Measurement of Farm Credit Risk: SUR Model and Simulation Approach

Transcription

1 Measurement of Farm Credt Rsk: SUR Model and Smulaton Approach Yan Yan, Peter Barry, Ncholas Paulson, Gary Schntkey Contact Author Yan Yan Unversty of Illnos at Urbana-Champagn Department of Agrcultural and Consumer Economcs 1301 West Gregory Drve Urbana, IL Tel: (952) Emal: Yan Yan s a PhD student, Peter Barry s a Professor, Ncholas Paulson s an Assstant Professor, and Gary Schntkey s a Professor at Department of Agrcultural and Consumer Economcs at the Unversty of Illnos at Urbana-Champagn. Selected Paper prepared for presentaton at the Agrcultural & Appled Economcs Assocaton 2009 AAEA & ACCI Jont Annual Meetng, Mlwaukee, WI, July 26-28, Copyrght 2008 by Yan Yan, Peter Barry, Ncholas Paulson, Gary Schntkey. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes. 1

2 Measurement of Farm Credt Rsk: SUR Model and Smulaton Approach Abstract The study addresses problems n measurng credt rsk under the structure model, and then proposes a seemngly unrelated regresson model (SUR) to predct farms ablty n meetng ther current and antcpated oblgatons n the next 12 months. The emprcal model accounts for both the dependence structure and the dynamc feature of the structure model, and s used for estmatng asset correlaton usng FBFM data for Farm rsk s then predcted by copula based smulaton process wth hstorcal default rates as benchmark. Results are reported and compared to prevous studes on farm default. Keyword: Credt Rsk Measurement, Seemngly Unrelated Regresson Model, Smulaton 2

3 Measurement of Farm Credt Rsk: SUR Model and Smulaton Approach Introducton In a value-at-rsk (VaR) framework, expected loss and unexpected loss at portfolo level are determned by probablty of default (PD), loss gven default (LGD), exposure at default (EAD), and default correlaton (Barry 2001 and 2004, Saunders and Allen 1999, Caouette et al 1998). When Merton s structure model (1974) s appled n credt rsk measurement, default probablty s often measured as the probablty of an agent s asset value fallng below a threshold pont, say total debt (Crouhy and Gala 1986, Crouhy et al. 2000, Gordy and Hetfeld 2001). Default correlaton s then determned by each agent s probablty of default and jont default for any two agents when a default event follows Bernoull dstrbuton. Snce margnal probablty of default and default correlaton are n practce closely assocated wth asset correlaton, credt rsk measurement under the approach generally reles on both the structure model and jont normal assumpton of asset returns (Grouhy et al 2000). Asset correlaton s often calbrated by factor models that relate change n asset values to changes n a small number of common economc factors for an ndustry, regon and/or country (Gordy 2003, Koyluoglu and Hckman1998). For example, Akhaven and Kocagl (2005) showed that average fve-year ntra-ndustry asset correlaton for US ssuers from a mult-factor model s 24.09% for In agrcultural lendng, the reported average assets correlaton s around 10.05% by applyng a sngle factor model to farm reported asset returns for (Katchova and Barry 2005). The man reason for adoptng the approach s to reduce dramatcally the number of asset correlatons to be calculated (Crouhy et al 2000). Although default correlaton, margnal probablty of default and asset correlaton are closely related, the connecton s not emphaszed by the approach. 1

4 Most popular credt rsk models based on the structure model n commercal lendng, such as KMV s 1 expected default frequency model (EDF), pre-requre nformaton on macroeconomc factors and long-tme loss data for computng asset correlaton and default rates. However, the prerequstes are hard to meet wth farm records on whch majorty of the lendng decsons are based. In ths sense, f only farm records are avalable for measurng credt rsk, t s mpossble to drectly use these models to assess asset correlaton and then default rsk. Of the econometrc methods, seemngly unrelated regresson (SUR) s a technque for analyzng a system of multple equatons wth cross-equaton parameter restrctons and correlated error terms. When covarance matrx of dsturbance s unknown, the parameters and correlaton coeffcents are estmated smultaneously by feasble generalzed least square method (FGLS) (Zellner 1962, Zellner and Huang 1962), whle the least squares resduals may be used (of course) to estmate consstently the elements of covarance matrx of dsturbance (Greene 2000). In addton, f workng wth a panel data, we may use statstcal classfcaton to reduce computng sze whle keepng smlartes wthn each class. Under the approach, ndvdual agents wthn each group are sad to have the same or smlar characters. By combne the classng and the SUR approach together wth the structure model, we may then have an approprate emprcal econometrc model that not only consders asset correlaton but also can take full use of farms accountng nformaton n descrbng potental rsk at group level. It s noted that the correlaton matrx obtaned from the emprcal model actually represents asset correlaton among the groups. As mentoned before, margnal probablty of default and jont default are n practce assocated wth asset correlaton. One way to connect them together s by copula based smulaton process that has been recently ntroduced n credt rsk measurement (Bouyé et al). In the paper, we wll llustrate that the estmated 2

5 correlaton matrx under the structure model and mult-normalty assumpton for the error terms s actually comparable to that by Gaussan copula. Thus, wth the asset correlaton obtaned from the econometrc model, t s straghtforward to apply Gaussan copula based smulaton procedure to predct margnal probablty of default and jont default. As mentoned earler, one of the dffcultes n measurng farm credt rsk s lack of long tme loss data from whch default thresholds used n default smulaton are derved. To address the ssue, hstorcal default rates used n the study are from two dfferent sources nstead. The frst one s from nvestgatng farm records by reconsderng defnton of default, and the other one s the default rates mpled by popular credt score models. In agrcultural lendng, credt scorng s a generally accepted method n borrower s ratng, and there are several studes connectng ratng crtera to default rate for each rsk class (Barry et al 2004, Featherstone et al 2006). In the study, asset correlaton between farm groups s frst estmated based on a prevous emprcal study on determnants of farm captal structure under the structure model (Yan et al 2008). An approach to ntegrate the model wth Gaussan copula based smulaton procedure s then proposed for predctng farm default at group level. Default defnton s nvestgated and default thresholds are nferred from farm records. On the bass, probablty of default (PD), expected loss (EL) and unexpected loss (EL) are predcted by Gaussan copula based smulaton procedure. Emprcal analyss wll apply Annual Farm Busness Farm Management (FBFM) for , and the results wll be reported and compared to prevous studes on farm default. Merton Model and Dstrbuton of Farm Fnancal Poston Under the framework of Merton s model (1974), the value of any farm s asset assumed to follow a standard geometrc Brownan moton At at tme t s 3

6 2 σ 1) At = A 0 exp(( µ ) t + σ tωt )) 2 where A 0 s the ntal asset value, µ s the nstantaneous expected rate of return, σ s the standard devaton of the return on the underlyng asset, and ω s of N (0,1). In the model, ω t actually represents the normalzed asset return at the tme that s equal to t 2) ω t A ln( = o 2 σ ) ( µ t A ) t 2 σ t For a known debt value D t at the tme, t s noted that the farm s fnancal poston can be represented by asset-to-debt rato ( A / D ). In agrcultural secton, low asset-to-debt t ratos are often nterpreted as an ndcator of farm fnancal stress. For example, n 1988, the U.S. Department of Agrculture (USDA) ndcated that farms wth debt-to-asset rato above 0.7 ( A / < ) were lkely to experence a very hgh level of fnancal stress, and t D t may have to lqudate certan assets n order to mprove ther fnancal poston. In ths sense, the probablty of asset value falls below ts debt value actually measures severty of fnancal stress for the farm. Gven quantle, the probablty s 2 A σ ln( o ) + ( µ ) t Dt 3) P(A D ) 2 t t = P ω t = Φ( zt ) σ t t where z t A σ ln( o ) + ( µ t D ) t = 2, Φ( ) s the standard normal cumulatve densty σ t 2 functon. On the other hand, f the farm s fnancal poston under the structure model s expressed as a dynamc regresson model 4) yt = x t β + ε t 4

7 where y t A t = ln, t Dt x s a vector of explanatory varables that contans some lagged values of y t, β s a vector of parameters to be estmated and ε t s the error term, an equvalent measurement of the probablty n expresson (3) s then 5) P(A D ) = P( ) = Φ( ) where υ = x β. t t t t ε t x t A major concern about the measurement s that the error terms between any two farms are actually correlated,.e. E( ε, ε ) 0 or E ( z, z ) 0 for j. The correlaton t jt n fact represents asset correlaton between the two farms accordng to the structure model. Obvously, the correlaton s related to credt rsk measurement. For a normal dstrbuton, such correlaton can be fully captured by correlaton coeffcent through seemng unrelated regresson (SUR) model. β t jt υ t Default Defnton and Its Implcaton to Farm Credt Rsk Crouhy and Gala (1986) suggested that default occurs once asset value falls below debt level. However, the scenaro may not mply real default. Altman (1968) once ponted out that, for a frm wth poor solvency, because of ts above average lqudty, the stuaton may not be consdered serous,.e. the frm could actually enter a state of fnancal stress nstead of default. Some studes on default, usng the structure model under the defnton, llustrated large dfferences between the predcted default rates and the reported values (Sten 2000, Crouhy et al 2000, Katchova and Barry 2005). The Basel II 2 (2004) also suggested a conservatve defnton of default for a bank, a default s consdered to have occurred wth regard to a partcular oblgor when ether or both of the two followng events have taken place, 5

8 The bank consders that the oblgor s unlkely to pay ts credt oblgatons to the bankng group n full, wthout recourse by the bank to actons such as realzng securty (f held). The oblgor s past due more than 90 days on any materal credt oblgaton to the bankng group. Overdrafts wll be consdered as beng past due once the customer has breached an advsed lmt or been advsed of a lmt smaller than current outstandng. The second event s close to the ndustry accepted standard that 90 days delnquency and assgnment to non-accrual loans (Barry et al 2004, Stam et al 2003). However, snce farm records are not lkely to cover real loss nformaton related to the standard, we pay more attenton to the frst scenaro,.e. unlkelhood of payng back on debt held by an oblgor. It s known that the farm fnancal crss n 1980s s assocated wth rapd deteroraton of farm return on asset and severe debt problems as measured by debt-to-asset rato and nterest rate. In corporate fnance, on the other hand, f an ssuer belongs to the speculatve grade under Moody s rsk ratng matrx, the frm wll be also assgned a speculatve-grade lqudty ratng (SGL) as an assessment of ts ablty to cover ts cash oblgatons by ts projected cash flow over the comng 12 months. The ratngs manly assess an ssuer s operatng ncome, current and antcpated cash balance, and nternal and external sources of lqudty. Puchalla and Marshella (2007) showed that weak SGL s hghly correlated wth hgh probablty of default, and every company that has defaulted n roughly the last fve years through a bankruptcy or mssed payment was rated SGL-4 (weak SGL) at the tme of default. By ncorporatng wth these fndngs and consderng that only farm records are avalable n the study, a farm s defned as defaulted f t can not meet ts current and antcpated cash balance over the comng 12 month (expected oblgaton) n combnaton wth poor poston n lqudty and return on asset (ROA) as well as heavy burden on nterest 6

9 payment relatve to ts operatng ncome. Specfcally, a farm s n default for any gven year f all of the followng condtons are satsfed, Rato of farm reported market value of asset over the expected oblgaton n the near future s less than 1; ROA s less than 0; Rato of current debt to current asset s hgher than 1.25; Rato of farm reported nterest expense and accrued nterests over value of farm producton (VFP) s hgher than 10%. When farm records ndcate the current porton of ntermedate and long-term labltes (TLD) as well as the total balances of these categores of labltes, a farm s current lablty plus one half of ntermedate and long-term labltes can be treated as a proper proxy for the expected oblgaton on debt. In statstcs, when nformaton on the TLD s term structure s unavalable, the value close to maturty could then be assumed unformly dstrbuted between 0 and TLD, resultng n an expected value of TLD/2. SUR Model and Asset Correlaton The emprcal seemngly unrelated regresson (SUR) model consdered here dffers from prevous models for study of captal structure usng farm records. The analyss emphases more on a farm s ablty to meet ts fnancal oblgaton n the next 12 months, rato of market value on farm asset-to-expected oblgaton s used as the dependent varable nstead of total debt (Barry et al 2000) or leverage rato (Jensen and Langemeer 1996, Yan et al 2008). Thus, the study extends beyond the verfcaton of the structure model and theores on farm captal structure by dentfyng the lnkage between farm s fnancal poston and credt rsk as well as potental determnants among a set of farm attrbutes and credt rsk factors. In the study, determnants of a farm s ablty to meet ts fnancal oblgaton wthn the next 12 months are 7

10 selected based on the structure model, credt scorng models, and theores on optmal captal structure. The followng factors, assocated wth a farm s asset dstrbuton, captal structure and credt rsk, are consdered as potental determnants of the strength of fulfllment. The Structure Model Factors The frst two factors enterng n the SUR model are drectly from the structure model. They are lag of log of asset-to-expected oblgaton/debt rato and the normalzed return on farm assets (NROA). If the structure model s stable, a less than 1 estmated coeffcent for lag of log of asset-to-expected debt rato s expected. NROA s calculated by rescalng return on asset by ts standard devaton for each farm record. A farm s asset-toexpected debt rato wll be negatvely nfluenced by NROA f the farm tends to make offsettng adjustments n ts captal structure n response to modfcatons of busness rsk as measured by the standard devaton of return on farm asset (Barry and Robson 1987, Gabrel and Baker 1980). Credt Rsk Factors Three key fnancal ratos employed by ratng agences and credt rsk model for farm lendng are consdered here, ncludng lqudty, fnancal effcency and VFP/Debt. Lqudty s calculated by dvdng workng captal by value of farm producton (WC/VFP), and s expected to have postve mpact on a farm s ablty to make tmely payment, and thus stay lqud. A farm s fnancal effcency s represented by rato of net ncome to value of farm producton (NETINC/VFP). Snce great fnancal effcency could strengthen farms rsk-bearng capacty and thus lower rsk of fnancal stress, t s expected to vary postvely wth the asset-to-expected debt rato. VFP/Debt s defned as log of value of farm producton to total debts rato and s an ndcator of farm proftablty. It s reasonably to say that farms wth hgher level of proftablty should be less lkely to default on ther expected oblgatons. 8

11 Captal Structure Factors Fve structure factors than has been ndentfed as mportant determnants of captal structure are also ncluded n the model. They are sze (log of farm cash sale), tenure (owned land to total tllable land rato), NGTA (annual growth n total assets dvded by ts volatlty), collateral rato (value of farmland plus machnery and equpment to total assets rato) and non-debt tax sheld (earnng before deprecaton dvded by total assets). If farms adjust to long term fnancal target of leverage rato wth addtonal fnancal needs followng peckng order theory and/or agency theory, the rsk of fallng short on ts fnancal oblgaton n the near future would be postvely nfluenced by proftablty and tenure poston whle t would be negatvely correlated to farm cash sale (sze). The low debt carryng capacty of farmland also justfes the expected postve tenure effect. The non-deprecaton property of farmland mples hgher lqudaton value, and thus t would be much easer for a farm wth hgher collateral poston to meet ts oblgaton n the next 12 months than otherwse. In ths sense, we would expect a postve relatonshp between farm collateral rato and the dependent varable. On the other hand, f farms wth large non-debt tax sheld tend to nclude less debt n ther captal structures as predcted by trade off theory, the ablty to pay back n full wll ncreases as non-debt tax sheld ncreases. It s noted that the emprcal SUR model ncludes lag value of the dependent varable and thus s a dynamc model. On the other hand, farm records are often characterzed by short tme perod and large number of farms. To address the two ssues, farms are grouped such that each group has enough degree of freedom. On the bass, a specfc sem-parametrc 3SLS estmator s then appled for the dynamc SUR model ((Yan et al 2008). Gven the regresson results and let the correlaton matrx among the farm groups be Σ, the consstently estmated elements of Σˆ s then gven by 9

12 6) ρˆ j e e = T j where e s the least square resduals from equaton or group, and T s the total number of observatons n each equaton/group (Greene 2000). Farm Credt Rsk Measurement It s noted that the calculated probablty of P(At Dt ) s not necessarly equvalent to probablty of default and an adjustment s often needed for more accurate predcton (Crouhy et al 2000, Altman 2002). For example, the reported default probablty for an ssuer by KMV s obtaned by mappng the DD ( z t ) to the actual probabltes of default for a gven tme horzon (Crouhy et al 2000). The actual probabltes of default, called default thresholds or hstorc default rates, are nferred from KMV s default database whle the mapped probablty s called expected default frequency (EDF). As ponted out earler, margnal probabltes of farm default are closely assocated wth asset correlaton. A popular way to connect both together s by copula approach (Nelson 1999). That s, gven margnal dstrbutons, we can derve correlaton structure by choosng a copula, whle gven a copula, margnal probablty of default for each agent can be predcted by smulaton. Of the copulas, Gaussan copula s fully characterzed by correlaton matrx Σ as multvarate normal dstrbuton does. In addton, when tme seres data of farm G assets are avalable, maxmum lkelhood estmate (MLE) of the elements of Σ G under Gaussan copula and the structure model s gven by ˆ δ j vˆ vˆ = T j, where vˆ s a vector of estmates generally obtaned by applyng kernel densty functon to the correspondng values calculated under the structure model wth respect to farm, for example ω t n expresson (2), and T s the total number of observatons for the farm (Magnus and Neudecker 1988). Clearly, 10

13 δˆ j s comparable to ρˆ j n expresson (6) under the multvarate normal dstrbuton assumpton. In ths sense, margnal probabltes of farm default and jont defaults can be predcted by Monte Carlo smulaton procedure for Gaussan copula wth the estmated correlaton matrx from the SUR model. Wth the predcted farm default and jont defaults from smulaton and assumng that the default event follows Bernoull dstrbuton, default correlaton τ j for a typcal farm n group and a typcal farm j n group j s gven by 7) τ j = P j P P P 1 P ) P (1 P ) ( j j j In the equaton, P( ) denotes the predcted margnal probablty of default for each farm and P j refers to the predcted jont probablty of default for farm and farm j. The standard devaton (std.) of farm s default and the jont probablty of default P j equal to 8) Std(farm n default) = P j = P P j / P (1 P ) where P / denotes the condtonal probablty of default for farm j gven that farm s n j default and s easy to calculate wth the smulaton results. Gven probablty of default, loss-gven-default, and default correlaton matrx, the expected loss (EL) and unexpected loss (UL) at portfolo level s then computed by meanvarance method, n whch EL = 9) UL = n = 1 w P LGD n n 2 2 w UL + = 1 = 1 n j w w ρ UL UL where UL = LGD P ( 1 P ), and w s the weght for farm and n s the total number of farms n the portfolo. j j j 11

14 Hstorcal Default Rates As mentoned above, one of the dffcultes n measurng farm credt rsk s lack of long-term loss data from whch hstorcal default rates are nferred. To address the ssue, FCS (Farm Credt System) default gudelne and hstorcal default frequences from farm records based on default defnton are used nstead. FCS Default Gudelne FCS default gudelne s summarzed based on two prevous studes on credt rsk model and default probablty for farm lendng (Barry et al 2004, Featherstone et al 2006). The credt score model was developed by Barry et al (2004) to dstngush between low credt rsk (less fnancally constraned) and hgh credt rsk (more fnancally constraned) farms. The model contans fnancal ratos recommended by the Farm Fnancal Standard Councl, representng a farm s solvency, lqudty, repayment capacty, proftablty, and fnancal solvency. The rsk ratng defnton, nterval ranges, and mpled default rates are llustrated n table 1. In the rsk ratng, each farm has fve scores rangng from 1 to 10 on solvency, lqudty, repayment, proftablty and effcency accordngly. The fve scores are then weghted to generate a fnal score between 1 and 10 by expresson (10), where each farm s then grouped to a ratng class wth respect to the fnal score. 10) score = 30% solvency + 20% lqudty+ 20% repayment + 20% proftablty + 10% effcency Default Frequences from Farm Records Hstorcal default frequences are nferred from Farm Busness Farm Management Assocaton (FBFM) data that contans farm accountng nformaton, such as ncome and 12

15 cash flow statement, as well as farm reported market value on assets and labltes durng the perod of Consstent wth Katchova and Barry (2005), farms wth no debt are excluded, resultng n approxmately 1,670 farms wth 11,745 farm observatons 3. Followng the default crteron and the noton for expected debt, a dscrete tme approxmaton of the nonparametrc contnuous-tme hazard rate approach (cohort method) s used to nfer margnal default rates from the FBFM data. The nonparametrc contnuous-tme hazard rate approach was frst proposed by Cutler and Ederer (1958) and has been commonly used by the ratng agences lke Moody and Ftch Ratngs for default and mgratng analyss. A pool of farms, called a cohort, s formed on the bass of ther rsk ratngs held n a gven calendar year, and the default status for the farms of the cohort s tracked over some stated tme horzon. In each tme nterval or horzon, some fracton of the cohort that has survved up to that tme may default. The margnal default rate s the probablty that a farm survved n the cohort up to the begnnng of a partcular tme nterval wll default by the end of the tme nterval. The cohort method assumes that wthdraws occurs randomly durng the nterval, and the probablty of survval/default at one nterval, though condtonal on survvng prevous ntervals, s ndependent of the probablty of survval at the pror nterval(s). Moreover, the nterval s often set evenly dstrbuted when long tme data s avalable. For example, the default rates calculated by most ratng agences under the method are based on more than 30 years annual or monthly observatons. In ths study, snce only 10 years annual data s avalable, the cohort spacng s selected based on data avalablty nstead. In total, 9 cohorts are formed from the data wth tme nterval rangng from 9 to 1. Consstent wth FCS default gudelne, the farms are grouped wth respect to ther rsk ratngs defned n expresson (10). Snce relatvely fewer farms are rated 7 and above, the farms wth rskng ratng greater than 7 are grouped together, the 9 cohorts are then created 13

16 for each of the 7 rsk ratng classes. The results are lsted n table 2. Overall, average default rate across all cohorts for each rsk ratng class s lower than the correspondng value n table 1. Small sample sze may be the reason. Loss-gven-default (LGD) for each cohort s calculated as the average LGD for the defaulted farms by usng reported marked values on asset and the expected oblgatons n the next 12 months and a 10% recovery rate (Featherstone and Boessen 1994, Featherstone et al 1993). The average values on LGD across all cohorts for each ratng class are also reported n table 2. On average, LGD s 23.91% for , whch s smlar to prevous reported values on farm LGD. For example, Stam et al (2003) reported that average LGD for all farm loans ssued by commercal banks, the FCS, lfe nsurance companes and the Farm Servce Agency was 24.26% for Accordng to Federal Depost Insurance Corporaton (FDIC) 4, average LGD on farm loans ssued by all commercal banks n Illnos s around 18.26% for Data and Estmaton Consstent wth prevous studes, the emprcal estmaton and predcton uses a subset of the FBFM annual farm data that ncludes only farm records wth a mnmum tme range of 10 years and the farms are grouped wth respect to ther credt rsk ratngs n 1995 pror to the estmaton perod of ((Barry et al 2004, Yan et al 2008). In total, we have 5,346 farm observatons wth 635 farms, and these farms are grouped nto 7 rsk classes. Table 3 shows defnton and summary statstcs of the varables ncluded n the dynamc SUR model. On average, the log of asset-to-expected debt rato for a typcal farm s 1.60 wth log of farm cash sale (sze) equal to The tenure poston and collateral rato for the typcal farm are 0.19 and 0.54 respectvely. The non-debt tax sheld (sheld) for the farm s wth a lqudty poston of The values of effcency (NETINC /VFP) and 14

17 proftablty (VFP/Debt) for the average farm are 0.20 and respectvely. In addton, the normalzed values of return on asset (NROA) and growth n total assets (NGTA) for the typcal farm are 1.26 and 0.34 respectvely 5. Snce mean values for most of the selected varables are hgher than ther correspondng medans, above half farms are ranked low n values as compared to the typcal farm. The regresson results are lsted n Table 4. Overall, most of the varables are sgnfcant at better than the conventonal level of 5%. In addton, the coeffcents for the lag of the dependent varables are all less than 1, ndcatng that the estmated dynamc model s stable. Results show that the ablty of payng back wthn the next 12 months s negatvely assocated wth NROA, sze and non-debt tax sheld, whle s postvely nfluenced by NGTA, tenure, collateral rato, VFP/Debt (proftablty), WC/VFP and NETINC/VFP. The postve sgnfcant sgns for the credt rsk components suggest that the probabltes of a farm s ablty to meet ts current and antcpated fnancal oblgatons over the comng 12 months are related to ts lqudty, fnancal effcency, proftablty as well as avalablty of secured assets. The estmated correlaton matrx s lsted n table 5. Overall, average correlaton coeffcent among the 7 rsk ratng classes s 20% wth a standard devaton of 5.6%, whch s clearly hgher than the reported average asset correlaton of 16% by KMV s rsk classng (Lopez 2002). Snce KMV s rsk classng s for publc frms, the result ndcates that agrcultural producton s more lkely to move n the same drecton than other ndustres, and thus comparatvely the systematc rsk plays a more mportant role n agrcultural producton. In addton, the estmated correlaton s also close to the reported ntra-ndustry average asset correlaton of 24.09% by Akhaven and Kocagl (2005) whle hgher than the reported value of 10.05% wth a smlar FBFM data by Katchova and Barry (2005). 15

18 It s noted that the matrx llustrates correlaton between farm groups; the order of farm observatons wthn each group s gnored. To further verfy that the estmated asset correlaton matrx n table 5 actually represents populaton correlaton, two statstcal tests, the log lkelhood rato test and the Jennrch s test for equalty of correlaton matrces, are appled n the study. The tests ndcate that the estmated correlaton metrcs s vald and can be used to predct farm default and default correlaton at group level (Appendx). Predcton of Farm Credt Rsk The default smulaton s at a tme horzon of 1 year. In the smulaton, the default threshold for any farm group s set to the quantle of the correspondng hstorc default rate gven n table 1 or table 2 under the standard normal dstrbuton. For example, for a default rate of 1.73% for group 7 n table 1, the default threshold s equal to Φ 1 (1.73%) = In each smulaton run, seven correlated random varables correspondng to each of the 7 farm groups are created by way of Cholesky decomposton gven the estmated asset correlaton matrx n table 5 (Bouyé et al 2000). Each random varable represents a standardzed asset return for the correspondng rsk class, and a default wll be regstered f ts value falls below the default threshold. A total of 50,000 scenaros for each rsk ratng class are generated, and the default probablty at group level s then defned as frequency of defaults out of the 50, 000 smulaton runs. In addton, jont default probablty s computed wth a procedure smlar to that for default probablty n whch jont default for any two farms s defned as concurrence of default for the two farms n a sngle smulatng run. The default correlaton s then calculated usng expresson (7) gven the predcted margnal probabltes of default and jont default probabltes. 16

19 Predcted probabltes of default are lsted n table 6. In the table, threshold 1 and threshold 2 correspond to the hstorc default rates n table1 and table 2 respectvely. From table 6, the order of the predcted default probabltes under both default thresholds s consstent wth the rsk ratng. Comparatvely, the predcted default rates under threshold 1 (FCS default gudelne) are relatvely hgher than those from threshold 2 (hstorcal default benchmark from FBFM data), and they are more close to ther correspondng benchmark rates than otherwse. Overall, the weghted average default probablty, weghted by the average debt n each group, s 0.895% for threshold 1 and s 0.643% for threshold 2. Accordng to FDIC, the average default rate for the agrcultural loans ssued by commercal banks n Illnos s 0.83% for Featherstone et al (2006) reported a default percentage of 1.83% for the loans ssued by the Seventh Dstrct durng 1995 to 2002, whle Stam et al (2003) reported a default rate of 1.02% for agrcultural banks 6 durng Obvously, the predcted default rates are close to those from FDIC and Stam et al (2003). Table 7 llustrates the estmated default correlaton nferred from the predcted defaults and jont defaults. Although average asset correlaton between the groups s around 20%, t s not surprsng to observe that default correlaton s much lower, mplyng that the two types of correlaton matrx are not equvalent although both are closely assocated. The result s consstent wth a prevous study by Crouhy et al (2000) who showed that for an asset correlaton of 20% for two rated AA and B ssuers by Moody s rsk ratng, the default correlaton s only around 1.9%, and thus, the rato of asset returns correlatons to default correlatons s approxmately 10-1 for asset correlatons n the range of 20-60%. In addton, the jont defaults are more lkely to occur among the hgher rsk groups. For example, when a farm of group 7 s n defaults, there s around 3% chance that another farm of group 6 wll be also n default whle the chance s less than 1% f another farm s from group 1 or group 2. These fndngs are consstent wth a prevous study by Hrvatn and Neugebauer (2004). They 17

20 showed that wth the same asset correlaton of 25%, the derved default correlaton s 3.5% between two ssuers wth default rates of 1% and 4% respectvely, and 8.1% f the default rates for the two ssuers are 4% and 10% respectvely. Gven probablty of default, loss-gven-default, and default correlaton matrx, the expected loss (EL) and unexpected loss (UL) for the farm portfolo s then computed usng equaton (9). The EL and UL at portfolo level and 1-year horzon are lsted n table 8. Overall, the average expected loss (EL) and unexpected loss (UL) for a typcal farm portfolo s 0.19% and 0.98% respectvely. The reported average loan loss allowance (EL) for agrcultural banks at a natonal level durng s around 0.33% (Stem et al 2003). Accordng to FDIC, the average loss for agrcultural loans ssued by commercal banks n Illnos s 0.18% for The data perod for estmaton of farm asset correlaton and predcton of EL and UL s The same perod should be consdered n comparson. Accordng to FDIC, the average default rate of agrcultural loans ssued by commercal banks n Illnos s 0.84% for , 0.74% for and 0.49% for , whle the correspondng EL are 0.18, 0.14% and 0.04% respectvely. Obvously, the predcted average PD and EL are close to the hstorcal average values of the perod , the same perod for the sample data. On the other hand, t s noted that the reported EL and PD by Stem et al (2003) s at a natonal level and for whle the predcton n the study focus on farms n Illnos and most of the farms are gran farms. In ths sense, t s not surprsng to see the dfference. Concluson As the regulatory requrements are movng towards economc-based measures of rsk, banks are urged to buld sound nternal measures of credt rsk, n whch predcton of a borrower or group of borrowers credt rsk plays a domnant role. The study addresses problems n 18

21 measurng credt rsk under the structure model, and then proposes a seemngly unrelated regresson model (SUR) to predct farms ablty n meetng ther current and antcpated oblgatons n the next 12 months. The emprcal model accounts for both the dependence structure and the dynamc feature of the structure model. On the bass, the SUR model s used for estmatng asset correlaton usng FBFM data for Wth the estmated asset correlaton, farm rsk s then predcted by copula based smulaton process n whch FCS default gudelnes and hstorcal default rates from the farm records are used to nfer default thresholds, where defnton of default s reconsdered and used for nvestgatng hstorcal default rates from farm records. Regresson results ndcate that the dynamc model s stable, and the structure model s confrmed by most of the farm records. Results also show that a farm s ablty to meet ts current and antcpated fnancal oblgatons n the next 12 months s assocated wth those factors related to the structural model, theores of farm captal structure, and the credt scorng model. The estmated asset correlaton s 20%, and the predcted default correlaton s lower than the correspondng asset correlaton. In addton, the predcted probablty of default and expected loss at portfolo level are close to the reported values for the same perod of and same regon. Results ndcate that the predcted probabltes of default at hgh-rsk groups are on average slghtly hgher than the correspondng FCS default gudelne (Fgure 1). The dfference may be characterzed by the approach. For example, some farms were grouped nto group 5 by ther own credt scores should be actually be classfed as group 6 by the predcted default rate. The study has mportant mplcatons to farm credt rsk management under the Basel II. Frst, although the study focuses on model testng, applcaton and comparson, the approaches ntroduced n the study are applcable to farm credt rsk management. For 19

22 example, gven a farm s accountng nformaton, we can use one of the equatons say the equaton for group 5 n the SUR model to estmate ts asset-to-expected debt rato. By comparng the estmated value to the observed one, we can statstcally test whether the farm belongs to group 5 or not. Second, dependence structure as well as level of the dependence for farm assets has sgnfcant mpact n measurng farm credt rsk, and thus should be emphaszed n loan prcng and n rsk dversfcaton. Thrd, asset correlaton as well as default correlaton may change under dfferent busness cycles. Applcaton of the approaches should pay attenton to possble changes n economc factors and update the nformaton accordngly. 20

23 Appendx The log lkelhood rato (LR) test s to test whether the correlaton matrx s dagonal or not (Greene 2000). If the estmated correlaton matrx does not pass the LR test, mplyng that observatons from any two dfferent rsk classes are ndependent, the problem of measurng credt rsk would be much smplfed than otherwse. Gven the regresson results for the SUR model, the lkelhood rato statstc s calculated by M 2 11) λ LR = T logσˆ log Σˆ mle = 1 2 e e where ˆ σ = and s calculated from the least square estmaton, and Σˆ mle s the maxmum T lkelhood estmator of the varance and covarance matrx for the regresson. Under the null 2 hypothess of no asset correlaton, the statstc has a lmtng χ dstrbuton wth M (M-1)/2 degree of freedom. In the study, M s the total number of equatons n the SUR model and s equal to 7. 2 Jennrch s χ test for homogenety of two correlaton matrces s based on a study by Jennrch (1970). Let R denote the correlaton matrx estmated by a sample of sze n from a p varate normal dstrbuton wth populaton correlaton matrx P r ), the test ( j statstc s then ) Jenn = ( tr( Z ) dg'( Z) S dg( Z)) 2 l= 1 wth 1 j Z = np ( R P), S = ( δ j + rjr ) and δ j beng the Kronecker delta. The null hypothess s that there s no dfference between the two correlaton matrces. Under the null 2 hypothess, the test statstc has an asymptotc χ dstrbuton wth p (p-1)/2 degree of freedom. In the study, the populaton correlaton matrx s assumed to be the matrx from the SUR process and s llustrated n table 5 wth p equal to 7. 21

24 Emprcal testng apples Bootstrap technques (Hollander and Wolfe 1999). A total of 5,000 random samples of resduals for each equaton were drawn from the least square regresson results for the SUR model. Each sample s randomly selected by the 7 rsk classes or equatons, and each class has 9 observatons randomly pcked out wth one for each year n the sample. In each samplng run, the random sample s then used to compute a value of λ LR and Jenn respectvely, n whch the correspondng sample correlaton matrx R s obtaned 2 by usng expresson (6). Both statstcs are of χ dstrbuton wth 21 degree of freedom. Overall, the mean value of λ LR s out of the total 5,000 calculated values, greater than the 1 percent crtcal value of So the null hypothess of dagonal for the correlaton matrx s rejected, and thus asset correlaton among farm rsk classes s confrmed statstcally 7. In addton, the average value for Jenn s as compared to the same crtcal value of 38.93, mplyng that statstcally, the order of farm observatons wthn each group has no sgnfcant mpact on the correlaton matrx 8. 22

25 Notes: 1 KMV s a trademark of KMV Corporaton. Stephen Kealhofer, John McQuown and Oldrch Vascek founded KMV Corporaton n Basel II s the second of the Basel Accords, whch are recommendatons on bankng laws and regulatons ssued by the Basel Commttee on Bankng Supervson. The purpose of Basel II s to create an nternatonal standard that requres fnancal nsttutons to mantan enough captal to cover rsks ncurred by operatons. 3 A farm s removed completely from the panel f t has zero debt n any year. In total, 137 farms are excluded wth a total of 650 observatons. 4 All FDIC nsured nsttutons are requred to fle consoldated Reports of Condton and Income (Call Report) as of the close of busness on the last day of each calendar quarter. FDIC constructed a database from the Call Report, and the database s publcly avalable on the webste startng In calculatng the standard devatons of return on asset (ROA) and annual growth n total assets (GTA) for each farm, a total of 10 records on farm asset and return are used. If there s any mssng value, the mssng value s replaced by mputed value through the multple mputaton method (Rubn 1987, Schafer 1997, Schafer and Schenker 2000, Relly 1993, L 1988). 6 A bank s defned as agrcultural bank f ts rato of farm loans to total loans exceeds percent (Stam et al 2003). 7 The LR test appled n the study s to test whether there s correlaton among farms of dfferent rsk classes. As for the farms wthn each class, t s reasonable to assume that they are dentcal and are derved ndependently from the same populaton, but we dd not test the assumpton here. 23

26 8 It s noted that the correlaton matrx n table 5 s calculated usng all the farm observatons n each group whle only 9 observatons n each group s used to calculate the sampled correlaton matrx n each samplng run. To account for any mpact of sample sze, we also dd a smlar test wth sample sze beng consdered. The testng result llustrates no such nfluence. 24

27 Reference Akhaven, J. D and Kocagl, A. E., A Comparatve Emprcal Study of Asset Correlaton, Structured Fnance, Credt Products Specal Report, Ftch Ratngs, July 2005 Altman, E. I., Fnancal Ratos, Dscrmnate Analyss and the Predcton of Corporate Bankruptcy, Journal of Fnance 23, Altman, E.I. Predctng Fnancal Dstress of Companes: Revstng the Z-score and ZETA models, Stern School of Busness, New York Unversty, New York, NY, workng paper, 2000 Altman, E.I., Revstng Credt Scorng Models n a Basel II Envronment, n Credt Ratngs Methodologes, Ratonale and Default Rsk, edted by M. Ong, London Rsk Books, 2002 Barry, P.J. Fnancal Management, markets and Models, Unversty of Illnos, 2004 Barry, P.J. and L. J. Robson, Portfolo Theory and Fnancal Structure: An Applcaton of Equlbrum Analyss, Agrcultural Fnance Revew, 47: , 1987 Barry, P.J., P.N. Ellnger, and B.J. Sherrck, Credt Rsk Ratng System: Tenth Farm Credt Dstrct, Unversty of Illnos, 2004 Barry, P.J. Modern Captal Management by Fnancal Insttutons: Implcatons for Agrcultural Lenders, Agrcultural Fnance Revew, 61, , 2001 Barry, P. J. W. R. W. Berlen and N. L. Sotomayor, Fnancal Structure of Farm Busnesses under Imperfect Captal Markets, Amercan Journal of Agrcultural Economcs, Vol. 82, No. 4. pp , November, 2000 Basel Commttee on Bankng Supervson, Internatonal Convergence of Captal Measurement and Captal Standards, A Revsed Framework, Bank for Internatonal Settlements, Basel, Swtzerland, June

28 Bouyé, E., V. Durrleman, A. Nkeghbal, G. Rbouletm, and T. Roncall, Copulas for Fnance: A Readng Gude and Some Applcatons. Unpublshed Manuscrpt, London: Fnancal Econometrcs Research Centre, Cty Unversty Busness School, 2000 Caouette, J. B., E. Altman and P. Narayana, Managng Credt Rsk: the Next Great Fnancal Challenge, New York: John Wley & Son, 1998 Crouhy M. and D. Gala, An Economc Assessment of Captal Requrements n the Bankng Industry. Journal of Bankng and Fnance, Vol.10, , 1986 Crouhy M., D. Gala and R. Mark, A Comparatve Analyss of Current Credt Rsk models, Journal of Bankng and Fnance, Vol.24, , 2000 Cutler S. J and F. Ederer, Maxmum Utlzaton of the Lfe Table Method n Analyzng Survval, Journal of Chronc Dseases, 8: , 1958 Featherstone, A.M. and C. R. Boessen, Loan Loss Severty of Agrcultural Mortgages, Revew of Agrcultural Economcs, 16: , 1994 Featherstone, A., L. Roessler and P. Barry, Determnng the Probablty of Default and Rsk- Ratng Class for Loans n the Seventh Farm Credt Dstrct Portfolo Revew of Agrcultural Economcs, Volume 28, Number 1, pp. 4-23(20), March 2006 Featherstone, A.M. B.W. Schurls, S.S. Duncan and K.D. Poster, Clearance Sales n the Farmland Market, Journal of Agrcultural and Resources Economcs, 18, , 1993 Gabrel, S. C. and C.B. Baker, Concepts of Busness Rsk and Fnancal Rsk, Amercan Journal of Agrcultural Economcs: 62: , 1980 Gordy M.B. A Rsk-factor Model Foundaton for Ratngs-Based Bank Captal Rules, Journal of Fnancal Intermedaton, Volume 12, Number 3, pp (34), July 2003 Gordy, M. and E. Hetfeld, Of Moody s and Merton: A Structural Model of Bond Ratng Transtons, workng paper, Board of Governors of the Federal Reserve System,

29 Greene W. H., Econometrc Analyss, Fourth Edton, Prentce Hall, 2000 Hollander, M. and D. A. Wolfe, Nonparametrc Statstcal Methods, 2nd Edton, Wley, 1999 Hrvatn R. V. and Neugebauer M., Default Correlaton and ts Effect on Portfolo of Credt Rsk, Structured Fnance, Credt Products Specal Report, Ftch Ratngs, February Jennrch R., An Asymptotc χ Test for the Equalty of Two Correlaton Matrces. Journal of the Amercan Statstcal Assocaton, Vol. 65, No. 330, pp , June 1970 Jensen F.E. and L. N. Langemeer, Optmal Leverage wth Rsk Averson: Emprcal Evdence, Agrcultural Fnance Revew vol. 56:85-97, 1996 Katchova, A.L. and Barry, P.J., Credt Rsk Models and Agrcultural Lendng. Amercan Journal of Agrcultural Economcs, 87, , 2005 Koyluoglu, H.U. and A. Hckman, Reconclable Dfferences, Rsk, 11(10): 56 62, 1998 Leland, H. E., Corporate Debt Value, Bond Covenants and Optmal Captal Structure, Journal of Fnance 49, , 37, 1994 L, K.H., Imputaton Usng Markov Chans, Journal of Statstcal Computaton and Smulaton, 30, 57 79, 1988 Lopez, J. The Emprcal Relatonshp between Average Asset Correlaton, Frm Probablty of Default and Asset Sze, FRBSF workng paper, Marceau, E. and H. Neudecker, Matrx Dfferental Calculus wth Applcaton n Statstcs and Econometrcs, Wley Seres n Probablty and Mathematcal Statstcs, John Wley & Sons, New York, 1988 Merton, R. C. On the Prcng of Corporate Debt: The Rsk Structure of Interest Rates, Journal of Fnance 29, May 1974 Nelson, R. B., An Introducton to Copulas, Sprnger, New York,

30 Puchalla, J and T. Marshella, Speculatve-Grade Lqudty: Some Early Casualtes of Credtor Rsk Averson, Moody s global Corporate Fnance, December 2007 Relly M. Data Analyss Usng Hot Deck Multple Imputaton, The Statstcan, 42, pp , 1993 Rubn, D.B. Multple Imputaton for Nonresponse n Surveys, New York: John Wley & Sons, Inc Saunders A. and Allen L. Credt Rsk Measurement, New approach to Value at Rsk and Other Paradgms, 2 nd Edton, John Wley & Sons, Inc Schafer J.L and N. S. Schenker, Inference wth Imputed Condtonal Means, Journal of the Amercan Statstcal Assocaton, Vol. 95, No. 449 pp , 2000 Schafer, J.L. Analyss of Incomplete Multvarate Data, New York: Chapman and Hall, 1997 Stam J., D. Mlkove, S. Koeng, J. Ryan, T. Covey, R. Hoppe and P. Sundell, Agrcultural Income and Fnance Annual Lender Issue, USDA, AIS-80, March 11, 2003 Sten, R M. Evdence on the Incompleteness of Merton-Type Structural Models for Default Predcton, techncal paper, Moody s KMV, 1-2-1, 2000 Yan, Y., X. Sh, P. Barry, N. Paulson and B. Sherrck, The Structure Model Based Determnants of Captal Structure: A Seemngly Unrelated Regresson Model, Presented at the Amercan Agrcultural Economcs Assocaton Annual Meetng, Orlando FL, Zellner, A. An effcent Method of Estmatng Seemngly Unrelated Regressons and Tests for Aggregaton Bas, Journal of the Amercan Statstcal Assocaton 57: , 1962 Zellner, A., and D. S. Huang, Further Propertes of Effcent Estmators for Seemngly Unrelated Regresson Equatons, Internatonal Economc Revew 3: ,

31 Fgure The SUR Model FSC Default Gudelne Probablty of Default (%) Rsk Class Fgure 1 Predcted Average PD by the SUR Model vs. FSC Default Gudelne 29

32 Tables Table 1 Credt Scorng Model and Proposed Probablty of Default (PD) by Farm Credt System Rsk Solvency Current Lqudty Assets to Repayment Earnngs Net Income Effcency to Proposed PD FCS Ratng Equty to Current Debt Return on Gross Farm Return Gudelnes (%) Gudelnes Class Assets Rato Rato CDRC* Rato Assets (%) Rato AAA to AA >0.80. > 2.5 > 1.6 >10 > AA to A A to A BBB+ to BBB BBB to BBB BB BB+ to BB BB to BB BB- to B and up B and down < 0.2 < 0.5 < 0.80 < -6 < 0 *CDRC rato= (farm and nonfarm net ncome + deprecaton+ debt servce-annual famly expendtures-ncome taxes)/debt servces Source: Farm Credt System rsk-ratng gudelnes defntons (Featherstone et al 2006) and Credt Rsk Ratng Systems: Tenth Farm Credt Dstrct (Barry et. al 2004) 30

33 Table 2 Hstorcal Default Frequency and Loss-Gve-Default (LGD) of FBFM Farms ( ) Rsk Ratng Class Cohort 1 ( ) Cohort 2 ( ) Cohort 3 ( ) Cohort 4 ( ) Cohort 5 ( ) Cohort 6 ( ) Cohort 7 ( ) Cohort 8 ( ) Cohort 9 (2003- Average 2004) # of Farms Default Rate # of Farms Default Rate # of Farms Default Rate # of Farms Default Rate # of Farms Default Rate # of Farms Default Rate # of Farms Default Rate # of Farms Default Rate # of Farms Default Rate % % 22.94% % % % 23.29% % % % % % 0.44% 23.69% % % % % % % % % % 1.54% 25.71% Default Rate LGD 31

34 Table 3 Basc Statstcs for Selected Varables of FBFM Farms ( ) Varable Descrpton Mean Medan Standard Devaton Log (asset to debt rato) Log of ( total assets to expected oblgaton rato) Sze Log of farm cash sale NROA Return on asset dvded by ts volatlty Tenure Owned land over total tllable land Collateral rato Machnery & equpment plus farmland value over total assets Sheld Earnng before deprecaton to total assets Lqudty Workng captal over value of farm producton (VFP) NETINC/VFP Netfarm ncome over VFP VFP/Debt Log of value of farm producton to total labltes rato NGTA Annual growth n total assets (GTA) dvded by ts volatlty