ESTIMATING THE MARKET VALUE OF FRANKING CREDITS: EMPIRICAL EVIDENCE FROM AUSTRALIA Duc Vo Beauden Gellard Stefan Mero Economc Regulaton Authorty 469 Wellngton Street, Perth, WA 6000, Australa Phone: (08) 6557 7900 Fax: (08) 6488 1016 Aprl 2013 * We are greatly ndebted to Greg Watknson, Rajat Sarawat and Bruce Layman for the support and constructve comments they have provded durng the wrtng of ths paper. Specal thanks to Keu Pham and Bll Scalan for ther proofreadng. The vews expressed heren n ths paper are those of the authors and do not necessarly represent those of the Secretarat or the Economc Regulaton Authorty. All remanng errors are ours.
ESTIMATING THE MARKET VALUE OF FRANKING CREDITS: EMPIRICAL EVIDENCE FROM AUSTRALIA Abstract The market value of frankng credts, known as theta, s an mportant nput for estmatng the weghted average cost of captal n Australan regulatory decsons. There s, however, a lack of consensus on an approprate estmate of the market value of frankng credts. Ths paper attempts to estmate the market value of frankng credts usng a dvdend drop-off methodology. A lst of 2,595 unque tckers was compled by observng stocks lsted on the ASX durng the perod 1 July 2001 to 1 July 2012. Dvdend dstrbuton events from 1 July 2001 to 1 July 2012 were obtaned and a dvdend sample was constructed usng flters dentfed n lterature on the topc. Regresson technques and parametrc forms of the dvdend drop off equaton were also sourced from relevant lterature. Intal estmates of the value of theta were calculated, and then a senstvty analyss was performed to ascertan the robustness of the estmates. It was found that due to the hgh multcolnearty between the net dvdend and the frankng credt, precse estmates of theta could not be readly obtaned.. Because of ths, t may be more approprate to use a range for the value of theta rather than a derved pont estmate. The approprate range suggested by ths study s between 0.35 and 0.55. JEL Classfcaton Numbers: G01; G11; G18 Keywords: Frankng credts; Dvdend events; Dvdend Drop-off methodology; regulaton; Australa. Aprl 2013
I Introducton Personal taxes mpact the requred rate of return an nvestor requres on both equty and debt. It s the post-tax (as opposed to pre-tax) rate of return that nvestors consder when evaluatng nvestment opportuntes. As a consequence, t s vtal to consder the mplcaton of personal taxaton on the WACC estmate. Specfcally, gven that Australa has an mputaton tax system; ts mpact on the requred return to equty must be consdered. The purpose of the mputaton tax system s to avod corporate profts beng taxed twce. Prevously, company profts were taxed at the corporate level, and taxed agan n the form of dvdends pad out to shareholders as personal ncome tax. Under the Australan mputaton tax system, a frankng credt s dstrbuted to ndvduals wth dvdends to offset personal taxaton lablty. The frankng credt represents the amount of personal taxaton already pad at the corporate level. Imputaton credts n Australa have a face value of one dollar per credt whch can be clamed as a rebate to offset personal tax labltes. Snce the 1st July 2000, a refund on any excess credts over personal tax labltes can be clamed. It s mportant to note that nternatonal nvestors cannot utlse mputaton tax credts. As such, mputaton tax credts provde benefts to Australan nvestors only. Any value generated by the presence of frankng credts n the Australan tax system must be accounted for n the requred return to equty, and n turn the weghted average cost of captal. Investors would be wllng to accept a relatvely lower requred rate of return on an nvestment that has frankng credts compared wth an nvestment wth smlar rsk and wthout a beneft of frankng credts. The precse value nvestors place on frankng credts s ambguous, gven that ndvdual nvestors have dfferng taxaton crcumstances and personal frankng credt valuatons. II Theoretcal Background () Gamma n the Weghted Average Cost of Captal Frankng credts represent a rebate whch reduces personal taxaton labltes. As frankng credts alter the effectve after-tax return on an equty nvestment; frankng credts wll alter the requred return on equty an nvestor requres. An early theoretcal framework presentng how frankng credts alter the after-tax cost of captal was proposed by Offcer (1994). The operatng ncome (or Earnngs before Interest and Tax, (EBIT) of a company s defned as follows: where X 0 s the operatng ncome, taxaton), X D s the debt holders share of operatng ncome and operatng ncome. X0 XG X D X E (1) X G s the government s share of operatng ncome (.e. company X E s the equty holder s share of The amount T ( XO X D) s the amount of company taxaton collected from the company by the government. However, a proporton of ths amount, whch s defned as γ (gamma), represents the tax collected from the company whch wll be rebated aganst personal ncome tax. It s convenent to consder gamma as the proporton of personal ncome tax collected at the company level. As a consequence, the effectve company taxaton s defned as: X T( X X ) T( X X ) G O D O D T( X X )(1 ) O D (2) Therefore, n ths representaton, gamma s the proporton of tax collected from the company whch gves rse to frankng credts. Gamma can be consdered as the proporton of company tax that s used as prepayment of personal tax labltes (Hathaway &Offcer 2004).
Substtutng (2) nto (1) yelds: X T( X X )(1 ) X X (3) 0 0 D D E Solvng for X 0 : X E X0 XD (1 T (1 )) (4) The weghted average cost of captal can be derved from (4) va the perpetuty defntons of value. Let E X r E D, D e X X O and V r r D O where E s the value of equty, re s the requred rate of return to equty holders after-company tax but before-personal tax, D s the value of debt, V s the sum of debt and equty, rd s the requred return to debt holders after tax, r O s the requred return before taxes or the before-tax weghted average cost of captal (WACC). Substtutng these defntons nto (4) yelds the before-tax cost of captal: r o e r. E rd. D (1 T(1- )) V V (5) The mpact of frankng credts on the WACC s therefore through the value of gamma. The WACC s consdered as the frm s weghted average cost of captal that represents the average return the frm must pay to ts nvestors (both debt and equty) to fund ts assets. Gven that equty holders consder the value of frankng credts when evaluatng nvestment opportuntes, ther value must be accounted for when calculatng the requred return of equty an nvestor requres. () Interpretaton of Gamma Gamma has the nterpretaton of beng the proporton of the company tax collected that wll be rebated aganst personal tax. Gamma s the product of two components (Monkhouse 2008): the fracton of mputaton credts created that are assumed to be dstrbuted to shareholders (F); and- the market value of mputaton credts dstrbuted as a proporton of ther face value (θ). F (6) Offcer (1994) argued that F s equal to one when consderng the cash flows from equty n perpetuty. In perpetuty, all dvdends and thus the correspondng frankng credts must eventually be pad out n each perod.
An alternatve approach outlned by Monkhouse (1996) ncorporates the tme value dscount assocated wth the retenton of mputaton credts nto the defnton of gamma: F (1 F) (7) Where: < due to the tme value loss assocated wth the retaned frankng credts. Ths specfcaton recognses the fact that not all dvdends and mputaton credts wll be pad out n each perod and as such, n perpetuty, the loss assocated wth tme value must be accounted for. Gven the extreme dffculty n estmatng the tme value dscount of retaned frankng credts, equaton (6) s used to calculate the value of gamma for the purposes of estmatng the WACC. Emprcal evdence suggests the annual payout rato of a company n Australa s 0.71 (Hathaway & Offcer 2004). As a consequence, 71% of the return of equty s assumed to be n the form of dvdends wth correspondng frankng credts attached. Therefore, t s assumed that 71% of all mputaton credts are dstrbuted to shareholders n the same year they are created. Ths s the man evdence cted n choosng the value of the payout rato for the calculaton of gamma. The market value of frankng credts,, can be defned as how much an nvestor would be wllng to pay for obtanng frankng credts, as a proporton of ther face value. It s the reducton n nvestor s personal taxes that determnes the value nvestors place on frankng credts. Investors who fully value frankng credts have a personal theta of 1; whlst nvestors who place no value on frankng credts have a theta of 0. As a consequence, the value of theta has a theoretcal nterval of 0. For the purposes of calculatng a frm s WACC, the approprate value of theta must represent a weghted average of all nvestor s ndvdual valuatons of frankng credts. Investors would be wllng to accept relatvely lower requred rates of return on equty nvestments f t comes attached wth frankng credts. Each nvestor would accept dfferent requred rates of return, based on ther own personal frankng credt valuaton. As a consequence, ths average requred rate of return depends on the weghted average of each nvestor s personal frankng credt valuaton. Investor s wll value frankng credts less than ther face value. In order to qualfy for frankng credts, nvestors must take on rsk by purchasng and/or holdng stocks. In addton, domestc nvestors forgo the benefts of nternatonal dversfcaton and ncur transacton costs by qualfyng for frankng credts. Internatonal nvestors, who cannot utlse frankng credts to reduce ther personal taxaton lablty, place no value on frankng credts. As a consequence, nvestors wll on average value frankng credts at less than ther face value. Unfortunately, frankng credts are not tradable, and prces are not drectly observable. However, the market value of frankng credts can be nferred by observng how the market prce of stocks reacts upon the dstrbuton of dvdends and frankng credts. In ths stuaton, the stock prce wll be reduced by the market value of both the cash dvdend and frankng credt pad. Econometrcs can then be employed to dstngush the component of the prce drop off due solely to the value of the frankng credts. By performng ths analyss over a long perod of tme and across a large number of dvdend events, an average market valuaton of frankng credts can be obtaned. () Dvdend Drop Off Studes Dvdend drop-off (DDO) studes nvolve examnng how much a frms stock prce changes after gong ex-dvdend. DDO studes are based on the assumpton of perfect captal markets n whch there are no transacton costs, no dfferental taxaton between dvdends and captal gans, and that share prces are not subject to any other nfluence other then the dstrbuton of dvdends and frankng credts. The theory of arbtrage predcts that n ths stuaton, the expected reducton of the share prce from cum-dvdend day to the ex-dvdend day (the prce drop off) should equal to the gross dvdend
whch ncludes the value of the cash dvdend and the value of the frankng credt. However, the assumpton of perfect captal markets s unlkely to hold n realty. In addton, gven that nvestors wll not fully value the combned package of the gross dvdend, the expected prce drop-off should be less than that of the face value. Formally, ths asserton can be expressed as: E P P D FC (8) c, x, 1 2 Where E Pc, Px, s the expected prce drop-off from the cum-dvdend day prce P c,, to the exdvdend day prce P x,. 1 s the value nvestors place on the cash dvdend (also referred to as the net dvdend) D, as a proporton of ts face value. 2 s the value nvestors place on the frankng credt FC, as a proporton of ts face value. To estmate the values of 1 and 2, regresson procedures are employed by collectng data on hstorcal dvdend events. The regresson equaton to be estmated s: P P D FC c, x, 1 2 (9) Where s an error term desgned to capture all other factors that nfluence the DDO outsde of the cash dvdend and frankng credt. It s assumed that s a normally dstrbuted random varable wth E[ ] 0. 1 Equaton (9) and ts varatons are used to estmate the values of 1 and 2 usng regresson analyss. The mpact that the net dvdend and frankng credt has on the prce drop-off, 1 and 2 can be nterpreted as the market value of each respectvely. It has been noted that DDO studes are vulnerable to heteroscedastcty (Beggs & Skeels 2006), multcolnearty (Mckenze & Partngton 2010), and the presence of outlers (Beggs & Skeels 2006). Heteroscedastcty refers to the non-constant varance of the error term. In partcular, the varance of the error term s condtonal on another varable related to the observaton. Formally, heteroscedastcty can be expressed as: Var[ x ] (10) 2 where x s a varable related to observaton. In the context of DDO studes, the varance of the error term s assumed to be related to the sze of the cum-dvdend prce or the sze of the dvdend. In order to perform Ordnary Least Squares (OLS) analyss, a constant varance term (or homoskedastcty) s requred. Performng OLS n the presence 1 The combned value of the net dvdend ( D ) and frankng credt ( FC ) s referred to as the gross dvdend, ( G ).
of heteroscedastcty wll result n an estmator wth a large varance, and ncorrect standard error (Hll, Grffths and Lm 2008). Multcolnearty s often cted as another ssue n the DDO studes. Multcolnearty refers to the stuaton where a lnear relatonshp exsts between the explanatory varables. Specfcally, the explanatory varables are correlated and tend to move together. Multcolnearty s a problem n that the data set does not contan enough nformaton n order to estmate the ndvdual effects of the varables n the model precsely. Multcolnearty causes an ncrease n the standard errors of the estmated regresson coeffcents, whch mples less precson n the resultng estmate. The consequences of multcolnearty arse f the purpose of regresson s explanaton; that s to explan the ndvdual effect each dependent varable has on the ndependent varable. If the purpose of regresson s predcton, multcolnearty s not an ssue as there s no need to separate out the ndependent effects of the correlated varables. It s well documented that n stuatons where extreme multcolnearty arses, t s nearly mpossble to separate the mpact that the ndependent varables have ndvdually on the dependent varable (Berry & Feldman 1985). Multcolnearty can cause the estmated model to be extremely senstve to changes n the underlyng sample, regresson technque used or the parametrc form 2 appled to the data (Berry & Feldman 1985). In dvdend-drop off studes, multcolnearty arses from the fact that the frankng credt s calculated from the sze of the net dvdend as follows: tc FC D f 1 t c (11) where t c s the corporate tax rate, f s the frankng proporton 3 and D s the net dvdend. In the stuaton where all dvdends are fully franked, f 1, perfect multcolnearty exsts and t s mpossble to estmate the value of frankng credts. In practce, as some dvdends are ether partally franked or have no frankng, t s possble to estmate the value of frankng credts. However, because most dvdends are fully franked, there exsts an extremely hgh degree of correlaton between the cash dvdend and the frankng credts. As a consequence, t becomes dffcult to dfferentate the nfluence on the prce drop off separately. The presence of outlers s cted as another weakness of DDO studes (McKenze & Partngton 2010). Outlers can have a large dsproportonate nfluence on the regresson coeffcents, maskng the underlyng trend of the rest of the data. Outlers are dstnct from heteroscedastcty n that they are not smply the result of a large varance, but rather ndcate the nadequacy of the current model n explanng the data. Excludng outlers based on ther nfluence on the regresson coeffcent can be seen as a form of data mnng, whch may exclude mportant nformaton from the analyss. An alternatve ntroduced by Truong and Partngton (2006) s to utlse varous forms of robust regresson; regresson technques that are not heavly nfluenced by the presence of outlers. 2 The parametrc form of a regresson model refers to the partcular form of the regresson equaton to be estmated. For example, multplyng equaton (9) by the nverse of the cum-dvdend prce for each event results n a new parametrc form of the model. 3 The frankng proporton represents the fracton of dvdends that have frankng credts attached to them. A frankng proporton of 1 ndcates that the dvdends are fully franked; a 0 frankng proporton ndcates no frankng credts are attached to dvdends.
() Hathaway and Offcer (2004) III Prevous Australan Dvdend Drop-Off Studes Hathaway and Offcer (2004) explore a slghtly dfferent parametrc form of the DDO equaton. Theoretcally, f both the cash dvdend and frankng credt are fully valued, ths leads to a prce dropoff equal to the value of both the cash dvdend and the face value of the frankng credt. Ths stuaton can be represented as: P D F (12) Where P s the change n stock prce from the cum-dvdend day to the ex- dvdend day, D s the net dvdend, F s the frankng credt and s an error term desgned to capture all other factors that nfluence the DDO outsde of the cash dvdend and frankng credt. The face value of the frankng credt can be expressed as follows: tc F D ( ) f 1 t c (13) Where f s the frankng proporton of the mputaton tax credt, tc s the corporate tax rate for observaton. Substtutng (13) nto (12) produces: tc P D D ( ) f 1 t c (14) Dvdng ths equaton by the cash dvdend produces the followng: P D tc ' 1 ( ) f 1 t c (15) It s noted that ths s the theoretcal case where the value of the cash dvdend and frankng credt s fully valued. In the stuaton where cash dvdends and frankng credts are not fully valued, the model becomes: P ' a b. f D (16) The nterpretaton of a s the drop-off proporton that s due to the cash component of the dvdend, and b s the drop-off proporton due to the frankng credt. Hathaway and Offcer noted that the error term was nversely proportonal to the dvdend yeld. To account for ths form of heteroscedastcty, equaton (16) was re-weghted by the dvdend yelds of each dvdend event to produce the followng equaton: P '' a. Dv / P b. Dv. f / P (17) P
The dvdend sample was constructed by complng a lst of all dvdend events for stocks lsted wthn the ASX/S&P 500 ndex between August 1986 and August 2004. OLS was appled to equaton (16) and (17) n order to produce an estmate of the value of frankng credts over ths perod. Hathaway and Offcer concluded that net dvdends are valued between 80 and 81 cents whle frankng credts are valued between 49 and 52 cents for large captalsed companes. Hathaway and Offcer noted that they dd not beleve that ther estmate of the value of frankng credts was precse; however they noted that attrbutng a zero value to frankng credts s ncorrect. 4 () Beggs and Skeels (2006) Beggs and Skeels (2006) utlse the DDO methodology n order to estmate the value of cashdvdends and frankng credts. Beggs and Skeels defne the Gross Drop-Off Rato (GDOR) as follows: GDOR P P G C X (18) Where P C s the cum-dvdend prce, PX s the ex-dvdend day prce, G s the gross dvdend. Based on the prevous lterature explored by Beggs and Skeels, t s expected that the GDOR<1. Ths mples that nvestors are valung the combned package of the net dvdend and frankng credts at less than ther face value. The DDO methodology n ther study assumes that: P P G (19) c, x, 0 1 Where 1 s the value that nvestors place on the gross dvdend. Separatng the gross dvdend of equaton (19) nto ts components yelds: P P D FC (20) * c, x, 1 2 * where: Pc, s the cum-dvdend prce of dvdend event, P x, s the market adjusted ex-dvdend day prce of dvdend event, 1 s the cash drop-off rato, 2 s the frankng credt drop-off rato, D s the net dvdend and FC s the face value of frankng credts. It s noted by Beggs and Skeels that DDO models suffer from heteroscedastcty. As such, OLS regresson s not approprate. Beggs and Skeels use the Feasble Generalsed Least Squares (FGLS) estmator approach by modellng the varance as follows: ˆ 2 ln 0 1W 2G 3 P c, u (21) Where ˆ are the OLS resduals from (20), market captalsaton as a proporton of the All ordnares Index, event and Pc, s the cum-dvdend prce of dvdend event. W s the company sze of dvdend event measured by G s the gross dvdend of dvdend
Wth ths model of varance, the ftted values of the varance are calculated for each ndvdual dvdend observaton: 2 ln 0 1W 2G 3 P c, (22) The estmated standard devaton of each dvdend event s then calculated usng the estmated regresson coeffcents of (22). The nverse of ths estmate s then used as weghts n the orgnal DDO equaton (20) and OLS s then appled to the followng: P P D FC * c, x, 1 2 (23) The Beggs and Skeels study was based on the Commsec Share Portfolo data. They showed that the GDOR was sgnfcantly less than 1 wth the mplcaton that net dvdends and/or frankng credts are not fully valued by the average nvestor. Between 2001 and 2004, ther estmated value was 80 cents for net dvdends and 57 cents for frankng credts. () Strategc Fnance Group Consultng (2011) Strategc Fnance Group (SFG) conducted a DDO study usng the Mornngstar DatAnalyss database (SFG 2011). Dvdend events that had data mssng or a market captalsaton of less than 0.03% of the All Ordnares Index were excluded from the analyss. Company announcements that occurred wthn 5 days of the ex-dvdend date that were consdered to be prce senstve resulted n the dvdend event beng removed from the sample. SFG appled varous scalngs to the DDO equaton n order to correct for heteroscedastcty. SFG concluded from ts survey of the DDO methodology that the heteroscedastcty was drectly proportonal to the cum dvdend prce, the sze of the dvdend pad and the hstorcal volatlty of excess returns of the stock. 5 To control for heteroscedastcty, SFG scaled the orgnal DDO equaton P P D FC, as follows: c, x, 1 2
Table 1 Parametrc form of DDO equaton used by SFG. Model Parametrc Form Scalng Factor 1 Pc, P x, FC D D D 2 P P D FC c, e, '' Pc, Pc, Pc, P c, 3 P P 1 FC D c, x, '' ' '' D D 4 P P D FC Pc, c, x, ' ' ' Pc, Pc, Pc, N Where 1 : ( t, ), t er er s the estmated standard devaton of excess returns of stock N, t 5 j j 1 N 1 over N tradng days, er, t : er, t tradng days,, t, t m, t return of stock at tme t ; N j 1 s the estmated mean of excess return of stock over N er : r r s the excess return of stock over the market at tme t and r s the return of the All Ordnares Index at tme t. mt, r s the t, Robust regressons were appled to these dvdend drops off models usng the MM regresson estmator. SFG beleved that model 4 showed the most consstent results across the robustness checks they performed. As a result, model 4 was assgned the most weght. An average estmate of theta usng model 4 was produced usng the varous robustness checks to produce an estmate for theta of 0.35. (v) Summary of Australan Dvdend Drop Off Studes A more extensve summary of Australan DDO studes can be found below:
Table 2 Summary of Australan Dvdend Drop Off studes. Author Year Data Technques Theta Brown & Clarke 1993 Walker & Partngton 1999 Hathaway & Offcer 2004 Statex, Melbourne and Australan Stock Exchange publcatons, 1973-1991 Securtes Industry Research Centre of Asa-Pacfc, 1995 to 1997 Australan Tax Offce and ASX/S&P 500, 1986-2004 OLS Regresson 0.72 Not Specfed 0.88 0.96 Generalsed Least Squares Bellamy & Gray 2004 1995-2002 Unknown 0.00 Beggs & Skeels 2006 SFG Feuerherdt, Gray & Hall 2007 2010 SFG 2011 CommSec Share Portfolo 1986-2004 Securtes Industry Research Centre of Asa-Pacfc and FnAnalyss, 1998-2006 Securtes Industry Research Centre of Asa-Pacfc, 1995-2002 DatAnalyss, 2000-2010 Generalsed Least Squares Generalsed Least Squares Generalsed Least Squares Generalsed Least Squares 0.49 0.57 0.23 0.00 0.35 The authors consder that studes carred out after 2001 are more relevant to the estmate of current market value of frankng credts. As such, other studes pror to 2001 were not consdered n ths study. Market value of frankng credts do vary sgnfcantly across studes. It s noted that one author, Gray, was nvolved n 4 dfferent studes as presented n Table 2 above, studes mplemented n 2004; 2007; 2010; and 2011. () Consderatons (IV) Analyss The company taxaton and mputaton credt system has undergone many changes as outlned n Beggs and Skeels (2006). A holdng perod of 45 days s necessary for total frankng credt enttlements below $5,000 to qualfy for frankng credts. In addton, f an nvestor hedges the prce rsk of the securty usng dervatves, the frankng credts are unable to be used. More recently, from 1 July 2000, any excess frankng credt can be rebated for cash and from 1 July 2001 the company taxaton rate has been reduced from 34 to 30 percent. As a consequence, the perod consdered n ths analyss s from 1 July 2001 to 1 July 2012 to avod structural changes n the company tax rate and mputaton credt system. Varous studes have noted that thnly traded stocks can have a confoundng effect on dvdend drop off regressons (Hathaway & Offcer 2004, Beggs & Skeels 2006, SFG 2011). Prces must be a reflecton of an effcent tradng mechansm whch s unlkely to be the case when a stock trades nfrequently. Hathaway and Offcer (2004) noted that:
There s no obvous reason why the cash dvdend for Bg Cap, Md Cap and Small Cap stocks should vary. That the results do s testament to the dffculty of estmaton among these smaller stock events. Implct n our expermental desgn s that stocks trade over the ex-date perod, but many stocks, partcularly small cap stocks, are rather llqud. They concluded that large captalsaton stocks to estmate the value of theta are the most relable. In addton, SFG(2011) and Beggs and Skells (2006) utlse a crteron of only ncludng stocks that have a market captalsaton greater than 0.03% market captalsaton of the All Ordnares Index. As a consequence, the dvdend sample used n ths analyss has been constructed usng the same 0.03% market captalsaton flter. Another mportant flter s the removal of stocks that undergo a captalsaton change (for example, undergo a stock splt) 5 tradng days before or after a dvdend event. Ths ensures that the prce drop off due to a captalsaton change has no mpact on the estmate of theta. Indvdual specal cash dvdends are consdered unrelable, as they are an rregular dstrbuton of excess cash reserves. As a consequence, dvdend events that are classfed as specal cash only were removed, consstent wth other DDO studes (Beggs & Skeels 2006). However, t s common for companes to dstrbute a specal cash dvdend n conjuncton wth a fnal or nterm dvdend. Removng specal cash dvdends n ths scenaro would mply that the prce drop off s due solely to the other dvdend, creatng an upward bas n the estmate of theta. Therefore, specal cash dvdends that occur on the same day as a normal dvdend event are aggregated n order to produce a combned dvdend as descrbed by Hathaway and Offcer (2004). The remanng ndvdual specal cash dvdends were then removed from the sample. Flters that exclude observatons based on prce senstve announcements have not been utlsed n ths study. SFG (2011) screen dvdend observatons based on prce senstve announcements that occur 5 days before the ex-dvdend date. The prce senstve flag for announcements s avalable on the ASX webste. After ths ntal screenng, SFG observe each observaton and decde f the announcement wll have a materal mpact on the stock prce. Observatons that have a prce senstve announcement close to the cum- or ex-dvdend date can be consdered as unbased nose, equally lkely to be postve or negatve. As a consequence, removng these observatons s unnecessary; dong so may ntroduce a subjectve element to the analyss that s undesrable. In prncple, data ponts should not be removed after the fnal sample of dvdends has been compled. Rather, dfferent econometrc methodologes that are not senstve to outlers should be employed, consstent wth objectve statstcal analyss. () Regresson Technques It has been noted that DDO studes are extremely senstve to the sample of dvdend events ncluded n the sample (McKenze & Partngton 2010). Ths s due to the assumptons of tradtonal Ordnary Least Squares (OLS) regresson analyss beng volated; specfcally the non-constant varance (heteroscedastcty); and non normalty of errors (presence of outlers). In addton, due to the hgh level of multcolnearty between the cash dvdend and the frankng credt, the coeffcent estmates are extremely senstve to small changes n the model or data. In mtgatng the problems that exst wth outlers, regresson technques that are less susceptble to ther presence wll be appled. Least Absolute Devaton (LAD) estmators of lnear models mnmse the sum of absolute values of the resduals whch can be expressed formally as: n ' mn y x β 1 (24)
Where y s the response varable of observaton ; s a vector of regresson coeffcents to be estmated; and x s a vector of the covarates for observaton. In contrast to OLS, LAD regresson does not gve ncreasng weght to larger resduals. As a consequence, t s less senstve to outlers then OLS regresson. The statstcal lterature has developed methodologes that are nsenstve to small changes to model assumptons; ncludng the presence of outlers. Robust statstcs are methodologes desgned to be nsenstve to devatons from the assumptons made n a statstcal analyss (Huber 1996). In partcular, varous forms of robust regresson have been developed n order to lmt the nfluence of outlers; and to deal wth the volaton of the normalty assumpton. Robust regresson has also been proposed as a method for dealng wth heteroscedastcty (Andersen 2008). A central concept of robust statstcs s the breakdown pont of an estmator; the smallest fracton of contamnaton that can cause the estmator to break down and no longer represent the trend n the bulk of the data. The effcency of an estmator s defned as the rato of ts mnmum possble varance to ts actual varance. It s desrable for an estmator to have an effcency rato close to 1, as ths ensures the estmator for the target parameter has the lowest varance possble. MM regresson s a form of robust regresson descrbed by Yoha (1987), whch has a hgh breakdown pont of 50% and hgh statstcal effcency of 95%. MM regresson has the hghest breakdown pont and statstcal effcency of robust regresson estmators currently avalable, and for ths reason, t wll be adopted n ths analyss. A trade-off between the breakdown pont and statstcal effcency of a MM estmator exsts - a hgher breakdown pont can be acheved by a reducton n statstcal effcency; or conversely, a hgher statstcal effcency can result from a lower breakdown pont. The tunng parameter s the varable n MM regresson that s chosen n order to acheve the desred breakdown pont and statstcal effcency. The choce of tunng parameter s an overlooked component of conductng MM regresson analyss, wth the choce of 50% breakdown pont and 95% statstcal effcency beng standard. Introducng the estmator; Yoha (1987) dscussed the choce of the tunng parameter and cautoned aganst relyng on the standard choce. () Regresson Models The tradtonal form of the DDO equaton s as below: 6 P P D FC (25) c, x, 1 2 Equaton (25) does not satsfy the assumptons requred to perform OLS due n part to the constant varance assumpton beng volated (Beggs & Skeels 2006, McKenze & Partngton 2010). The standard form of adjustng equaton (25), assumes that the error varance s proportonal to the sze of the cum-dvdend prce, that s: 2 ~ N(0, ) k P (26) 2 2 c, Intutvely, ths mples that the dfference between the predcted value of the DDO and the actual value of the dvdend drop off, the error, s lkely to be larger for stocks wth a hgher stock prce. To counter ths, equaton (25) s dvded (scaled) by the cum-dvdend prce as follows: P P D FC (27) c, e, ' 1 2 Pc, Pc, Pc, 6 Ths assumes no ntercept term.
Equaton (27) s the standard choce of adjustment to the DDO equaton whch s used to mtgate the mpact of heteroscedastcty. Other varables dentfed n the lterature nfluencng the error varance nclude market captalsaton (Hathaway & Offcer 2004), dvdend yeld (Mchaely 1991, Hathaway & Offcer 2004), and nverse stock return varance (Bellamy & Gray 2004). Intutvely, the dvdend yeld results n heteroscedastcty as stocks wth larger dvdends wll cause a larger prce drop-off, and as a consequence have a proportonally larger error. Stock prce return varance refers to the hstorcal volatlty of the stock. A stock that s hstorcally volatle over a long perod of tme s lkely to have a larger error varance then a stock wth low hstorcal volatlty, regardless of the sze of the dvdend pad. As a consequence a measure of hstorcal stock return volatlty s requred n order to reduce ths form of heteroscedastcty. Market captalsaton s generally not used as a weghtng varable n the DDO equaton, as the 0.03% of the All Ordnares ndex flter of the data appled n DDO studes reduces the mpact that low market captalsaton has on stocks (Beggs & Skeels 2006, SFG 2011). Table 3 presents the results of applyng these scalng, ncludng jont scalng, to equaton (25) as follows: Table 3 Models used n ths analyss. Model Parametrc Form Scalng Factor Form of Heteroscedastcty Model 1 P P D FC c, e, ' ' ' 1 2 Pc, Pc, Pc, P c, k P 2 2 c, Model 2 P P FC D c, x, '' '' '' 1 2 D D 7 k D 2 2 Model 3 P P 1 FC Ds, c, x, ''' ''' ''' 1 2 D se, se, D se, e k ( D s ) 2 2 e, Model 4 P P D FC c,, c, x, '''' '''' '''' 1 2 Pc, se, Pc, se, Pc, se, 2 P s 2 e k P s c, e, Where P c, s the cum-dvdend prce of dvdend event, Px, s the ex-dvdend day prce of dvdend event, D s the cash dvdend of dvdend event, FC s the frankng credt of dvdend event, 1 s 2 the market value of the cash dvdend, 2 s the market value of the frankng credt, s the varance 2 of the error term of dvdend event, Var[ ] and s e, s the hstorcal excess return volatlty of stock. 7 Usng equaton (27), Model 2 can also be derved by scalng by the dvdend yeld, D P. c,
Table 3 contans the 4 models that wll be employed n the analyss to estmate theta. SFG (2011) also utlsed these models n ther DDO study. Model 1 and 2 are equvalent to the models utlsed by Hathaway and Offcer n ther 2004 study (Equaton 16 and 17), although they use frankng proporton as opposed to the frankng credt varable. 8 The Feasble Generalsed Least squares approach utlsed by Beggs & Skeels (2006) s not attempted n ths study. Gven the large multcolnearty that exsts between the frankng credt and net dvdend, an analyss of the gross dvdend s warranted. As dscussed prevously, multcolnearty s an ssue f the purpose of regresson s explanaton, not predcton. By consderng the gross dvdend, an estmate of the expected prce drop off caused by the combned package of the net dvdend and frankng credt can be obtaned. Ths allows us to predct the mpact the gross dvdend has on the stock prce, as opposed to explanng the mpact each component has on the stock prce. In order to estmate the market value of the gross dvdend, the models n table 3 are rewrtten n terms of the gross dvdend as shown n Table 4. 9 The coeffcent of the gross dvdend can be nterpreted as the Gross Drop-Off Rato (GDOR), defned n equaton (18). Here, can be nterpreted as the estmated market value of $1 of gross dvdend. Table 3 Models used n estmatng value of gross dvdend. Model Parametrc Form Scalng Factor Form of Heteroscedastcty Model 5 P P G P, c, e, ' Pc, Pc, c k P 2 2 c, Model 6 P P G D c, e, '' D D 10 k D 2 2 Model 7 P P G e, c, x, ''' D se, D se, k ( D s ) 2 2 Ds e, Model 8 P P G c, e, c, x, '''' Pc, se, Pc, se, 2 P s 2 k P s c, e, 8 It can be shown they are equal. 9 By defnton, G = FC + D D P. 10 Usng equaton (31), Model 2 can also be derved by scalng by the dvdend yeld,, c
(v) Market Returns Correcton Several DDO studes utlse an adjustment n ther study for takng nto account the market returns on the ex-dvdend day prce (Beggs & Skeels 2006, SFG 2011): P * x, x, (28) 1 P r mt, Where Px, s the prce of the stock on the ex-dvdend day, r, Index on the ex-dvdend day. mt s the return of the All Ordnares Ths assumpton assumes that each stock has a beta of 1, and returns are fully explaned by the Sharp- Lnter Captal Asset Prcng Model. Ths s an extremely strong assumpton; especally gven the dvdend sample conssts only of stocks that have a market captalsaton greater than 0.03% of the All Ordnares Index. In addton, the error term of each regresson represents all other factors that nfluence the DDO apart from the cash dvdend and the frankng credt, ncludng market fluctuatons. As a consequence, ths adjustment s unnecessary. It has been argued by Mckenze and Partngton (2010) that ths adjustment wll have no mpact on the fnal value of theta. Beggs and Skeels (2006) note that ths adjustment s mperfect, however as the adjustment s a common practce across the fnancal lterature; the adjustment s performed n order to enable comparson of results across the lterature. As a consequence, the regresson analyss wll be performed by applyng the market return correcton as well as abstanng from t. (v) Collecton of Data A lst of Australan securtes was developed by observng all securtes lsted on the Australan Stock Exchange (ASX) from 1 July 2001 up untl 1 July 2012 usng Bloomberg s equty screenng functon eqs. Only equtes lsted on the ASX were ncluded. A lst of 2,595 unque tckers was compled by observng stocks lsted on the ASX durng ths perod. Of these, anythng that was not classed as common stock was excluded. Dvdend dstrbuton events from 1 July 2001 to 1 July 2012 were obtaned usng the Bloomberg spreadsheet calculator xdvd. Any dstrbuton event that was not classed as regular cash, nterm, fnal or specal cash was removed. It s common for companes to dstrbute a specal cash dvdend n conjuncton wth a fnal or nterm dvdend. As a consequence, all dvdends that occurred on the same day for a partcular stock were aggregated. Gven that ndvdual specal cash dvdends are consdered unrelable they were removed from the sample, consstent wth other DDO studes (Beggs & Skeels 2006). In addton, companes that engaged n stock splts/share buy backs 5 days ether sde of a dvdend event where removed from the sample. Ths left a lst of 8,224 dvdend events for 827 unque tckers. The followng felds were collected for each dvdend event: The pre ex-dvdend date prce at the close of tradng 1, 2 and 3 days prevous. 11 The ex-dvdend date closng prce. 12 The gross dvdend. 13 The net dvdend. 14 11 Usng the PX_LAST feld n Bloomberg. 12 Ibd. 13 Feld part of the xdvd spreadsheet.
The market captalsaton of the underlyng stock on the ex-dvdend date. 15 The market captalsaton of the all ordnares ndex on the ex-dvdend date. 16 The currency of the dvdend event. 17 The exchange rate for the dvdend currency on the ex-dvdend date. 18 The return of the All Ordnares Index on the ex-dvdend date. 19 The cum-dvdend prce was calculated by observng the closng prce of the relevant stock on the tradng day pror to the ex-dvdend date. For example, f the ex-dvdend date fell on a Tuesday, the cum-dvdend prce would be the closng prce of the stock the prevous Monday. A stock wth an exdvdend date on Monday would have a cum-dvdend date the prevous Frday. The frankng credt for each dvdend event s the resdual between the gross dvdend and net dvdend. Any dvdend event whch had mssng data was removed from the sample. The sample was further reduced to nclude only companes that make up at least 0.03% of the All Ordnares ndex on the day of the ex-dvdend date. Ths s consstent wth other dvdend drop off studes (Beggs & Skeels 2006, SFG 2011). Any stock found to be payng a dvdend denomnated n currency other than the Australan dollar was converted to Australan dollars usng the closng prce exchange rate on the ex-dvdend date. The fnal sample contans 3,309 dvdend events. The stock return varance was estmated usng a tme seres of each stocks hstorcal prces, n addton to the hstorcal value of the All Ordnares Index. From ths the daly returns of both the stock and All Ordnares Index was calculated. The daly excess return of the stock s defned as the dfference between the stocks daly return and the return of the All Ordnares Index. The volatlty of the excess returns s calculated, over a year nterval as follows: 20 1 s er er s the estmated standard devaton of excess returns of stock over N N (, t N j 1, t 5 j t, ) 1 N N j 1 tradng days; er, t er, t days;, t, t m, t s the estmated mean of excess return of stock over N tradng er r r s the excess return of stock over the market at tme t ; stock at tme t ; r s the daly return of the All Ordnares Index at tme t. mt, r s the daly return of t, Ths s the method employed by SFG (2011) n ther DDO analyss when consderng stock return volatlty. Ths method allows for stocks volatlty above the daly market fluctuatons to be accounted for, and as such t s adopted n ths analyss. Our notaton s slghtly dfferent to avod confuson wth the varance of the error term. 14 Ibd. 15 Usng the feld n Bloomberg CUR_MKT_CAP. 16 Ibd. 17 Feld part of the xdvd spreadsheet. 18 Usng the PX_LAST feld for the gven currency. 19 Calculated by observng the prce of the all ordnares ndex on the ex-dvdend day and the prevous tradng day usng the PX_LAST feld n Bloomberg. 20 Calculated by observng all avalable excess returns wthn a one year nterval, 5 days prevous of the Ex-dvdend date.
(v) Summary of Data The data from DDO studes can be summarsed by consderng the drop-off rato, dvdend yeld and frankng proporton of each dvdend event. The drop-off rato s calculated by the change n stock prce from the close of the cum-dvdend day to the close of the ex-dvdend day, dvded by the amount of the gross dvdend. Dvdend yeld s calculated by the amount of the net dvdend dvded by the stock prce at the close of tradng on the cum-dvdend day. The frankng proporton represents the fracton of dvdends that have frankng credts attached to them. A frankng proporton of 1 ndcates that the dvdends are fully franked; a 0 frankng proporton ndcates no frankng credts are attached to dvdends. Table 5 below summarses these varables n addton to the market captalsaton and volatlty of excess returns 21 for the dvdend sample: Table 4 Summary data of the dvdend sample. Drop-off Rato Dvdend Yeld Frankng Proporton Market Cap% Volatlty of excess returns (daly) Net Dvdend Frankng Credt Mean 0.56 0.02 83.2% 0.57% 0.019 $0.27 $0.073 Medan 0.70 0.02 1 0.13% 0.018 $0.10 $0.037 Standard devaton 1.81 0.013 0.34 1.55% 0.0076 $3.35 $0.20 Mnmum -50.4 22 0.0001 0 0.03% 0.0061 $0.0025 $0.00 Maxmum 16.2 23 0.14 1 16.9% 0.11 $140 $9.65 The hstogram of the frankng proporton s shown n Fgure 1. Ths demonstrates the extreme multcolnearty present n DDO studes, as a large proporton of the sample of frankng credts are fully franked, approxmately 75% of the entre sample. Recall that as the frankng credt s a lnear functon of the net dvdend and frankng proporton (13), a wde dstrbuton of the frankng proporton s a necessary condton for low correlaton between the frankng credt and net dvdend. Gven the extreme dstrbuton of the frankng proporton below, we can conclude that ths sample s nflcted wth severe multcolnearty. The extreme multcolnearty between the net dvdend and frankng credt s confrmed by the value of the Pearson Correlaton, 0.81. As prevously dscussed, a fully franked dvdend does not contrbute any nformaton about the separate mpact a net dvdend and frankng credt has on the prce drop off. As a consequence, only the 25% of the sample that s not fully franked contans nformaton that s used to dstngush the market value of the frankng credt from the market value of the net dvdend. 21 As descrbed n paragraph 73. 22 Coal & Alled Industres pad a gross dvdend of $0.36 on 28 Feb 2008, wth the Cum-dvdend prce of $82 and an Exdvdend prce of $100. 23 NewCreast mnng pad a gross dvdend of $0.20, wth the prce fallng from $36.10 from the cum-dvdend day to $32.86 on the ex-dvdend day.
Frequency 0 500 1000 1500 2000 2500 Fgure 1 Frequency dstrbuton of frankng proporton Hstogram of Frankng Proporton 0.0 0.2 0.4 0.6 0.8 1.0 Frankng Proporton Whlst t s dffcult to vsualse multvarate data for Models 1 to 4, we can gan a general overvew of the data by plottng the prce drop off aganst the gross dvdend, dvded by the approprate scalng factor. Ths corresponds to a vsualsaton of Models 5 to 8. The graph of the relevant varables s shown below: Fgure 2 Scatter plot of prce drop-off aganst gross dvdend, scaled by cum prce (Model 5)
Fgure 3 Scatter plot of prce drop-off aganst frankng credt, scaled by net dvdend (Model 6) Fgure 4 Scatter-plot of prce drop-off aganst gross dvdend, scaled by net dvdend and volatlty (Model 7)
Fgure 5 Scatter-plot of prce drop-off aganst gross dvdend, scaled by cum-prce and volatlty (Model 8) Fgure 2, 4 and 5 demonstrates that a postve relatonshp exsts between the prce drop-off rato and the gross dvdend when scaled by the applcable varable. Ths s to be expected, gven the emprcal results of the lterature attrbutng a postve value to both the net dvdend and frankng credt. It s however hard to decpher a postve relatonshp between the prce drop-off rato and the gross dvdend when scalng by the net dvdend, as llustrated n Fgure 3. Fgure 3 reveals the extreme clusterng of the data found when usng model 2. The dependent varable can be expressed as: tc D. f FC 1 tc tc. f D D 1 tc (29) As the tax rate s constant, the dependent varable n model 2 s a lnear functon of the frankng proporton, f. Gven that the frankng proporton s between 0 and 1, clustered around whole percentages, ths results n model 2 beng clustered, explanng the clusterng found n fgure 3. Clusterng of ths form s undesrable n regresson as t results n hgh standard errors of the estmated coeffcents, n addton to beng senstve to the observatons present. (v) Statstcal Packages Used The R statstcal package has been used n order to mplement the requred regresson methodologes. OLS was performed usng the lm() functon whch s bult nto R. 24 Robust regresson was performed usng the rlm() functon found n the MASS package, usng the MM regresson settng, wth all optons set to default. 25 Least absolute devatons regresson was appled usng the rq() functon n the quantreg package, usng a value of tau=0.5. 26 24 lm() functon documentaton can be found at: http://127.0.0.1:20803/lbrary/stats/html/lm.html. 25 rlm() functon documentaton can be found at: http://127.0.0.1:20803/lbrary/mass/html/rlm.html. 26 rq() functon documentaton can be found at: http://127.0.0.1:20803/lbrary/quantreg/html/rq.html.
(V) Results The results of applyng OLS, LAD and MM robust regresson to the data set usng the models n Tables 3 and 4 are shown below. It s noted that no weght s placed on the results derved from applyng OLS to the varous models, due to the assumptons for OLS not beng met. However, as other DDO studes have utlsed OLS t s ncluded for comparson.
Table 5 Regresson results for Models 1 to 4 No Market Correcton Market Correcton Regresson Model Regresson Methodology Estmated Value of Cash Dvdend Estmated Value of Frankng Credt Standard Error of Frankng Credt Estmated Value of Cash Dvdend Estmated Value of Frankng Credt Standard Error of Frankng Credt Ordnary Least Squares 0.83 0.11 0.13 0.84 0.12 0.11 Model 1 Robust Regresson usng MM Estmator 0.84 0.35 0.09 0.90 0.30 0.08 LAD Regresson 0.84 0.38 0.16 0.90 0.29 0.08 Ordnary Least Squares 0.57 0.54 0.28 0.66 0.37 0.27 Model 2 Robust Regresson usng MM Estmator 0.77 0.39 0.11 0.85 0.35 0.11 LAD Regresson 0.77 0.53 0.16 0.83 0.44 0.15 Ordnary Least Squares 0.64 0.60 0.22 0.74 0.45 0.21 Model 3 Robust Regresson usng MM Estmator 0.79 0.44 0.11 0.86 0.39 0.10 LAD Regresson 0.79 0.49 0.15 0.87 0.38 0.13 Ordnary Least Squares 0.88-0.11 0.11 0.90-0.07 0.1 Model 4 Robust Regresson usng MM Estmator 0.87 0.32 0.09 0.92 0.33 0.08 LAD Regresson 0.86 0.33 0.15 0.94 0.21 0.12 Average (excludng OLS) 0.82 0.40-0.88 0.34 -
Table 6 Regresson results for Models 5 to 8 No Market Correcton Market Correcton Regresson Model Regresson Methodology Estmated Value of Gross Dvdend Standard Error of Gross Dvdend Estmated Value of Gross Dvdend Standard Error of Gross Dvdend Ordnary Least Squares 0.63 0.01 0.65 0.01 Model 1 Robust Regresson usng MM Estmator 0.68 0.01 0.73 0.01 LAD Regresson 0.70 0.01 0.73 0.01 Ordnary Least Squares 0.56 0.03 0.58 0.03 Model 2 Robust Regresson usng MM Estmator 0.68 0.01 0.71 0.01 LAD Regresson 0.70 0.01 0.72 0.01 Ordnary Least Squares 0.63 0.02 0.66 0.02 Model 3 Robust Regresson usng MM Estmator 0.69 0.01 0.73 0.01 LAD Regresson 0.70 0.01 0.73 0.01 Ordnary Least Squares 0.60 0.01 0.62 0.01 Model 4 Robust Regresson usng MM Estmator 0.72 0.01 0.76 0.01 LAD Regresson 0.70 0.01 0.73 0.01 Average (excludng OLS).70-0.73 -
The robust MM estmaton method produces an estmate of the frankng credt between 0.32 to 0.44, whlst applyng the market correcton produces a robust MM estmaton of between 0.30 to 0.39. LAD regresson produces an estmate of the frankng credt between 0.33 to 0.53 and usng the market correcton produces estmates between 0.21 to 0.44. Wth the excepton of OLS, the results of applyng robust MM regresson and LAD regresson to the gross dvdend models show only a small varaton, between 0.68 and 0.72. The varaton between the models and regresson types for the estmated value of the gross dvdend s consderably less than the varaton n the estmated value of the frankng credt. Whlst not drectly comparable, the standard error of the estmate of theta tends to be lower for robust MM regressons than for LAD regressons. Producng estmates of confdence ntervals and p-values, as s standard n statstcal analyss, s not approprate for LAD and MM regresson. Dong so requres strong assumptons on the asymptotc dstrbuton of the regresson coeffcents and standard 2 errors, whch could gve msleadng results. The coeffcent of determnaton, R, quoted n other dvdend drop off studes s also napproprate as a measure of model relablty gven that OLS models wll always maxmse ths statstc. However, as OLS s napproprate n DDO studes, the coeffcent of determnaton s also napproprate as a measure of model relablty. Varance nflaton factors are also quoted when data s nflcted wth multcolnearty, n order to gauge the mpact multcolnearty has on the estmated regresson coeffcents. Gven that ths s only approprate for OLS models, varance nflaton factors are not calculated. The mproved confdence n the estmaton of the market value of the gross dvdend over the frankng credt can be seen by the comparatvely smaller standard errors of the regresson coeffcents. Ths confrms the mpact of multcolnearty; on average we expect $1 of gross dvdend to cause a reducton n prce from the cum-dvdend prce to the ex-dvdend prce of $0.70. However t s dffcult to solate the contrbuton of the net dvdend and the frankng credt to the prce-drop off, wth the market value of the frankng credt varyng substantally between models and regresson procedures employed. Interestngly, the use of the market correcton results n a sgnfcant reducton n the estmate of theta, contradctng Mckenze and Partngton (2010) and the analyss conducted by Skeels (2009) n analyss of SFG s frst report. The market value of the gross dvdend generally ncreases upon applcaton of the market correcton. () DFBETAS (VI) Senstvty Analyss It s undesrable that the estmates of theta show consderable varaton across the dfferent models. Ths varaton s compounded further f the market correcton s utlsed. It s valuable to nvestgate the mpact on the estmate of theta on removng sgnfcant observatons from the data set. Ths analyss was performed n order to ascertan the senstvty of the estmates to changes n the underlyng sample of dvdend events. As noted prevously, DDO studes are extremely senstve to the choce of the underlyng sample of dvdend events. As a consequence, t s necessary to use a statstcal crteron n order to assess the mpact that each observaton has on the estmated value of theta. In partcular, how would removng a specfc dvdend event mpact the estmated value of theta? The DFBETAS crteron s approprate as by defnton chooses the pont that has the most mpact on the value of a regresson coeffcent. It s also applcable across a range of dfferent regresson methodologes, unlke other crterons such as Cooks Dstance. DFBETAS s a standardsed measure of the amount by whch a regresson coeffcent changes f a partcular observaton s removed. Formally, DFBETAS k s the standardsed measure of the amount,