Testing Benjamin Graham s Net Current Asset Value Strategy in London

Transcription

1 Testng Benjamn Graham s Net Current Asset Value Strategy n London Yng Xao and Glen Arnold Centre for Economcs and Fnance Research Salford Busness School Unversty of Salford Salford Manchester M5 4WT, UK e-mal: y.xao@pgr.salford.ac.uk G.C.Arnold@salford.ac.uk Salford Busness School Workng Paper Seres Paper no. 109/07 31 January 2007

2 Testng Benjamn Graham s Net Current Asset Value Strategy n London Yng Xao and Glen Arnold Centre for Economcs and Fnance Research, Salford Busness School, Unversty of Salford, Salford, Manchester, M5 4WT, UK. Abstract It s wdely recognzed that value strateges - those that nvest n stocks wth low market values relatve to measures of ther fundamentals (e.g. low prces relatve to earnngs, dvdends, book assets and cash flows) - tend to show hgher returns. In ths paper we focus on the early value metrc devsed and employed by Benjamn Graham - net current asset value to market value (NCAV/MV) - to see f t s stll useful n the modern context. Examnng stocks lsted on the London Stock Exchange for the perod 1981 to 2005 we observe that those wth an NCAV/MV greater than 1.5 dsplay sgnfcantly postve market-adjusted returns (annualzed return up to 19.7% per year) over fve holdng years. We allow for the possblty that the phenomenon beng observed s due to the addtonal return experenced on smaller companes (the sze effect ) and stll fnd an NCAV/MV premum. The proftablty of ths NCAV/MV strategy n the UK cannot be explaned usng Captal Asset Prcng Model (CAPM). Further, Fama and French s three-factor model (FF3M) can not explan the abnormal return of the NCAV/MV strategy. These premums mght be due to rratonal prcng. Key words: Market effcency; Net asset value; Benjamn Graham. The nterpretaton of the excess returns to value strateges s controversal and has been explaned n two ways. Frst, the excess return assocated wth value stocks s due to the propensty of value portfolos to be dsproportonately small frms, and so what s really beng observed s a low market captalsaton effect. Second, value strateges are fundamentally rsker. For example, Fama and French (1993, 1996) created ther three-factor prcng model (market factor, small mnus bg sze factor and hgh mnus low book-to-market factor) n an attempt to provde a rsk compensaton explanaton of value premums. However, many other researchers, partcularly behavoural fnance adherents, dspute whether the FF3M really measures rsk nduced equty return premums. Accordng to ths vew hgh returns to small companes and hgh returns to low market-to-book rato companes are caused by nvestors beng less than completely ratonal, leadng to neglected, under-researched stocks and temporary under-prcng, followed by a convergence to ntrnsc value. 2

3 Amongst the array of value strateges the net current asset value (NCAV/MV) approach has been successfully used n practce, most famously by Benjamn Graham n the early twenteth century, brngng hgh profts from the 1930s to There have been very few studes examnng the NCAV/MV strategy. Graham s NCAV/MV strategy calls for the purchase of stocks at a prce 2/3 or less of the NCAV. Per share NCAV, as defned by Graham (Graham and Dodd (1934), Graham (1976)), s the balance sheet current assets mnus all the frm's (current and long-term) labltes dvded by the number of shares outstandng. Long-term assets (e.g. ntangble assets and fxed assets) values are not counted. Graham found that companes satsfyng the NCAV/MV strategy were often prced at sgnfcant dscounts to estmates of the value that stockholders could receve n an actual sale or lqudaton of the entre corporaton. Thus, the NCAV/MV rule, n theory, not only protects captal from sgnfcant permanent loss but also generates a portfolo of stocks wth excellent prospects for advance n prce. It s clear that these ssues were sellng at a prce well below the value of the enterprse as a prvate busness. No propretor or majorty holder would thnk of sellng what he owned at so rdculously low a fgure In varous ways practcally all these bargan ssues turned out to be proftable and the average annual result proved much more remuneratve than most other nvestments Graham (2003). An adherent to the effcent markets hypothess would advance the argument that nvestors ratonally push down a stock s prce to below NCAV n antcpaton of the corporaton contnung to nvest ts resources n wasteful ways, gradually dranng the company of much of ts shareholder wealth. However, Graham reasoned that the majorty of these value stocks wll survve and produce good returns because of the potental for one of a number of developments to occur preventng management from contnung on a path of value destructon through the gradual dsspaton of assets: Earnng power would be lfted to the pont where t was commensurate wth the company s asset level. Ths could come about n two ways: a general mprovement n the ndustry entry and ext dynamcs mean that low ndustry proftablty s frequently not as persstent as many market pessmsts beleve - and; a change n the company s operatng polces management runnng a company wth such a low stock prce relatve to assets ether respond voluntarly to take correctve acton or they (or ther replacements) are forced to by stockholders, such as adoptng more effcent methods or abandonment of unproftable lnes. A sale or merger wth another corporaton that could employ the frm s assets would take place. It would pay at least the lqudaton value. Complete or partal lqudaton could release value. The management of a corporaton sellng at below lqudaton value need to provde a frank justfcaton for contnung to operate. Graham used the NCAV/MV crteron extensvely n the operatons of the Graham-Newman Corporaton and report that shares selected on the bass of the NCAV/MV rule earn, on average, about 20percent per year over the 30-year perod to 1956 (Graham and 3

4 Chatman (1996)). More recently, Oppenhemer (1986) tested returns of NCAV/MV portfolos wth returns on both the NYSE-AMEX value-weghted ndex and the small-frm ndex from 1971 through He found that returns are rank-ordered: securtes wth the smallest purchase prce as a percentage of NCAV show the largest returns. Over the 13-year perod, the Graham crtera NCAV/MV portfolos on average outperformed the NYSE-AMEX ndex by 1.46percent per month (19 percent per year) after adjustng for rsk. When compared to the small-frm ndex, these portfolos earned an excess return of 0.67% per month (8 percent per year). In the frst study outsde of the USA, Bldersee, Cheh and Zutsh (1993) s paper focuses on the Japanese market from 1975 to In order to mantan a sample large enough for cross-sectonal analyss, Graham s crteron was relaxed so that frms are requred to merely have an NCAV/MV rato greater than zero. They found the mean market-adjusted return of the aggregate portfolo s around 1 percent per month (13 percent per year). The objectve of ths paper s to study NCAV/MV strategy n London snce we are not aware of any work done on the UK market. The Study The research perod s from January 1980 to December 2005 (company data pror to 1980 s unrelable and ncomplete Nagel (2001)). Two databases are used: monthly return data and general nformaton s from the London Share Prce Database (LSPD), and; annual accountng data s from Datastream. In order to calculate NCAV, current assets, current labltes, long-term debt and preferred stock are downloaded from balance sheet entres on Datastream. Because of potental problems defnng accountng varables and equty captalsaton, we exclude companes wth more than one class of ordnary share and foregn companes. Also excluded are companes on the lghtly regulated markets and companes belong to the fnancal sector. We nclude companes that have been de-lsted from the exchange due to merger, lqudaton or any other reason n the holdng perod, thus avodng survvorshp bas. Returns for each company, ncludng dvdends, are adjusted for changes n stock splts, rghts ssues and stock repurchases. The total number of companes n the full sample s 2438, whch covers 90 percent of all corporatons n LSPD (.e. 90 percent of the London man market), and the number n the market ndex s 3086 (ths ncludes fnancal companes). The average number of companes at the 20 portfolo formaton dates s Portfolos of stocks are formed annually n July. To be ncluded n the sample for year t, frms must have data for NCAV n December of t-1, and at least one return observaton n the post-formaton perod. The sx-month lag between the measurement of NCAV and return data allows for the delay n publcaton of ndvdual companes accounts, thus ensurng that the fnancal statements are publc nformaton before the returns are recorded. Only those stocks wth NCAV/MV hgher than 1.5 are ncluded n the NCAV/MV portfolos. Buy-and-hold portfolos held for one, two, three, four or fve years are constructed; the frst formaton s n July 1981 and the last formaton s n July The numbers of companes fulfllng Graham s NCAV/MV crtera are lsted n table 1. Clearly, a potental dffculty n ths area of 4

5 research s the low number of frms that can be ncluded n the portfolos n recent tmes. However, n ths work there are a suffcent number to provde meanngful results overall. Results Wthn each of portfolos stocks are frst weghted equally and then value weghted (whch means that each stock s weghted n proporton to ts market captalsaton at the date of portfolo formaton). To examne the senstvty of the results to the choce of a market ndex, frstly, the results are presented usng an equally weghted market ndex, then they are presented wth a value-weghted ndex. The market ndex, used to adjust returns, comprses all of companes n Offcal lst. Panel A of table 2 presents raw returns, together wth the market ndex returns. Panel B shows the market-adjusted returns together wth tests of statstcal sgnfcance. We fnd that Graham s NCAV/MV stocks substantally outperform the stock market over holdng perods of up to fve years. The average 60-month buy-and-hold raw return s 254 percent wth equal weghtng wthn the NCAV/MV portfolo and 216 percent wth value weghtng, whch are much hgher than market ndces of only 137 percent and 108 percent. One mllon pounds nvested n a seres of NCAV/MV (equal weghted) portfolos startng on 1 st July 1981 would have ncreased to 432 mllon by June 2005 based on the typcal NCAV/MV returns over the study perod. By comparson 1,000,000 nvested n the entre UK man market would have ncreased to 34 mllon by end of June For almost all post-formaton lengths, and regardless of wthn portfolo weghtng, the NCAV/MV portfolo outperforms ether equal weghted or value weghted market ndces wth hgh statstcal sgnfcance. Market-adjusted returns rse to 117 percent and 146 percent after fve years f the stocks are equally weghted; and 78 percent and 108 percent after fve years f the stocks are value weghted. Inspecton of table 2 clearly shows that there are substantal benefts from selectng hgh NCAV/MV stocks. Rsk analyss If NCAV/MV stocks bear rsk, ther average returns may be smply compensaton for ths. We examne rsk from a number of perspectves: Consstency If the NCAV/MV strategy performs badly aganst the market ndex regularly then the nvestor may be faced wth a form of rsk that may be unacceptable. Table 3 shows the number NCAV/MV portfolos (out of 20) that faled to pay-off (compared wth an nvestment n the market). We fnd that n only 20 percent -25 percent of cases (4 or 5 out of 20 years) do the NCAV/MV portfolos under perform the market ndex over the fve-year holdng perod. Few of the formatons under-perform the market n the 1980s: f equal weghtng s used n portfolo formaton and benchmark constructon, the NCAV/MV strategy consstently outperforms the market for 8 of 10 years. Ths would have looked a good strategy f the 5

6 nvestor had downsde constrants. The results for the 1990s are not quet so encouragng, but, at least when equal weghts are gven to NCAV/MV stocks outperform on most occasons. We conclude, therefore, the strategy s farly, but not completely, relable. Deletons and lqudatons Another concern for nvestors s the lkelhood of lqudaton. Table 4 presents average percentage of stocks remanng durng the test perod and the cause of deletons. Panel A shows that a hgher percentage of NCAV/MV companes reman on the market after fve years than s the case for companes generally. The removal rate of the NCAV/MV portfolo s percent whle for the market ndex t s percent for 60-month holdng perods. The reason for removal from the portfolo s mportant because, for example, mergers have a dfferent mpact on portfolo than lqudatons. A hgher lqudaton rate provdes a sgnfcant downward push to portfolo test perod performance. Panel B shows that wthn 60 months 2.6 percent of the NCAV portfolo on average faled (deleted due to lqudaton) compared wth 4.2 percent of the companes n the market ndex. Ths evdence does not support a rsk-based explanaton for the out-performance of NCAV/MV stocks, based on dstress (Fama and French (1996) refer to fnancal dstress rsk). Beta and standard devaton We also conducted rsk analyses based on tradtonal beta and standard devaton calculatons. The test for CAPM-beta rsk does not provde support for the vew that the NCAV/MV strategy s fundamentally rsker see table 5. The ntercepts of regressons (alpha- a ) are postve wth statstcal sgnfcance n the whole perod and the betas ( b ) are relatvely low up to fve years postformaton. For example, the average beta of NCAV/MV portfolos for 20 formatons s only f buy-and-hold for frst 12 months regressons. CAPM provdes low explanatory power of the tme seres varaton n returns for NCAV/MV portfolos because R 2 s very low (less than 20 percent) for the holdng perods. The standard devatons of monthly returns for NCAV/MV portfolos are slghtly hgher than the market, but we need to consder the fact that these portfolos contan a small number of companes and so would be expected to exhbt greater volatlty. The sze effect Frm sze has been shown to be nversely related to future returns. If NCAV/MV stocks are generally small companes the sze effect may explan ther extra returns. To construct table 6, at each formaton date, , all London lsted UK shares n the sample are sorted accordng to sze and allocated to one of ten portfolos. Separately, stocks are allocated to an NCAV/MV portfolo f ther rato s hgher than 1.5. The numbers shown are the percentage of the average NCAV/MV portfolo fallng nto each sze decle. For Benjamn Graham s NCAV/MV portfolo, nearly 79 percent number of companes are very small (belong to sze 1 and sze 2). The sze effect may therefore be causng the abnormal performance of the NCAV/MV strategy. Table 7 confrms the presence of a sze effect over the study perod. It records the value 6

7 weghted returns for all man market London shares after sortng by market captalsaton The raw return for the smallest sze portfolo s 209 percent over 60 months, whle that for the largest s only 105 percent. The results are consstent wth Levs (1989) and show that there s a strong sze effect n the UK stock market. To nvestgate the relatonshp between the NCAV/MV effect and the small frm effect, we use sze-control portfolos. To generate these we frst select shares that qualfy by Benjamn Graham s crtera. Then for each NCAV/MV portfolo n each year we observe the sze of each company. Ths provdes a profle for each NCAV/MV portfolo n terms of the dstrbuton of the component shares wth respect to sze decles. Once the sze profle of an NCAV/MV portfolo s known, the returns over the subsequent 1 to 5 years s calculated on the assumpton that return s due only to sze-decle make up of the portfolo. Sze-control portfolos are constructed to have the same sze composton as the correspondng NCAV/MV portfolo. The sze-adjusted return of an NCAV/MV portfolo s computed as the average raw return on the portfolo (value weghtng of shares wthn portfolos) mnus the average return on the value weghted sze-control portfolo. (The results of equal weghtng are smlar to value weghted returns.) Ths procedure s carred out for each of the portfolo formatons and the reported numbers are averages over 20 test perods. Controllng for sze reduces the return premum of NCAV/MV portfolos consderably for all holdng perods (see table 8). The fve year sze-adjusted return of NCAV/MV stocks reduce to 71 percent compared to 108 percent market-adjusted returns (as shown n table 2). For holdng perods of one, two and three years we fnd evdence that t s possble that the NCAV/MV effect s subsumed wthn the sze effect (gven the poor statstcal sgnfcance of the sze-adjusted returns). However, wth the four and fve holdng perods we can observe statstcal sgnfcance at the 95 percent level. Then the abnormal buy-and-hold performance controlled by sze s 50 percent for four years and 71 percent for fve years. Thus even after allowng for sze effects n returns, there s an average NCAV/MV premum of 11.3 percent per annum for fve years holdng. The sze effect does not fully explan the abnormal return of the NCAV strategy. Usng Fama and French s three factor model We now ask whether the dfferences n the returns of NCAV/MV portfolos can be explaned by the loadngs that these portfolos have on the three common factors dentfed by Fama and French (1993), namely the market factor, and the mmckng portfolos for the book-to-market and sze factors. Fama and French (1993) argued that f assets are prced ratonally, varables that are related to average returns, such as sze and book-to-market equty, must proxy for senstvty to rsk factors n returns. The FF3M factors serve as ndependent varables n the followng regresson: R R a b ( R R ) t ft Mt ft s SMB h HML e t The market factor (R Mt -R ft ) s the equty market premum and s defned as the monthly 7

8 return of the average of all London man market companes mnus the monthly Treasury bll rate. Followng Gregory, Harrs and Mchou (2001), the mmckng portfolos for the sze and book-to-market factors are constructed. At the end of June each year t from 1981 to 2000, stocks are allocated nto two groups, small (S) and bg (B) by the medan of the largest 350 companes n the sample. Stocks are also allocated n an ndependent sort to three book-to-market groups, low (L), medum (M) or hgh (H). These groups reflect the breakponts for the bottom 30 percent, mddle 40 percent, and top 30 percent of the values of BM recorded for the largest 350 companes at the end of year t-1. Sx sze-bm portfolos (S/L, S/M, S/H, B/L, B/M, B/H) are created from the ntersectons of the two sze and three BM groupngs. Monthly value weghted returns for the portfolos are calculated for 12 months from July of year t to June of year t+1. In respect of the sze factor, the small-mnus-bg (SMB) return s defned as the dfference each month between the average of the returns on the three small portfolos (S/L, S/M, S/H) and the average of the returns on the three bg-stock portfolos (B/L, B/M, B/H). In relaton to the book-to-market factor, the hgh-mnus-low (HML) return s defned as the dfference between the average of the returns on the two hgh BM portfolos (S/H, B/H) and the average of the returns on the two low BM portfolo (S/L, B/L). Fama and French (1993, 1996) estmate three-factor models for portfolos by regressng excess returns for each portfolo on the excess market return and the returns to the most recently formed HML and SMB portfolos up to 12 months. In respect of each portfolo, we estmate fve separate regresson models correspondng to each of the post-formaton years. Usng Gregory, Harrs and Mchou (2001) s method, for the one year horzon, we regress monthly excess returns on the portfolo for July of year t to June of year t+1 on the contemporaneous excess market return and the returns to the HML and SMB portfolos formed n December of year t-1 and June of year t respectvely. The one-year horzon regresson s estmated usng the 240 monthly returns for the perod July 1981 to June For the second test perod year, we regress monthly excess return on the portfolo thrteen months to twenty-four months after portfolo formaton on the contemporaneous excess return on the market factor and on the HML and SMB portfolos formed n the frst test perod year. The method used for three-, four- and fve-year horzons s analogous. The slopes and R 2 value show whether mmckng portfolos for rsk factors related to sze and B/M capture shared varaton n stock returns not explaned by other factors. And the estmated ntercepts provde a smple return metrc and a formal test of how well dfferent combnatons of the factors capture the cross-secton of average returns. The results (shown n table 9) dsplay ntercepts, a, that are sgnfcantly dfferent from zero for each of the frst fve years followng portfolo formaton. Further, low fgures of R 2 (less than 35 percent for all years) represent a market factor and proxes for rsk factors related to sze and B/M seem not to explan NCAV/MV stock returns well,.e. SMB, HML and the market premum do not capture the varaton n NCAV stock returns. Fama and French clam that these factors represent rsk premum demanded by nvestors, but ths s much dsputed (see Lakonshok, Shlefer and Vshny (1994), Danel and Ttman (1997)) who are prepared to accept market neffcency due to nvestor error. 8

9 Concluson Graham defned a bargan ssue as one whch appears to be worth consderably more than t s sellng for. He suggested that an ssue s not a true bargan unless the ndcated value s at least 50 percent more than the prce. The type of bargan ssue that can be most readly dentfed s a stock that sells for less than the company s net workng captal alone, after deductng all pror oblgatons. We fnd evdence that buyng stocks n companes wth a per share net current asset value greater than 1½ tmes the current share prce has produced returns superor to those of the market. Although the NCAV strategy exhbts a small frm effect, when we delve deeper nto the out performance we fnd that the phenomenon s not fully explaned by the fact that these types of stocks tend to be smaller companes and exhbt hgh book-to-market ratos. 9

10 References Bldersee, J. B., Cheh, J. J. and Zutsh, A. (1993). "The performance of Japanese common stocks n relaton to ther net current asset values." Japan and the World Economy 5: Danel, K. and Ttman, S. (1997). "Evdence on the characterstcs of cross-secton varaton n stock returns." Journal of Fnance 52(1-33). Fama, E. F. and French, K. R. (1993). "Common rsk factors n returns on stocks and bonds." Journal of Fnancal Economcs 33: Graham, B. (1976). "A conversaton wth Benjamn Graham." Fnancal Analyst Journal Sep./Oct. Graham, B. (2003). The ntellgent nvestor, New York: HarperCollns World. Graham, B. and Chatman, S. (1996). Benjamn Graham: The memors of the dean of wall street. New York, the McGraw-Hll companes. Graham, B. and Dodd, D. (1934). Securty analyss. New York, McGraw-Hll. Gregory, A., Harrs, R. D. F. and Mchou, M. (2001). "An analyss of contraran nvestment strateges n the UK." Journal of Busness Fnance & Accountng 28 (9) & (10)(Nov./Dec.): Lakonshok, J., Shlefer, A. and Vshny, R. W. (1994). "Contraran nvestment, extrapolaton, and rsk." The Journal of Fnance XLIX(5): Levs, M. (1989). "Stock market anomales a re-assessment based on the UK evdence." The Journal of Bankng and Fnance 13: Nagel, S. (2001). "Accountng nformaton free of selecton bas: A new UK database " workng papers London Busness School. Oppenhemer, H. R. (1986). "Ben Graham's net current asset values: a performance update." Fnancal Analysts Journal:

11 Table 1 Number of companes ncluded n NCAV/MV portfolos at formaton date Year Number of companes

12 Table 2 Raw returns and market-adjusted returns for NCAV/MV portfolos London Stock Exchange lsted UK shares are allocated to NCAV portfolos f ther NCAV/MV ratos are hgher than 1.5 at the begnnng of July 1981 and all subsequent July to Average raw and market-adjusted returns for shares wthn a portfolo are calculated for perods of 1,2,3,4 and 5 years post-formaton. The market ndces nclude all lsted shares except nvestment trusts and overseas companes. All numbers presented are averages over the 20 test perods computed for correspondng portfolos. One sample t-tests based on annually excess returns over the market are shown. Panel A. Average raw buy-and-hold test perod returns Months after portfolo formaton Equally weghted NCAV/MV return Equally weghted market ndex return Value weghted NCAV/MV return Value weghted market ndex return Panel B. Average market-adjusted buy-and-hold test perod returns Months after portfolo formaton Portfolo equal weghts, ndex equal weghts t-test p-value Portfolo equal weghts, ndex value weghts t-test p-value Portfolo value weghts, ndex equal weghts t-test p-value Portfolo value weghts, ndex value weghts t-test p-value Note: a fgure of ndcates a return of 10.68% 12

13 Table 3 Number of occasons when the NCAV/MV strategy produces negatve market-adjusted returns when portfolos are held for fve years Portfolo weghtng Market ndex weghtng Out of 10 years Out of 10 years Out of 20 years Equal Equal Equal Value Value Equal Value Value Table 4 Average percentage of stocks remanng durng the test perod and the reason for deleton of companes Panel A: The percentage of shares remanng after 1,2,3,4 and 5 years averaged for the 20 portfolo formatons Months after formaton NCAV/MV > % 96.33% 89.91% 84.14% 78.22% 73.18% Market ndex 100% 93.63% 86.79% 80.28% 74.18% 68.43% Panel B: Percentage of companes deleted (cumulatve) due to mergers, lqudatons and other reasons. L = percentage of companes deleted due to lqudaton compared to sample n ths portfolo M = percentage of companes deleted due to beng acqured n merger/takeover compared to sample n ths portfolo O = percentage of companes deleted due to other reasons compared to sample n ths portfolo 12-month 24-month 36-month 48-month 60-month M L O M L M M L M M L M M L M NCAV/MV> Market ndex

14 Table 5 Beta and standard devaton for NCAV/MV portfolos For the frst test perod year followng portfolo formaton we observe the raw returns of the portfolo relatve to the Treasury bll rate and the return on a value-weghted market portfolo relatve to the Treasury bll rate. The regressons are based on the 12 monthly observatons for portfolos, drawng on all 20 portfolo formatons. The analyss s repeated for each of the test years. Usng the 20 formaton perods, we also compute the standard devaton of returns n the 12 months after formaton and n each of the test years. R ft s the Treasury bll (30 days) rate at the begnnng of the month, t. R mt s the monthly return of the all companes n the sample. R R a b ( R R ) t ft Mt ft e t 1-12 months months months month months a b t(a) t(b) R 15.5% 16.8% 9.5% 10.8% 19.3% St de (NCAV/MV) St de (market) Table 6 Percentage of frms wthn the NCAV/MV portfolos fallng n sze decles Sze1(smallest) Sze 2 Sze 3 Sze 4 Sze 5 Sze 6 Sze 7 Sze 8 Sze 9 Sze 10 (bggest) NCAV/MV> % 15.43% 7.31% 4.03% 3.81% 1.20% 2.66% 2.25% 0.07% 0.00% 14

15 Table 7 Returns for Offcal lst companes followng allocaton to sze decles London Stock Exchange lsted UK shares are ranked and assgned to decles annually on the bass of ther market captalzatons from end June 1981 and all subsequent Junes to Startng at the begnnng of July each year 1981 to 2000 average raw returns for shares wthn a value-weghted decles portfolo are calculated for perods of 1, 2, 3, 4 and 5 years post-formaton. The returns n the rankng perod are raw returns wth no market adjustment. All numbers presented are averages over the 20 test perods computed for correspondng portfolos. 12-month 24-month 36-month 48-month 60-month Sze 1 (smallest) Sze Sze Sze Sze Sze Sze Sze Sze Sze 10 (bggest) Table 8 Average test perod returns for NCAV/MV portfolo, sze control portfolos and sze-adjusted returns London Stock Exchange lsted UK shares are allocated to NCAV portfolos f ther NCAV/MV ratos s hgher than 1.5. Average raw returns wth value weghtng for shares wthn NCAV/MV portfolo are calculated for perods of 1,2,3,4 and 5 years post-formaton. In order to compute sze-control portfolo, London Stock Exchange lsted UK shares are ranked and assgned to decles annually on the bass of ther market captalzatons from end June 1981 and all subsequent Junes to Average raw returns for shares wthn a value-weghted decles portfolo are calculated up to fve years. Sze-control portfolos are constructed to have the same sze composton as the correspondng NCAV/MV portfolo. The sze-adjusted return of an NCAV/MV portfolo s computed as the average raw return on the portfolo mnus the average return on the value weghted sze-control portfolo. One sample t-tests based on annually excess returns over the market are shown under returns. NCAV/MV Portfolo Raw returns Sze-control portfolo returns Sze-adjusted returns t-test p-value 12-month month month month month

16 Table 9 Three-factor regressons for monthly excess returns for portfolos R R a b ( R R ) t ft Mt ft s SMB h HML e t R ft s the monthly Treasury bll rate. R Mt s the monthly return of all London Stock Exchange lsted UK shares. One-sample t-tests for each coeffcent provded n t( ). The constructon of SMB and HML s explaned n the man text. 1-year 2-year 3-year 4-year 5-year a b s h t(a) t(b) t(s) t(h) R 19.7% 32.7% 19.4% 18.8% 30.0% Cross-reference lsts of LSPD company numbers and Datastream codes to SEDOL numbers provde a startng pont of matchng two databases. Then LSPD and Datastream are matched usng tme seres unadjusted stock prces. To check the matchng, company name, base date, end date, prevous name and date of last name change are also used. We also tred equal weghtng for sze effect (and FF3M) n the UK market and found smlar results to value weghtng. The use of the largest 350 companes rather than the whole sample to defne the breakpont for the sze splt reduces the mbalance on the market captalzaton of small and large groups. Ths s consstent wth Gregory, Harrs and Mchou (2001) and Levs and Lodaks (1999). 16