rsk or deren nvesors expecaons make dcul o orm a unque prce or each opon. Black and choles (973) developed a mehod o value opons. he model s complex, and he dervaon. s beyond he scope o hs paper, bu e ll presen he basc seps n he dervaon o he Black and choles opon prcng model. hs overve s based on Hull (989). Assume ha he prce movemen o a share n a resource sock can be descrbed, usng dscree orm, as: ' P ' ' z here represens he share prce, P represens expeced rae o reurn and s he share prce m 3

4 volaly, and 'z s a Wener process. hs equaon s knon as a geomerc Bronan moon and s a sochasc process around a mean h a me rend. Io s lemma proos ha a uncon, hch depends on and, ollos a parcular process, knon as Io process; shon belo n dscree orm: ' P ' ¹ here s he prce uncon or a gven dervave on shares h prce. Invesors can reduce rsk by buyng boh socks and opons on a specc sock. By akng oppose sands on he sock and opons marke, he nvesor can elmnae he uncerany descrbed by he Wener process, 'z. he value o a porolo h a shor dervave and a long share poson s: 3 and he change n value s hen: '3 ' ' nce hs ould be a rsk-ree porolo, mus earn he same rae o reurn as oher rsk-ree nvesmen opporunes n a orld h no ransacon coss. Hence, he change n he value o he porolo over a small me nerval s: '3 r3' and subsung equaons () and () no equaon () gves us he Black-choles-Meron derenal equaon. r hs equaon s a general ormula h many deren soluon dependng on he boundary condons on he derenal equaon. he mos amous soluon s he Black-choles opon prcng model or valuaon o European call opons. he soluon or a European Call opon has he boundary condon as: max( X,) hen here s he sock prce, X s he srke prce, and sands or me. Usng he above boundary condon o solve equaon (3) gves he Black-choles model, generally represened h hree equaons: ee Hull, 989 p. 6 r ' z here d d N( d ) Xe ln( d X ) ( r r N( d ) ) Hence, he value o an opon depends upon ve acors, he sock prce,, he srke or exercse prce, X, he rsk ree neres rae, r, he me o maury,, and he sock prce volaly,. O hese, he rsk-ree neres rae, sock prce, and he sock volaly can be regarded as exogenous o he value o he opon. he oher acors are chosen by he nvesor ho res he opon. Hoever, ha does no ener he value o he opon s he nvesor's expeced rae o reurn. Hence he opon prce or a gven srke prce gves valuable normaon abou he overall marke expecaons on he value o he uncerany o he underlyng asse. he boundary condon (4) s really he nrnsc value o he opon,.e., he value o he opon. he oal value o an opon s hen s nrnsc value plus s me value. A smple graph belo explans ho changes n one o he parameers aec he oal opon value. $ P P Call C B A Asse po Prce Fgure : Opon value and deren me perods Fgure shos he value o a European Call opon a a gven srke prce, compared o he value o he underlyng asse. he 45 degree lne represens he derence beeen he spo prce(s) and he srke prce(s). he dsance beeen pons A and B represens he nrnsc value o he opon, or he derence beeen he spo prce and he srke prce. hs ould be he value o he opon ere exercsed mmedaely, snce he exercse prce s hgher han he curren spo prce. I he opon expres some monhs laer, s value ould be P. he oal value o he opon s hen he nrnsc value (B A) plus he 4

5 me value (C B), hch represens he rsk premum. I s he me value ha conans he mos mporan normaon, snce depends on he volaly o he prce o he asse. Changes n me value ll, hereore, gve he holder o he asse valuable normaon on he changes n perceved rsk o he asse. $ P P Asse po Prce Fgure : Opon value and changes n asse prce Fgure shos ho he opon value changes hen he underlyng asse ncreases n prce. We begn h an asse prce, and opon value P, or a srke prce equal o he curren spo prce (also called a-hemoney). No assume ha an exogenous even causes he asse prce o nsananeously ncrease. he asse s no more valuable, bu he queson remans, ha happens o he value o he opon? In hs example, he prce o he a-he-money opon (P ) has ncreased. nce me o maury has no changed, he comparson o he a-he-money opon mmedaely beore and aer he exogenous even reveals normaon abou perceved rsk. In hs example, perceved rsk ncreased aer he exogenous even. 4. Usng marke normaon o evaluae managemen pracces Frs, le's look a he sgnals ha he resource manager receves rom he spo marke. here are several reasons hy a share n he resource mgh ncrease n value. here mgh be ncreased demand or he produc rom he resource, leadng o hgher prces, and hence, makng he curren value o holdng a share n he resource hgher. hs mgh happen despe he ac uure susanably o he resource may be hreaened. econd, he ncrease mgh be due o beer managemen pracces leadng o a more valuable asse, such as conservaon mehods ha lead o larger sh socks n he uure. hrd, he buyer mgh have expecaons o ncreased prce n he uure, and ourh he buyer mgh have some knoledge abou uure saus o he resource, or producs derved rom, hch he resource manager s unaare o. I s clear ha smply observng he spo prce o he sock sends mxed sgnals o he resource manager. he manager canno make srong conclusons abou he eecveness o he managemen plan n place and, hereore, needs more normaon. I here s an acve marke or opons n he shares o he reneable resource, he marke ll reveal he expecaons abou he rsk o he resource rom hose ho parcpae n he radng. hose mos lkely o parcpae are he curren oners, processors ha use he resource, and speculaors. LEAP could gve he resource manager he mos valuable nsgh no he expeced sae o he resource n he uure snce hey have an expraon perod o several years. 3 For a gven r and, he opmal premum ncreases, he raders mus be expecng a decreases n prce volaly o he share and/or he share spo prce, and vce versa or a prce decrease o he opon. As prevously llusraed, e look n combnaon a he spo prce and he opons prce, he resource manager can deduce some valuable normaon abou curren expecaons regardng he uure sae o he reneable resource n queson. Frs, le's assume e have a shery h an Is managemen sysem. he sheres managemen announces he AC or he nex ve years, gven no envronmenal or ecologcal changes. Hence, here s uncerany abou he acual AC or any gven year n he uure. here s a publc, ell developed spo marke or share quoas and opons, here parcpans can buy or sell hou resrcons. Prces or quoa shares depend on he expeced prce or he nal sh producs, AC, and quany o avalable shares or sale. he objecve o he sheres manager s o maxmze he oal resource value over me. Le's examne ha happens he prce o quoa shares on he spo marke ncreases hou any announced changes n he AC. hs could happen or o reasons; eher he expeced prce or sh producs ncreased, or he perceved volaly o he value o he asse has declned, all else consan. I he spo prce or shares ncreases due o an ncrease n expeced sh prces, he me value o he opon ll no change. I he spo prce or shares ncreases because o decreased volaly, me value o he opon ll declne. 3 Currenly, LEAP h hree-year maury are beng raded on he CBOE. 5

6 Anoher example ould be he sheres manager chooses o se he AC. hs ll lkely change he perceved volaly o share value. nce he AC s hgher, he prces o shares n he harvesng rghs o he resource are lkely o ncrease, especally he dscoun rae s hgh. Hoever, o deermne, n ac, he change n AC ncreases he perceved volaly o he share, he manager should look a he opon value. I volaly (lkelhood o sock collapse) s perceved o ncrease, he opons value ll ncrease. Wha becomes mporan or sheres managers o an I shery h acve opon radng or he underlyng share n he shery s o monor he neracon beeen he spo prce and he opon prce. By so dong, he sheres manager can beer make he radeo beeen maxmzng he value o he resource, and reducng perceved rsk o he resource. Hence, acve opons radng can be used as a valuable ool or sheres managers n undersandng he volaly (susanably) o he resource. 5. Dscusson and concluson hares n he AC or a gven sh sock are lke share n a publcly raded company. he ools and rades o modern sock radng can, hereore, be appled o radng n shares o he cach rom a sh sock. In hs paper, e have reveed classcal nancal heory and shon ho he ools o he nancal markes can be used o exrac useul normaon or hose parcpang n he shery, as ell as sheres managemen. We also dscussed Mnmum Inormaon Managemen ysems or sheres and poned ou ha some o he model lmaons become less severe opon radng s aken no accoun. I radng h quoa shares does develop o he same exen as modern sock radng, varous normaon on he sh sock and he expecaons o hose ho rade producs rom he sh sock could be exraced. hs could be done by smply monorng he rade o shares and by monorng he rade n opons or quoa shares. I s our bele ha prvae propery rghs ll develop n mos o he orld's sheres over he nex e decades. he need or asse and dervave prcng or quoa radng s lkely o rse sgncanly over he nex e years. here s much o be done hn hs eld o sheres economcs. Boeconomc analyss s knon o be complcaed heorecally and dcul o es emprcally. Opons prcng s also dcul, requrng knoledge o sochasc calculus and dynamc opmzaon. he nex sep ould be o ormalze he deas se orh n hs paper o nclude normaon rom opons radng hn a dynamc boeconomc model. hs s needed n order o sho ho opon prces could be used drecly o enhance he normaon avalable or sheres managemen, and by so dong, ncrease he overall ecency o he shery n queson. Reerences Andersen, P. "On ren o shng grounds": A ranslaon o Jens Warmng's 9 arcle, h an nroducon. Hsory o Polcal Economy 5, no. 3(983): Arnason, R. he Icelandc Fsheres: evoluon and managemen o a shng ndusry. Oxord, London, Ednburgh, Cambrdge, Carlon: Fshng Nes Books, 995. Arnason, R. Mnmum Inormaon Managemen n sheres. Canadan Journal o Economcs 33, no. 3(99): Baldursson, F. M., and G. Magnusson. Porolo shng. candnavan Journal o Economcs 99, no. 3(997): Black, F. and M. choles. "he Prcng o Opons and Corporae Lables." Journal o Polcal Economy 8(May-June 973): Chance, D. M. An Inroducon o dervaves. 4 ed. Orlando: he Dryden Press, 998. Chrsy, F. J. Fsherman uoas: A enave suggeson or domesc managemen. Occasonal Paper. he La o he ea Insue, November, 973. Clark, C. W. oards a Predcve Model or he Economc Regulaon o Commercal Fsheres. Canadan Journal o Fsheres and Aquac cences 37, no. 7(98): -9. Copeland,. E. W., J.F. Fnancal heory and corporae polcy. Ne York: Addson-Wesley publshng company, 99. Copes, P. A crcal reve o he ndvdual quoa as a devce n sheres managemen. Land Economcs 6, no. 3(986): Gordon, H.. he economc heory o a common propery resource: he shery. Journal o Polcal Economy 6(954): 4-4. Graon, R.., D. qures, and J. Krkley. Prvae Propery Rghs and Crses n World Fsheres: urnng he de? Conemporary Economc Polcy 4, no. Ocober(996):

7 Hannesson, R. Fsheres Msmanagemen. Oxord: Fshng Nes Book, 996. Hannesson, R. From common sh o rghs based shng. Fsheres managemen and he evoluon o exclusve rghs o sh. European Economc Reve 35(99): Hardn, G. he ragedy o he Commons. cence 6, no. 968(968): Homans, F. R., and J. E. Wlen. A model o Regulaed Open Access Resource Use. Journal o Envronmenal Economcs and Managemen 3(997): -. Hull, J. C. Opons, Fuures & Oher dervaves. orono: Prence-Hall Inernaonal, Inc., 989. Lndner, R. K. C., H.F.; Bevn, G.F. Ren generaon durng he ranson o a managed shery: he case o he Ne Zealand I sysem. Marne Resource Economcs 7, no. 4(99): Mahasson,. Consequences o local governmen nvolvemen n he Icelandc I marke. Marne Resource Economcs, no. (997): 7-6. Moloney, D. G., and P. H. Pearse. uanave Rghs as an Insrumen or Regulang Commercal Fsheres. Journal o Fsheres Research Board o Canada 36(979): Runolsson, B. (999) he Icelandc ysem o Is: Is naure and perormance, ed. R. Arnason, and H. H. Gssurarson. Reykjavík, he Unversy o Iceland Press. Runolsson, B.. A., Ragnar (996). Evaluaon and Perormance o he Icelandc I sysem. Icelandc Economc Papers. Economc Insue, Unversy o Iceland. co, A. he Fshery: he objecves o sole onershp. Journal o Polcal Economy 63(955): 6-4. olo, R. An almos praccal sep oard susanably. Resource or he uure, An nved lecure on he occason o he 4h annversary, no. Ocober(99): 5-. qures, D., and J. Krkley. Indvdual ranserable quoas n a mulproduc common propery ndusry. Canadan Journal o Economcs 4, no. (996): qures, D., J. Krkley, and C. A. sdell. Indvdual ranserable uoas as a Fsheres Managemen ool. Reves n Fsheres cence 3, no. (995): evenson, G. G. Common propery economcs: A general heory and land use applcaons. ed. Ne York: Cambrdge Unversy Press, 99. Wlen, J. E. oards a heory o he regulaed shery. Marne Resource Economcs, no. 4(985): Yamamoo,. Y. Developmen o a Communy- Based Fshery Managemen ysem n Japan. Marne Resource Economcs (995):