Estimating the Utilisation of Franking Credits through the Dividend Drop- Off Method

Transcription

1 Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop- Off Method Basc statstcal dagnostcs and alternatve models Stefan Mero, Rohan Sadler and Rchard Begley Secretarat Workng Paper 9 February 2017 Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method

2 200x> Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method

3 Economc Regulaton Authorty 4th Floor Albert Facey House 469 Wellngton Street, Perth Mal to: Perth BC, PO Box 8469 PERTH WA 6849 T: F: E: W: Natonal Relay Servce TTY: (to assst people wth hearng and voce mparment) We can delver ths report n an alternatve format for those wth a vson mparment Economc Regulaton Authorty. All rghts reserved. Ths materal may be reproduced n whole or n part provded the source s acknowledged. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method

4 Contents Executve Summary 1 Further Informaton 3 1 Introducton 4 2 The Dvdend Drop-off Study Framework 7 3 Addressng ssues rased by SFG and Fronter Consultng Market corrected data and senstvty analyss What do the senstvty analyses tell us? 12 4 Are the models that produce the theta estmates meanngful? 15 5 Better fttng models 25 6 Concluson 34 Appendx 1 Models for the Estmaton of θ 36 Appendx 2 Regresson Dagnostcs 39 Potental Issues n Regresson Modellng 39 Outlers 39 Multcollnearty 40 Nonlneartes 41 Heteroskedastcty 41 SFG and Fronter s Senstvty Analyss 42 DFBETAs 42 Crtque of the DFBETAs Stablty Analyss 44 Robust Models 49 Heteroskedastcty 55 Dfferences n Estmates of θ 60 Dfferences n the Standard Error of θ 62 Appendx 3 Alternatve Models 66 Broken-Stck Model 67 Defnton 67 Results and Dscusson 67 Fnte Mxture-of-Regressons 72 Defnton 72 Results and Dscusson 73 An Interacton Model 76 Defnton 76 Results and Dscusson 76 Conclusons 79 Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method

5 Tables Table 1 Ramsey RESET tests of model specfcaton error 16 Table 2 Breusch-Pagan Test for Heteroskedastcty n resduals from OLS/MM regressons 17 Table 3 Measures of dstrbuton shape of model resduals 21 Table 4 Jarque-Bera tests of normalty n the dstrbuton of regresson resduals 22 Table 5 Kolmogorov-Smrnov tests for changes n dstrbuton of resduals 25 Table 6 Model 1 - Broken-stck model theta estmates 27 Table 7 Model 4 - Broken-stck model theta estmates 28 Table 8 Interacton model results based on market corrected data 29 Table 9 Skewness and kurtoss n resduals of orgnal and addtonal models 30 Table 10 Breusch-Pagan tests for heteroskedastcty n orgnal and addtonal models 31 Table 11 Summary of the models and the outcomes of the dagnostcs on ther resduals ranked from uncertan to relatvely more uncertan 32 Table 12 Parametrc form of DDO equatons used by SFG for estmaton of theta. 38 Table 13 Percentage overlap n outlers: SFG versus standard DFBETAs procedure 46 Table 14 Statstcs descrbng the bootstrapped dstrbuton of θ 53 Table 15 Varance nflaton factors for the varous scalng factors. 55 Table 16 Breusch-Pagan (BP) tests for heteroskedastcty n OLS models. 57 Table 17 Skewness and kurtoss of resduals from the dfferent OLS models. 58 Table 18 Mean θ as a functon of scalng factor components and estmaton method 60 Table 19 Mean θ as a functon of estmaton method and market correcton 60 Table 20 Mean θ as a functon of scalng factor components and market correcton 61 Table 21 Mean standard error of θ as a functon of scalng factor and estmaton method 62 Table 22 Table 23 Table 24 Mean standard error of θ as a functon of estmaton method and market correcton 62 Mean standard error of θ as a functon of scalng factor components and market correcton 62 Summary of volatons of the standard lnear model for the DDO model gven dfferent scalng factors 64 Table 25 Broken-stck estmates of θ for non-market corrected data 70 Table 26 Broken-stck estmates of θ for market corrected data 71 Table 27 Mxture-of-regresson results 74 Table 28 Interacton model results 78 Table 29 Estmates of θ as a functon of the quantles of the scaled net dvdend, appled to the market corrected data 79 Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method

6 Fgures Fgure 1 Senstvty analyss of OLS theta estmates wth and wthout market correcton 10 Fgure 2 Senstvty analyss of MM theta estmates wth and wthout market correcton 11 Fgure 3 Senstvty analyss of LAD theta estmates wth and wthout market correcton 11 Fgure 4 Parwse vs one-at-a-tme removal n stablty tests on model 3 OLS estmates 14 Fgure 5 Fgure 6 Model 4 MM regresson resduals plotted aganst correspondng frankng credt values (market corrected data) 18 Model 4 OLS regresson resduals plotted aganst correspondng frankng credt values (market corrected data) 19 Fgure 7 Dstrbuton of Model 4 MM regresson resduals based on market corrected data 20 Fgure 8 Fgure 9 Fgure 10 Dstrbuton of Model 4 OLS regresson resduals based on market corrected data 21 Model 1 OLS regresson resduals plotted aganst correspondng frankng credt values (market corrected data) 23 Comparson of resdual dstrbuton between lower and upper half of resdual sample based on frankng credt value - Model 1 OLS regresson resduals 24 Fgure 11 Stablty analyses on postvely skewed smulated data 47 Fgure 12 CPR Plots for the OLS estmaton of Model 1: market corrected data 50 Fgure 13 CPR Plots for the MM estmaton of Model 1: market corrected data 51 Fgure 14 Scale-locaton plots for the market corrected Models Fgure 15 CPR Plots for the broken-stck model appled to the market corrected Model 1 69 Fgure 16 CPR Plots for the broken-stck model appled to the market corrected Model 4 69 Fgure 17 CPR plots for mxture-of-regressons appled to the market corrected data 75 Fgure 18 Estmates of θ for the market corrected model 4 as a functon of the quantles of the scaled net dvdend 80 Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method

7 Executve Summary Gamma s a parameter whch accounts for that part of the return on equty that s realsed through mputaton credts an nvestor receves on ther tax return. As a general rule, nvestors who are able to utlse frankng credts wll accept a lower requred rate of return, before personal tax, on an nvestment that has frankng credts, compared wth an nvestment that has smlar rsk and no frankng credts, all other thngs beng equal. The Economc Regulaton Authorty (ERA) n ts decsons has consdered that the beneft arsng from mputaton credts, gamma, can be nterpreted as the proporton of frankng credts that are dstrbuted, multpled by the proporton of these, theta, that are utlsed by the representatve nvestor. The ERA n recent decsons has consdered three dfferent approaches to estmatng the utlsaton rate, theta: the equty share approach; the taxaton statstcs approach; and the dvdend drop-off method. Ths Secretarat Workng Paper s concerned wth the statstcal aspects of the dvdend drop-off method. It explores some recent crtcsms of the ERA s approach to dvdend dropoff estmaton, and s ntended to advance the debate n ths area. Specfcally, the valdty of the dvdend drop-off (DDO) approach has been an mportant focus for recent debates about valung gamma n a regulatory settng. For example, n ts 2013 Rate of Return Gudelnes, the ERA reled on the 2013 Vo, D., Gellard, B., Mero, S. conference paper on Estmatng the Market Value of Frankng Credts, when establshng ts range for theta to apply n ts gas decsons. Ths paper concluded that the state-of-theart theta estmates of the tme whch were based on the models orgnally used by SFG Consultng n a seres of estmatons undertaken n 2012 were hghly unstable. Subsequently, n March 2014, SFG Consultng was retaned and nstructed by Aurzon Network to provde ts vew on ssues relatng to the estmaton of gamma, ncludng those relatng to the stablty of dvdend drop-off estmates of theta, whch were rased n Vo et al. s study. Ths SFG Consultng report contended that the analyss of Vo et al was nonstandard, and hence flawed, because: the stablty analyss dd not apply a correcton for broader market movements to the data; and t mplemented a stablty analyss where data observatons beleved to be nfluental were removed one-at-a-tme, nstead of n pars. Further, n December 2014, DBP submtted to the ERA a report prepared by SFG Consultng n response to an nvtaton for submssons on the ATCO Gas Draft Decson. Ths report rased the same techncal ssues related to the Vo et al. stablty analyss as had been rased n SFG s report prepared for Aurzon n March SFG also emphassed that t had submtted ts results to an expanded set of stablty tests. Most recently, n March 2016 Fronter Economcs submtted a further report to the ERA on ssues n relaton to the regulatory estmate of gamma on behalf of Damper Bunbury Ppelne. Ths report presented smlar materal to that set out n SFG Consultng s prevous reports. Specfcally, t rased the same techncal ssues related to the Vo et al. stablty Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 1

8 analyss and agan emphassed that SFG s theta estmates are relable and stable n lght of the tests undertaken n a report for APA Group. Ths study examnes the crtcsms of Vo et al. made by SFG Consultng/Fronter, fndng that: generally, all theta estmates based on the market corrected data tend to fluctuate around a lower value, wth a smaller range, than estmates based on uncorrected data; however, SFG s asserton that a falure to apply the market correcton to the data results n relatvely unstable theta estmates s only mnmally supported by the analyss; - the scale of fluctuaton n the results, wth the market corrected data, tends to reman large relatve to the value of the theta estmate; accordngly, the results wth the market corrected data are not stable, as they change consderably, dependng on the model and regresson technque chosen; further, removng nfluental observatons n pars, as s done by SFG, nstead of one-at-a-tme, as s done by Vo et al, nduces smoothness, whch falsely ncreases the appearance of stablty n the theta estmates. More mportantly, whle SFG/Fronter have pad consderable attenton to these stablty analyses, they have done so wthout consderng more commonly used econometrc dagnostcs. Ths study apples these econometrc dagnostcs to SFG/Fronter s models. The results of the dagnostcs show that SFG/Fronter s models are a very poor ft on the data. Applyng better fttng models can produce much hgher estmates of theta than those proposed by SFG/Fronter. Despte fndng superor fttng models, all dvdend drop-off models stll ft the data very poorly, renderng theta estmates from the dvdend drop-off method hghly uncertan. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 2

9 Further Informaton Further nformaton regardng ths report can be obtaned from: Stefan Mero Regulaton and Inqures Dvson Economc Regulaton Authorty Ph (08) Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 3

10 1 Introducton 1. Gamma s a parameter n the Weghted Average Cost of Captal that accounts for that part of the return on equty that s realsed through mputaton credts an nvestor receves on ther tax return. As a general rule, nvestors who are able to utlse frankng credts wll accept a lower requred rate of return, before personal tax, on an nvestment that has frankng credts, compared wth an nvestment that has no frankng credts (all other thngs beng equal). 2. The Economc Regulaton Authorty (ERA) estmates gamma ( ) as the product of the dstrbuton rate F and the estmate of the utlsaton rate (theta): 1 F (1) 3. The beneft arsng from mputaton credts s nterpreted as the proporton of frankng credts dstrbuted ( F ) multpled by the proporton of these that are utlsed by the representatve nvestor ( ). 2 The ERA s nterpretaton s consstent wth that of the Australan Energy Regulator, whch descrbes the utlsaton rate as the utlsaton value to nvestors n the market per dollar of mputaton credts dstrbuted The ERA n recent decsons has consdered three dfferent approaches to estmatng the utlsaton rate, theta: 4 the equty share approach; the taxaton statstcs approach; and the dvdend drop-off method. 5. Ths paper s concerned wth the statstcal aspects of the dvdend drop-off method for estmatng the utlsaton rate. 5 Issues relatng to whether dvdend drop-off studes correctly estmate theta as defned are not examned n ths statstcal revew. The ERA has observed that dvdend drop-off studes may not correctly estmate the utlsaton rate. Ths means that theta ( ), whch s estmated n the dvdend dropoff framework set out n ths study, s not necessarly the same theta that s expressed n equaton (1). 6. Dvdend drop-off studes observe the change n the prces of stocks when they go from tradng cum-dvdend, where the current holder s enttled to the dvdend, to 1 Ths follows the analyss by Monkhouse n relaton to the mpact of mputaton credts on the effectve tax rate of companes. See equaton 2.5 n P. Monkhouse, The valuaton of projects under the dvdend mputaton tax system, Accountng and Fnance, 36, 1996, p. 192; Goldfelds Gas Ppelne, Access Arrangement Revson Proposal: Supportng Informaton, 15 August 2014, Appendx 1. 2 Economc Regulaton Authorty, Fnal Decson on Proposed Revsons to the Access Arrangement for the Damper to Bunbury Natural Gas Ppelne , Appendx 5 Gamma, 30 June 2016, p Australan Energy Regulator, AusNet Servces dstrbuton determnaton fnal decson , Attachment 4, p For a detaled consderaton of each approach, see Economc Regulaton Authorty, Fnal Decson on Proposed Revsons to the Access Arrangement for the Damper to Bunbury Natural Gas Ppelne , Appendx 5 Gamma, 30 June See Economc Regulaton Authorty, Fnal Decson on Proposed Revsons to the Access Arrangement for the Damper to Bunbury Natural Gas Ppelne , Appendx 5 Gamma, 30 June 2016, pp ). Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 4

11 tradng ex-dvdend, where any new holder of the stock s no longer enttled to the dvdend yet to be pad. The dea behnd these studes s that the observed change n prce should reflect the market s value attached to the gross dvdend beng pad. 7. However, the gross dvdend conssts of both cash (or net ) dvdends and company tax pad on the gross dvdend. The franked proporton of gross dvdends return the tax pad to nvestors n the form of mputaton credts. Econometrc regresson technques are employed to quantfy the change n prce across a sample of stocks and estmate the quantty of the change that can be attrbuted to net dvdends and mputaton credts. Theta ( ) s the proporton of prce change attrbutable to gross dvdend payment that s n turn, attrbuted to mputaton credts. 8. In ts Rate of Return Gudelnes the ERA reled on dvdend drop-off studes undertaken by both Vo et al and SFG Consultng to establsh a permssble range for theta of Vo et al. s dvdend drop-off study rased ssues relatng to the stablty of estmates produced by the technque employed by SFG. Vo et al. s study tested stablty usng a method that sequentally removes an ncreasng number of nfluental data ponts, re-estmatng theta each tme a data pont s removed. The results ndcated that dvdend drop-off estmates of theta are senstve to ncluson or excluson of a small number of hghly nfluental observatons. 9. In March 2014, SFG Consultng was retaned and nstructed by Aurzon Network to provde ts vew on ssues relatng to the estmaton of gamma, ncludng those relatng to the stablty of dvdend drop-off estmates rased n Vo et al. s study. 7 Ths report proposed that the analyss of Vo et al was non-standard because: the stablty analyss dd not apply a correcton for broader market movements to the data; and t mplemented a stablty analyss where data observatons beleved to be nfluental were removed one-at-a-tme, nstead of n pars The market correcton ssue relates to the preparaton of the prce data used n the dvdend drop-off analyss. Some of the change between cum-and ex-dvdend prce wll stem from movement n the stock market as a whole. To factor the market movement out of the prce change, market returns are dscounted out of ex-dvdend prces. SFG Consultng s report to Aurzon, to some extent, attrbutes Vo et al. s fndng of nstablty n estmates to the omsson of applyng a market correcton to the data The ssue relatng to parwse removal of observatons concerns the applcaton of the stablty test n Vo et al. As mentoned above, the Vo et al study tested stablty by removng an ncreasng number nfluental data ponts, and re-estmatng theta each tme a data pont s removed. Ths method begns by detectng the most nfluental observaton through a DFBETAs statstc, remove ths observaton from the sample, 6 Economc Regulaton Authorty, Explanatory Statement for the Rate of Return Gudelnes, 16 December 2013, pp Vo, D., Gellard, B., Mero, S., Estmatng the Market Value of Frankng Credts, Emprcal Evdence From Australa Conference Paper, Australan Conference of Economsts SFG Consultng, Dvdend drop-off estmate of theta, Fnal Report, 21 March SFG Consultng, Estmatng Gamma: Report for Aurzon Network, 6 March 2014, p.1. 8 Ibd, pp Ibd, p.11. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 5

12 and then re-estmate theta. Ths process s repeated one observaton at a tme untl 30 observatons were removed. 12. SFG have mplemented tests that remove outlers and then re-estmate theta n a number of dfferent ways. One of ther methods for testng stablty nvolves removng observatons n pars nstead of one-at-a-tme. The pars consst of observatons where the frst observaton has the most nfluental upward effect on the estmate of theta, and the second observaton has the most nfluental downward effect on the estmate. SFG Consultng s report to Aurzon concludes that the fndng of nstablty n estmates s lkely to be manfest n the Vo et al. non-standard approach appled In December 2014, DBP submtted a report prepared by SFG Consultng to the ERA n response to an nvtaton for submssons on the ATCO Gas Draft Decson. Ths report rased the same market correcton ssue dscussed n SFG s report prepared for Aurzon n March In relaton to the stablty analyss, SFG emphassed that t had subjected ts results to an expanded set of stablty tests. It appears that SFG was makng reference to ts report prepared n May 2014 on behalf of APA, and submtted as part of the proposed revsons to the Goldfelds Gas Ppelne access arrangement. In ths report, SFG submtted that t appled the one-at-a-tme nfluental observaton approach that Vo et al. used n ther study and n addton conducted a randomsed bootstrappng analyss. Ths analyss randomly elmnates 5 per cent of the data and re-estmates theta. The procedure s repeated 1000 tmes to produce a dstrbuton for theta estmates. 11 SFG concludes that ths analyss corroborates the stablty and nsenstvty of ts theta estmates to the removal of outlers. 14. In March 2016 Fronter Economcs submtted a report on ssues n relaton to the regulatory estmate of gamma behalf of DBP. Ths report submtted the materal presented n SFG Consultng s prevous reports. Specfcally, t rased the market correcton ssue and agan emphassed that SFG s theta estmates are relable and stable n lght of the tests undertaken n ts report for APA n May Ths study seeks to address the ssues orgnally rased n SFG s report prepared for Aurzon n March The mpact of the market correcton on Vo et al. s senstvty analyss s assessed by comparng the orgnal results wthout the market correcton to results based on the orgnal data that nclude the market correcton. It demonstrates that there are other statstcal ssues affectng certanty around theta estmates that are more mportant than the market correcton. 16. The effect of perceved outlers on estmates of theta have been a man pont of contenton. Ths study assesses the value of senstvty analyses whch repeatedly remove what are beleved to be outlers and re-estmate theta. More meanngful tests are then appled to the dvdend drop-off study methods employed by both Vo et al and SFG to determne whether the methods volate standard statstcal assumptons. Ths study then moves on to demonstrate that, n the face of non-normally dstrbuted data, model specfcaton combned wth choce of estmaton method s the prmary 10 Ibd, p SFG Consultng, An approprate regulatory estmate of gamma: Report for Jemena Gas Networks, ActewAGL, APA, Networks NSW (Ausgrd, Endeavour Energy and Essental Energy), ENERGEX, Ergon, Transend, TransGrd and SA Power Networks, 21 May 2014, pp Fronter Economcs, Issues n relaton to the regulatory estmate of gamma: A report prepared for DBP, March SFG Consultng, Estmatng Gamma: Report for Aurzon Network, 6 March 2014, p.1. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 6

13 drver of dfferences and thus uncertanty n dvdend drop-off analyss results. The ssue of assessng the ft of a specfed model s addressed and an estmate of theta based on a better fttng model s produced. 2 The Dvdend Drop-off Study Framework 17. The basc model employed n dvdend drop-off studes s shown n equaton (2). Where: P Net Dvdend Frankng Credt (2) P s the change n the prce across the cum-and ex-dvdend date of a gven stock ; s the change n P per dollar change n net dvdend; Net Dvdend s the sze of the net dvdend credted to the holder of stock at a gven on the cum-dvdend date; (theta) s the change n P per dollar change n frankng credt; Frankng Credt s the sze of the frankng credt that s credted to the holder of stock on the cum-dvdend date; and t,. s the error between the regresson predcton and observaton on stock. 18. Ths equaton expresses the change n stock prces between the cum-and ex-dvdend date as reflectng the net or cash dvdend, frankng credt measured on observed data wth some random error (whch s zero on average). Ths model s typcally mplemented n a statstcal regresson framework. Ex-and cum-dvdend date prce data s observed on a number of stocks across a number of dvdend payment events for each stock through tme. Ths s then regressed on the correspondng observatons of net dvdend and frankng credt data n order to estmate the parameters and whch are nferred to be the market value of the net dvdend end and frankng credt, respectvely The standard regresson method s ordnary least squares (OLS). OLS reles on the assumpton, among others, of a constant varance n the error terms t, (no heteroskedastcty). When ths assumpton s volated the estmated standard errors from the model used to test the statstcal sgnfcance of estmated parameters tend to be too small, resultng n a falure to correctly conclude parameters are not statstcally dfferent from zero (type I error). The prce data used n the dvdend drop- 14 As noted above, ssues relatng to whether dvdend drop-off studes correctly estmate theta as defned are not examned n ths statstcal revew. The ERA has observed that dvdend drop-off studes may not correctly estmate the utlsaton rate (Economc Regulaton Authorty, Fnal Decson on Proposed Revsons to the Access Arrangement for the Damper to Bunbury Natural Gas Ppelne , Appendx 5 Gamma, 30 June 2016, pp ). Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 7

14 off studes tend to exhbt non-constant varance (heteroskedastcty). Ths means the estmated parameters and may produce estmates that appear statstcally dfferent from zero when n fact, ths s not the case. Varous reasons for the observed heteroskedastcty have been posted, however t appears no consensus has been reached as to the exact causes SFG s approach attempts to address the heteroskedastcty ssue by specfyng four addtonal forms of the model shown n equaton (2). 16 Ths approach scales the observatons of varables used n the model by dvdng them through varables beleved to be related to potental patterns observed n the (non-constant) varance, thereby removng those patterns to produce constant varance. 21. The four models are shown below. P Net Dvdend Frankng Credt (3) P P P Cum, Cum, Cum, 22. The model shown n equaton (3) assumes varance s related to cum-dvdend prces. Dvdng each term by cum-dvdend prce expresses all of the varables n n the regresson terms of yeld on the cum-dvdend prce. Ths s referred to as model 1 n ths study. P Net Dvdend Frankng Credt (4) Net Dvdend 23. The model shown n equaton (4) assumes varance s related to the net dvdend. Note the net dvded dsappears from the rght sde of the equaton as a result of beng dvded by tself. Ths s referred to as model 2 n ths study. P Net Dvdend Frankng Credt (5) Net Dvdend 24. The model shown n equaton (5) assumes that varance s related to the standard devaton of stock s returns n excess of the market return ( ). 17 Ths s referred to as model 3 n ths study. 15 The sze of varance n the error terms may be related to the net dvdend and frankng credt, but not detected as havng a relatonshp wth the prce drop-off because they are related to absolute sze of the drop-off as opposed to the sgn of the drop-off. Another hypothess s that larger companes tend to trade more frequently and so have lower varance n ther error terms that can stem from sporadc prcng n less traded smaller stocks. See Beggs and Skeels, Market Arbtrage of Cash Dvdends and Frankng Credts, The Economc Record, vol.82, no.258, 2006, p SFG Consultng, Dvdend drop-off estmate of theta, Fnal Report, 21 March 2011, pp N : ( t, ), t er er N, t5j j1 N tradng days. 1 er, t : er, t, t, t m, t N j 1 s the estmated standard devaton of excess returns of stock over N s the estmated mean of excess return of stock over N tradng days. er : r r s the excess return of stock over the market at tme t. tme t. r s the return of stock at t, r s the return of the All Ordnares Index at tme t. More detals are gven n Appendx 1. mt, Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 8

15 P Net Dvdend Frankng Credt (6) P P P Cum, Cum, Cum, 25. The model shown n equaton (6) assumes that varance s related to the cum-dvdend date prce multpled by the standard devaton n excess returns. Ths s referred to as model 4 n ths study. 26. The ERA n ts 2013 Rate of Return Gudelnes reled upon Vo et al. n estmatng parameters for all four of these specfcatons. 27. A number of dfferent lnear regresson methods can be, and have been, used to estmate the parameters and n these models. These methods nclude OLS, MM robust regresson (MM) and least absolute devaton (LAD) regresson. The robust regresson methods have been appled by SFG and Vo et al. n an attempt to mtgate the nfluence of what are perceved to be outlers n the regresson. 3 Addressng ssues rased by SFG and Fronter Consultng 3.1 Market corrected data and senstvty analyss 28. As outlned n the ntroducton, SFG Consultng have rased concerns that the stablty analyss of Vo et al., reled upon by the ERA n ts 2013 Rate of Return Gudelnes, dd not apply a correcton for broader market prce movements to the data. 18 Vo et al. appled ths stablty analyss to show that removng a very small number of outlers can vary the estmate of theta from 0.3 to Ths was stll the case when robust regresson technques were appled. 29. SFG and Fronter Economcs partly attrbutes Vo et al. s fndng of nstablty n estmates of theta to the omsson of applyng ths market correcton to the data. 30. The market correcton of data s appled as shown n equaton (7). Where: P P Adjust Ex, Ex, (7) 1 rm, P Ex, s the prce of stock on the ex-dvdend day at tme t ; and r m, s the daly return on the All Ordnares ndex on the ex-dvdend date. 31. To test SFG s asserton, that a falure to apply ths market correcton results n nstablty n theta estmates, the same stablty tests on the same data set n the Vo et al. analyss are undertaken below, but wth the market correcton appled. These results are compared to the orgnal results below. 18 Vo, D., Gellard, B., Mero, S., Estmatng the Market Value of Frankng Credts, Emprcal Evdence From Australa Conference Paper, Australan Conference of Economsts Ibd, p.31 Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 9

16 32. Fgure 1 compares the results of senstvty analyss appled n Vo et al. based on the OLS regresson estmates. The senstvty analyss removes the most nfluental data ponts and re-estmates theta 30 tmes to observe the consequent effect on theta. Data ponts are classfed as nfluental accordng to the DFBETAs crteron (see Appendx 2 for techncal detals). Ths s a standardsed measure of the amount by whch a regresson coeffcent, such as theta, changes f a partcular observaton s removed. Each teraton on the x axs s a re-estmate of theta. Each of the four models for estmatng theta outlned n chapter 2 are shown n ther respectve panels. 33. These results nclude those based on market corrected data, whch tend to fluctuate wthn a reduced range, as compared to those based on uncorrected data. The estmates based on market corrected data also tend to fluctuate around a lower estmate of theta than the estmates based on the orgnal data. Fgure 1 Senstvty analyss of OLS theta estmates wth and wthout market correcton Source: ERA Analyss 34. Fgure 2 compares the results of the MM regresson estmates. In ths case, wth the excepton of model 2, the results based on market corrected data tend to fluctuate wthn a reduced range. The estmates based on market corrected data, agan, also tend to fluctuate around a lower estmate of theta than the estmates based on the orgnal data. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 10

17 Fgure 2 Senstvty analyss of MM theta estmates wth and wthout market correcton Source: ERA Analyss 35. Fgure 3 compares the results of the LAD regresson estmates based on data wth no market correcton to results based on data that ncorporates the market correcton. Vo et al. dd not report LAD stablty test results for models 3 and 4. Fgure 3 Senstvty analyss of LAD theta estmates wth and wthout market correcton Source: ERA Analyss 36. The concluson drawn from Fgure 1 and Fgure 2 can be also be drawn from Fgure 3. The results based on market corrected data tend to fluctuate wthn a reduced range and around a lower estmate of theta. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 11

18 37. Applcaton of the market correcton to the data seeks to control for market wde effects n the drop-off. However, SFG s asserton that a falure to apply the market correcton to the data results n nstablty n theta estmates s only mnmally supported by the analyss above. 38. Wth the excepton of the model 2 MM estmate, all theta estmates based on the market corrected data tend to fluctuate around a smaller range than estmates based on uncorrected data. However, the scale of fluctuaton tends to reman large relatve to the value of the theta estmate. 39. Moreover, t s evdent from the fgures above that the results are not stable from the perspectve that they change consderably dependng on the model and regresson technque chosen. The most stable estmate n the analyss above s the LAD estmate based on model 2 (Fgure 3), however, changng from model 2 to model 1 results n greater fluctuaton n the estmate around a lower level of theta. The fluctuaton ncreases wth MM and OLS estmates. Ths rases two questons. Frstly, what does the senstvty analyss tell us? Secondly, what model and regresson technque s the most approprate? 3.2 What do the senstvty analyses tell us? 40. The senstvty analyses appled by SFG and subsequently Vo et al. nvolve removng outlers and re-estmatng theta to observe the consequent effect on theta. These tests have been mplemented n a number of ways ncludng: comparng estmates of theta before and after removng the most nfluental 1 per cent of observatons; 20 parwse removal; 21 one-at-a-tme removal; 22 and bootstrappng (smulatng dstrbutons) removng 5 per cent of data Comparng estmates of theta before and after removng the most nfluental 1 per cent of observatons uses 'Cook's dstance' to measure and rank the nfluence of observatons n the data set on the fnal parameter estmates. Cook's dstance measures the effect of removng a gven observaton on estmates of the regresson parameters. The most nfluental one per cent of observatons n terms of Cook s dstance are removed from the data set (all at once) and theta s re-estmated. 20 SFG Consultng, The mpact of frankng credts on the cost of captal of Australan companes: Report prepared for Envestra, Multnet and SP Ausnet, 25 October SFG Consultng, Dvdend drop-off estmate of theta, Fnal Report, 21 March 2011, p SFG Consultng, An approprate regulatory estmate of gamma: Report for Jemena Gas Networks, ActewAGL, APA, Networks NSW (Ausgrd, Endeavour Energy and Essental Energy), ENERGEX, Ergon, Transend, TransGrd and SA Power Networks, 21 May 2014, p. 95. Vo, D., Gellard, B., Mero, S., Estmatng the Market Value of Frankng Credts, Emprcal Evdence From Australa Conference Paper, Australan Conference of Economsts 2013, p SFG Consultng, An approprate regulatory estmate of gamma: Report for Jemena Gas Networks, ActewAGL, APA, Networks NSW (Ausgrd, Endeavour Energy and Essental Energy), ENERGEX, Ergon, Transend, TransGrd and SA Power Networks, 21 May 2014, p. 98. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 12

19 42. Parwse removal of observatons frst determnes whch sngle observaton, f removed, would result n the greatest ncrease n the estmate of theta (see Appendx 2 on SFG and Fronter s stablty analyss for further dscusson). Next t determnes whch sngle observaton, f removed, would result n the greatest decrease n the estmate of theta. Both observatons are then removed and theta s re-estmated. Ths process s repeated by removng another par of observatons reestmatng theta. Ths contnues untl 25 pars of observatons have been removed n total. The parameter estmates are then plotted sequentally on a graph n the same way as shown n secton As shown and dscussed n secton 3.1, one-at-a-tme removal of observatons uses the DFBETAs crteron to dentfy nfluental data ponts nstead of other measures such as Cook s dstance. DFBETAs s a standardsed measure of the amount by whch a regresson coeffcent changes f a partcular observaton s removed. 24 The parameter estmates are then plotted sequentally on a graph n the same way as shown n secton Bootstrappng smulates a dstrbuton for the theta parameter. A random fve per cent of the data sample s elmnated, wth theta re-estmated from the remanng 95 per cent of the observatons. Ths process s repeated 999 tmes to create 1000 estmates of theta (by ncludng the full sample estmate). The resultant bootstrapped estmates are plotted as a hstogram to show the dstrbuton of the estmates. 45. The tests based on one-at-a-tme and parwse removal of observatons descrbed above are typcally employed to address concerns that a tme seres model s parameters may be dfferent durng a forecast perod to what they are durng the sample perod. Use of such tests n the current context of estmatng theta, whch s based on observatons on a cross-secton of stocks, s unusual. 25 In ths context the movement n the sequental plot of recursve estmates reflects removal of data that least comply wth the assumed ft. 46. For OLS regresson, greater movement n the stablty plots wll tend to ndcate a poorer fttng model. Ths s because the OLS regresson method does not downweght extreme data ponts n the model fttng process and takes them nto account to provde the best ft. For ths reason, the removal of extreme data ponts wll have a stronger effect on the OLS ft and theta estmate than for MM and LAD regresson, whch are desgned to mtgate the effect of extreme data ponts. When the model s a poor ft to the data, removng several of the most extreme data ponts wll tend to alter ths ft and theta estmate, more so than the removal of less extreme data ponts. Each subsequent pont removed wll tend to have less of an mpact on the ft (and thus theta parameter), gvng the mpresson of stablty. If a large proporton of extreme observatons n the sample have been removed by a flterng process pror to ths type of stablty test then the plots are lkely to converge and stablse more quckly. 47. The plot of robust regresson estmates (MM and LAD) derved from recursvely removed data wll provde an mpresson of greater stablty than OLS. Ths s because these regresson methods down-weght, and hence mtgate, the effect of extreme data ponts wth each sequental theta estmate. The recursve plots based on MM and LAD regresson are therefore predsposed to show a lack of movement by already 24 Techncal detals are gven n Appendx 2 n the secton on SFG and Fronter s stablty analyss. 25 Whle the observatons used n the theta regressons span a perod of tme, the models themselves do not ncorporate changes n tme reflected n the data. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 13

20 beng relatvely nsenstve to extreme data ponts. Ths relatve nsenstvty of robust regresson estmates s evdent n the comparson of Fgure 2 and Fgure 3 to Fgure 1. The estmates based on OLS n Fgure 1 fluctuate substantally, whle the MM and LAD estmates n Fgure 2 and Fgure 3 fluctuate less so. 48. Removng pars of observatons wth offsettng mpacts on theta tends to smooth the stablty plots. The effect of usng parwse removal versus one-at-a-tme removal s shown n Fgure 4. More techncal detals regardng the smoothng effect of parwse removal can be found n Appendx 2 n the secton Crtque of the DFBETAs Stablty Analyss. Fgure 4 Parwse vs one-at-a-tme removal n stablty tests on model 3 OLS estmates Source: ERA Analyss 49. Ths apparent stablty s smlarly observed when comparng estmates of theta before and after removng the most nfluental 1 per cent of observatons usng Cook's dstance. Removng extreme observatons s lkely to assst n stablsng estmates In short, these methods nduce stablty through removng or mtgatng the effect of non-complant observatons usng robust regresson or removng pars of observatons wth offsettng effects. Instead of specfyng a model that comples wth the data the focus of these analyses has been to mtgate the effect of non-complant data to create smlar lookng sets of theta estmates. Because of ths, the smlar or stable lookng sets of theta estmates provde lttle nformaton about certanty around parameter estmates or robustness of the estmates to possble volatons of other basc modellng assumptons. 51. Bootstrappng by randomly removng 5 per cent of observatons and re-estmatng theta dffers from the other senstvty analyses n that t does not target nfluental observatons. It demonstrates the senstvty of theta to removng random 26 Ths s evdent n SFG s analyss of sub-perods across table 3 and 4 n SFG Consultng, The mpact of frankng credts on the cost of captal of Australan companes, 12 November 2008, pp Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 14

21 observatons regardless of whether they are nfluental or not. In effect, removng 5 per cent of the observatons slghtly thns the sample. The results based on the thnned sample wll be expected to produce a smlar estmate of theta. Ths s because the full sample and any large subsample of the observatons are not lkely to have substantally dfferent dstrbutons. Due to the central lmt theorem, the bootstrapped dstrbuton of ether the full sample, or a thnned sample, wll be approxmately normal. The only dfference wll be that the thnned sample wll have a slghtly larger standard error assocated wth theta (see dscusson n Appendx 2, A Comment on the SFG Bootstrap Senstvty Analyss ). Ths type of bootstrappng analyss therefore says lttle, f anythng, about the stablty of estmates because t s predsposed to producng a largely smoothed and normally dstrbuted hstogram of the samplng dstrbuton of theta. 52. All of the senstvty analyses appled (ncludng bootstrappng) are focussed on the behavour of estmated parameters. The tests gnore the behavour of dscrepances between the ftted models predctons (resduals) and the actual data. Rather than focus on the stablty of parameter estmates, conventonal regresson dagnostcs assess the behavour of these resduals to nform the approprateness of the proposed model wth respect to the data. That s, once a model s ftted and parameters are estmated the resduals are observed to determne f they exhbt any remanng patterns that have not been adequately captured by the model specfcaton. The resduals are also observed to determne whether they follow the dstrbuton assumed when specfyng the model and regresson fttng procedure. The emphass of dagnostcs should be focused on the model fttng process, rather than reteratng parameter estmaton over dfferent truncated samples. 4 Are the models that produce the theta estmates meanngful? 53. As mentoned above, conventonal statstcal dagnostcs assess the behavour of the dscrepances between the ftted model and actual data, as measured by the resduals, before settlng on a model and regresson technque to produce the requred parameter estmates Although the classcal lnear regresson model s ntutvely appealng n the sense of the drop-off beng composed of a lnear combnaton of net dvdends and frankng credts, few dagnostcs have been undertaken to determne whether ts modfcaton wth scalars (such as those appled n models 1 through to 4) results n a nonlnear relatonshp. If ths s the case a lnear model s lkely to be a poor ft and assocated wth relatvely hgher uncertanty n the estmates. 55. Hence, regresson dagnostcs should be desgned to test for volatons of the classcal lnear regresson model (CLRM) assumptons. These assumptons are: The response varable, for example, the dvdend drop-off, s a lnear functon of the predctor varables (net dvdend and theta). Values observed for the predctor varables (for example net dvdends and frankng credts) are randomly sampled. 27 The ssue of assessng resduals was ndrectly rased n Lally. M, The Estmated Utlsaton Rate for Imputaton Credts, 12 December 2012, p.21. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 15

22 No multcollnearty - the predctor varables are not an exact lnear functon of each other. The resduals at any gven value of the predctor varables have a mean of zero. No heteroskedastcty - the resduals exhbt constant varance as a functon of the predctor varables. No correlated errors - the resduals do not exhbt a pattern across tme or wthn dfferent groupngs of the data. No correlaton between resduals and predctor varables. The regresson model s correctly specfed the relatonshp between the predctor varables and the response varable s correctly stated by the model. The number of observatons must be greater than the number of parameters to be estmated. 56. Testng for volatons of these assumptons asssts n producng meanngful parameter estmates. Such technques nvolve vsual analyss of the resduals and testng them va a sute of statstcal procedures. Such dagnostcs have receved lttle attenton n Australan theta studes so far despte beng standard practce n appled econometrcs. 57. To test the assumpton of a lnear regresson beng the correct specfcaton Ramsey s RESET test s appled to each model. The test s commonly used n basc econometrcs courses. An F-statstc larger than the crtcal value or p-value less than 0.05 ndcates rejecton of the hypothess that the lnear model s the correct specfcaton at the 5 per cent sgnfcance level. 28 Table 1 Ramsey RESET tests of model specfcaton error Model F-statstc p-value outcome < Reject hypothess model correctly specfed Do not reject hypothess model correctly specfed Reject hypothess model correctly specfed < Reject hypothess model correctly specfed Source: ERA Analyss Note: the resettest functon n R package lmtest yeld dentcal results for MM regressons 58. The results ndcate that a lnear specfcaton s only approprate for model 2 whch s scaled by net dvdends. Ths suggests that nonlnear patterns n the raw drop-off and frankng data are adjusted out by dvdng the data by net dvdends. The results ndcate that t s napproprate to apply classc lnear regresson technques to the other models because they produce a relatvely poor ft compared to nonlnear estmates. Ths ssue s examned n further detal n the dscusson of robust models n Appendx 2. Other regresson technques, however, may produce more meanngful estmates for models 1, 3 and The conventonal default assumpton of addng a square and cubc term to the alternate specfcaton s appled. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 16

23 59. The assumpton of varablty and random samplng n the predctor varables may be volated by systematc removal of observatons from the dvdend events observed over a gven perod, by applyng flterng technques or removng observatons based on some other crtera. The ssue of removng extreme data ponts has been hghlghted at length n secton 3.2. Volaton of ths assumpton potentally nduces bas n estmates. 60. Multcollnearty s an nherent ssue n dvdend drop-off studes. The net dvdend and frankng credt are hghly correlated and dsplay a strong lnear relatonshp. Ths s because n the majorty of cases the frankng credt equals 30 per cent (corporate tax rate) of the gross dvdend whle the net dvdend comprses the remanng 70 per cent. In regresson analyss usng multple varables, multcollnearty can obscure the true relatonshp between each ndvdual predctor varable and the dependent varable whle the predctve accuracy of the whole regresson remans vald. In addton, the standard errors on the affected parameters tend to be nflated, whch results n ncorrectly concludng that parameters are not statstcally dfferent from zero (type II error). For example, the stuaton could arse where one ncorrectly concludes that theta s not sgnfcantly dfferent from zero. 61. The lnear relatonshp between net dvdends and frankng credts s not perfect n the current context because t s obscured by dfferences n the proporton of gross dvdends that are franked. That s, the frankng credt n some nstances s less than 30 per cent of the gross dvdend due to less than 100 per cent of the gross dvdends beng elgble for frankng credts. Consequently, the ssue of multcollnearty does not completely nvaldate the DDO study, but s a source of ncreased uncertanty n the estmates. Further detals on the extent to whch ths s an ssue are covered n the dscusson of multcollnearty n Appendx Varance n the resduals of each model may be dependent on the level of frankng credts. Such a relatonshp volates the assumpton of no heteroskedastcty. A formal test of ths s the Breusch-Pagan test. The Breusch-Pagan test appled here tests for a relatonshp between the explanatory varables n each model (such as net dvdends and frankng credts) and varance n the resduals such as that shown n Fgure 5. The null hypothess s that there s no relatonshp. A large Breusch-Pagan statstc relatve to the crtcal value (not shown here), or small p-value, ndcates rejecton of the null hypothess of no relatonshp and we conclude that heteroskedastcty s present. Table 2 Model Breusch-Pagan Test for Heteroskedastcty n resduals from OLS/MM regressons Breusch-Pagan Statstc p-value outcome Do not reject hypothess of no heteroskedastcty Do not reject hypothess of no heteroskedastcty Do not reject hypothess of no heteroskedastcty Reject hypothess of no heteroskedastcty Source: ERA Analyss Note: Results are dentcal between OLS and MM regressons usng bptest n R package lmtest. 63. In Table 2 model 4 reports a large test statstc wth a p-value less than Ths ndcates rejecton of the hypothess of no heteroskedastcty at the 5 per cent sgnfcance level. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 17

24 Fgure 5 Model 4 MM regresson resduals plotted aganst correspondng frankng credt values (market corrected data) Source: ERA Analyss Note: The plot has truncated a sngle observaton for a frankng value credt valued between 9 and 10 n order to show the pattern n the bulk of the data. In the context of the model 4 regresson frankng credt values would be of a dfferent scale due to beng dvded by cum prce multpled by the standard devaton n excess returns. 64. Fgure 5 shows a dstngushable relatonshp between the resduals and frankng credt value. Lower values of frankng credts are assocated wth a hgher dscrepancy between the model predctons and the actual data than lower values. Ths ndcates that a relatonshp between frankng credts and varance n parameter estmates exsts n the resduals whch s not adequately captured by model 4. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 18

25 Fgure 6 Model 4 OLS regresson resduals plotted aganst correspondng frankng credt values (market corrected data) Source: ERA Analyss Note: The plot has truncated a sngle observaton for a frankng value credt valued between 9 and 10 n order to show the pattern n the bulk of the data. 65. Fgure 6 based on the OLS regresson resduals of model 4 ndcates an almost dentcal relatonshp. Agan, ths confrms that a relatonshp between frankng credts and varance n parameter estmates exsts whch s not adequately captured by model The consequence of ths heteroskedastcty n the resduals of model 4 s that estmated standard errors from the model used to test the statstcal sgnfcance of estmated parameters tend to be too small. The smaller standard errors produced by the model were one of the factors behnd SFG s preference for model The presence of heteroskedastcty n the resduals generated by the model ndcates that the small standard errors are unrelable and that model 4 s not a wholly vald specfcaton. Further detals on ths ssue are gven n the dscusson of heteroskedastcty n Appendx Fgure 2 shows model 4 as beng relatvely stable. SFG also expressed a preference for ths model on the bass of ts estmate of theta beng very stable. 30 The dagnoss of resduals for heteroskedastcty shows that the stablty tests are an nadequate test of model valdty. 68. Asde from volatons of the CLRM assumptons, an mportant aspect to note n the models ftted n the dvdend drop-off studes s that the resduals are not normally dstrbuted. Ths s a fundamental assumpton behnd evaluatng the statstcal sgnfcance of parameters n models ftted to a fnte data set. 29 SFG Consultng, Dvdend drop-off estmate of theta: Fnal Report, 21 March 2011, pp Ibd. Estmatng the Utlsaton of Frankng Credts through the Dvdend Drop-Off Method 19