Two previous CTAHR Economic Issues publications,

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1 Economc Issues Apr EI-9 Growth and Stablty of Agrcultural Producton n Hawa: A Portfolo Analyss Junnng Ca and PngSun Leung Department of Molecular Boscences and Boengneerng Two prevous CTAHR Economc Issues publcatons, EI-3 (Agrculture s Contrbuton to Hawa s Economy An Update) and EI-4 (The Lnkages of Agrculture to Hawa s Economy) have examned agrcultural ndustres economc contrbuton and ther lnkages to the rest of Hawa s economy 1 (see Notes, p. 11). The present publcaton examnes the growth and stablty of agrcultural producton n Hawa over the past four decades. Ths examnaton provdes nformaton about ndvdual agrcultural ndustres growth and stablty characterstcs as well as ther mpacts on the growth and stablty of the entre agrcultural sector. 2 We have also assessed how dversfcaton wthn Hawa s agrcultural sector has affected ts stablty. A portfolo of agrcultural ndustres Hawa s agrcultural sector s lke a portfolo composed of a varety of ndvdual agrcultural ndustres (Table 1). Ths ndustry portfolo s performance s determned by the performance of each ndustry n t as well as ts ndustry composton (.e., each ndustry s weght n the portfolo). Hgh growth of ndvdual agrcultural ndustres would lead to hgh growth of the entre agrcultural sector; and an agrcultural sector made up of a hgher percentage of rapdly growng ndustres would grow faster. 3 Smlarly, low (growth) varaton (.e., more consstent growth rates) of an ndvdual agrcultural ndustry would tend to make the entre agrcultural sector grow more stably. Varaton of the entre agrcultural sector s also affected by co-varaton between agrcultural ndustres. For example, an ndustry wth a tendency to move n the opposte drecton, relatve to the general agrcultural trend, could help reduce the varaton of the entre agrcultural sector. Varaton of the entre agrcultural sector depends not only on ndvdual ndustres varatons and co-varatons but also on ther composton n the sector. 4 The followng analyss also examnes the mpacts of dversfed agrculture on the stablty of Hawa s total agrcultural sector. On the one hand, as new ndustres tend to have relatvely hgh growth varatons at ther startng stages, dversfcaton towards them (.e., ncreasng ther shares n the total agrcultural sector) may have a negatve mpact on Hawa s agrcultural stablty. However, as a hghly dversfed agrcultural sector s generally beleved to be more stable than one concentrated n a few ndustres, dversfcaton may enhance the stablty of Hawa s agrcultural sector. Growth and stablty characterstcs of Hawa s agrcultural ndustres Table 2 shows the annual growth rates of total producton value of Hawa s agrcultural sector from 1964 to These four decades of agrcultural development could be dvded nto two two-decade perods. Durng the frst perod from 1964 to 1983, Hawa s total agrcultural producton value was on a slghtly upward trend but had fluctuated sgnfcantly. 6 From 1984 to 2003 the producton value declned for most of the tme but remaned relatvely flat n the early 2000s (Table 2 and Fgure 1). These aggregate agrcultural growth patterns were shaped by the growth and stablty performance of ndvdual agrcultural ndustres, whch s llustrated by the two graphs n Fgure 2. Publshed by the College of Tropcal Agrculture and Human Resources (CTAHR) and ssued n furtherance of Cooperatve Extenson work, Acts of May 8 and June 30, 1914, n cooperaton wth the U.S. Department of Agrculture. Andrew G. Hashmoto, Drector/Dean, Cooperatve Extenson Servce/CTAHR, Unversty of Hawa at Mänoa, Honolulu, Hawa An equal opportunty/affrmatve acton nsttuton provdng programs and servces to the people of Hawa wthout regard to race, sex, age, relgon, color, natonal orgn, ancestry, dsablty, martal status, arrest and court record, sexual orentaton, or status as a covered veteran. CTAHR publcatons can be found on the Web ste <

2 UH CTAHR Growth and Stablty of Agrcultural Producton n Hawa... EI-9 Apr Table 1. Industry portfolo of Hawa s agrcultural sector n 1964 and (For each commodty and year, producton s expressed n farmgate sales n 2003 dollars and the percentage relatve to total agrcultural producton.) (1,000 $) (%) (1,000 $) (%) Crops 774, , sugarcane 497, , frut 207, , pneapples 195, , papayas 5, , bananas 3, , guavas tropcal specalty frut 2, , vegetables and melons 28, , tomatoes 5, , taro 3, , herbs 7, gnger root , others 19, , tree nuts 23, , macadama nuts 6, , coffee 16, , florculture and nursery products 14, , orchds 23, le flowers 3, folage 16, cut flowers 14, potted flowerng plants 5, other nursery products 30, seed crops 50, other crops 4, , Lvestock 195, , mlk 63, , cattle 53, , eggs 46, , hogs 19, , honey , others 12, , Aquaculture 27, algae 11, shellfsh 9, fnfsh 1, others 4, Total 970, , Data source: Statstcs of Hawa Agrculture, varous ssues. The upper graph n Fgure 2 shows the growth and stablty performance of Hawa s agrcultural ndustres durng Three ndustres (.e., macadama nuts, florculture and nursery products, and papayas) were located n the northwest quadrant of ths graph. These ndustres have the most desrable growth and stablty characterstcs (.e., above-average growth rates but belowaverage growth varatons) durng Coffee, gnger root, guavas, honey, and seed crops were located n the northeast quadrant wth above-average growth rates and above-average growth varatons. Most of Hawa s agrcultural ndustres (.e., bananas, pneapples, tropcal specalty frut, taro, tomatoes, other vegetables and melons, other crops, cattle, eggs, hogs, mlk, and other lvestock) were located n the southwest quadrant, ndcatng that they had below-average growth rates durng ; yet ther growth was steader than the average. Sugarcane was the only ndustry located n the southeast quadrant, whch ndcates that ts growth performance was slghtly below average durng , whle the varaton of ts growth rate was above average. The lower graph n Fgure 2 shows the growth and stablty performance of Hawa s agrcultural ndustres durng , whch has changed sgnfcantly compared to the stuaton durng Only florculture and nursery products stll stayed n the northwest quadrant, whle papayas and macadama nuts have slpped nto the southwest quadrant wth ts below-average growth rate durng Although tomatoes growth and stablty performance durng was very smlar to ts stuaton durng , tomatoes has relocated from the southwest to the northwest quadrant because of Hawa agrcultural sector s reduced average growth rate durng compared to the stuaton durng Four ndustres (coffee, guavas, honey, and seed crops) stll remaned n the northeast quadrant despte ther declned mean growth rates durng compared to , whle the declne n gnger root s growth rate was too large to reman n ths quadrant. Wth ts deteroratng growth performance but mprovng stablty performance, sugarcane had relocated from the southeast to southwest quadrant. Smlar to the stuaton durng , pneapples, lvestock, and vegetables and melons (excludng tomatoes) stll remaned n the southwest quadrant wth lackluster but more steady growth performance. 2

3 UH CTAHR...A Portfolo Analyss EI-9 Apr Table 2. Annual growth n the value of Hawa s agrcultural sector. Year Growth Year Growth Year Growth Year Growth % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % Calculatons are based on data from varous ssues of Statstcs of Hawa Agrculture and State of Hawa Data Book. Percentages are the annual growth rates of Hawa s total agrcultural farmgate sales measured n 2003 dollars. Fgure 1. Annual value of agrcultural producton n Hawa, ,000,000 1,500,000 1,000, , Note: Agrcultural producton s measured by total agrcultural farm-gate sales n thousands of 2003 dollars. 3

4 UH CTAHR Growth and Stablty of Agrcultural Producton n Hawa... EI-9 Apr Fgure 2. Growth and stablty of Hawa s agrcultural ndustres. HIGH GROWTH HIGH GROWTH HIGH STABILITY gnger root honey coffee LOW STABILITY macadama nuts guavas seed crops 20% 15% florculture and nursery products 10% papayas other crops sugarcane 5% other vegetables tomatoes and melons tropcal bananas cattle specalty pneapples mlk frut taro other lvestock 0% hogs eggs LOW GROWTH LOW GROWTH HIGH STABILITY LOW STABILITY -5% -5% 5% 15% 25% 35% 45% 55% 65% 75% 85% HIGH GROWTH HIGH STABILITY aquaculture HIGH GROWTH LOW STABILITY 15% seed crops herbs coffee 10% bananas tomatoes florculture and nursery products topcal specal frut honey guavas 5% other vegetables and melons taro macadama nuts papayas gnger root other crops 0% pneapples mlk eggs other lvestock cattle hogs sugarcane % -10% LOW GROWTH HIGH STABILITY LOW GROWTH LOW STABILITY -15% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% Vertcal and horzontal axes measure agrcultural ndustres growth and stablty, respectvely. The coordnate of each ndustry measures the mean (vertcal axs) and standard devaton (horzontal axs) of ts growth rates durng or The orgn n each graph represents the average growth and standard devaton of all the agrcultural ndustres durng each of the two perods. The coordnate of the orgn n the upper graph s (21.9%, 6.3%), whch ndcates that agrcultural ndustres average growth rate durng s 6.3%; and the average standard devaton of ther growth rates s 21.9%. The coordnate of the orgn n the lower graph s (17.5%, 1.5%). 4

5 UH CTAHR...A Portfolo Analyss EI-9 Apr Idosyncratc growth and stablzng capacty of Hawa s agrcultural ndustres The above analyss has examned ndvdual agrcultural ndustres growth and stablty characterstcs. We now examne ther dosyncratc growth and stablzng capacty, whch, based on Wllam Sharpe s portfolo analyss model, can be measured by ther alphas and betas. 7 Conceptually, the growth performance of an agrcultural ndustry s affected by common and dosyncratc factors. Common factors are those that tend to affect most of agrcultural ndustres (e.g., weather, land prces, transportaton costs, government polces, etc.). In contrast, factors that only affect specfc ndustres are dosyncratc factors (e.g., dseases, export market condton, mport competton, etc.) Based on Sharpe s approach, an agrcultural ndustry s responsveness to the common factors can be measured by ts beta. A negatve beta ndcates that ths ndustry tends to grow when the common factor makes the entre sector declne, whle a postve beta ndcates that ths ndustry tends to move n the same drecton as the entre sector. Agrcultural ndustres betas can be used to measure ther stablzng capacty. An ndustry wth ts beta lower than the portfolo beta has hgh stablzng capacty snce t s less responsve to the general agrcultural trend or even countercyclcal when ts beta s negatve. 8 On the contrary, an ndustry wth ts beta hgher than the portfolo beta has low stablzng capacty. In general, the hgher an ndustry s beta, the lower ts stablzng capacty and vce versa. Besdes respondng to the common factor, the growth of an agrcultural ndustry s also nfluenced by factors ndependent of the general agrcultural trend. Such dosyncratc growth can be measured by ts alpha. An ndustry wth alpha greater than the portfolo alpha has hgh dosyncratc growth, whle an ndustry wth alpha below the portfolo alpha has low dosyncratc growth. 9 Based on Sharpe s approach we have estmated the alpha and beta of each agrcultural ndustry n Hawa durng each of the two perods (.e and ). The results are reported n Table 3 and llustrated n Fgure For the perod of , there were eght ndustres (papayas, guavas, vegetables and melons, gnger root, coffee, macadama nuts, florculture and nursery products, and honey) n the northwest quadrant of the left graph n Fgure 3. These ndustres alphas were greater than the portfolo alpha, ndcatng that they had hgh dosyncratc growth durng (Table 3). Ther betas were smaller than the portfolo beta, ndcatng that they had hgh stablzng capacty durng the perod. Such ndustres wth both hgh dosyncratc growth and hgh stablzng capacty are often called star ndustres because of ther outstandng contrbuton to both growth and stablty of the entre agrcultural sector. Vegetables and melons and florculture and nursery products contnued to be star ndustres durng (Fgure 3). Ths may reflect ther comparatve advantage n servng local markets over Hawa s major crops (e.g., sugarcane and pneapples) that are manly for export. Besdes, the hgh dosyncratc growth of florculture and nursery products may also beneft from federal research funds and the ntroducton of new varetes from UH-CTAHR. Guavas, gnger root, and honey also margnally remaned n the star quadrant durng (Fgure 3). Coffee, the most shnng star durng , has shfted to the northeast quadrant durng (Fgure 3). Industres n ths quadrant are often called queston mark ndustres n that they have outstandng dosyncratc growth but below-average stablzng capacty. Coffee s persstent hgh dosyncratc growth may reflect the fact that Hawa s the only U.S. state growng coffee and has benefted from ts dstnct regonal brandng such as Kona coffee. Papayas and macadama nuts were another two ndustres turnng from star ndustres durng to queston-mark ndustres durng (Fgure 3). Pneapples and other lvestock also belonged to the queston-mark quadrant durng , shftng from the southwest quadrant (Fgure 3). Industres n the southwest quadrant are often called cash cow ndustres because of ther below-average dosyncratc growth but above-average stablzng capacty. Whle pneapples, bananas, tropcal specalty frut, tomatoes, taro, seed crops, cattle eggs, hogs, and mlk were cash-cow ndustres durng , only the lvestock ndustres remaned so durng (Fgure 3). As the exact opposte of a star ndustry, a dog ndustry s located n the southeast quadrant wth an alpha smaller than the portfolo alpha and a beta greater than the portfolo beta. Such dog ndustres have not only below-average dosyncratc growth but also rela 5

6 UH CTAHR Growth and Stablty of Agrcultural Producton n Hawa... EI-9 Apr Table 3. Idosyncratc growth and stablzng capacty of Hawa s agrcultural ndustres Stablzng capacty Idosyncratc growth Stablzng capacty Idosyncratc growth Industry (beta) 2 (alpha, %) 2 (beta) 2 (alpha, %) 2 sugarcane fruts pneapples papayas bananas guavas tropcal specalty frut vegetables and melons tomatoes taro herbs gnger root other vegetables and melons tree nuts macadama nuts coffee florculture and nursery products seed crops lvestock mlk cattle eggs hogs honey other lvestock aquaculture Portfolo An ndustry s dosyncratc growth and stablzng capacty characterstcs are measured by ts alpha and beta, respectvely. For example, coffee s beta of 1.3 and alpha of 22% durng ndcate that t tended to grow (or declne) by 1.3% when the entre agrculture declned (or grew) by 1% durng ths perod; and ndependent wth the general agrcultural trend, ts dosyncratc growth was 22%. 2 Industres alphas and betas are estmated based on Sharpe s portfolo analyss model. Alphas and betas nsgnfcant at 20% were set to zero. 3 Includes beef, dary, and dary replacement operatons. 4 The portfolo alpha and beta of each year are the weghted sums of ndvdual ndustres alphas and betas; each ndustry s weght s ts share n the agrcultural sector n that year. The portfolo alpha and beta durng or are the average portfolo alpha and beta durng these two perods. tvely low stablzng capacty. Sugarcane s the only below-average dosyncratc growth durng , dog ndustry dentfed n our study (Fgure 3). whle the latter had below-average overall growth but A comparson of Fgure 2 and Fgure 3 ndcates that above-average dosyncratc growth durng most agrcultural ndustres dosyncratc growth (cap- The comparson of Fgure 2 and Fgure 3 also ndtured by Fgure 3) s consstent wth ther overall growth cates that although some dversfed agrcultural ndus (captured by Fgure 2). That s, an ndustry wth rela- tres (e.g., coffee durng , aquaculture and tvely hgh dosyncratc growth also tends to have rela- herbs durng , and guavas, gnger root, seed tvely hgh overall growth. Seed crops and other veg- crops and honey durng both perods) had relatvely hgh etables and melons were two exceptons durng 1964 growth varatons by themselves (Fgure 2), they had The former had above-average overall growth but relatvely hgh stablzng capacty for the entre agr 6

7 UH CTAHR...A Portfolo Analyss EI-9 Apr Fgure 3. Idosyncratc growth and stablzng capacty of Hawa s agrcultural ndustres. STAR coffee gnger root QUESTION MARK guavas honey macadama nuts florculture & nursery products other vegetables and melons papayas pneapples cattle tomatoes tropcal specalty frut sugarcane CASH COW DOG STAR QUESTION MARK coffee taro aquaculture herbs seed crops other vegetables and melons mlk eggs cattle hogs florculture and nursery products pneapples macadama nuts papayas other lvestock sugarcane CASH COW DOG 1. Vertcal and horzontal axes measure agrcultural ndustres alphas and betas, respectvely. Industres n the northwest quadrant have alphas greater than the portfolo alpha (ndcatng ther relatvely hgh dosyncratc growth ndependent of the general agrcultural trend); and they have betas less than the portfolo beta (ndcatng ther relatvely hgh stablzng capacty). Industres n the northeast quadrant have relatvely hgh dosyncratc growth (.e. ther alphas greater than the portfolo alphas) but relatvely low stablzng capacty (.e., ther betas greater than the portfolo beta). Industres n the southwest quadrant have relatvely low dosyncratc growth but relatvely hgh stablzng capacty; and ndustres n the southeast quadrant have relatvely low dosyncratc growth as well as relatvely low stablzng capacty. 2. The trangle symbol n the left graph represents seven ndustres (bananas, taro, seed crops, hogs, mlk, eggs, and other lvestock) durng that have both alphas and betas nsgnfcantly dfferent from zero. Sx ndustres (bananas, guavas, tropcal specalty frut, tomatoes, gnger root, and honey) durng belonged to ths category. 7

8 UH CTAHR Growth and Stablty of Agrcultural Producton n Hawa... EI-9 Apr Fgure 4. Industry composton n Hawa s agrcultural sector. 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% florculture and nursery products vegetables and melons seed crops macadama nuts other fruts aquaculture coffee others lvestock pneapples sugarcane An ndustry s rato represents the share of ts producton n Hawa s total agrcultural producton. cultural sector (Fgure 3). Ths phenomenon reflects the power of dversfcaton, whch allows ndvdual ndustres varatons offsettng one another and hence reduce the varaton of the entre sector. Dversfcaton and agrcultural stablty n Hawa Dversfed agrculture has been proposed as a strategy for sustanable agrcultural development n Hawa snce the early 1900s. 11 One purpose of ths dversfcaton strategy s to enhance agrcultural stablty by actvely encouragng a shft from plantaton crops such as sugar and pneapples, to a cornucopa of agrcultural products. Fgure 4 shows that durng the perod , Hawa s agrculture has successfully changed from hghly dependent upon sugar and pneapples nto one that contans a varety of agrcultural ndustres. As ndcated by the entropy ndex (as a measure of dversty) n Table 4, 12 these changes n ndustry composton have ncreased the dversty of Hawa s agrcultural sector for most of the tme durng The dversty has ncreased most sgnfcantly durng the second perod (.e., ), especally from md 1980s to md 1990s, and seems to reach a plateau snce 1997 (Fgure 5). To assess how dversfcaton has affected agrcultural stablty n Hawa durng , we have computed Hawa agrcultural sector s portfolo standard devaton (as a measure of ts stablty) n each year durng ths perod. 13 The results are llustrated n Fgure 5. Fgure 5 shows that Hawa s agrcultural sector s portfolo standard devaton has manfested a downward trend for most of the tme durng before levelng off n the early 2000s. It also shows an obvous negatve correlaton between the portfolo standard devaton and the entropy ndex. These results ndcate that ncreased agrcultural dversty has contrbuted to reducng agrcultural varaton n Hawa durng

9 UH CTAHR...A Portfolo Analyss EI-9 Apr Fgure 5. Entropy ndex and portfolo standard devaton of Hawa s agrcultural sector, % 2.5 5% 2 Entropy ndex (left axs) Portfolo standard devaton (rght axs) 4% 1.5 3% 1 2% 0.5 1% % The entropy ndex measures the degree of dversfcaton wthn Hawa s agrcultural sector; a hgh ndex ndcates a more dversfed agrcultural sector. The portfolo standard devaton measures the stablty of Hawa s agrcultural growth; a small devaton ndcates that the sector grows more steadly. Smple correlaton, r, between the portfolo standard devaton and the entropy ndex s 0.90 (p-value = 0.000). Table 4. Agrcultural dversty n Hawa, as expressed by entropy ndex. 1 Year Index Year Index Year Index Year Index Average 1.67 Average 1.74 Average 2.15 Average The dversty of Hawa s agrculture s measured by ts entropy ndex. The mnmum entropy ndex s zero, whch would occur when the sector s completely specalzed n a sngle ndustry. The greater the entropy ndex s, the more dversfed the sector would be. 9

10 UH CTAHR Growth and Stablty of Agrcultural Producton n Hawa... EI-9 Apr Concludng remarks We have appled portfolo analyss to assess the growth and stablty characterstcs of Hawa s agrcultural ndustres as well as ther dosyncratc growth and stablzng capacty durng and Our analyss has dentfed several star ndustres (e.g., aquaculture, herbs, seed crops, vegetables and melons, and florculture and nursery products) durng Expanson of these ndustres durng ths perod has helped ncrease both Hawa s agrcultural sector s growth and stablty. If these ndustres mantan ther dosyncratc growth and stablzng capacty, ther expanson would contnungly beneft the growth and stablty of Hawa s agrcultural sector. Our analyss has also shown that several matured agrcultural ndustres (e.g., pneapples, papayas, and macadama nuts) have become queston-mark ndustres durng wth slghtly above-average dosyncratc growth and below-average stablzng capacty. In the future, whether these ndustres wll return to the star quadrant where they (except pneapples) used to belong durng , or become dog ndustres lke the sugarcane ndustry, depends on whether they wll utlze ther own comparatve advantages to stmulate growth. We have also assessed dversfcaton wthn Hawa s agrcultural sector and ts mpact on the sector s growth and stablty. The results show that Hawa s agrcultural sector has become ncreasngly dversfed durng the four decades from 1964 to 2003, especally for the last two decades; and the ncreased dversty has enhanced the stablty of Hawa s agrculture. As the degree of agrcultural dversty has ceased to ncrease snce the late 1990s, the mpact of Hawa s agrcultural sector s ndustry composton on ts stablty has remaned relatvely steady n the early 2000s. It remans to be seen whether ths s merely a temporary pause or reflects that agrcultural dversfcaton n Hawa has reached a plateau. Due to data lmtatons we have used agrcultural producton value as a measure of the general performance of the agrcultural sector. Pendng data avalablty, smlar portfolo analyss can also be conducted usng agrcultural ncome or employment, whch would provde more nsghts about the contrbuton of ndvdual ndustres and ther composton to agrcultural growth and stablty n Hawa. Whle the present study shows that agrcultural dversfcaton has had a postve mpact on the stablty of Hawa s agrculture, a step further would be to use portfolo analyss models to examne growth-stablty tradeoffs n Hawa s agrculture and dentfy ndustry compostons that would lead to optmal growth-stablty tradeoffs. Acknowledgments Ths document benefted greatly from the constructve comments and suggestons of the followng colleagues: Jm Hollyer (ADAP/CTAHR, UHM), Vctor Huang (Fnance, UHM), Matthew Loke (HDOA), James Mak (Economcs, UHM), and Stuart Nakamoto (HNFAS/ CTAHR, UHM). The remanng errors are ours. Fundng support from the Offce of Assocate Dean and Assocate Drector for Research n CTAHR s greatly apprecated. 10

11 UH CTAHR...A Portfolo Analyss EI-9 Apr Notes 1 The two publcatons are avalable at hawa.edu/oc/freepubs/pdf/ei-3.pdf and hawa.edu/oc/freepubs/pdf/ei-4.pdf. 2 Whle growth measures an ndustry or sector s development performance, measure of stablty provdes another mportant dmenson, especally for agrcultural ndustres that tend to have hgher crop-specfc varaton due to varatons n weather patterns, pest nfestatons, dsease outbreaks, etc. 3 The entre agrcultural sector s growth rate (G) s equal to the weghted sum of ndvdual agrcultural ndustres growth rates (g ) wth the weght (s ) beng the share of ndustry n G = s g the sector,.e.,. 4 The volatlty of the entre agrcultural sector can be measured by ts portfolo varance, whch s equal to the weghted sum of ndvdual agrcultural ndustres varance σ = s σ + s s σ σ 2 p j p and covarance,.e., j j, where, σ 2, and σ j denote, respectvely, the portfolo varance, the varance of ndustry, and the covarance between ndustres and j. 5 The producton value of agrculture s measured by the value of agrcultural farm-gate sales n constant dollars (.e., adjusted for nflaton). 6 Both of the extremely hgh agrcultural growth perods n 1974 and 1980, and subsequent declnes, were manly caused by fluctuatons n sugar prces. 7 Wllam Sharpe s paper, A smplfed model for portfolo analyss (Management Scence, vol. 9, no. 2, 1963, ), ntroduced a smplfed way of conductng meanvarance portfolo analyss. Deborah J. Brown and Jm Pheasant s paper, A Sharpe portfolo approach to regonal economc analyss (Journal of Regonal Scence, vol. 25, no. 1, 1985, 51 63), appled Sharpe s approach to ndustry portfolo analyss. See also Deborah J. Brown and Keth C. Brown s paper, Usng the Sharpe Portfolo Model to choose economc sectors for expanson n a rural Indana county (Interfaces, vol. 13, June 3, 1983, 13 19). 8 The portfolo beta of the agrcultural sector measures agrcultural ndustres average responsveness to the common factors. It s equal to the weghted sum of the betas of ndvdual agrcultural ndustres n the sector,.e., Β = s β, where B, β, and s denote, respectvely, the portfolo s beta, ndustry s beta, and ndustry s weght n the entre agrcultural sector. 9 Smlar to the portfolo beta explaned n footnote 8, the portfolo alpha of the entre agrcultural sector measures agrcultural ndustres average dosyncratc growth. It s equal to the weghted sum of the alphas of ndvdual ndustres n the sector,.e., Α = s α, where A, α, and s denote, respectvely, the portfolo s alpha, ndustry s alpha, and ndustry s share n the entre agrcultural sector. 10 The model used to estmate alphas and betas s g = α + β G + ε, whch mples that ndustry s annual growth rate g s determned by ts dosyncratc growth rate α, ts response to the growth of the entre agrcultural sector β G (where G represents the annual growth rate of the entre agrcultural sector; and β s a stablty parameter measurng the responsveness of ndustry to the entre sector s volatlty), and the random element ε. 11 Smth, J.G., Annual Report of the Hawa Agrcultural Experment Staton n 1901, U.S. Department of Agrculture, Offce of Experment Statons, page 361. N 12 A sector s entropy ndex s computed by s ln s, where =1 s represents ndustry s share n the sector s revenues; and N represents the number of ndustres n the sector. The mnmum entropy ndex s zero, whch would happen when a sector completely specalzes n only one ndustry. The more ndustres a sector contans, the hgher ts entropy ndex would be. Gven the number of ndustres, a sector s entropy ndex would be hgher when ts revenues are dstrbuted more evenly across these ndustres. 13 The agrcultural sector s portfolo standard devaton s equal to the square root of ts portfolo varance, whch can be computed accordng to the formula ntroduced n footnote 4. 11