Low-risk anomaly everywhere: Evidence from equity sectors

Transcription

1 Low-rsk anomaly everywhere: Evdence from equty sectors Forthcomng: Rsk-Based and Factor Investng, Elsever Scentfc Publcatons, September 2015 Raul Leote de Carvalho s deputy-head of fnancal engneerng at BNP Parbas Investment Partners n Pars, France. raul.leotedecarvalho@bnpparbas.com, Tel. +33 (0) Majdoulne Zakara s a quanttatve analyst n the fnancal engneerng team at BNP Parbas Investment Partners n Pars, France and doctoral student at Dauphne Unversty n Pars, France. majdoulne.zakara@bnpparbas.com, Tel. +33 (0) Xao Lu s head of quanttatve research n the fnancal engneerng team at BNP Parbas Investment Partners n Pars, France. xao.lu@bnpparbas.com, Tel. +33 (0) Perre Mouln s head of marketng nnovaton and research at BNP Parbas Investment Partners n Pars, France. perre.mouln@bnpparbas.com, Tel. +33 (0) We are grateful to Franços Soupé and Gullaume Kovarck for ther nsghtful dscussons and to Chrs Montagu, Erc Melka, Gurvnder Brar, Ingo Fraser-Jenkns, Marco Don, Mchael Sommer and Yn Luo for ther nsghtful vews. 30 October 2014 BNP Parbas Investment Partners, 14 rue Bergère, Pars, France 1

2 Abstract: We gve strong emprcal evdence of a rsk anomaly n equty sectors n a number of regons and countres of developed and emergng markets, wth the lowest rsk stocks n each actvty sector generatng hgher returns than would be expected gven ther levels of rsk, and the converse outcome for the rsker stocks. We beleve ths evdence s a lkely consequence of the fact that equty analyst and actve fund managers tend to specalze n partcular sectors and to manly select stocks from those sectors. Addtonally, constrants restrctng the devaton of sector weghts n actve portfolos aganst ther market captalzaton benchmarks are often used by actve fund managers, n partcular by quanttatve managers whch tend to go as far as beng sector neutral. As a consequence, we fnd that sector-neutral, low-rsk approaches appear more effcent at generatng alpha than non-sector neutral approaches, wth the latter showng strong sector allocaton towards fnancals, utltes and consumer staples than sector neutral, at least when appled to developed countres n a global unverse. We also dscuss some propertes of low-rsk nvestng such as tal rsk, turnover and lqudty. JEL classfcaton: G11, G12, G14 Keywords: low rsk, low volatlty, equtes, factor nvestng, market effcency, CAPM 2

3 Low-rsk nvestng n equtes has been n the spotlght n recent years probably due n partcular to the dsappontng performance of equty markets snce the start of the new mllennum and untl the 2008 crss. The man focus of low-rsk nvestng s to reduce portfolo rsk, defendng the portfolo n equty market downturns, whle capturng the postve alpha from low-rsk stocks to mprove rskadjusted returns. Indeed, the postve alpha found n low-rsk stocks explans why the Sharpe rato of strateges nvested n these stocks has been larger than that for the market captalzaton ndex. Lowrsk nvestng also naturally excludes the rsker stocks whch have been delverng the poorest rskadjusted returns and have had sgnfcant negatve alpha. Low-rsk nvestng dates back to the semnal paper of Haugen and Hens (1972) wth emprcal evdence that between 1926 and 1969 portfolos systematcally nvestng n U.S. low-volatlty stocks would have delvered much larger returns than expected from ther low level of beta, whle portfolos nvested n hgh-volatlty stocks would have delvered returns much below what should have been expected from ther hgh level of beta. Brennen (1971) and Black (1972) showed that the volaton of one of the assumptons behnd the Captal Asset Prcng Model (CAPM) that nvestors have no constrants, e.g. on leverage or borrowng s suffcent to reduce the slope of the relatonshp between returns and beta. Bltz (2014) has recently revewed the academc lterature and summarzed the dfferent effects that have been proposed by academcs to explan the low-rsk anomaly. The low-rsk anomaly appears almost unversally. Haugen and Baker (2012) demonstrated emprcally that t can be found n the cross-secton of stock returns of almost all developed and emergng market countres n the world. The comprehensve emprcal analyss of De Carvalho, Dugnolle, Lu and Mouln (2014) strongly suggests that the low-rsk anomaly goes beyond equty markets and can also be found n the cross-secton of bond returns of all major segments of fxedncome markets and regons. Ther results show that portfolos nvested n low-rsk bonds wth the lowest beta generated the largest postve alpha, whle portfolos nvested n the rsker bonds wth the hghest beta generated the most negatve alpha. Ths result was found for government bonds, quas & foregn government bonds, securtzed & collateralzed bonds, corporate nvestment-grade bonds, corporate hgh-yeld bonds, emergng market bonds and aggregatons of some of these unverses, and for bonds n USD, EUR, GBP and JPY. Frazzn and Pedersen (2014) suggest that the low-rsk anomaly s also observed n commodtes, currences and at top-down level n fxed ncome and equtes,.e. n the cross-secton of the returns of currency forwards, ndex futures, equty and Treasury country ndces, portfolos aggregated by ratngs, and n the cross-secton of all these put together. Baker, Brendan and Talaferro (2014) have recently looked at the decomposton of the lowrsk anomaly nto top-down country and ndustry contrbutons and bottom-up contrbutons. They found a rsk anomaly n the cross-secton of country returns and, to a lesser extent, n the cross- 3

4 sectonal of ndustry returns. Asness, Frazzn and Pedersen (2014) gave stronger evdence of a lowrsk anomaly n the cross-secton of ndustry returns by usng more granular ndustry defntons. The low-rsk anomaly s not only found n the cross-secton of asset classes but also n the tme seres of asset class premums and n the tme seres of factor premums. Perchet, De Carvalho, Heckel and Mouln (2014) showed that the tme seres of asset class returns shows volatlty clusterng,.e. the volatlty forms two dstnct volatlty regmes, one wth low volatlty and hgh average returns and on wth hgh volatlty and low average returns, or even negatve, for most asset classes. In turn, Perchet, De Carvalho and Mouln (2014) showed that the tme seres of value and momentum factor returns n equty, government bonds and currency markets also shows volatlty clusterng, wth two dstnct volatlty regmes: hgher returns for the low volatlty regme and lower returns for the hgh volatlty regme. In ths paper we am ) to nvestgate the unversalty of the rsk volatlty anomaly by focusng on the cross-secton of stock returns n equty sectors n developed countres and emergng market countres, n aggregate and at ndvdual country level; and ) to compare sector-neutral low-rsk nvestng wth the tradtonal sector-based low-rsk approaches that are typcally over-exposed to defensve sectors. We also am to shed addtonal lght on the results of Baker, Brendan and Talaferro (2014), who found that the rsk anomaly s stronger at stock level by neutralzng ndustry exposure than n the cross-secton of ndustry returns, contrary to what should have been expected from the suggeston by Samuelson (1998) that stocks are prced more effcently than ndustres because ndustres have fewer substtutes than stocks, an argument they used to motvate ther research. The results of Asness, Frazzn and Pedersen (2014) also pont n the same drecton,.e. that the rsk anomaly can be more effcently captured by neutralzng ndustry exposures than by nvestng at top-down level n low rsk ndustres and avodng the rsker ndustres. Moreover, we dd not fnd any explct effect that could explan these results n the avalable lterature. In fact, we wll argue that one possble explanaton comes from the actve management ndustry and the way actve managers tend to pck stocks for ther actve portfolos. Ths explanaton s thus closely related to what Bltz (2014) calls relatve utlty and agents maxmze opton value, but s lkely to be a consequence of the practcaltes of how fund managers tend to operate and manage portfolos wth the objectve of out-performng a benchmark ndex. LOW VOLATILITY OR LOW BETA? Nether the stock volatlty nor the stock beta s constant over tme. Hence, low-rsk nvestng requres perodc rebalancng to take nto account that some stocks whch have been low rsk n the past may no longer be low rsk n the future. A strategy perodcally rebalancng the stock allocaton towards 4

5 the mnmum varance portfolo s an example of a low-rsk strategy that can be shown to have delvered hgher rsk-adjusted returns than expected from ts low level of beta. However, as shown by De Carvalho, Lu and Mouln (2012), the mnmum varance portfolo can be replcated by smple portfolo strateges based on equally overweghtng low beta stocks and underweghtng hgh beta stocks. We thus prefer to use smpler strateges that nvolve selectng stocks from rsk rankngs to buld low-rsk portfolos, rather than usng mnmum varance strateges. Research on the low-rsk anomaly often reles on buldng portfolos nvested n a selecton of stocks wth the lowest ex-ante beta, e.g. Baker, Brendan and Talaferro (2014) and Asness, Frazzn and Pedersen (2014), and often n a selecton of stocks wth the lowest ex-ante volatlty, e.g. Baker and Haugen (2012) and L, Rodney, Sullvan and Garca-Fejóo (2014). We chose to use ex-ante volatlty nstead of ex-ante beta for the reasons lsted below. We bult two strateges and appled them to the MSCI World Index 1 stock unverse. In the frst strategy, stocks are frst ranked every month by ther level of ex-ante beta 2 calculated at that pont n tme from a two-year rollng regresson of the stock total returns n excess of cash aganst the total returns of MSCI World Index n excess of cash, wth returns n USD. Every month we bult an equally-weghted portfolo nvested n the stocks wth the lowest ex-ante beta at the start of the month holdng ths portfolo untl the next monthly re-balancng. We kept only 10% of the stocks n the unverse. The hstorcal smulaton of ths strategy runs from January 1995 through August 2013 and ts results are compared wth a smlar strategy, whch dffers only n the fact that nstead of ex-ante beta we used a two-year rollng standard devaton of returns 2. Low-volatlty stocks have low beta because beta s smply the product of the stock volatlty by the correlaton of returns wth the market returns dvded by the market volatlty. But not all low-beta stocks have low volatlty. Some hgher-volatlty stocks can be low beta due to the low correlaton wth the market. If we look at the average overlap between the portfolos behnd the two strateges we fnd that t s hgh, at 55%. Ths s n fact hgh knowng that there are about 1,700 stocks on average n the MSCI World ndex and that we retan only 10% of those stocks n each case. But despte beng hgh, the unverse of low-volatlty stocks s not exactly the same as the unverse of low-beta stocks. We also observe that the strategy based on low beta has a hgher turnover at 19% (two-way) per month than the strategy based on low volatlty at only 13%. That s a sgnfcant dfference and shows that the persstence of beta s less strong than the persstence of volatlty, whch should have been expected snce the beta wll change n tme not only because of changes n volatlty but also because of changes n correlaton wth the ndex. We have thus ncluded a thrd strategy whereby the selecton s based on a Bayesan estmaton of the beta, thus followng the procedure proposed by Vascek (1973), whch ams at mprovng the estmaton of beta. 5

6 The results of the smulatons can be found n exhbt 1. We use US T-bll 3-month rates obtaned va FactSet as the proxy for the rsk-free rate and no transacton cost or market mpact was consdered. As we can see, the dfferences among the strateges are not large, n partcular f we take nto account the length of the back-test. Nevertheless, we fnd that when selectng the lowest beta stocks, the strategy delvers a slghtly lower beta and alpha than when selectng the lowest volatlty stocks. In turn, the volatlty s slghtly lower when selectng the lowest volatlty stocks than when selectng the lowest beta stocks. Not surprsngly, we also fnd that the results based on a Bayesan estmaton of the beta are closer to those based on volatlty than those based on the standard beta estmaton. Exhbt 1: Annualzed returns, volatlty, Sharpe rato, alpha and beta for monthly rebalanced low rsk strateges based on rankng approaches usng beta and volatlty estmators. Selected low-rsk stocks are equally weghted. World unverse. Jan-95 Aug-13. Low Beta Low Volatlty CAPM Bayesan Annualzed Excess return over Cash 7.6% 7.9% 8.1% Volatlty 11.4% 11.1% 10.9% Sharpe Rato Annualzed alpha 5.7% 6.0% 6.0% Beta Selectng low-volatlty stocks generates much lower turnover, creates margnally more alpha and results n a beta that s almost as low as when selectng by low beta. For these reasons we shall use volatlty nstead of beta for the selecton of stocks n the remander of ths paper. An addtonal reason for usng volatlty nstead of beta s the non-unversalty of beta. From a CAPM pont of vew the beta should be based on the market portfolo. But for a portfolo manager benchmarked aganst a segment of the market portfolo what really matters s the beta measured aganst the market captalzaton-weghted portfolo for the stocks n that market segment. Thus, the relevant measure of beta s not the same for all market partcpants f we take nto account ther dfferent objectves. SECTOR-NEUTRAL LOW-RISK INVESTING Motvaton The CAPM assumes that nvestors are rsk-averse and maxmze the expected utlty of absolute wealth, carng only about the mean and the varance of returns. Ths s a large assumpton whch does not actually apply to all nvestors. Professonal actve portfolo managers are apprased on ther performance relatve to a benchmark ndex, typcally a market-captalzaton portfolo of a gven 6

7 segment of the equty market, usually a country or regon. Consequently, these professonal nvestors do not care about absolute wealth or rsk, but only about the relatve performance n excess of the benchmark and the trackng-error rsk. They often have targets and constrants on the trackng-error rsk they can take. As argued by Falkensten (2009), f CAPM was observed, actve portfolo managers would then maxmze ther utlty by nvestng n hgh-beta stocks nstead of low-beta stocks. Under CAPM, gven two stocks wth the same level of trackng-error rsk, one wth hgh beta and one wth low beta, the portfolo manager preference would necessarly be for the hgh-beta stock whch, wth a beta hgher than one, would be expected to out-perform the market captalzaton ndex n the medum to long term thanks to ts hgher exposure to the market rsk premum. In turn, the low-beta stock, wth beta below one, would be expected to under-perform the market captalzaton ndex thanks to ts low market exposure. The hgher demand for hgh-beta stocks created by these nvestors should push up the prces of such stocks and make cheaper the low beta stocks that are less n demand. As shown by Falkensten (2009), the expected return for each stock s then the same n equlbrum. Even f these nvestors represent just part of the unversal nvestor populaton and other nvestors maxmze the expected utlty of absolute wealth, a rsk anomaly should stll expected, even f less strong, as shown by Brennan (1993) and Brennan, Cheng and L (2012). A related explanaton of the low-rsk anomaly was proposed by Baker and Haugen (2012). They focus on the typcal compensaton structure of professonal actve portfolo managers and show that the ncentve structures resemble a call opton. The value of call optons ncreases wth volatlty and thus, assumng that actve portfolo managers seek to maxmze the expected value of the call optons upon whch ther compensaton s based, they are ncentvzed to take rsk and should prefer to nvest n hgh-rsk stocks than low-rsk ones. Falkensten (2009) goes further, argung that snce rewards are typcally much larger for top quntle portfolo managers than for second quntle portfolo managers, the ncentve to take rsk and nvest n rsky stocks s heghtened. Baker and Haugen (2012) also argue that the nvestment teams responsble for selectng the stocks for actvely-managed funds are usually ncentvzed to focus on hgh-rsk stocks, manly due to career pressure. It s those who select stocks wth stellar performances that are more lkely to be promoted, and stocks wth stellar performances can be more lkely found n the unverse of rsker stocks, even f the average returns of the unverse of all rsker stocks s shown to be poor. They are also under pressure to focus on stocks whch are n the spotlght and receve above medan coverage, the hottest stocks n the market, whch are typcally rsky stocks. Dscussons wth lead portfolo managers and wth clents are much easer when t comes to explanng the decson to nvest n a gven stock f they 7

8 are also famlar wth that partcular stock. Fnally, prvately-owned asset management frms sellng actvely-managed funds have an ncentve to generate more volatle fund performances, as dscussed by Chevaler and Ellson (1997) and Srr and Tufano (1998). Ths s because the funds wth the top performance relatve to peers, n partcular followng perods of good market performance, tend to receve the largest nflows. The relatonshp between fund flows and performance supports the dea that asset management frms should concentrate ther efforts on hgh-beta funds to maxmze ther profts. In concluson, there s strong evdence that the way n whch the actve management ndustry operates creates strong demand for rsker stocks. But none of the authors above explores the practcaltes of managng actve funds. In partcular, they do not take nto account that, n most asset management frms managng actve funds based on fundamental approaches, the stock selecton s typcally made by sector specalsts who pck the stocks wth the hghest expected returns from ther sector. There are reasons for ths. Stocks from any gven sector tend to be exposed to a number of common factors and are thus easer to compare. The decson behnd stock selecton s easer when apples are compared to apples. Analysts can also specalze and focus only on more manageable unverses n terms of the number of stocks to cover. Analysts nvolved n stock selecton at asset management frms are nearly always organzed by sector. And analysts nvolved n stock research n brokerage frms, provdng company research to asset management frms, are also almost nvarably organzed by sector. We asked seven heads of research at large nternatonal brokerage frms 3 wth bases n the U.S., Europe and Asa, how many of ther clents operate on ths bass and the answers suggested that the vast majorty do. They also confrmed that the equty analysts at ther brokerage frms are ndeed also organzed by sectors, much n lne wth ther clent base. When asked about the most commonly used sector defnton used to delneate sector coverage we were told that even f the 10 sector GICS 4 defnton s not always strctly used, for the most part, some relatvely smlar defnton s employed wth occasonally one or another sector broken nto some of ts consttuent ndustres. Only one brokerage house hghlghted that some clents tend to go down to the 24 ndustry GICS defnton when managng portfolos benchmarked aganst broader ndces. Actve portfolo managers tend to nvest n a lmted number of selected stocks from the nvestment unverse to whch they are assgned. Sector actve weghts n portfolos are often constraned as a crude way of managng trackng-error rsk. When asked about how many of ther clents tend to keep tght-to-moderate sector constrants, the brokerage frms gave essentally the same answer. When t comes to portfolo constructon, quanttatve actve managers, those who rely on quanttatve systematc approaches for stock-pckng and whch have represented a large porton of the actvely 8

9 managed funds market n the past seem nvarably to use tghter sector constrants than fundamental managers, who follow the process descrbed above. When asked to put a number behnd ther answer we were gven results wth some level of dsperson. In terms of average, the brokerage frms put at about 40% the percentage of fundamental actve managers who mpose strong-to-moderate controls on actve sector exposures, whle for quanttatve actve managers ths fgure rses to about 70%. Moreover, quanttatve managers often seem to add constrants on the beta of ther portfolos, restrctng t to be above one for benchmarked funds and above zero for long-short portfolos. We beleve ths evdence s supportve of the results of Baker, Brendan and Talaferro (2014) and Asness, Frazzn and Pedersen (2014) and probably explans why ther results are not n lne wth what should have been expected from the reasonng advanced by Samuelson (1998),.e. that stocks are prced more effcently than sectors or ndustres. The fact that the stocks are almost nvarably pcked usng sector-based approaches and that a large percentage of portfolo managers apply some level of sector control when buldng ther portfolos s consstent wth a stronger rsk anomaly n the cross-secton of stock returns wthn each sector rather than n the cross-secton of sector returns. The evdence collected from heads of research at brokerage frms ponts towards a more wdespread use of the 10 sector GICS defnton than the more granular ndustry defnton used by ether Baker, Brendan and Talaferro (2014) or the sub-ndustres defnton used by Asness, Frazzn and Pedersen (2014). For ths reason we concentrate our research on sectors rather than ndustres or sub-ndustres. Unversalty of the low-rsk anomaly n equty sectors In ths secton we present results from hstorcal smulatons desgned to compare the return and rsk of systematc strateges nvested n the lowest volatlty stocks of each sector wth those from a smlar strategy nvested n the rsker stocks of the same sector. We run the analyss through a number of developed and emergng markets. We used the followng lst of ndces: Developed countres: MSCI World Index (MSCI Inc.). From U.S.: S&P 500 Index (U.S. stock exchanges). From Europe: Stoxx Europe 600 Index (18 countres of the European regon whch today are Austra, Belgum, Czech Republc, Denmark, Fnland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Span, Sweden, Swtzerland and the Unted Kngdom). From Japan: Topx 500 Index (Tokyo stock exchange). From Canada: S&P/TSX Composte Index (Toronto stock exchange). From Emergng Markets: MSCI Emergng Markets Index (MSCI Inc.). From Chna: CSI 300 Index (Shangha and Shenzhen stock exchanges). From

10 Brazl: IBrX Index (São Paulo stock exchange). From Tawan: TWSE Index (Tawan stock exchange). From South Korea: Kosp Index (Stock Market Dvson of South Korea exchange). From For each unverse of stocks defned by these ndces we used the longest hstory we avalable. Snce not all ndexes have the same startng dates, the results cover dfferent perods varyng from nne to 24 years. All data was collected usng FactSet and the orgnal data provders are ndcated adjacent to each ndex. In the hstorcal smulatons for each ndex above we started by estmatng the hstorcal volatlty of each stock n the ndex unverse at the end of each month from the past two years 2 of total returns n local currences. The stocks n each sector were then ranked by ther hstorcal volatlty 2 nto three portfolos wth the same number of stocks. Stocks n each of these three portfolos were then equallyweghted. We used the 10 sector defnton of GICS 4 ; n cases where the GICS classfcaton was mssng for a gven stock, the FactSet ndustry classfcaton was used nstead. A small number of stocks that had nether GICS nor FactSet classfcaton were excluded. Only sectors wth at least 15 stocks were consdered at each pont n tme,.e. a mnmum of fve stocks n each tercle portfolo was requred. Over the perod of the smulaton the portfolos were rebalanced once every month at the start of each month to take nto account changes n the hstorcal volatlty. In exhbt 2 we show the results from these hstorcal smulatons for developed markets and for emergng markets, respectvely. In these exhbts we nclude the beta of the portfolo strategy nvested n the lowest volatlty stocks of each sector, LowestRsk, and the beta of the portfolo strategy nvested n the hghest volatlty stocks of each sector, HghestRsk. These two metrcs were calculated from a regresson over the entre perod of the monthly returns, n excess of cash, of each portfolo strategy aganst the monthly returns, n excess of cash, of the underlyng benchmark ndex whch ncludes all sectors. The alpha generated from the lowest rsk portfolo strategy for a gven sector can be estmated from the same regresson: Lowest Rsk R R R R (1) LowestRsk Cash LowestRsk BenchmarkIndex Cash wth R LowestRsk the annualzed performance of the lowest rsk portfolo strategy, Benchmark Index R the annualzed performance of the market captalzaton-weghted benchmark ndex and 10 R Cash the annualzed return of money market nstruments n the currency used. A smlar equaton can be used to estmate the alpha from the hghest-rsk portfolo strateges, HghestRsk. The alpha n each sector,, shown n these exhbts s gven by:

11 1 LowestRsk HghestRsk (2) LowestRsk HghestRsk Here s the constant that s requred for the volatlty of the returns to be exactly 5% annualzed over the entre perod of the smulatons: r t 1 rt r, LowestRsk t, Cash LowestRsk rt r, HghestRsk t, Cash HghestRsk (3) r t s the tme seres of monthly returns to a long-short portfolo, long the portfolo strategy wth the lowest rsk stocks and monthly returns r t, LowestRsk, wth a weght 1 /, and short portfolo LowestRsk strategy wth the hghest rsk stocks and monthly returns r t, HghestRsk, wth weght 1 / HghestRsk. The weghts are such that the fnal beta of the long-short portfolo s exactly zero and the strategy has zero exposure to the benchmark ndex n the perod 5. We call ths long-short portfolo strategy Low Volatlty mnus Hgh Volatlty (LVMHV). The results n exhbt 2 show that the lowest-volatlty stocks of each sector n developed countres tend to have a beta below one wth the excepton of those n the nformaton technology sector for whch the beta s close to one or even hgher, as s the case for the U.S. and Europe. The hghestvolatlty stocks tend to have a beta above one wth the excepton of those from the defensve sectors,.e. consumer staples, health care and utltes. In Canada, defensve sectors dd not have enough stock representaton for the analyss to be carred out. Here, the lowest-rsk stocks from the materals sectors have a beta above one. The alpha from the LVMHV strategy s postve for all sectors n the MSCI World ndex, the ndex wth the largest number of stocks. In the other unverses, wth smaller number of stocks, the alpha s postve wth a few exceptons lke fnancals n the U.S. and Japan, energy and nformaton technology n Europe and materals n Canada. All these levels of alpha are for exactly 5% annualzed volatlty. They are sgnfcant more often than not. Exhbt 2: Alpha from LVMHV for dfferent sectors and countres or regons. The beta of the long portfolo, nvested n the lowest-volatlty stocks, and the short portfolo, wth the hghest-volatlty stocks, are also shown. In A) developed countres and n B) emergng countres. T-stat s estmated at 5% sgnfcance level. Jan-95 Dec-14. A) 11

12 Consumer Dscretonary Consumer Staples Energy Fnancals Health Care Industrals Informaton Technology Materals Telecommuncaton Servces Utltes α (t-stat) 2.6% (2.22) 4.5% (3.89) 2.0% (1.72) 1.8% (1.49) 2.0% (1.70) 3.2% (2.73) 1.0% (0.80) 1.7% (1.42) 2.4% (2.06) 2.7% (2.34) Developed Markets MSCI World Index β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) 0.83 (30.7) 0.47 (13.4) 0.79 (14.0) 0.82 (24.3) 0.55 (15.3) 0.75 (26.3) 1.05 (26.4) 0.91 (23.8) 0.73 (19.0) 0.26 (5.89) α (t-stat) U.S. S&P 500 Index β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) 1.34 (28.5) 1.1% (1.00) 0.89 (24.7) 1.42 (21.0) % (21.1) (1.81) (12.2) (20.2) % (13.5) (1.77) (11.8) (11.8) % (24.9) (-0.0) (19.4) (22.7) % (15.0) (1.56) (15.7) (17.1) % (27.9) (2.60) (24.4) (24.7) % (16.9) (0.49) (28.2) (18.1) % (18.0) (0.78) (21.5) (16.3) 1.44 (15.8) % (14.5) (2.22) (5.59) (8.92) Europe Stoxx Europe 600 Index α (t-stat) 2.0% (1.75) 1.5% (1.33) -0.6% (-0.5) 2.3% (2.04) 3.0% (2.79) 2.0% (1.82) -0.3% (-0.2) 0.7% (0.51) 2.8% (2.09) 2.4% (2.19) β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) 0.87 (28.1) 0.50 (13.7) 0.86 (17.7) 0.80 (28.4) 0.52 (13.6) 0.78 (25.3) 1.23 (21.0) 0.88 (24.5) 0.73 (11.9) 0.41 (10.3) α (t-stat) Japan Topx 500 Index β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) Canada S&P/TSX Composte Index α (t-stat) β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) 1.38 (25.2) 1.4% (1.27) 0.71 (24.7) 1.17 (27.6) 1.3% (0.91) 0.50 (8.35) 1.20 (10.3) % (20.4) (2.65) (12.0) (16.8) % (12.1) (2.71) (12.3) (15.7) % % (26.5) (-0.8) (13.5) (12.4) (2.03) (12.9) (14.4) % (16.2) (1.36) (10.0) (13.3) % % (28.1) (0.53) (23.1) (24.6) (3.43) (11.9) (10.5) % (17.8) (2.54) (25.8) (24.0) % % (19.0) (0.60) (22.7) (22.0) (-0.5) (14.5) (9.72) 1.46 (12.1) (16.2) B) Consumer Dscretonary Consumer Staples Energy Fnancals Health Care Industrals Informaton Technology Materals Telecommuncaton Servces Utltes Emergng Markets Chna Brazl South Korea Tawan MSCI Emergng Markets Index Cs 300 Index IBrX Index Kosp Index TWSE Index α (t-stat) 3.0% (2.01) 3.7% (2.49) 3.2% (2.16) 2.9% (1.97) 3.1% (1.88) 1.3% (0.89) 3.4% (2.30) 2.1% (1.43) 1.9% (1.31) 1.6% (1.07) β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) 0.77 (22.5) 0.59 (17.8) 0.93 (23.8) 0.79 (28.3) 0.57 (9.32) 0.77 (26.5) 0.85 (18.1) 0.87 (30.2) 0.52 (16.5) 0.53 (16.1) α (t-stat) β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) α (t-stat) β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) α (t-stat) β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) α (t-stat) β Lowest Rsk β Hghest Rsk (t-stat) (t-stat) 1.27 (23.7) -0.2% (-0.1) 0.94 (18.4) 1.13 (21.1) % (0.74) 0.78 (21.5) 0.91 (12.5) 4.6% (3.24) 0.76 (18.6) 1.28 (16.9) % % % (24.8) (2.08) (11.9) (13.3) (0.14) (15.7) (8.70) (4.01) (12.8) (12.6) % (23.5) (-0.0) (21.0) (14.5) % % % (31.0) (0.70) (22.2) (22.9) (-0.1) (15.7) (13.2) (-0.4) (14.4) (11.6) % (8.64) (2.02) (14.5) (10.4) % % % (23.3) (-1.3) (22.6) (24.2) (1.50) (20.2) (12.0) (3.72) (17.0) (16.1) % % (15.8) (1.51) (23.5) (11.4) (3.02) (19.1) (16.3) % % % % (28.8) (-0.7) (23.9) (23.7) (-0.0) (11.4) (12.7) (0.96) (21.4) (12.4) (3.28) (14.5) (12.1) 1.01 (16.4) % % (16.8) (0.47) (15.4) (12.9) (0.94) (9.94) (6.82) The results for the MSCI Emergng Markets ndex n exhbt 2 B) are comparable to those for the MSCI World ndex n exhbt 2 A), wth the alpha also postve for all sectors n emergng markets. However, we fnd that the rsker stocks n each sector are more lkely to have a beta above one than n developed markets, snce now only hgh-rsk consumer staples have a beta below one. And smlarly, low-rsk stocks from all sectors seem more lkely to have a beta below one. Carryng out the analyss n each ndvdual emergng market country was not as easy as for developed countres because of the smaller number of stocks n each sector, n partcular n Brazl, and because of shorter hstory of returns, n partcular n Chna. The evdence of a low-rsk anomaly seems stronger for South Korea and Tawan than for Chna or Brazl. In the latter, only two sectors had enough stocks to perform the analyss and only n utltes s there evdence of postve alpha, despte the fact that the beta of hgh-rsk utltes s below one. In Chna, stronger evdence of a 12

13 postve alpha s found only n consumer staples, along wth some weak evdence n fnancals and utltes. But the hstory of returns s relatvely short. In Tawan, the evdence s stronger and only fnancals do not have a strong postve alpha. Evdence s less strong for South Korea than for Tawan, wth two sectors n seven no showng sgnfcant alpha. Dversfcaton n sector-neutral low-volatlty nvestng In exhbt 3 we show the par-wse correlaton of the tme seres of return for the LVMHV strateges defned n (3) for any two pars of sectors, for the MSCI World ndex and for the MSCI Emergng Markets ndex. The correlaton of LVMHV returns for any two sectors s always postve wth the excepton of the correlaton between the LVMHV returns for the energy sector and the LVMHV returns for the health care sector n emergng markets. Nevertheless, the average correlaton of LVMHV returns from sectors n the MSCI World ndex s low, at 34%, and from the MSCI Emergng Markets ndex s only 20%. These results show a potental dversfcaton gan from nvestng n low-volatlty stocks from dfferent sectors. We shall dscuss ths pont later. Exhbt 3: Correlaton of LVMHV returns for any two sectors from A) the MSCI World ndex and B) the MSCI Emergng Markets ndex. Jan-95 Dec-14. A) Developed countres Consumer Health Informaton Telecom. Energy Fnancals Industrals Materals Staples Care Technology Servces Utltes Consumer Dscretonary 45% 31% 42% 41% 58% 43% 31% 37% 39% Consumer Staples 28% 45% 39% 51% 20% 20% 35% 41% Energy 31% 33% 23% 33% 11% 45% 26% Fnancals 20% 38% 22% 15% 31% 47% Health Care 45% 52% 8% 51% 26% Industrals 34% 48% 42% 46% Informaton Technology 13% 40% 25% Materals 21% 17% Telecom. Servces 33% B) Emergng countres Consumer Health Informaton Telecom. Energy Fnancals Industrals Materals Staples Care Technology Servces Utltes Consumer Dscretonary 41% 20% 50% 8% 51% 17% 34% 14% 19% Consumer Staples 9% 38% 16% 17% -3% 22% 10% 16% Energy 12% -10% 23% 1% 18% 7% 10% Fnancals 17% 52% 13% 52% 22% 39% Health Care 4% 4% 12% 4% 21% Industrals 20% 52% 11% 24% Informaton Technology 11% 12% 11% Materals 15% 21% Telecom. Servces 24% 13

14 In exhbt 4 we show the correlaton of the returns to LVMHV strateges appled to the dfferent sectors of the MSCI World ndex and MSCI the Emergng Markets ndex wth the returns to equvalent strateges postvely exposed to small captalzaton, value and momentum. What we call SMB (Small-mnus-Bg) s a long-short strategy that nvests n the one-thrd of stocks n the unverse wth the smallest captalzaton n the MSCI ndces and sells short the one-thrd of stocks wth the largest captalzaton. The stocks are equally weghted n the long and short legs of the portfolo. The beta s neutralzed as before by allocatng a weght 1/ to the long leg and Smallest MarketCap 1/ to the short leg fully neutralzng the beta, wth LargestMarketCap Smallest MarketCap and LargestMarketCap the ex-post beta for each leg over the entre perod. The fnal leverage s adjusted so that the ex-post volatlty s exactly 5% over the perod. A smlar strategy s bult, ths tme rankng stocks every month by prce-to-book and nvestng n the stocks wth the lowest prce-to-book whle sellng short the stocks wth the largest prce-to-book. We call ths strategy HML (Hgh-mnus-Low) n analogy to the HML strategy as defned by Fama and French (1992), although we follow a somewhat dfferent approach. Fnally, we construct another smlar strategy but wth stocks now ranked by momentum defned as the past 11-month return of each stock measured one month before portfolo formaton. We call ths portfolo Mom n analogy to what was defned by Carhart (1997), although agan our strategy s not exactly the same. Exhbt 4: Correlatons between the returns to LVMHV strateges appled to the sectors n A) MSCI World ndex and B) MSCI Emergng Markets ndex wth the returns to SMB, HML, and Mom returns appled to the same unverses, respectvely. In A) the perod s Jan-95 to Aug-14 and n B) Jan-02 to Aug-14) markets. Monthly USD total returns. A) Developed countres LVMHV HML Mom Consumer Consumer Health Informaton Telecom. Energy Fnancals Industrals Materals Dsc. Staples Care Technology Servces Utltes SMB 50% -45% -4% -13% -13% -12% -7% -3% -7% -2% -7% 2% HML -69% 11% 12% 20% -7% 43% 21% 28% 1% 21% 19% Mom 16% 3% 10% 18% -6% 0% 1% 3% 11% 5% B) Emergng countres LVMHV HML Mom Consumer Consumer Health Informaton Telecom. Energy Fnancals Industrals Materals Dsc. Staples Care Technology Servces Utltes SMB 51% -57% -26% -9% -20% -6% -6% 1% -5% 8% -1% 11% HML -57% -19% -18% -22% -15% 1% -18% 3% -7% -11% -2% Mom 22% 1% 16% 12% 15% 4% 7% -13% 13% -5% 14

15 The average correlaton of the returns to LVMHV strateges wth the returns to SMB, HML and Mom s only 5% when formed usng stocks from the MSCI World ndex and -3% when formed wth stocks from the MSCI Emergng Markets ndex. Ths shows clearly that the returns to LVMHV strateges are uncorrelated from the returns of these other strateges, SMB, HML and Mom. Tal rsk n sector-neutral low-volatlty nvestng We shall now show that low-rsk nvestng has only a small or no exposure to stocks wth future poor performances. In a smple exercse, each month we ranked stocks n each sector of the MSCI World ndex 1 by hstorcal volatlty 2 and formed decle portfolos n each sector. We then put together the correspondng decle portfolos from each sector to form 10 portfolos, from 1, the lowest volatlty n each sector, to 10, the hghest volatlty n each sector. We then checked the future returns of the stocks n each of these portfolos and asked the queston of how many had monthly returns below -50%, or nferor to -70%, n subsequent months. The results can be found n exhbt 5, where we show the probablty that a stock wth a monthly return nferor to -50% n A) or nferor to -70% n B) was n found n a gven decle portfolo up to three months before that month and up to three months after that month. The perod of the analyss s Jan-95 to Mar-14. Ths corresponds to 231 months wth a total of 390,380 monthly stock returns observed,.e. 1,689 stocks on average per month. Of these we fnd 53 monthly returns observed to be nferor to -70% from 46 unque stocks and 356 observatons nferor to -50% wth 275 unque stocks. In exhbt 5 we show the results of our analyss. We found no stock wth a monthly return nferor to -70% n a gven month rankng n the lowest volatlty decle n the precedng month, or n the precedng two or three months. These stocks are found wth ncreasng frequency n the most volatlty decles. Only 10% of these observatons come from stocks rankng n the half of the unverse wth the lowest-volatlty stocks n the precedng month, 16% two months before and 17% three months before. If we put the threshold at -50%, then there s a largest percentage found n the lowest volatlty unverse but most stocks wth the poorest performances stll come from the rsker half of the unverse. Only 18%, 21% and 23% of these observatons were from stocks rankng n the lowest volatlty half of the unverse one, two and three months before the event, respectvely. Exhbt 5: Percentage of the stocks wth an absolute monthly return nferor to -50% A) or nferor to - 70% B) found n each decle portfolo before and after that event. USD returns. Stocks from the MSCI World ndex unverse 1. Jan-95 to Mar

16 A) Probablty that a stock wth monthly return < -50% s observed n one gven decle Lowest volatlty Hghest volatlty Volatlty decle % 2% 6% 5% 8% 6% 6% 17% 17% 31% Months 2 2% 1% 6% 5% 7% 4% 8% 15% 16% 36% before 1 1% 2% 4% 5% 6% 5% 6% 16% 19% 36% Month of observaton 1% 1% 5% 4% 5% 5% 7% 16% 17% 39% 1 1% 0% 3% 5% 5% 5% 5% 13% 22% 41% Months 2 0% 0% 1% 3% 3% 4% 2% 11% 23% 53% after 3 0% 0% 1% 3% 2% 3% 2% 10% 19% 61% B) Probablty that a stock wth monthly return < -70% s observed n one gven decle Low volatlty Hgh volatlty Volatlty decle % 2% 5% 5% 5% 2% 2% 14% 14% 51% Months 2 0% 0% 7% 2% 7% 0% 5% 9% 16% 55% before 1 0% 2% 2% 4% 2% 7% 2% 9% 17% 54% Month of observaton 0% 0% 4% 2% 2% 4% 0% 11% 20% 57% 1 0% 0% 2% 0% 2% 2% 2% 5% 21% 65% Months 2 0% 0% 0% 0% 0% 0% 0% 0% 9% 91% after 3 0% 0% 0% 0% 0% 0% 0% 0% 4% 96% SECTOR-NEUTRAL VERSUS NON-SECTOR NEUTRAL LOW-RISK INVESTING In ths secton we compare tradtonal low-rsk nvestng based on nvestng n the lowest-rsk stocks and strongly based towards defensve sectors wth sector-neutral low-rsk nvestng. We focus only on the MSCI World ndex unverse for developed countres wth the larger number of stocks and suffcently long hstory, from January 1995 through May Performance and sector exposures In exhbt 6 we compare the alpha of two beta-neutral strateges, both wth exactly 5% annualzed volatlty. The frst strategy, whch we call sector neutral, s an aggregaton of LVMHV sector longshort portfolos, one for each sector, as defned before but usng decles nstead of tercles. Each sector LVMHV s allocated a weght nversely proportonal to ts volatlty over the entre perod, and the leverage of aggregaton of these 10 sector LVMHV s such that the ex-post volatlty s exactly 5%. The second strategy, whch we call non-sector neutral, s based on a LVHMV long-short portfolo whch does not take nto account sectors. The stocks are ranked by hstorcal volatlty once a month and the portfolo s rebalanced once at the start of each month. Stocks are equally weghted just as before. But ths portfolo nvests n the decle of stocks wth the lowest hstorcal volatlty and short sells the decle of stocks wth the hghest hstorcal volatlty, rrespectve of ther sectors. As before, 16

17 the weght of the long and short legs are equal to the nverse of each observed beta, 1 / and Hghest Rsk 17 LowestRsk 1/ respectvely, and the allocaton s re-scaled by as n (2) so that the ex-post volatlty s 5%. In exhbt 6 we also consder the same strateges but now mplemented wth a sx month lag,.e. the portfolo s mplemented sx month after formaton. Exhbt 6: Alpha and nformaton rato for two LVMHV strateges, one based on nverse volatlty weghted of ndvdual LVMHV sector strateges, whch we call sector-neutral, and one applyng the LVMHV across the entre stock unverse gnorng sectors, whch we call non-sector neutral. The beta of both strateges s zero and the volatlty s 5% by constructon. We also consder the same strateges mplemented wth sx months lag. MSCI World Index Jan May-2013 Sector neutral Non-sector neutral 1 month 6 months 1 month 6 months Alpha 3.7% 3.9% 3.2% 3.2% Informaton rato The results n exhbt 6 show an mprovement of 14% n the nformaton rato of the sector-neutral strategy when compared to that of the non-sector neutral. It s also nterestng to see that the strateges wth lower turnover reach the same levels of alpha as those rebalanced more frequently. Ths seems to ndcate that the rotaton of stocks n the portfolos s low, somethng we shall nvestgate n the next secton. In exhbt 7 we show the average net sector weghts n each of these two strateges. The net sector weght s the sum of the weghts allocated to each stock n a gven sector. The sector-neutral strategy has a postve weght n all sectors. Ths s because, n order to neutralze the market exposure and reach a beta equal to zero, the strategy allocates a larger weght to the low-volatlty stocks t buys than to the hgh-volatlty stocks t sells short. The sze of the net sector weghts s a functon of the dsperson of beta,.e. the larger the dfference between the beta of low-volatlty stocks and hgh volatlty stocks, the larger the net sector weght. The man dfference between the sector-neutral strategy and the non-sector neutral s the much larger weght allocated to consumer staples, fnancals and utltes and the much smaller weght allocated to nformaton technology, consumer dscretonary and energy found n the non-sector neutral strategy. The non-sector neutral strategy has always been strongly based towards fnancals except for a few months n the aftermath of the 2008 crss. Exhbt 7: Average net sector weghts for sector-neutral and non-sector neutral LVMHV strateges for stocks from the MSCI World ndex 1. Jan-95 to May-14.

18 A) 14% 12% Developed countres 10% 8% 6% 4% 2% 0% -2% -4% -6% Consumer Dscretonary Consumer Staples Energy Fnancals Health Care Industrals Informaton Technology Materals Telecommuncaton Servces Utltes Sector Neutral Non-Sector Neutral Persstence of volatlty We now focus on the reasons why, n exhbt 6, the turnover could be reduced sgnfcantly wthout a reducton n the alpha of the LVHMV strateges. Ths s n fact due to the persstence of volatlty. Perchet, De Carvalho, Heckel and Mouln (2014) have recently nvestgated the persstence of volatlty at aggregate market level, for dfferent asset classes, and Perchet, De Carvalho and Mouln (2014) have done the same for value and momentum factor premum. They found that the persstency of volatlty s strong at the aggregate level, whch explans why volatlty can to some extent be predcted at an aggregate level. In exhbt 8 we show transton probablty matrces for stocks n the MSCI World ndex and MSCI Emergng Markets ndex, respectvely. Wth the sector-neutral portfolo, stocks n each sector are ranked by hstorcal volatlty 2 every month and then, n each sector, the unverse of stocks s ranked by hstorcal volatlty and dvded nto tercles. For the non-sector neutral portfolo, ths s done across the unverse defned by the ndex rather than on a sector-by-sector bass. Ths exercse s repeated each month. We then calculated the average number of stocks whch ranked as beng of low volatlty n a gven month and also n the mmedately followng month. We repeated the exercse for stocks that ranked as md-volatlty and hgh-volatlty. The probabltes are the average percentage of stocks stayng n the same tercle of volatlty from one month to another. 18

19 Smlarly, we also estmated the probablty that a stock remans n the same tercle of volatlty sx months after beng ranked. And we also ncluded the probablty that a stock leaves the ndex n the followng month or wthn the followng sx months. These are ndcated as out. Exhbt 8: Probabltes that a stock rankng n a gven tercle of volatlty n a gven month s stll found n the same tercle of volatlty n the followng month. Also shows the probablty of that stock beng found n the same tercle of volatlty n the followng sx months. Results for sector-neutral and non-sector neutral portfolos are ncluded. In A) the unverse s defned from the MSCI World ndex 1 and the perod s Jan-95 to May-14. In B) the unverse f defned from the MSCI Emergng Markets ndex 1 and the perod s Jan-02 to May-14. A) MSCI World Index Jan May-2014 Sector Neutral Non-Sector neutral 1-month transton probablty matrx Volatlty tercle next month Volatlty tercle next month Low Md Hgh Out Low Md Hgh Out Volatlty Low 95% 5% 0% 0% 96% 4% 0% 0% tercle Md 5% 90% 4% 1% 4% 92% 4% 1% today Hgh 0% 4% 94% 1% 0% 4% 95% 1% 6-month transton probablty matrx Volatlty tercle next month Volatlty tercle next month Low Md Hgh Out Low Md Hgh Out Volatlty Low 83% 14% 1% 2% 85% 12% 1% 2% tercle Md 14% 69% 14% 3% 12% 72% 13% 3% today Hgh 0% 13% 80% 6% 0% 12% 82% 6% B) MSCI Emergng Markets Index Jan May-2014 Sector Neutral Non-Sector neutral 1-month transton probablty matrx Volatlty tercle next month Volatlty tercle next month Low Md Hgh Out Low Md Hgh Out Volatlty Low 94% 5% 0% 2% 95% 4% 0% 2% tercle Md 5% 89% 5% 1% 4% 91% 4% 1% today Hgh 0% 5% 93% 2% 0% 4% 94% 2% 6-month transton probablty matrx Volatlty tercle next month Volatlty tercle next month Low Md Hgh Out Low Md Hgh Out Volatlty Low 80% 13% 1% 6% 81% 12% 0% 6% tercle Md 14% 67% 13% 6% 13% 69% 13% 6% today Hgh 1% 15% 77% 8% 0% 15% 78% 8% 19

20 The results n exhbt 8 show a strong persstency n the volatlty of stocks. For the sector-neutral strategy, 95% of the stocks ranked lowest volatlty n the MSCI World ndex n a gven month then remaned ranked lowest volatlty n the followng month and the other 5% ranked md-volatlty. The results are comparable for the non-sector neutral strategy, wth 96% and 4%, respectvely. The results are also comparable for the stocks n the MSCI Emergng Markets ndex, wth 94% of stocks ranked lowest volatlty stll remanng lowest volatlty one month later for the sector-neutral approach and 95% for the non-sector neutral approach. Sx months after beng ranked, 83% of lowest volatlty stocks n the MSCI World ndex stll rank lowest volatlty for the sector neutral approach and 85% for the non-sector neutral approach. For the MSCI Emergng markets ndex ths s just slghtly lower at 80% and 81%, respectvely. It s also nterestng to note that the probablty of stocks leavng the ndex s hgher for the hghest-volatlty stocks than for the lowest-volatlty stocks. Lqudty of low-volatlty strateges Low-volatlty nvestng s an actve strategy that nvests away from the market captalzaton portfolo and requres re-balancng. Lqudty s thus an mportant ssue. Here we gve some crude dea of the lqudty of smple low-volatlty strateges and compare ths lqudty to other smple style strateges for small captalzaton, value and momentum. We consder both sector-neutral and nonsector neutral low-volatlty strateges. In exhbt 9 we show the average number of days needed to lqudate a USD 100 mllon portfolo nvested n the decle of stocks wth lowest volatlty, sector-neutral and non-sector neutral, and compare ths to the average number of days to lqudate a portfolo of a smlar sze nvested n the decle of stocks wth the smallest market captalzaton, the stocks wth the lowest prce-to-book rato and momentum stocks wth the hghest 11-month return measured one month before portfolo constructon. The averages are based on the allocaton at the start of each month. The number of days requred to lqudate the portfolo assumes that a maxmum of 30% of the monthly volume of each stock can be traded every day. We ran the analyss between 2008 and Stock volume data s provded from MSCI. The results are for stocks n the MSCI World ndex. Not surprsngly, the market captalzaton ndex has the greatest lqudty and can be lqudated wth the least dffculty. There s not a large dfference between the sector-neutral and the non-sector neutral low-volatlty portfolos, wth perhaps no sgnfcant advantage for the non-sector neutral portfolo seen at the level of full lqudaton only. Lqudty of the low-volatlty portfolos s large at ths level and comparable to that of momentum portfolos. Not surprsngly, the small captalzaton portfolo has the poorest lqudty. Value also shows poor lqudty because we dd not remove the small captalzaton bas that a selecton based on the lowest prce-to-book ratos tends to create. 20