Construction of Investment Risk Measure by the Dispersion Degree of Estimation Errors of Working Capital

Transcription

1 Journal of Applied Finance & Banking, vol., no.1, 01, ISSN: (prin version), (online) Inernaional Scienific ress, 01 Consrucion of Invesmen Risk Measure by he Dispersion Degree of Esimaion Errors of Working Capial Shen-Ho Chang 1, Shaio Yan Huang, An-An Chiu 3 and Mei-ing Huang 4 Absrac his sudy is based on invesors viewpoin and adops he accruals qualiy model [1] as proxy variable of earning qualiy. By applying he process capabiliy concep in engineering applicaion, we esablish capabiliy index of basis accrual qualiy and ransform i ino he invesmen risk assessmen. I provides invesors an effecive way o conrol invesmen risk and o improve he invesmen decision-making process. 1 Deparmen of Accouning, Feng Chia Universiy, 100 Wenhwa Rd., Seawen, aichung, aiwan, R.O.C., shchang@fcu.edu.w Deparmen of Accouning and Informaion echnology, Advanced Insiue of Manufacuring wih High-ech Innovaions, Naional Chung Cheng Universiy, 168, Universiy Rd., Min-Hsiung, Chia-Yi 61, aiwan, R.O.C., acsyh@yahoo.com.w 3 Deparmen of Accouning and Informaion echnology, Naional Chung Cheng Universiy, 168, Universiy Rd., Min-Hsiung, Chia-Yi 61, aiwan, R.O.C. 4 Docoral rogram in Accouning, Graduae School of Managemen, Naional Yunlin Universiy of Science and echnology, Universiy Road, Secion 3, Douliou, Yunlin, aiwan, R.O.C., g960806@yunech.edu.w Aricle Info: Received : December 1, 011. Revised : January 3, 01 ublished online : February 8, 01

2 17 Consrucion of Invesmen Risk Measure... JEL classificaion numbers: M41 Keywords: esimaion errors of working capial, accrual qualiy, invesmen risk 1 Inroducion Financial saemens play an imporan role when invesors make invesmen decisions. Invesors are able o effecively evaluae business performance by inerpreing informaion hrough financial saemen analysis [10]. here are some uncerain facors in operaing aciviies of a company. herefore, here is room for he adminisraion o do wihin-gaa adjusmen. hese uncerain facors will appear in financial informaion evenually and make i have informaion risk []. When invesors use he risk informaion provided by he adminisraion, i can cause invesors invesmen loss. Afer Enron scandal, invesors learn ha financial saemens are unable o reveal he rue value and poenial risks of a company. hey also quesion he soundness of he financial reporing. A comparison of financial saemens of Enron before and afer bankrupcy revealed major inconsisencies beween he operaing cash flow and ne income afer axes. hus, he accrual qualiy repored was suspicious. Dechow and Daichev [1] poined ou he bases of measures of earning are divided ino accrual basis and cash basis. he difference of he wo bases is he esimae of he adminisraion for assuming and recognizing fuure cash flow under accrual basis. he accrual qualiy model, DD model [1], is used as he proxy variable of earning qualiy. Recenly, he sudies of informaion risk and have increased a lo [3, 8]. Oher sudies sugges D&D accruals qualiy model as he measuremen of informaion qualiy o discuss he relaion wih earnings [4, 5].

3 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 173 he DD model uses he regression model o make he accrual changes of working capial correspond o he cash flows of operaing aciviies from previous, curren, and fuure period and uses regression residual sandard deviaion as reverse measure. As a resul, when he qualiy of accruals is poor, he residual sandard deviaion of he DD model is larger and informaion risk invesors face will rise. However, he viewpoin of he DD model does no consider individual decision-making crieria of invesors. I hinks boh esimaion error and error correcion influence accrual qualiy bu does no ake anipahy and olerance of invesors decision-making crieria oward esimaion error and error correcion ino accoun. he firs quesion raised by our sudy is Is i proper o ake DD as accrual qualiy indicaor? Besides, our sudy brings up how we can measure he esimaion error of he chosen invesmen objec no wihin invesors olerance when invesors esimae cash flow from informaion of uncerain accruals wihin olerance of esimaion error. herefore, our sudy addresses invesor firs-order loss funcion in accordance wih invesors anipahy level and olerance oward DD and includes he concep of consrucion qualiy o build he accrual qualiy capabiliy index as subsiuion variable for informaion risk. hen, we conver he accrual qualiy capabiliy index ino he loss probabiliy of invesors. Since his probabiliy is caused by he uncerainy of accrual qualiy, we define i as Invesmen Risk. In applicaion, firs, we derive he saisic of he accrual qualiy abiliy indicaor as base of saisical confidence. If he accrual qualiy abiliy indicaor of he invesmen objec is greaer han or equal o one, he invesmen objec has accrual qualiy abiliy. We coninue o he second sep. Oherwise, we sop. Second, we develop he saisic of homogeneiy es and run homogeneiy es on invesmen objecs passing he abiliy es on he same basis. If invesmen objecs mee he requiremen of he homogeneiy es, here is no significan difference among invesmen objecs; conversely, if no mee he requiremen, he invesmen

4 174 Consrucion of Invesmen Risk Measure... objecs coninue o he final sep. hird, if he invesmen objecs do no mee he requiremen of he homogeneiy es, we have o compare he accrual qualiy abiliy of invesmen objecs wo by wo. herefore, on he relaive basis, our sudy develops he saisics of accrual qualiy abiliy of invesmen objecs in wo by wo comparison es and applies he es saisics o run he es. By his applicaion, invesors can clearly choose beer invesmen objecs when facing differen accrual qualiy abiliy of hem. he main conribuion of our sudy is o exend DD s accrual qualiy o accrual qualiy abiliy indicaor, and conver i ino invesmen risk under accrual qualiy measure. Furher, we ge a series of es saisics o help invesors choose beer invesmen objecs. he remainder of his paper is organized as follows. he second secion discusses analysis model. he hird secion probes ino daa resource and esimaor. he fourh secion is empirical resuls. he fifh secion is conclusion. Analysis Models We aim a building a measure of invesmen risk. he relaing discussions are as follows:.1 Accrual Qualiy In financial saemens, here are wo accouning bases o assess he business performance. One is ne profi afer ax in accrual basis and he oher is cash flow from operaing aciviies in cash basis. If here is a large difference beween ne profi afer ax and cash flow from operaing aciviies in he company s financial saemens, which means he repored earning canno be recovered in cash. his may lead he company o bankrupcy crisis because of he shorage of cash. of

5 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 175 course, his will also decrease he reliabiliy of he accrual qualiy [9, 11]. herefore, we adop he DD model o assess accrual qualiy 5. I is as follows: WC CFO CFO CFO (1) ΔWC : Change in working capial,= -[ΔA/R (Change in accouns receivable)+ : 1 ΔINV (Change in invenory)-δa/ (Change in accouns payable)-δ/ (Change in axes payable)+δoa (Change in oher asses (ne)) ]; CFO Cash flow from -1 operaing aciviies; CFO : Cash flow from operaing aciviies; CFO Cash flow from +1 operaing aciviies; : 1 : Residuals (esimaion errors) from Eq. (1). Dechow and Dichev [1] poined ou ha from Eq. (1) sands for he esimaion errors of working capial, whereas sandard deviaion of is he index of accrual qualiy. When σ ( ) is larger, he accrual qualiy is worse; on he conrary, when he σ ( ) is smaller, he accrual qualiy is beer.. Invesmen Loss he concep of qualiy loss is a measure model of consumer loss o judge if qualiy of merchandise is good or bad. he crieria for judgmen are based on he qualificaion of specific requiremens. here are only wo resuls eiher o accep or o rejec he merchandise. his concep is applied o he measure of accrual qualiy. he invesmen loss funcion (Figure 1) from accrual qualiy is as follows: 5 Dechow and Dichev [1] believed ha accruals are also affeced by firm and indusry s aribues. o eliminae he scale facor, he menioned variables are he deflaor of he oal asses of he curren year. However, he residuals of he DD model include inenional and random esimaion errors effecs. he residual in McNichols (00) adding he effec of Jones model is smaller han adding he effec of he DD model. he connoaions are so differen, and i could be discussed in fuure sudies.

6 176 Consrucion of Invesmen Risk Measure... 0, if S L A, oher () L : Invesmen loss of accrual qualiy; when he esimaion errors of working capial for he invesmen objecs are wihin he range of S, he invesmen loss is 0. On he conrary, when he esimaion errors of working capial for he invesmen objecs are ouside he range of S, he invesmen loss is A; S : An accepable range of he esimaion errors of working capial; he range is : se by sandard deviaion of esimaion errors of working capial for poenial invesmen objecs; Esimaion errors of working capial of invesmen objecs; : arge value of esimaion errors of working capial of poenial invesmen objecs; USL (Upper Specificaion Limi) : Maximum accepable specificaion limi of esimaion errors of working capial of invesmen objecs; LSL (Lower Specificaion Limi) : Minimum accepable specificaion limi of esimaion errors of working capial of invesmen objecs. Figure 1: Invesmen Loss Funcion of Accrual Qualiy in a Specific eriod

7 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 177 In general, invesors refer o financial saemens of invesmen objecs when hey are making invesmen decisions. Furher, hey build an invesmen porfolio. As menioned earlier, higher sandard deviaion from he Eq. (1) shows lower accrual qualiy and hus high invesmen risk. For he long-erm, he losses of invesors will be affeced by accrual qualiy of invesmen objecs. his implies he invesmen loss for bad accrual qualiy of invesmen objecs will be bigger. he expeced invesmen loss is expressed as follows: N ELoss ( ) Li i (3) E (Loss):expeced losses from decline of accrual qualiy on invesmen objecs; L i :he invesmen losses from decline of accrual qualiy on invesmen objeci; N:he number of invesmen objecs; i :he probabiliy of invesmen losses from invesmen objec i. Invesors are unable o expec and avoid invesmen losses resuling from decline of accrual qualiy on invesmen objecs in advance when esablishing heir invesmen porfolio. Given consan invesmen losses L i, he higher he probabiliy of invesmen losses i, he higher he expeced losses E(Loss). Moreover, o lower E(Loss), invesors need o focus on he reducion of i under risk aversion. herefore, his sudy regards i as invesmen risk from he decline of accrual qualiy. he quesion would be how o reduce he invesmen risk caused by he lowered accrual qualiy. i1.3 Basic Capabiliy Index of Accrual Qualiy We exploi he rocess Capabiliy Index, proposed by Kane [7], o consruc a basic capabiliy index of accrual qualiy, C, and furher infer i o invesmen risk i. ha is, we inroduce he concep of process capabiliy used in indusrial

8 178 Consrucion of Invesmen Risk Measure... engineering ino he error erm derived from Eq. (1). Under he normal disribuion assumpion, we esablish he olerable upper bound and lower bound on he basis of 90% probabiliy disribuion of residuals for all poenial invesmen objecs. Assuming a normal disribuion, 3.9 imes poenial invesmen objecs σ ( ) is he olerance as well as he numeraor of C. We assume ha σ ( ) of invesmen objecs is equal o σ ( ) of he poenial invesmen objecs a mos. In his circumsances, he corresponding olerance forms 3.9 imes σ ( ) of invesmen objecs, which is also he denominaor of C. When all poenial invesmen objecs are equal o σ ( ) of invesmen objecs, C is 1. he invesmen risk is 10% (=1-90%). hen he equaliy of basic capabiliy index of accrual qualiy 6 for porfolio in our sudy is: C USL LSL 3.9 p (4) USL (Upper Specificaion Limi): Maximum accepable specificaion limi of of poenial invesmen objecs (i.e. USL= ) Z ( 1 / ); LSL (Lower Specificaion Limi): Minimum accepable specificaion limi of of poenial invesmen objecs. (i.e. LSL= ) Z ( 1 / ); : Mean of of he poenial invesmen objecs 7 ; : Sandard deviaion of of he poenial invesmen objecs; : Sandard deviaion of of porfolio and assume ha > 0 In Eq. (4), given consan USL and LSL, C changes inversely o. he disribuion of residuals of invesmen porfolio ges more dispersed, hen is 6 According o he Cenral Limi heorem, if he sample size is large, i is close o he normal disribuion ε ~N (0,σ ε ). 7 We adop he DD model in pooled Regression mehod and assume =0 based on Eq. (1).

9 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 179 bigger and C is smaller and vice versa. herefore, we esablish a measuremen benchmark of accrual qualiy for he DD model and furher infer he invesmen risk i from he perspecive of invesmen porfolio. hus, we exend he DD model and develop a basic capabiliy index of accrual qualiy, which is based on invesors perspecive..4 Invesmen Risk Afer he esablishmen of accrual qualiy capabiliy index (C ), we resolve he measuremen of invesmen risk caused by lowered accrual qualiy. In his sage, Eq. (4) will be changed furher and he mahemaic relaionship beween C and i will be consruced. Under he normal disribuion assumpion, i is expressed as follows 8. USL LSL i 1 ( Z ) ( Z ) (5) i sands for invesmen risk caused by lowered accrual qualiy in sampling invesmen porfolio i. Le SL=USL-LSL or SL=(USL- )=(LSL- ). he upper specificaion limi and lower specificaion limi disribue symmerically given normal disribuion assumpion. Accordingly, SL=*USL=*LSL and Eq. (5) can be rewrien as follows. USL LSL i 1 ( Z ) ( Z ) (6) Apparenly i can be seen from Eq. (6) ha he higher he C is, he lower he i is, hereby he lower invesmen risk is, and vice versa. As long as C of invesmen porfolio was esimaed, he corresponding invesmen risk i will be 8 Esablishing C. assuming =

10 180 Consrucion of Invesmen Risk Measure... obained. (6) is revised as follows if we consider 90% probabiliy of he accepable range: USL LSL 1 ( Z ) ( Z 1. ) i ( Z 1.645C 1 1 ( Z 1.645C ( Z 1.645C ( Z 1.645C ) ) ( Z 1.645C ) ( Z 1.645C ) ( Z 1.645C ) ) ) wihin (7) In Eq. (7), i is obvious ha i is smaller when C is larger. ha means he invesmen risk is lower. On he conrary, i is larger when C is smaller, which means he invesmen risk is higher. herefore, we should know invesmen risk given he C. We develop a measure model of i aking esimaion errors of working capial as he foundaion of our sudy. In oher words, we esablish he mahemaical relaionship beween and i. Our model no only complemens he deficiencies lef by he DD model bu also provides invesors wih a useful decision-making model for esimaing invesmen risk. 3 Informaion Sources and Discussion of Esimaes 3.1 Informaion Sources, Sampling and Sudy Duraion We have seleced financial daa from he financial daabase of lised companies provided by he aiwan Economic Journal (EJ) as our samples. I akes a long ime o esimae and so we adoped he SE and OC Lised Companies from year 1996 o 007 as our samples, and excluded hose companies from he insurance, securiy indusry and wihou sufficien informaion. Furhermore, he sample companies had o be lised a or before he end of year 005. Since we need a leas 3 years of consisen daa for he calculaion of

11 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 181 variables, he sampling duraion is divided ino 10 periods based on his crierion 9. here is sample informaion from a leas 6 periods for a single company. In he end, we obain 8,346 firm-years from 93 companies. 3. Esimaes and Examinaion of C In he calculaion of C, we esimae he populaion basing on he sample informaion. From Eq. (4), he esimaion saisics of 10 is S ( ) n 1. Hence, he predicor of C can be wrien as: C USL LSL 3.9 USL LSL S ( n 1) 3.9 S ( n1) p ˆ C n 1 (8) From Eq. (8), he relaionship beween C and Ĉ is: C Cˆ ( v n 1) (9) v Invesors may face a siuaion where hey have o deermine wheher he accrual qualiy of a paricular porfolio is good since invesmen decisions are diversified. On he oher hand, invesors have o selec an invesmen porfolio of minimum risk from poenial invesmen objecs. herefore, we divide he C examinaion ino 3 sages: firs of all, we es C of porfolio o see if i is larger han 1. Secondly, we conduc Harley s Homogeneiy es for he C of 9 he 10 periods are divided as: 1 s period is year 95-97; nd period is year 96-98; 3 rd period is year and so on. 10 So he esimae of is S.

12 18 Consrucion of Invesmen Risk Measure... invesmen se. Finally, basing on he resul of invesmen se 11 es, we make wo-pair C es beween wo porfolios. Consequenly, we provide a reference for invesors when hey are making invesmen decisions Capabiliy es of C When esablishing C, we assume he degree of variance beween poenial invesmen objecs and invesmen porfolio is equal. Hence, invesmen risk is i =10% when C equals 1. We examine if C is larger han 1 by means of one-ailed es, and he null hypohesis should be: H1: orfolio C 1 By now, we obain a confidence inerval of he lef-ailed es as below (Appendix A): Cˆ ( n1, ) n 1 C (10) 3.. Homogeneiy es of invesmen se Assuming ha we selec hree invesmen porfolios from he poenial invesmen objecs, we use he F max mehod, which is inroduced by Harley [6] o es if here are significan differences among 3 ses of C. he chosen orfolios C i (i=1,,3) are classified as C 1, C and C 3, and examined by he Harley s homogeneiy es. Null hypohesis should be: H: C 1 =C = C 3 We obain a es saisic of homogeneiy es for hree porfolios as follows: F max Min{ C Max{ C 1 1, C, C, C, C 3 3 } } (11) 11 An invesmen se is formed by our choosing muliple invesmen porfolios from he poenial invesmen objecs.

13 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 183 I proves ha F ~ max max[ 3, 1 ] F (Appendix B) wo-pairs Comparison of C If he resul of he above homogeneiy es rejecs he null hypohesis, ha means a leas one C i is unequal. In his circumsances, we have o compare wo C i each oher. We compare he value of C i and C j, and he null hypohesis is: H3: i C j C / =1 By now, i is proved ha he 1-α maxima and minima confidence inerval (Appendix C) of C / C ) are: ( i j UCI ( C i/ C j ) F ( v, v ) (1) 1 LCI ( C i/ C j ) F ( v, v ) (13) 1 1 When confidence inerval of C / C ) are boh larger han 1, i C j ( i j C. When confidence inerval of C / C ) are boh smaller han 1, i C j ( i j C. When confidence inerval of C / C ) include 1, Ci C j may happen. ( i j 4 Empirical Resuls We measure and analyze he capabiliy index of accrual qualiy and invesmen risk basing on he above conceps.

14 184 Consrucion of Invesmen Risk Measure Regression Analysis Regression analysis is conduced according o Eq. (1). he resuls are shown on anel A of able 1. From anel A of able 1, we know ha he regression resuls are exacly he same as hose of Dechow and Dichev [1]. In addiion, he explanaory power (Adj. R ) of he regression model is 5.9%, which is very close o he explanaory power of Dechow and Dichev[1], 9%. From anel B of able 1, he mean of residual is 0, which complies wih he basic assumpion of he linear regressive model. he sandard deviaion of he residual is 0.079, which is S and is he numeraor in calculaingĉ. 4. Saisical ess of C 4..1 Capabiliy es of C We sar wih discussing he formaion of he porfolio of a paricular company. We assume invesors decision-making crierion orfolio equals o poenial invesmen objecs a mos. hus, i is necessary o es wheher or no C is larger han 1. We selec orfolios A, B, C, D, E from 5 companies respecively and calculae heir S Ĉ, i and he lower confidence inerval according o Eq. (10). he resuls are indicaed in able. We know from able ha C of he five porfolios are 3.039, 1.50, 1.000, 0.7 and respecively. hen he i of five porfolios are 0%, 1.4%, 10%, 3.5% and 5.% respecively. I is obvious ha he resul of orfolio C ( C =1, i =10%) fis our previous assumpion. Apparenly, if S is higher in he chosen porfolio, C is smaller, whereas he i is higher. On he conrary, if

15 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 185 S is lower in he chosen porfolio, C is larger and he i is lower. hus, here is a regular paern among S, C and i. able 1: Regression Resuls and Residuals Analysis (N=8,346) anel A: Regression Resuls Variable Expeced Symbol Coefficien Inercep 0.03 VIF value CFO *** 1.07 CFO *** 1.44 CFO *** 1.07 Sample 8,346 F Value DW Adj. R 5.9% anel B: Descripive saisic of residuals from Eq.(1) Mean Median Minima Maxima Sandard Deviaion Explanaions: 1. *** sands for <0.01; ** sands for 0.01<<0.05; * sands for 0.05<<0.1.. WC 0 1CFO 1 CFO 3CFO 1 WC : changes of working capial in period ; CFO -1 : cash-flow of operaing aciviies in period -1; CFO : cash-flow of operaing aciviies in period ; CFO +1 : cash-flow of operaing aciviies in period +1. o enhance saisical confidence, we furher examine he resul by means of a one-ailed confidence inerval ( a 0.1). In able, he lef-ailed confidence inerval of orfolio A, B and C is larger han 1, so he null hypoheses H1 are

16 186 Consrucion of Invesmen Risk Measure... rejeced. In oher words, A, B and C have accrual qualiy capabiliy. When he lef-ailed confidence inerval of orfolio D and E is smaller han 1, he null hypoheses H1 canno be rejeced. In oher words, D and E do no have accrual qualiy capabiliy. orfolio able : es of Capabiliy of orfolio C ( a 0.1) S C Lower Limi of Inerval Esimaion Resuls A Rejec H1 B Rejec H1 C Rejec H1 D Did no rejec H1 E Did no rejec H1 he above resuls mach up our prerequisie assumpion: when C =1 and i =10%. his can be a es basis for porfolio comparison, which helps invesors find ou wheher or no a paricular porfolio possesses accrual qualiy capabiliy. 4.. Homogeneiy es of Invesmen Se he homogeneiy es we conduc is based on invesmen se formed by muliple porfolios. Firs of all, we use, C 1, C and 3 C which are proved o possess accrual qualiy capabiliy in able o conduc he homogeneiy es. In he es, we also refer o he F max mehod in Eq. (11). hen we calculae he values max of S, S mix and F max, and he resuls are lised in able 3.

17 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 187 V (Average Degree of Freedom) able 3: Homogeneiy es of orfolio C ( a 0.05 ) S max S mix max F hreshold F max (K=5,V=8) Resuls Rejec H Explanaions: 1. he F max hreshold able provided by Harley [6] only provided 0.05 and and did no have 0.1 hreshold. Hence, we selec α=0.05 for he es. In able 3, resul for he homogeneiy es rejecs he null hypohesis H, so a leas one ou of he hree chosen porfolios is unequal o C. his proves here is significan difference in he accrual qualiy capabiliy among he hree chosen porfolios. A furher es aiming a comparing C s of porfolios is needed if we wan o discover he difference among porfolios wo-pairs Comparison of C Since he previous es resuls of C are unequal, we should compare C i and C j individually. hree compared combinaions are formed by pairing up hree porfolios. We pair up orfolio A wih orfolios B and C (hereafer AB and AC ) and so on. hen we calculae Cˆ / Cˆ, UCI and LCI of each i j mach using Eq. (1) and (13). he resuls are indicaed in able 4. he resuls shown in able 4 obviously poin ou ha only Cˆ i / Cˆ j inerval esimaion range for Mach BC includes 1, so i canno rejec null hypohesis H3. herefore, wheher invesors eiher choose orfolio B or C, heir accrual qualiy capabiliy is no differen in erms of saisical confidence. Cˆ / ˆ Inerval esimaion ranges are boh larger han 1 for oher maches i C j

18 188 Consrucion of Invesmen Risk Measure... (AB and AC), so hey rejec null hypoheses H3. In erms of saisical confidence, orfolio A ouperforms orfolios B and C. From our resuls above, invesors can pick he bes porfolio by conducing wo-pair comparison agains he chosen porfolio from invesmen se. orfolio i orfolio j able 4: wo-pairs Comparison of C Cˆ / ˆ UCI LCI Resuls i C j A B Rejec H3 A C Rejec H3 B C Did no rejec H3 Remark: UCI LCI, are calculaed based on Eq. (1), Eq. (13) and he resuls are F (α/,ν1, ν) =3.717 and F (1-α/, ν1, ν) =0.69 respecively Saisical es for diversified orfolio C o go a sep furher, we discuss he diversified orfolios, X, Y and Z from 3 differen companies and calculae he S, C and i and lower limi of confidence inerval. he resuls are lised in able 5. From able 5; we know ha orfolios X, Y and Z have accrual qualiy capabiliy. able 5: es of Capabiliy of Diversified orfolio C ( a 0.1) orfolio S C Lower Limi of confidence inerval Resuls X Rejec H1 Y Rejec H1 Z Rejec H1

19 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 189 In addiion, we conduc he homogeneiy es on orfolios X, Y and Z and calculae heir max S S mix 及 F max. Resuls are lised in able 6. able 6:Harley s Homogeneiy es for Diversified orfolio C ( a 0.05 ) EMBED Equaion.3 ( Average Degree of Freedom) EMBED Equaion.3 EMBED Equaion.3 Saisic F ma hreshold F max (K=3,V=8) Resuls Rejec H Explanaions: 1.F ma conduced by Harley [6] did no obain hreshold K=3, V=8. So we replace i wih he mean of F max hreshold from: K=3, V=0, F max hreshold=.9 and K=3, V=30, F max hreshold. From able 6, we know ha here are significan differences in he capabiliy of accrual qualiy among orfolios X, Y and Z. Hence, we ake wo-pair es for diversified orfolios X, Y and Z, and he maches are XY, XZ and YZ and so on. Cˆ / ˆ, UCI and LCI are calculaed by using Eq. (1) and (13). he i C j resuls are lised in able 7. able 7: Join Confidence Inervals es on Diversified orfolio C orfolio i orfolio j Cˆ i / Cˆ j UCI LCI Resuls X Y Did no rejec H3 X Z Rejec H3 Y Z Rejec H3 I is clear ha orfolios X and Y have he same accrual qualiy capabiliy in erms of saisic confidence. he accrual qualiy capabiliies of orfolios X and Y also ouperform ha of orfolio Z.

20 190 Consrucion of Invesmen Risk Measure Invesmen Decision rocess A flow char of he invesmen decision process is illusraed in Figure for invesors who ake he firm s accrual qualiy ino consideraion in invesmen decision-making. In Figure, he original decision-making poin from he invesmen risk is calculaed o be wihin he risk olerance range of invesors. Even so, he decision-making poin can be moved forward anoher sep - he capabiliy index analysis C of accrual qualiy, which provides for invesors use of he es procedures developed in our sudy. Informaion cos can be saved during he invesmen decision-making. Figure : Flow Cha of Invesmen Decision rocess

21 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang Conclusions When invesors are making invesmen decisions, accrual qualiy decreases due o esimaion errors of working capial, and he invesmen risk increases as a consequence. o reduce invesmen risk in erms of accrual qualiy, we refer o he concep of qualiy capabiliy. We also adop he regression model of accrual qualiy ha inroduced by Dechow and Dichev [1]. he capabiliy index of basic accrual qualiy was esablished in order o disinguish he degree of accrual qualiy. o go a sep furher, we develop he mahemaical relaionship beween he capabiliy index of basic accrual qualiy and invesmen risk from he viewpoin of invesors. Our empirical resuls show ha he higher he capabiliy index of basic accrual qualiy for porfolio, he lower he invesmen risk, and vice versa. endency range and dispersion range can be considered in fuure sudies abou capabiliy index of accrual qualiy o develop a modifying capabiliy index of accrual qualiy. References [1].M. Dechow and I.D. Dichev, he qualiy of accruals and earnings: he role of accrual esimaion errors, Accouning Review, 77, (00), [] D. Easley, S. Hvidkjaer and M. O'Hara, Is Informaion Risk a Deerminan of Asse Reurns?. he Journal of Finance, 57, (00), [3] D. Easley and M. O Hara, Informaion and he Cos of Capial, Journal of Finance, 59(4), (004), [4] J. Francis, R. LaFond,. Olsson and K. Schipper, Cos of equiy and earnings aribues, he Accouning Review, 79, (004), [5] J. Francis, R. LaFond,. Olsson and K. Schipper, he marke pricing of accruals qualiy, Journal of Accouning and Economics, 39, (005),

22 19 Consrucion of Invesmen Risk Measure... [6] H.O. Harley, he Maximum F-Raio as a Shor-Cu es for Heerogeneiy of Variance, Biomerika, 37(3/4), (1950), [7] V.E. Kane, rocess capabiliy indices, Journal of Qualiy echnology, 18, (1986), [8] C. Leuz and R.E. Verrecchia, Firms capial allocaion choices, informaion qualiy, and he cos of capial, Working paper, Universiy of ennsylvania, (004). [9] M. McNichols, Discussion of he qualiy of accruals and earnings: he role of accrual esimaion errors, he Accouning Review, 77(Supplemen), (00), [10] K.G. alepu,. M. Healy and V.L. Bernard, Business Analysis and Valuaion Using Financial Saemens, Souh Wesern ublishing co, 005. [11] K. Schipper and L. Vincen, Earnings qualiy, Accouning Horizons, 17(Supplemen), (003),

23 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 193 Appendix A o es wheher he capabiliy of C is larger han 1, we exend he basic concep of confidence inerval of variance o wrie Eq. (A1): n 1) S ( n1,1 / ) ( 1) S ( n1, / ) ( n (A1) o furher work ou Eq. (A): ( n1, / ) 1 ( n1,1 / ) ( n 1) S ( n 1) S USL LSL 3.9S * ( n1, / ) ( n 1) USL LSL 3.9 p USL LSL * 3.9S ( n1,1 / ) ( n 1) Cˆ ( n1, / ) n 1 C Cˆ ( n1,1 / ) n 1 Because we adop he lef-ailed es, he confidence inerval is (A) Cˆ ( n1, ) n 1 C (A3) Appendix B If null hypohesis H1: C 1 =C =C 3 is rue, and hen Eq. (11) can be wrien as: F max MinC MaxC 1 1, C, C, C, C 3 3

24 194 Consrucion of Invesmen Risk Measure... C1 C C3 Max,, C 1 C C 3 C 1 C C3 Min,, C 1 C C 3 (B1) If d USL LSL, hen: d C S S ( n 1) * ( n1) S * 1 vn1 (B) C d ( n1) n1 v 1.645S o subsiue F C C BEQi ~ / v i i ino Eq. (B1), i is wrien as: BEQi Max / v, / v, / v v1 1 v v3 3 max Min v / v 1 1, v / v, v / v 3 3 (B3) Furhermore, if we conduc a variance es oward he five porfolios by F max mehod in Harley [6], is null hypohesis is Hb: saisic is: = = and is es 1 3 F s Max{ s, s, s } (B4) {,, } max 1 3 max smin Min s1 s s3 If Hb is rue, and hen Eq. (B4) can be: F max[5, v1] v 1s1 vs v3s3 Max / v 1, / v, 1 3 v 1s1 vs v3s3 Min / v 1, / v, 1 3 Max v / v1, /, 1 v v v3 Min / v, / v, v 1 1 v v 3 / v / v 3 3 / v3 / v3 (B5) Since (B3)=(B5), so F ~ max max[ 3, 1 ] F, in which v / 3. v i

25 Shen-Ho Chang, Shaio Yan Huang, An-An Chiu and Mei-ing Huang 195 Appendix C o es wheher he confidence inerval of C / C includes 1, we come i j up wih equaliy according o Eq. (B): C C C C i i j j C C C C i j i j v / v 1 i ~ F( v1, v) / v v j herefore, we obain he Upper Confidence Inerval (hereafer UCI) and he Lower Confidence Inerval (hereafer LCI) of 1-α for he following equaliy: UCI ( Ci/ Cj ) F ( v 1, v ) (C1) ( C i / Cj ) and provide (C) LCI ( / ) F ( v 1, v Ci Cj ) 1- (C3) hen he UCL and LCI of 1-α for C / C ) is as below respecively: UCI ( Ci/ Cj ) F ( v1, v) ( i j (C4) LCI ( / ) (, Ci Cj F v1 v ) 1 (C5)