Decomposing the Price-Earnings Ratio

Transcription

1 Decomposng the Prce-Earnngs Rato Keth Anderson, ISMA Centre, Unversty of Readng Chrs Brooks, Cass Busness School, Cty of London May 2005 Correspondng author. Faculty of Fnance, Cass Busness School, Cty Unversty, 106 Bunhll Row, London EC1Y 8TZ, UK. t: (+44) (0) ; f: (+44) (0) ; e-mal

2 Abstract The prce-earnngs rato s a wdely used measure of the expected performance of companes, and t has almost nvarably been calculated as the rato of the current share prce to the prevous year s earnngs. However, the P/E of a partcular stock s partly determned by outsde nfluences such as the year n whch t s measured, the sze of the company, and the sector n whch the company operates. Examnng all UK companes snce 1975, we propose a modfed prce-earnngs rato that decomposes these nfluences. We then use a regresson to weght the factors accordng to ther power n predctng returns. The decomposed prce-earnngs rato s able to double the gap n annual returns between the value and glamour decles, and thus consttutes a useful tool for value fund managers and hedge funds. 1 Introducton The prce-earnngs (P/E) effect has been wdely documented snce Ncholson (1960) showed that low companes havng low P/E ratos on average subsequently yeld hgher returns than hgh P/E companes, and ths dfference s known as the value premum. A low prce-earnngs rato s used as an ndcator of the desrablty of partcular stocks for nvestment by many value/contraran fund managers, and the P/E effect was a major theme n Dreman (1998). The value premum s mostly postve through tme, and a large number of studes have confrmed ts presence. Whle the contnued exstence of a value premum s puzzlng for academcs, a plausble explanaton s that t provdes compensaton for the extra rskness of value shares. However, the CAPM beta does not ncrease as the P/E decreases; f anythng, t decreases (Basu, 1977), so the rsk must resde n other measures. Accordng to Dreman and Lufkn (1997), sector-specfc effects are also unable to explan the value premum, and more complex multfactor models have smlarly faled to ratonalse the outperformance of value stocks (see, for example, Fuller et al., 1993). Others have proposed behavoural explanatons (e.g., Lakonshok, Schlefer and Vshny, 1994), ascrbng the extra returns from value shares to psychologcal factors affectng market partcpants. However, the P/E as t s commonly used s the result of a network of nfluences, smlar to the way n whch a company s share prce s nfluenced not only by dosyncratc factors partcular to that company, but also by movements n prces on market as a whole, and the sector n whch the company operates. A large number of studes have examned the decomposton of stock returns nto market-wde and sector nfluences, and n ths paper we propose and show the usefulness of an analogous approach n deconstructng the P/E rato. We dentfy four nfluences on a company s P/E, whch are: 1) The year: the average market P/E vares year by year, as the overall level of nvestor confdence changes. 1

3 2) The sector n whch the company operates. Average earnngs n the computer servces sector, for example, are growng faster than n the water supply sector. Companes n sectors that are growng faster n the long-term should warrant a hgher P/E, so as correctly to dscount the faster-growng future earnngs stream. 3) The sze of the company. There s a close postve relatonshp between a company s market captalsaton and the P/E accorded. 4) Idosyncratc effects. Companes examned n the same year, operatng n the same sector and of smlar szes nevertheless have dfferent P/E s. Idosyncratc effects, that do not affect any other company, account for ths. Such effects could be the announcement of a large contract, whether the drectors have recently bought or sold shares, or how warmly the company s recommended by analysts. Usng data for all UK stocks from , we take these four nfluences n turn, lookng at the extent to whch they affect the P/E, and how closely they are correlated wth subsequent returns. We decompose the nfluences on each of our company/year data tems, and we then run a regresson to get a weght for each nfluence. Usng these weghts, we construct a new sort statstc for assgnng companes to decles, and we are able to double the dfference n returns between the glamour and value decles. Fnally, we show, va a portfolo example, the practcal effect of the new statstc on the values of the glamour and value decles through tme. The remander of ths paper proceeds as follows. Secton 2 descrbes our data sources, and the methodology we used n our calculatons of P/E ratos and decle portfolo returns. Secton 3 descrbes our results from decomposng the nfluences on the P/E, assgnng sutable weghts to them, and creatng a more powerful weghted P/E statstc. Secton 4 shows how the factor weghtngs are vtally affected by the bd-ask spread. In Secton 5, we demonstrate the utlty of the new statstc by comparng the fortunes of four sample portfolos. Secton 6 concludes. 2 Data Sources and Methodology Intally, we collated a lst of companes from the London Busness School s London Share Prce Database (LSPD) for the perod 1975 to The LSPD holds data startng from 1955, but only a sample of one-thrd of companes s held untl Thereafter, data for every UK lsted company are held, so we took 1975 as our start date. We excluded two 2

4 categores of companes from further analyss. These were fnancal sector companes, ncludng nvestment trusts, and companes wth more than one type of share - for nstance, votng and non-votng shares. Apportonng the earnngs between the dfferent share types would be problematc. Earnngs data are avalable on LSPD, but only for the prevous fnancal year. We therefore used Datastream, as ths servce s able to provde tme seres data on most of the statstcs t covers, ncludng earnngs. A four-month gap s allowed between the year of earnngs beng studed, and portfolo formaton, to ensure that all earnngs data used would have been avalable at the tme. We therefore requested, as at 1 st May n each year , normalsed earnngs for the past eght years, the current prce, and the returns ndex on that date and a year later, for each company. A common crtcsm of academc studes of stock returns s that the reported returns could not actually have been acheved n realty, due to the presence of very small companes or hghly llqud shares. In an attempt at least to avod the worst examples, we excluded companes f the share md-prce was less than 5p, and we also excluded the lowest 5% of shares by market captalsaton n each year. We checked whether ths removal of mcro-cap and penny shares had a serous effect on returns. Penny shares and mcro-caps dd ndeed contrbute to returns, although ths contrbuton was across all decles, not just for value shares. Average returns were 1-1.5% hgher when all companes are ncluded, across all decles and holdng perods. An arbtrage strategy that s long n value companes and short n glamour companes would therefore be largely unaffected by the excluson of very small companes and of penny shares. We also examne the mpact of transactons costs, whch are lkely to be larger for small frms, n Secton 4. A further crtcsm of many studes s that they do not deal approprately wth bankruptces. Companes that faled durng the year are flagged n the LSPD. In such cases, we set the RI manually to zero, as n Datastream t often becomes fxed at the last traded prce. We assumed a 100% loss of the nvestment n that company n such cases. 3 P/E Decomposton In ths secton, we solate the varous nfluences on the PE, then develop a model for puttng them back together agan n a new P/E statstc that more accurately reflects ther power n predctng returns. 3

5 The P/E Rato Through Tme Market average P/E s vary through tme, as nvestor confdence waxes and wanes. We show average P/E s and average subsequent returns for each base year n Table 1. A major peak n P/E s can be observed n 1987, representng the run-up to the crash n October of that year. Average P/E s were farly constant throughout the perod marked a major recent low for the average market P/E, as t reached a level last seen n the md-1970 s. However, note that the data were read as at 1 st May 2003, only a few weeks nto the market recovery of that year, so the average P/E for 2004 would be hgher. The correlatons between the market average P/E and subsequent returns are shown n the frst row of Table 2. Compared to the other nfluences, the correlaton s qute hgh, at 0.12 for the correlaton of the market E/P to one-year returns. Sector Effects on the P/E Feld G17 n the LSPD holds each company s FTSEA ndustral classfcaton. We calculated the average P/E for each sector wth more than ten company/year returns. There were 151 of these, rangng from a P/E of 20.9 for Semconductors, to 5.5 for Publshng. Note that these averages are for the sector across all years. In order to splt the year effect from the sector and sze effects, we must make the assumpton that sector and sze effects do not have ther own year-dependent varaton. The correlaton between sector E/P and subsequent returns s shown n the second row of Table 2. In ths table, we examne holdng perods from 1 to 8 years. In contrast to the year returns, the contrbuton of the sector to the E/P has a correlaton that s small but usually negatve,.e. a hgher sector E/P (lower P/E) means poorer returns. We assume that ths s because, for example, the software sector wth ts average P/E of 17.1, as a whole really does gve better returns on average than the water supply sector wth ts average P/E of 8.8, because software s growng more quckly n the long term, regardless of the returns on ndvdual companes. Thus, the contrbuton of the sector has an opposte effect on the overall P/E, compared to that of the other effects. Therefore, t s desrable to negatvely weght the nfluence of the sector P/E when constructng the modfed P/E statstc. Usng ths, unloved companes from growth sectors wll have a greater chance of beng ncluded n any value portfolo than they do wth the tradtonal P/E. Ths s a useful result, for t suggests 4

6 that whle tradtonal value funds may comprse a mxture of stocks from value sectors and value stocks from glamour sectors, the latter are lkely to produce hgher returns. Sze Effects on the P/E Larger companes usually command a hgher P/E than smaller companes. Lqudty constrants suffered by large fund managers may account for a sgnfcant proporton of ths premum snce only the largest companes can offer the necessary lqudty n ther shares f the fund manager s not to move the market prce adversely. Managers of large funds therefore naturally gravtate towards nvestng n larger companes. Market captalsatons of companes vary hugely, but the dstrbuton s skewed by the presence of a modest number of very large companes. A common approach to ths ssue s to rescale the market cap data by takng ther logarthms. However, nstead of takng logs, we took a more ntutvely meanngful route and dvded companes nto categores. For each year, we dvded companes nto 20 categores by market value, and calculated the average P/E and average returns for each category. The results are shown n Table 3. Note that the P/E and returns quoted are averaged over all 29 years, but the category lmts are specfc to each base year, as the average captalsaton changes so much from year to year. As the companes get larger, the P/E s ncrease but the returns fall: note the very hgh returns for categores 1 and 2 of 28%. However, ths s for the smallest 10% of companes. In 2003, only companes wth a market captalsaton of less than 7.6m fell nto categores 1 and 2. Lqudty constrants on the shares of such companes would be a very real problem for even a small fund, and the wder bd-ask spread for small companes would further erode returns. The close relatonshp between the sze category and average P/E can more clearly be seen n Fgure 1. There s a very hgh correlaton of 0.82 between P/E and market sze category, and ths can clearly be seen here. Lookng at the thrd row of Table 2, the 0.07 correlaton of the sze category of ndvdual companes to one-year returns s larger than that of the ndustry, but smaller than that of the year average P/E. A Model for Deconstructng the Influences on the P/E We have now assessed the strengths of the dentfable nfluences on the P/E. Unlke the other nfluences, the dosyncratc part of the E/P (termed IdoEP) cannot be ndependently 5

7 observed: t s merely that part of the overall E/P that s unexplaned by the year, market value and ndustry factors. We assumed a multplcatve arrangement of the nfluences, so that ActualEP YearEP SzeEP SectorEP IdoEP = AverageEP AverageEP AverageEP AverageEP (1) AverageEP where the average E/P s the average over all companes and years. Note that s not a regresson equaton, and there s no error term: IdoEP s smply a way of relatng what would be expected for the E/P, gven the year, company sze and ndustry, to what has been observed. Thus, for a company wth unformly average characterstcs, the actual, year, market cap and sector E/P terms (each ncludng the denomnator) would be unty, so the dosyncratc E/P term would be unty also. On the other hand, a company wth a low observed E/P (hgh P/E) wth average year, market cap and sector E/P s would be assgned a low dosyncratc E/P, and ths term would make t less attractve as an nvestment accordng to the E/P statstc developed below. Rearrangng (1), we calculate the dosyncratc E/P for each company/year return as 3 ActualEP AverageEP IdoEP = YearEP SzeEP SectorEP As can be seen n the fnal row of Table 2, the dosyncratc E/P has a postve correlaton of wth one-year returns, so ts nfluence s n the same drecton as the year and market cap E/P s, but ts correlaton s somewhat weaker than that of the market value E/P. Fgure 1 summarses the varous nfluences on the prce-earnngs rato, showng that overall, low P/E ratos lead to hgh returns, whle returns are lkely to be hgh f the P/E that year s uncharacterstcally low. Returns are also lkely to be superor for hgh P/E sectors, for small frms (that typcally have lower P/E ratos), and f the dosyncratc P/E s low. Havng calculated all four nfluences on the P/E, we can now show the correlatons between the dfferent nfluences, n Table 4. The nfluences all have very lttle correlaton wth each other, whch should mean that there s no problem of multcollnearty n the subsequent regressons. (2) We now combne the four nfluences n the model Rtn 01 β β IdoEP + u (3) = 0 + β1yearep + β2szeep + β3sectorep + 4 where Rtn01 s the 1-year return for frm-year, the β terms are parameters to be estmated, and u s a dsturbance term. Here we are tryng to predct one-year returns by gvng weghts to the four decomposed nfluences on the P/E that we have just revealed. Note that there are 16,000 company/year returns and 16,000 dfferent IdoEP values, but only 29 dfferent 6

8 YearEP s, 20 dfferent SzeEP s and 151 dfferent SectorEP s. The dosyncratc contrbuton to the E/P turns the E/P that one would expect to observe, gven the year, ndustry and sze, nto the E/P actually observed. A lnear regresson of ths model results n the followng estmated coeffcents and standard errors: Rtn01= YearEP SzeEP SectorEP IdoEP (0.0269) (0.1051) (0.2305) (0.1636) (0.0348) (4) All coeffcents are sgnfcant at the 0.1% level, except for the sector term, whch has a p- value of Of the E/P varables ncluded n the regresson, the year E/P s roughly as useful n predctng returns as the market captalsaton (sze) category E/P, but these two domnate the other two factors. The ndustry classfcaton E/P s the only predctor varable to have a negatve coeffcent, as foreshadowed earler by ts negatve correlaton wth returns. The effect of the weghts s to make t more lkely that small companes, whch on average have a hgher E/P (low P/E) wll be selected as part of the value decle. Companes from faster-growng sectors that usually have a low E/P (hgh P/E) are also more lkely to be selected. We now offer a couple of examples to llustrate the dfferences that our approach would make to the selected portfolos. Stanley Gbbons appears n the 2003 value decle. Based on the tradtonal P/E, the company appears n decle 4, but ts sze (market cap category 2) propels t nto the value decle. Stanley Gbbons shares trpled n value between 1 st May 2003 and 1 st May At the other end of the value-glamour scale, Imperal Tobacco s the least attractve company on the whole UK market n 2003 usng the decomposed P/E, yet when usng the tradtonal P/E t falls nto decle 3. It s very large (market cap category 20), the Tobacco sector has a lower than average sector P/E of 9.5, but the company s overall P/E of 15.3 results n a hgh dosyncratc P/E of All three factors count aganst t n the new weghtng system. In total returns on Imperal Tobacco shares were 25%, compared to the overall market gan of 55%. Do the regresson weghts allow us to acheve a P/E statstc wth a hgher resoluton between the glamour and value decles? We calculated a sort statstc for each company/year return, that s the weghted average of ts decomposed E/P nfluences, where the weghts are as shown n (4). The sort statstc s 7

9 EP β + β YearEP + β SzeEP + β SectorEP + β IdoEP = 4 j = 1 β j 3 4 (5) where EP s the new statstc for company/year, and the rght-hand sde of the equaton s a weghted average of the four decomposed nfluences on the E/P, dvded by the sum of the weghts. The new sort statstc can be understood as meanng that a company s most lkely to be ncluded n the value decle f t s small and operates n a sector that usually has hgh P/E s, but has a low dosyncratc P/E 1. We use the sort statstc to assgn companes to decles, wth the results shown n column 1 of Table 5. In order to gauge the relatve effects of each part of the E/P, columns 2 to 4 of Table 5 also show the returns by decle when sortng by each of the component E/P s alone. For comparson, the results for the tradtonal P/E are shown n column 5. The market captalsaton factor has the largest effect on the E/P of the three nfluences, provdng a D10-D1 resoluton of 13%. (Ths s however reduced f transactons costs are taken nto account; see Secton 4). The ndustry factor gves a resoluton of only around 5%, but t works n the opposte drecton to the other two factors. Puttng all three together usng the weghts suggested by the lnear regresson, wth the ndustry factor gven the approprate negatve weght, results n a remarkably powerful statstc: the resoluton of the undfferentated statstc s multpled two-and-a-half tmes to 15.4%, and a value decle s dentfed that has average one-year returns of 28.6%. 4 The Effect of the Bd-Ask Spread In Secton 3, the returns were calculated usng md-md prces,.e. not takng account of the bd-ask spread. However, t s well known that smaller companes shares suffer from much wder bd-ask spreads than those of larger companes, and the major contrbuton to the 15.4% dfference between the value and glamour decles returns n Secton 3 s because the value decle conssts of a hgher proporton of small companes, and the glamour decle of large 1 Note that n fact, the ntercept and year factor do not need to be ncluded when calculatng the modfed EP statstc snce we are sortng wthn each year separately, and the constant wll adjust each modfed EP by the same amount, leavng the rank orderng of frms unaffected. 8

10 companes, than would be the case f the tradtonal E/P were used. Is the dfference n decle returns much reduced f bd-ask spreads are taken nto account? 2 Bd and ask prces were frst recorded on Datastream n 1987, and for the majorty of companes are only avalable from Where the actual bd-ask spread was avalable for that company on that day, we used t, calculatng the returns after allowng for costs due to the bd-ask spread as where P P PB Rtn 01Sprd = (6) PA0 P0 P1 P n s the md-prce at tme n, PAn s the ask prce at tme n, and PBn s the buy prce at tme n. The frst fracton n (6) represents the notonal loss when buyng, the second fracton s the md-md return as used n Secton 3, and the thrd fracton s the notonal loss when sellng. To cater for companes for whch bd and ask prces were not avalable, we calculated the average bd-ask spread for each market value category. The results can be seen n Fgure 3. The spreads vary monotoncally from over 10% for the smallest 5% of companes, to 1.15% for the largest 5%. Ths wll clearly have a major mpact on any strategy based largely on nvestng n small rather than large companes, such as we developed n Secton 3. Where companes bd-ask spreads were not avalable, we employed the average bd-ask spread for that sze category for calculatng returns. Where a share remans n the decle portfolo for more than one year, we appled no spread on sellng f a company would reman n the same decle next year, and appled no buyng spread f the company had already been n the same decle portfolo the prevous year. Snce the returns have now changed, we re-ran the lnear regresson from Secton 3, usng returns after spread costs as the new dependent varable, whch gave the followng coeffcents and standard errors: Rtn01= YearEP SzeEP SectorEP IdoEP (0.0257) (0.1004) (0.2204) (0.1564) (0.0332) (7) All coeffcents are sgnfcant at the 0.1% level, except for SzeEP and SectorEP wth p- values of 0.02 and 0.03 respectvely. The company sze E/P nfluence has lost three-quarters of ts predctve power now that we are allowng for the effect of bd-ask spreads on returns. 2 In the UK, a tax known as stamp duty of 0.5% must be pad on all share purchases; we do not nclude ths n our calculatons. 9

11 The effect of spread costs on decle returns can be seen n Table 6. The weghtng scheme from Secton 3, developed usng md-md returns, suffers a major reducton n ts resoluton, from 15.4% to 9.4%. Ths s due to ts heavy relance on the sze effect, so that the value decle, full of small companes, s much more serously affected by the bd-ask spread than the glamour decle. The new weghtng scheme, wth ts lesser weght on market cap, shows a hgher resoluton of 10.49%, double that of the tradtonal P/E, and moreover the returns for the value decle are now much less relant on the sze of the company. The value decle s average market value category of 5.64 corresponds to a market captalsaton of 16.2m n 2003, compared to a market value category of 2.21 ( 5.7m) for the value decle usng Secton 3 weghts, and ths would present much less of a lqudty problem for a large nvestor. It s mportant to note that the D10-D1 fgure n Table 6 s lterally just that, and does not represent the returns that would actually be avalable from an arbtrage strategy that s long n the value decle and short n the glamour decle. The larger the glamour portfolo spread costs are, the wder the D10-D1 fgure s, whereas n realty spreads should be a cost to the arbtrageur on both sdes of the arbtrage trade. The effect of spreads on the glamour portfolo returns are 4.07%, 0.85% and 1.39% for the tradtonal P/E, the Secton 3 weghts and the Secton 4 weghts respectvely. Doublng these and subtractng them from the D10-D1 fgures gves realsable arbtrage returns of 2.89%, 7.7% and 7.71%. Ths result shows that after allowng for reasonable transactons costs n the approprate way, arbtrage rules based on the tradtonal P/E rato wll actually lose money, whereas the new statstc stll yelds postve returns. Can the superor returns from the value decle be explaned as a far return for havng taken on extra rsk? The Sharpe ratos when usng the new lnear regresson weghts are shown n Fgure 4. We calculated the Sharpe ratos of the portfolos as the excess return of the portfolo over the rsk-free rate, dvded by the standard devaton, usng the three-month Treasury bll rate as the proxy for the rsk-free rate. Although the varablty of returns s somewhat hgher for the low P/E decles, the standard devaton does not rse as quckly as the returns, so that the Sharpe ratos for the low P/E decles are much hgher. The Sharpe rato of the value decle s almost four tmes that of the glamour decle. If one expects returns over the rsk-free rate to 10

12 be proportonal to the varablty of returns, then the low P/E decle seems to represent very good value 3. 5 Portfolo Illustraton Ths example shows n a more concrete manner the extra return that can be obtaned by decomposng the P/E. We calculated the performances of the value and glamour decles dentfed usng the weghts arrved at through the lnear regresson developed above, and compared them to the returns for the decles calculated usng the tradtonal P/E, n whch the nfluences of year average E/P, sze E/P and ndustry E/P had not yet been dfferentated. All portfolos use annual rebalancng. Table 7 shows the percentage returns and portfolo values for the glamour and value decles for the two sort statstcs. Snce the decomposton weghts were based on returns after spread effects (.e. net of transactons costs), the values n Table 7 are also calculated on ths bass. For the value decle, average returns are 2.5% better for the new statstc than for the tradtonal E/P, and for the glamour decle, average returns are 2.74% worse. The mpact of ths s that the new value decle portfolo ends up beng worth almost double the old value decle based on a 30-year nvestment horzon. The modfed E/P statstc also provdes a more consstent profle of postve returns, yeldng only 7 years where the long-value-shortglamour arbtrage portfolo lost money. If the tradtonal E/P were used to assgn companes, the number of years where the arbtrage strategy would lose money s rased to Conclusons Although the P/E effect was frst documented almost ffty years ago, and t s well-known that non company-specfc nfluences affect ndvdual company P/E s, as far as we are aware we are the frst to nvestgate whether accountng for these varous nfluences can delver a P/E effect of greater value n predctng returns. Usng data for all UK companes from , we mposed a model of performance attrbuton onto the P/E rato. We dentfed the nfluences on a company s P/E as the annual market-wde P/E, the sector, the company sze, 3 These results can farly be crtcsed as sufferng from a look-ahead bas, n that the regresson weghts could only have been known n May 2004, but we use them to calculate annual returns for the whole dataset from We used a rollng ten-year sub-sample to check whether the results would be affected by the use of tralng wndows of hstorcal data to calculate the regresson weghts. We found that the returns are slghtly degraded, but snce the mpact s not marked, to avod repetton we do not report these results. 11

13 and dosyncratc nfluences. We solated the power of each of these effects. Company sze has a hgh correlaton wth the P/E and wth subsequent returns, so t s apportoned a hgher mportance n the fnal statstc than the other factors. The ndustry classfcaton has a decdedly moderate predctve power for returns, but ts effect upon the P/E s n the opposte drecton compared to the other factors. Reversng the drecton of the sector nfluence on the P/E so that t produces better company sorts s, we feel, an mportant nnovaton of ths paper. Havng solated these nfluences, we developed a model that provdes weghts for them, so that company sze s weghted more heavly than the others, and the ndustry factor s assgned ts approprate negatve weght. However, the weghtng for company sze E/P s very much dependent on whether bd-ask spreads are taken nto account, and t loses threequarters of ts predctve value f returns are calculated after transactons costs. We found that the new statstc usng these weghts was consderably better than the tradtonal P/E n predctng future returns. Usng the optmum weghtngs suggested by the lnear regresson, we doubled the average annual dfference n returns between the glamour and value decles from 5.25% to 10.5%. The hgher returns for the value decle cannot be explaned as payment for greater rsk (at least n the sense of the Sharpe rato), and the factor weghts are reasonably robust whchever sub-perod of returns s chosen. Our portfolo llustraton shows that the value and glamour decles chosen usng the new weghted P/E bracket the value and glamour decles chosen usng the tradtonal P/E, and the new value portfolo comfortably outperforms the old by 2.4% annually. These results should be of nterest even to managers of large funds, snce the value decle after spreads are taken nto account s much less dependent on the sze of the company than f spreads are gnored. Future work n ths area could nvolve replcatng ths result for the much larger US markets. Addtonally, our lst of nfluences on the P/E s lkely not exhaustve: gearng, for example, may be a further sgnfcant explanatory varable, snce of two otherwse dentcal companes, the one wth hgher gearng wll mert a lower P/E. 12

14 References Dreman, D.N. Contraran Investment Strateges: The Next Generaton. (1998) New York: Smon & Schuster. Dreman, D.N. and E.A. Lufkn. Do Contraran Strateges work wthn Industres? Journal of Investng, 6 (1997), pp Fuller, R.J., L.C. Huberts, and M.J. Levnson. Returns to E/P Strateges, Hggeldy Pggeldy Growth, Analysts' Forecast Errors, and Omtted Rsk Factors. Journal of Portfolo Management, Wnter (1993), pp Lakonshok, J., A. Schlefer, and R. Vshny. Contraran Investment, Extrapolaton, and Rsk. Journal of Fnance, 49 (1994), pp Ncholson, S.F. Prce-Earnngs Ratos. Fnancal Analysts Journal, 16 (1960):

15 Table 1: Market average P/E's and subsequent 1-year returns for each year, Year Average P/E Return Year Average P/E Return Year Average P/E Return % % % % % % % % % % % % % % % % % % % % % % % % % % % % % Table 2: Correlatons between the dfferent nfluences on the P/E and subsequent 1-8 year returns, Year 2-Year 3-Year 4-Year 5-Year 6-Year 7-Year 8-Year YearEP SectorEP SzeEP IdoEP Table 3: Average P/E's and returns, , categorsed by market captalsaton Market Cap Category Avg P/E Return Market Cap Category Avg P/E Return 1 (smallest) % % % % % % % % % % % % % % % % % % % 20 (largest) % Table 4: Correlatons between P/E nfluences SzeEP SectorEP IdoEP YearEP SzeEP SectorEP

16 Table 5: E/P deconstructon model returns, Lnear Regresson 2 SzeEP alone 3 SectorEP alone 4 IdoEP alone 5 Tradtonal P/E Weghts assgned SzeEP SectorEP IdoEP One-year returns Hgh P/E 13.17% 15.48% 24.42% 18.08% 17.83% Decle % 18.19% 22.54% 20.36% 19.89% Decle % 17.92% 19.59% 17.06% 18.40% Decle % 17.68% 20.34% 18.41% 16.90% Decle % 18.99% 19.39% 18.55% 18.39% Decle % 20.24% 18.00% 20.12% 18.79% Decle % 19.01% 20.14% 19.00% 21.62% Decle % 21.80% 17.90% 21.51% 20.89% Decle % 22.84% 19.47% 21.99% 22.89% Low P/E 28.59% 28.48% 18.61% 24.93% 24.39% D10 D % 12.99% -5.81% 6.85% 6.56% Notes: Each column shows frst the weghts used to construct the sort statstc, then the decle returns resultng from assgnng companes to decles usng that sort statstc. Column 1 shows the returns when usng the lnear regresson weghts. Columns 2 to 4 show the returns when sortng by each E/P nfluence on ts own, so as to ndcate the relatve effectveness of each nfluence as a predctor of returns. Column 5 shows the returns when usng the tradtonal P/E, whch has not been decomposed nto the dfferent nfluences. 15

17 Table 6: The effect of bd-ask spreads on returns, Tradtonal P/E Weghts from Rtn01 regresson Weghts from Rtn01Sprd Returns after spread Average Sze Category Returns after spread Average Sze Category regresson Returns after spread Average Sze Category Weghts assgned SzeEP SectorEP IdoEP One-year returns Hgh P/E 13.76% % % Decle % % % Decle % % % Decle % % % Decle % % % Decle % % % Decle % % % 9.69 Decle % % % 8.25 Decle % % % 6.87 Low P/E 19.01% % % 5.64 D10 D1 5.25% % % - Notes: We show the decle returns after allowng for the bd-ask spread, and each decle s average market value category, usng three dfferent P/E ratos to assgn companes to decles: the tradtonal P/E, the decomposed P/E wth a heavy weghtng on SzeEP as suggested by the lnear regresson on one-year bd-bd returns, and the decomposed P/E wth a lower weghtng on SzeEP, as suggested by the lnear regresson on one-year returns after takng nto account bd-ask spreads. 16

18 Table 7: Portfolo values and percentage returns for the glamour and value decles from the E/P decomposton lnear regresson and from the tradtonal undfferentated E/P, Value Decle Value Decomposed E/P Value Decle % Glamour Decle Value Glamour Decle % Value Decle Value Tradtonal E/P Value Glamour Decle % Decle Glamour Decle % Value , % 1, % 1, % 1, % , % 1, % 1, % 1, % , % 1, % 1, % 1, % , % 2, % 2, % 1, % , % 2, % 4, % 2, % , % 2, % 3, % 2, % , % 3, % 5, % 3, % , % 2, % 5, % 3, % , % 3, % 7, % 4, % , % 4, % 11, % 6, % , % 5, % 13, % 6, % , % 7, % 22, % 7, % , % 10, % 33, % 12, % , % 10, % 37, % 12, % , % 11, % 47, % 15, % , % 10, % 35, % 12, % , % 9, % 30, % 9, % , % 9, % 27, % 8, % , % 10, % 30, % 8, % , % 12, % 40, % 11, % , % 11, % 41, % 10, % , % 14, % 46, % 13, % , % 14, % 46, % 15, % , % 15, % 50, % 17, % , % 16, % 44, % 16, % , % 17, % 53, % 29, % , % 14, % 65, % 20, % , % 13, % 67, % 13, % , % 10, % 53, % 9, % ,475 13,973 80,904 15,517 17

19 Fgure 1: Average P/E's by market captalsaton category, P/E Market Value Category Fgure 2: Influences on the P/E rato Year Low P/E Hgh returns P/E Low P/E Hgh returns Sector Hgh P/E Hgh returns Sze Low P/E Hgh returns Idosyncratc Low P/E Hgh returns 18

20 Fgure 3: Bd-offer spreads by market captalsaton category, all UK companes % 10% 8% Bd/Offer Spread 6% 4% 2% 0% MV Category Fgure 4: Sharpe ratos of one-year returns when assgnng companes to decles usng E/P decomposton lnear regresson weghts, Hgh P/E Decle 2 Decle 3 Decle 4 Decle 5 Decle 6 Decle 7 Decle 8 Decle 9 Low P/E 19