xt7xgx44sb7j https://nyx.uky.edu/dips/xt7xgx44sb7j/data/mets.xml Agricultural Experiment Station, Department of Agricultural Economics, University of Kentucky 1974 journals kaes_research_rprts_20 English University of Kentucky Contact the Special Collections Research Center for information regarding rights and use of this collection. Kentucky Agricultural Experiment Station Research Report 20 : July 1974 text Research Report 20 : July 1974 1974 2014 true xt7xgx44sb7j section xt7xgx44sb7j EFFECTS OF LOCATION BASIS VARIABILITY ON LIVESTOCK HEDGING IN THE SOUTH By Barry W. Bobsf · I RESEARCH REPORT 20 : July I974 University of Kentucky : : College of Agriculture Agricultural Experiment Station :·: Department of Agricultural Economics Lexington . I ` J x x * a ’ CONTENTS V Page Foreward ........................................... 4 Introduction ......................................... 5 Theoretical Issues ...................................... 6 Location Basis Variability ............................... 6 Imperfect Spatial Competition ............................. 7 Alternative Measures of Location Basis Variability ................... 7 Hedging Error and Bias ................................. 8 Summary ........................................ 10 Location Basis Variability for Slaughter Hogs ........................ 10 Markets and Grades Selected .............................. IO Hedging Systems .................................... 10 Method of Calculation ................................. 11 Results ......................................... 11 Location Basis Variability for Fed Cattle ........................., 15 · Markets, Grades, and Hedging Periods ......................... 15 Results ......................................... 17 Further Tests ...................................... 22 Special Analysis for Choice Steers .............................. 26 Concluding Remarks ..................................... 33 References .......................................... 35 Appendix .......................................... 36 1 I I I ~. ` i i LIST OF TABLES ; , i Page i F 1 Hog Price and Hedging Revenue Summary Statistics, by Grade, Four Markets, 1971 . . 12 1 1* , ii , i _ 2 Bartlett’s Test of Equality of Variance of Cash Hog Prices and Hedging Revenues, by j p Grade, Four Markets, 1971 ,.., , ..........,.....,.......... 14 * V 3 Realized Basis Statistics for Hog Hedging Revenues, by Grade, Four Markets, 1971 . . 16 V 4 Feeding — Hedging Periods for Selected Feeder Cattle Types ............. 19 i i j 5 Summary Statistics for Fed Cattle Hedging Revenues, Four Markets, january § I Qi , 1969-june 1972 .................................... 20 l 6 Bartlett’s Test of Equality of Variances of Fed Cattle Prices and Hedging Revenues, by g Grade, Four Markets,january 1969-june 1972 ..................... 23 Q 1 E Q 1 i E 7 Individual F-Ratios of Cash Price and Hedging Revenue Variances for Choice Steers in i 1 . i _ Three Markets Compared to Omaha,january l969·june 1972 ............ 24 . l 2 I ` . il 8 Ratios of Hedging Revenue Variances to Cash Market Price Variances, Four Markets, [ ' · Q1 january 1969-june 1972 .,,.......i.. . . . . . a ..,...... 25 A r _ i 9 Realized Basis Means and Variances by Grades, Four Markets, january 1969-june 1972 27 I 10 Ratios oft Realized Basis Variances to Cash Market Price Variances, by Grades, Four 1 i Markets,january 1969-june 1972 ,.,...,.. . . . ............. 28 I p 11 Choice Steer Price and Hedging Revenue Summary Statistics, Four Markets, january i _ § 1969-june 1972 .........,.....,,....r...,.......... 30 12 Individual F-Ratios of Choice Steer Cash Price and Hedging Revenue Variances, Three j Markets Compared with Omaha,january 1969-june 1972 ...,...,....... 31 ; 13 Covariances and Correlations of Choice Steer Prices with Hedging and Covering Futures I Prices, Four Markets,january 1969-june 1972 ..,, , . . . ........... 32 ’ 2 , 1 APPENDIX TABLE Page 1 Means, Variances, and Covariances of Choice Steer Futures, by Length 0f Hedge, january 1969-june 1972 . , .......................... 36 2 i . i . l ‘ ¤ ~ i ; . I Foimwoao s » i ~. I The research summarized in this report represents Kentucky’s contribution to the Southern = ii T regional livestock marketing research project, "Economic Evaluation of Alternative Forms of I Vertical Coordination in the Livestock-Meat Industry." lt was performed under the auspices of the Chicago Mercantile Exchange’s "Research in Futures" fellowship program. Some of the material contained in this report has been published in the form of two articles in the 1973 I volume of the Southern joumal ofAgrz`cultuml Economics. One article dealt with slaughter hogs ~ I ? I and the other with slaughter cattle. This paper brings these two topics together and expands upon ` I 1 them. Much new material, particularly on cattle hedging, has been added. I spect; I Q ii with I I the I . I comn I slaug} I I estab} I I l IT in thc I I I Yet ; I ; Qi repre: 1 I . comp l L ’i livest· I I ` I educ: i i I made I i l_ For t I Z I I A sanct I Yi been I I comm I . » Arthi I towai . . notec i alterr I I n hog descr I coorc s betw· I simpl livest mark packi ? I the 1 Ll Z 1 EFFECTS OI· LOCATION BASIS VARIABILITY ON LIVESTOCK HEDGING IN THE SOUTH by Barry XV. Bobst Introduction offered, or price. If one takes the open _ market as a base, a spectrum of alternative 7 Live animal futures contracts have had a coordinating arrangements can exist, ranging spectacularlysuccessfuldevelopment Starting from informal agreements through written with a radical departure in futures markets, contracts, which specify one or more of the the concept of trade in a nonstorable terms of trade, to vertical integration, in commodity, contracts in choice steers, which feeding and packing are carried out by slaughter hogs, and feeder cattle have been the same firm and coordination becomes a established. Trading volume and open interest matter of adminstrative arrangement. Hedging in these contracts are increasing year by year. fits into this spectrum in avariety of ways. It Yet at the same time, the hedging activity can be used in conjunction with open represented tn these contracts is very small markets, with various kinds of contracts, or compared with the potential afforded by the even by vertically integrated firms. The livestock industry Public relations and potential for hedging in a region, therefore, is educational efforts have been and are being an important aspect of efforts to devise . made to arouse interest in potential hedgers vertical coordination methods to improve the For potential hedgers in business circles, the effrciency of livestock marketing in the sanction of the Harvard Business School has region. been placed on hedging in livestock and other Regionaltty is stressed because of the commodtties by the publication of a book by geographic structure of livestock feeding in Arthur Efforts have been directed the United States. The traditional heartland towards farmers too, with some success, as of cattle and hog feeding is the Corn Belt, and noted by Futrell (6). most livestock futures contract delivery Live animal futures contracts provide an points have been located there. The presence alternative marketing procedure for cattle and or absence of futures contract delivery points hog producers This alternative is best is an important factor influencing the described in the context of the vertical potential of hedging in a region. Hedging in coordination of marketing that takes place areas remote from contract delivery points between livestock producers and buyers. The can be rendered ineffective by a condition simplest means of coordination between known as location basis variability. In general, livestock feeders and packers ts the open the Southeastern and South Central states market: feeders sell to the highestrbiddrng lack contract delivery points. None of the packer with no prior arrangements concerning delivery points for hogs is located in this ' the timing of the sale, quality of livestock region. No delivery point for choice steers was 5 l ' i l 2 I 6 i Wl is . ° { located in the region until August 1971, when Theoretical Issues F;“CCS _ l Guymon, Okla., in the westernmost part of UC r . § the study area, was so designated. Since Location Basis Variability l"Cd‘C i i Southern livestock markets are susceptible to PHCCS if location basis variability, the object of the Location basis variability can be defined C0“Cl* l Yi study was to measure the degree of location as the distortion in hedging results that occurs l'“C#“» basis variability occurring in these markets by virtue of the hedger’s location at some $e*U`*C» e ’ p and to assess its effects on hedging. point distant from a futures contract delivery PUCC S _ l C; The basic procedure of this study was to point market. Location basis is by its very I ’ l generate hedging revenues for Southern nature unhedgeable. At the same time, C"’fCl* i A markets, €Sti1T1¤t€ th€if Vafiabilitifis, and variation in location basis does not necessarily Vumlbl E p compare them with similar measures for a exist. If it does exist, it has its origin in the C°mPC r I _ y central futures contract delivery market. It is state of spatial competition in a br C"l . i · in the nature of location basis that, if it exists, geographically dispersed market for the Shork , it will result in higher variabilities in the commodity in question rather than in the bmkcl A i if i distant markets. The point of view taken in futures market for that commodity It can be ls fom the study was that of livestock producers. shown that in a perfectly competitive spatial I i That is, short hedges intended to avert the market, with free trade, perfect knowledge, Rljgt 1 Q risk of price declines on inventories of large numbers of buyers and sellers, and so A p' , livestock on feed were postulated, and the on, price differences between any two points “'hC’C i timing of hedges was tailored to fit various cannot exceed the transfer cost between them "Cg“’“ * · C feeding situations. Since timing is an in the short run (2). In the long run, entry, g Wim [ F , i important aspect of hedging management, the exit, and resource price revaluation will cause Comm results of the study HIC less applicable t0 the price differences to just equal transfer costs. on C ( I y situation of long hedgers, such as packers, Short run or long run, the perfectly Comm ° l E whose timing requirements are likely to be competitive spatial market implies stable price PHCC H l 1 different from those of feeders. differentials among points in a geographic dam [ A l C i No Sig'¤ifiCaI1t effects due to location market-—otherwise known as a price surface. CPPYOP l i if basis variability W€T€ found f01` Slaughwf hogs Fluctuations in demand or supply at various mls *5 H for the mafkcts, St¤dY period, and hffdgiflg points in the market cause fluctuations in “*‘*O“’ " jé systems used in the study. Southern hog price which are reflected evenly across the MC CV · E C feeders in the markets studied would have price surface, leaving the transfer hcdsm l l C ,_ found hedging as effective in averting the risk cost-generated gradient of the surface Cash IT Q i ig of price change as would feeders in the unchanged, hCd§C$ i ii C€l’l’CI`8.l, Corn Belt COl’1tI`aCt delivery market. Stability of the price gurface for a illgcblf l . However, significant location effects were commodity has two implications of interest in CCl“i“" : il found for fed cattle in the Southern and an analysis of hedging in a spatial market. *1 l'“Ci ; r 1 Southern Plains markets studied. Hedging was Frrst, the stability of the surface itself C"“m* , p generally not so effective as in the central suggests predictability. If prices at points A m Cq“* . 1 i ` delivery market. ln some instances, hedging and B bear a certain relationship to one ~ h would actually have increasedprice risk rather another at one point in time, the same Vikllg ‘ than reducing it. Details and interpretations relationship can be safely predicted to hold in i i . of these findings are presented later in this the future, given only that transfer costs ‘2CV(l YCPON- remain constant. While the absolute level of r · where l ’ i 7 prices at A and B may be very unpredictable, covariance respectively, and T is the total the relationship between them is highly number of sales dates. This variance equation predictable 'I`he other implication is that applies to any given market region i. Where prices at points A and B will be perfectly prices have equal variances and are perfectly correlated, so that, when price changes are correlated, the variance and covariance linear, price variance will be everywhere the components of equation (2) are equal in all same, even though means will vary along the markets, and hedging revenue variances are , price surface everywhere the same. Whatever risk lt also follows from the perfect transference can be accomplished through , correlation among prices that location basis hedgrng can be accomplished equally in all variability will not exist in a perfectly markets competitive spatral market This can be seen by examinrng the variance components of a slrort·hedge revenue equation Omittrng ImperfectSpat1al Competition brokerage fees, the hedgrng revenue function is formulated as follows: In the real world, knowledge is imperfect because large numbers of buyers and sellers Rljgt = Plgl + lljm - Cml (1) are not present in all areas, rigidities in commodity transport exist, and quality where Rljgl is hedgrng revenue in marker differences represented by commodity grades region 1, hedge length j, for commodity grade are not perceived rn the same way at all places g which is sold on date t; lljm is the futures and at all times Leads and lags in price contract price at which the hedge vvas placed adjustments among markets can exist. Under A on a date specified by hedge length j in the these conditions of imperfect spatial contract mattrrrng in period m; Cm; is the competition, location basis variability may price at vvhich the contract rs repurchased on occur With less than perfect correlations date t All variables are measured in units between futures contract delivery market and appropriate to the commodity For livestock, distant market prices, and possibly different this is dollars per hundredweight for the variances as well, hedging revenue variances various grades Since futures contract prices may be higher in distant markets than at the are everywhere the same at a given time, contract delivery market. This is anempirical hedging revenues among markets will vary as question, however. The existence of cash market differentials vary For a series of significant location basis variability cannot be hedges over time, mean hedgrng revenue is the inferred a przorz from an imperfect state of algebraic srim of thc means of the prices in spatial competition. The question of how equation (1), and hedgrng revenue variance is much of an effect there rs must be addressed. a linear combination of the variances and covariances of its price componcnrs, as shown in equation (2): Alternative Measures of Location Basis Variability Vfkijgl : Vfpigl + Vflljml * Vfcml + 2CV(l’lg, Hjm) - 2CV(l’gg,Cm) The foregoing discussion leads to two -2CV(Hjm, Cm), t = 1, 2, . T (2) alternative measures of location basis variability: (a) comparisons of cash market where V and CV stand for variance and correlation coefficients between contract 1 - i { . V ! 1 _ t, Z I 8 E ( 3EY 1 is . delivery markets and distant markets, and (b) specifically directed toward measuring exactl· i l comparison of hedging revenue variances location basis variability without at the same with f· ’ through estimates of equation (2) for various time trying to solve hedging management not pe Q markets. The latter procedure was chosen for problems in a number of regions, was E r this study. A comparison of cash market adopted. the foj l l correlations has the virtue of simplicity, but it would not capture the time dimension of _ ` E(Rijg ¤ hedging. Equation (2) shows that hedging Hedgrng Lrror and Bias _ j ( revenue variance is affected by the where l relationship between cash and futures prices EQUHUOIIS (1) and (2) provide measures Ieljmis at two different Points in time Cevtujtmee of hedging performance which are essentially and Z j terms relate local price to the futures priee at ex post in outlook. That is, hedging results are the f , ( , which a hedge is plueed stud to the fututes measured at the end of the marketing process situati { Price at which it is lifted Ot eOveted_ A and incorporate cash market prices actually grade, A I eeutempemueeus eeytelatjem between loca] received. Consideration of futures price bias reflect ( ‘ j u Cash prices and eash prjcgg in the delivery follows from this ex post outlook. Bias is Expec · · ( gf market ignores the lagged relationship, and a essentially comparison of hedging revenue an obj ) _ lagged` correlation `ignores the with the revenue that would have been price) , contemporaneous relationship. For these obtained had hedging not been undertaken. hedger I ( V T reasons, a direct comparison of variances An alternative to the ex post point of view is f , V seems the better alternative. to evaluate hedging performance from the betwe< i i A third analytical alternative is to use a standpoint of expectations held at the time revenu ( ( Q portfolio-type procedure of the sort suggested hedges are placed. Hedging error is an ex ante ] ( ij Yi by Ward and Fletcher (13) and applied measure of the deviation of results from lfigt { ft Qi empirically by Heifner (7) and by Holland, expectations. * g l i i Purcell, and Hague Certainly, work on In the textbook example of the perfect Substi I 1 j ( optimal and minimum—risk hedging strategies, hedge, a commodity is sold short in futures, equati i ( ; as used in these studies, is necessary, and the convergence betweenash and futures prices in i { , Q type of analysis implied by alternative (b) is the delivery month is exact, and the Uigt i Y no substitute for micro-analysis of hedging for commodity is sold and the short position ¤ local markets. However, data problems crop covered to achieve an outcome just equal to Note ( I { up when portfolio—type analyses are used for the short sale price. Expectations are exactly hedgir ( » interregional comparisons. This type of realized Realism calls for two modifications equati ( analysis requires knowledge of the production of this concept. First, the assumption that the (Pigt · · function in each area of application. As expected revenue equals the short sale price 4 ln the ( Ehrich (5, pp. 31-32) points out, available implies not only location at the par delivery be zer V _ (secondary) cost data may not represent the point but also that the hedger has no price is exe _ minimum-cost situation foraregion.Also,the expectation of hrs own other than what is perfec degree of upgrading of livestock while on feed reflected in the futures price. As antic introduces a bias unless the degree of Hieronymous (8) has indicated, hedging is nonco , upgrading is known and taken into account. really done with some price expectation in Y€Z1liZ€ 1 Thus, intimate knowledge of local conditions mind. The other point is that convergence hffdgir t is necessary for the successful application of between cash and futures prices is seldom 0¤ UW portfolio-type procedures. Under these exact, nor do the price changes in the two F circumstances, the simpler model, which is markets necessarily parallel each other €¤iif€¥ ( basis, l ‘ 1 . r J i 9 exactly. Cash prices will be highly correlated the hedger, and so cannot be measured except with futures prices in the nearby contract, but on a case by case basis. However, the realized not perfectly so. basis component can be estimated from Basis expectation can be quantified in market data. Estimates of this component are the following manner: useful, because they give a measure of the error agamst which a hedger must work in his E(Rijg[) = Hjm + Zlgt (3) particular market. The realized basis , component of hedging error will be referred where E(Rijg[) is expected hedging revenue, to as U’jgt and is _ Hjmis the hedging price as previously defined, and Zigl is the basis differential which relates U’]g[ = Pigt - Cmt (6) the futures price to the hedger`s own situation. The basis differential has spatial, with variance grade, and time dimensions, and it may also reflect the hedger`s own price forecast. V(U’ig) = V(Pig) + V(Cm) - Expected hedging revenue therefore contains an objective component (the futures contract 2CV(P,g, Cm), t = 1, 2, ...T. (7) price) and a subjective component (the hedger’s estimate of the basis differential), Realized basis variance is a major component Hedging error is defined as the difference of hedging revenue variance and both may be between received and expected hedging affected by location. revenue, or An intriguing aspect of hedging error is the role of the individual in anticipating basis Uigt = Rijgt · E(R,jgt) (4) change. It is clear from equation (5) that hedging error will always be zero if the Substituting equations (1) and (3) into anticipated basis is of an appropriate value. equation (4), hedging error reduces to This is to say that a clever forecaster can overcome the difficulties imposed by Uigt = Pigt - Cmt — Zig,. (5) imperfect convergence, location, and grade basis variability, at least in principle. Of t Note that length of hedge does not affect course, the ability of our hypothetical clever hedging error Hedging error as expressed in forecaster to know fairly precisely the equation (4) is composed of the realized basis outcome of a hedge does not mean that he (Pigt - Cmt), less the anticipated basis Zlg;. will necessarily place that hedge, which brings In the par delivery market, realized basis will us to the bias. be zero for the delivery grade if convergence Bias is usually defined as the persistent is exact. This meets the condition for a deviation of futures prices at different points perfect hedge, so hedging error will be zero, if in time. A downward bias is said to exist anticipated basis was also zero For when futures prices persistently tend to nonconvergence and for other cash markets, underestimate eventual cash prices; upward realized basis will be different from zero, but bias is the reverse of this. From the point of hedging error may be zero or not, depending view of the hedger, bias is equivalent to an ex on the level of the anticipated basis. post evaluation of hedging results which Hedging error cannot be estimated in its compares hedging revenues with the revenue entirety without knowledge ofthe anticipated that would have been received without basis, which is fundamentally in the mind of hedging. In the context of the prices models { 1 I r j V 3 l0 i id ` developed here, this is to extend the analysis further back because of in W} 5 Q illiquidity in the live hog futures market prior and {7 i v i B- = R-- . P- (3) to 1971. Daily price observations were used eorree g 18* ilgt ISV bc t. h t. t. , h f , , , ,, cause 0 t e requency o price c ange or run where Bjgt = Hjm - Cm,. (9) hogs. Lags in price change between markets frrrror E i which might be apparent in daily data might when ( Notc that bias is not affcctcd by location well be covered up in weekly averages. later, S Bias, if it is present in a futures market, be H r l , Q affects hedgers in all locations equally. €¤i€1'| l Because Of its neutrality respect {O Markets and Grades Selected placet ; V location, bias was of only passing concern in purcli i f I this study. Southern markets selected for use in the finish I Y g study were the Western Kentucky (Purchase the h . 1 ( Area) buying stations, the Southeast direct were i l l Summary : Theoretical Issues market (Southwestern Georgia and adjacent grow; i areas of Alabama and Florida), and the North time 1 l Three measures of hedging effectiveness Carolina auctions. By Southern standards, 225 I; P l Q have been developed in this section. The first, these are regions of concentrated slaughter grgiyl g ) l and the one of primary importance in the hog production and marketing. Their markets wcrgh i , 1 if gi empirical portion of the study, is hedging also have the virtue of having daily price so rh; ( l A i revenue variance, While hedging revenue reports made for them. Omaha was selected as any c ‘ , ` is variance will be the same everywhere in a the reference delivery market, even though I perfectly competitive spatial market, in the deliveries at Omaha are discounted relative to | ( . " real world market imperfections may give rise P€0Tl3·, which I5 thi? PHY delivery m¤fl<€f- The Metht i ( l E to locational differences. The second measure Omaha market was selected because of the { 1 ’ 1 of effectiveness was hedging error, in which wider distribution of price reports for it in I l j Z A expected hedging revenue is taken as the basis market news media available to Southern comb i of comparison. While hedging error is not producers. syster ( ,2- observable in its entirety, its realized basis Prices in Kentucky, the Southeast deserr g . component can be measured from market market, and at Omaha were reported on the Calcu 2 data. Since location enters into the realized basis of USDA grades. Prices for North date, , i i basis component, its variance may differ by Carolina, however, were reported on the basis prior ) 2 __ location. Last, the concept of bias was of a state grade, called "North Carolina Top and xt l · examined, to find that location was not a Hog." Prices were not reported for any lower hedge ( i factor in it. grades in North Carolina. While a state grade hog ft . does not necessarily conform to U.S. grade D = N ‘ standards, "North Carolina Top Hogs" are contra r Location Basis Variability for Slaughter Hogs reported to be essentially comparable to U.S. hedge , ls and 2s weighing 200-220 pounds mont} — ( Location basis variabilities for three were T _ Southern markets and a central delivery point contrz market were estimated and compared. Two Hedging Systems mont} i production-hedging systems with differing for ja lengths of hedge were assumed. Daily market The two hog production-hedging systems hedge z price data for calendar year 1971 were used in which were assumed were a farrow-finish for F the analysis. It was not considered worthwhile SYSYCIU and (b) Z1 specialized feeding enterprise Arpil ‘ n 1 l in which 50—pound feeder prgs are purchased contract month was used as the cut-off point and fed to market weight. So far as hedging is rather than the 20th, when contracts i concerned, the systems differ by the length of normally expire, to avoid liquidity problems run of the hedge ln the longer run, that might arise nearer the expiration date. farrow-finish system, the hedge was placed Daily closing prices of futures contracts when pigs were farrowed and lifted 174 days and the midpoints of daily trading ranges for later, when the finished hogs were assumed to cash market hogs were the prices used in the / be marketed In the feeder pig finishing calculations. Means, variances, and covariance enterprise, the hedge was assumed to be components for hedging revenues and realized , placed at the time the feeder pigs were hedging error were calculated. These statistics purchased and lifted 106 days later, when the were adjusted for missing cash price data. No finished hogs were marketed The lengths of attempt was made to rnterpolate missing data the hedges, 174 and 106 days, respectively, from nearby prices. were derived from National Research Council growth rate standards and expected lengths of time necessary to achieve a market weight of Results 225 pounds (12). Variation around the mean growth rate would cause a dispersion of Hedging revenue results are summarized weights and grades around this mean weight in Table 1. In respect to location basis so that individual lots of hogs might fall into variability, the focus of attention is on the any of the reported grade and weight ranges. variances presented in the table. To review the conditions of the hypothesis of location basis variability, if it can be shown that hedging Method of Calculation revenue variances are not equal, given equality of cash market price variance, then it is lledging revenues were calculated for all concluded that location basis variability is combinations of markets, grades and hedging present. Inequality of cash market price systems for calendar year 1971 Equation (1) variances would indicate a highly imperfect describes the calculation process employed state of spatial competition in which location Calculations were oriented on the marketing basis variability would be presumed to be date, with hedges placed 17+ and 106 days large. Bartlett’s test of equality of variances prior to that date Adjustments for holidays was used to test the null hypothesis of and weekends were made by placing or lifting equality in cash market price variances and in hedges on the next available date on which hedging revenue variances. Results of these hog futures contracts were traded tests are presented in Table 2. 1\larketings which were scheduled for a The figures in the top portion of Table 2 contract delivery month were assumed to be are the Bartlett`s test statistics for equality of hedged in that contract up to the 15th of the variances of prices and hedging revenues by month. l\larketings scheduled after the 15th grade. The figures in the lower portion of the were assumed to be hedged in the next table show the critical values of F against contract, as were marketings in noncontract which the test statistics should be compared. months. For example, marketrngs scheduled No test statistic exceeds its critical value of F, · for jan. 1 · Feb. 15, 1971 were assumed to be indicating no significant differences in hedged in the February contract Marketrngs variances among the variables tested. Cash for Feb. 16 - April 15 were hedged in the prrce variances within grades were not Arpil contract, and so on. The 15th of a significantly different from one another, nor i Y E i 1 E fj 12 ( Qih Table 1.--Hog Price and Hedging Revenue Summary Statistics, by Grade, Tat ‘ ¥ il? Four Markets, 1971. 2 Gr: g {Q_ ·—-— dollars per cwt and (dollars per cwt) ...- 1 g 1; A. Omaha Terminal Market (252 observations) Ca: . 1 C?. Grade U.S. 1-2 U.S. 1-3 U.S. 2-4 g A (200-220 lb) (200-240 lb) (240-270 lb) ‘ 1 He< Q g Cash Market Price I (_ Mean . 19.31 19.03 18.36 i ( Variance 2.39 2.45 2.45 1 ;l Hedging Revenue $ i‘ 1. Farrow-Finish { 1- Mean 20.36 20.09 19.41 j ¥ Variance 2.57 2.61 3.01 2 I ( fC 2. Feeder Pig-Finish ’ . . Mean 19.25 18.97 18.29 Gr: § · s Variance 4.58 4.78 5.20 l , 1 ( . . 1/ C3 ; 1 ( » B. Kentucky Buying Stations- (254 observations) 1 g. § 4 Grade U.S. 1-3 U.S. 2-4 U.S. 2-4 · 1 (200-240 lb) (190-240 lb) (240-260 1b) He· . i 1 Cash Market Price I j Mean 18.56 18.14 17.73 2 Variance 2.72 2.79 2.85 1 Hedging Revenue g 1. Farrow—Finish § Mean 19.61 19.20 18.79 1 i Variance 2.83 2.88 2.89 — 2. Feeder Pig-Finish " ( i Mean 18.48 18.07 17.66 1/ ( g Variance 4.77 4.81 4.84 _ . 1 i (continued) 13 Table l.——Continued C. Southeast Direct (251 observations) Grade U.S. 1-2 U.S. 2-3 U.S. 2-4 (200-230 lb) (190-240 1b) (240-270 lb) Cash Market Price f Mean 18.46 17.83 17.33 Variance 2.52 2.62 2.66 Hedging Revenue 1. Farrow—Finish Mean 19.51 18.88 18.39 Variance 2.97 3.06 3.10 2. Feeder Pig—Finish Mean 18.41 17.77 17.28 Variance 4.81 4.88 4.90 D. North Carolina Auctions (242 observations) Grade North Carolina Top Hog Cash Market Price 1 Mean 17.96 Variance 2.71 Hedging Revenue 1. Farrow—Finish Mean 19.03 Variance 2.98 2. Feeder Pig—Finish Mean 17.91 Variance 4.79 if A fourth grade of heavy hogs is reported for Kentucky but not included here. i , S Y Q ‘ 14 Table 2.--Bart1ett's Test of Equality of Variance of