Volume1 Number 5 December 1998 Investment …...Is small-cap investing worth it? Two decades of...

Is small-cap investing worth it?Two decades of research

on small-cap stocks

Volume 1 • Number 5 • December 1998

Investment InsightsCreating, transforming and sharing knowledge

∫

Laurence B. Siegel

Director of Investment Policy Research

Ford Foundation

Guest co-author Laurence B. Siegel is director of investment policy

research at the Ford Foundation in New York, where he has worked

since 1994. Previously, he was a managing director of Ibbotson

Associates, a Chicago-based investment consulting and data firm

he helped to establish in 1979. He has also worked at the Marmon

Group and the American Enterprise Institute. Larry is editor of

Investment Policy Magazine and has published over 40 articles in

professional journals and magazines. He is also on the editorial

board of the Journal of Portfolio Management and the Journal ofInvesting. Larry received his BA in urban studies and his MBA in

finance from the University of Chicago.

M. Barton Waring

Manager, Client Advisory Group

Principal

Barton Waring joined Barclays Global Investors in 1995. He has an

extensive background in asset allocation, investment strategy and

quantitative asset management issues from his work with large defined

benefit and defined contribution plans. He has held senior positions at

Morgan Stanley Asset Management, Towers Perrin Asset Consulting

and Ibbotson Associates. Barton received his BS in economics from the

University of Oregon, his JD from Lewis & Clark University and his

MPPM in finance from Yale University. He frequently writes and speaks

on investment strategy issues.

Eric Clothier

Client Relationship Officer

Managing Director

Eric Clothier joined Barclays Global Investors in 1987 and is responsible

for a team that serves and advises over 100 BGI clients. He has broad

experience in investment management having managed BGI’s tactical asset

allocation, global trading and index strategies groups in the past. Prior to

joining BGI, Eric was with Mellon Bank where he held positions in struc-

tured equity and fixed income portfolio management. He received an MBA

in finance from Temple University and is a chartered financial analyst.

1

Investment Insights December 1998

It has long been part of market folklore that stocks of smaller companies are high-returning

investments, due perhaps to aggressive management and the fact that they have room to grow,

or because such issues are neglected by many investors.1 This folklore is consistent with the

intellectual constructions of the 1960s and 1970s—the efficient market hypothesis and the

Capital Asset Pricing Model (CAPM)—only if small stocks have greater risk, with high returns

being a compensation for bearing that risk. Because the stakes were high among both aca-

demics and practitioners for finding convincing evidence that the market is not efficient, or

that the CAPM does not hold, a great deal of effort has been devoted to searching for market

“anomalies.”2 The first big payoff was the discovery (or rediscovery, if one counts the folklore)

of high returns earned by small-capitalization stocks in the United States, as documented by

Banz (1981).

Is small-cap investing worth it?Two decades of research on small-cap stocks

The astonishment, skepticism anddelight that greeted this finding are difficult to overstate. By 1981, the effi-cient market hypothesis was so deeplyingrained in academic financial thinkingthat a simple beat-the-market rule (buyan index of small-cap stocks) wasalmost inconceivable. That it appearedto work on a risk-adjusted basis wascontrary to the CAPM, which appearedto many academics to be true by con-struction and thus unlikely ever to beoverturned.3 Practitioners, for their part, were generally pleased to seerespected academics chipping away attheir own efficient-market framework,for if one major anomaly was discov-ered, then others would surely be found,vindicating the active manager’s craft.

Over the period since Banz’s discov-ery, researching the small-stock effecthas become a favorite pastime of aca-demics and research-oriented practition-ers so that the volume of writing on thistopic is enormous. This paper reviewsthe most influential papers on smallstocks, classifying them into “threads” or intellectual themes that tie themtogether. Criteria for including a paperhere are: (1) authorship by respected academics and research-oriented practi-tioners; (2) influence on later writingand on portfolio management; and (3)where these criteria are met onlymarginally, an innovative approach orunexpected conclusion that helps onethink about small-capitalization stocks in a new way.

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Is small-cap investing worth it? Two decades of research on small-cap stocks

Threads of research on small-cap stocks

The following are the principal threads by which we classify research conclusions onsmall-capitalization stocks and the size effect, and will serve as the basis for organiz-ing this paper. Of course, the researchers themselves knew no such neat categories,and a given article may well be categorized in multiple threads.

T H R E A D 1

Discovery and measurement of a historical small-stock premium

T H R E A D 2

Evidence that the small-stock premium is a payoff for the greater risk of small stocks2a The premium is a payoff for risk that is captured by properly measured beta2b The premium is a payoff for risk that is not captured in beta2c An argument that one would observe some small-stock premium even if small

stocks are fairly priced

T H R E A D 3

Evidence that the small-stock premium is compensation to the investor for transaction,information and other costs

T H R E A D 4

Evidence that the small-stock premium is unreliable or does not exist4a Arguments that the small-stock premium derives from a single observation or one-

time repricing of these stocks4b Arguments that the small-stock effect is really a proxy for other effects such as

low P/E

T H R E A D 5

Behavioral explanations for the small-stock effect

T H R E A D 6

Evidence that the small-stock premium is a true anomaly (that is, that small stocks offeran excess expected return after controlling for risks, marketability, and other investorcosts)

T H R E A D 7

Short-term timing of the small-stock effect (the January effect, etc.)

T H R E A D 8

Long-term timing of the small-stock effect

T H R E A D 9

The small-stock effect internationally

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T H R E A D 1

As noted in the introduction, the modernhistory of research on the small-stockeffect begins with Banz (1981). A youngNorthwestern University professorwhose research on the topic was actual-ly finished in 1979, Rolf Banz summa-rized his predecessors’ efforts as follows:

[R]ecent evidence suggests the exis-tence of additional factors [beyondthe CAPM beta] which are relevantfor asset pricing. Litzenberger andRamaswamy (1979) show a signifi-cant positive relationship betweendividend yield and return of commonstocks for the 1936–1977 period.Basu (1977) finds that price-earningsratios and risk adjusted returns arerelated.…This study contributesanother piece to the emerging puzzle.

Banz then set up a two-factor regres-sion in which one factor is the marketor beta factor and the other is the sensi-tivity of the stock’s return to its marketcapitalization, or size. This is a joint testof the efficient market hypothesis andthe CAPM; that is, if the CAPM is cor-rectly specified and the market is effi-cient, the coefficient on the second (size) factor should be zero. Using datafor all New York Stock Exchange (NYSE)stocks over the period 1926-1975, Banzfound that even after controlling forbeta, the smallest firms outperformedthe largest ones by about 5% per year,and that the effect is concentrated

among very small firms (the fourth andfifth quintiles of NYSE stocks ranked bysize). This is a very large effect, andBanz emphasizes that “the magni-tude…during the past 45 years is suchthat it is of more than just academicinterest.”

Banz’s speculations at the end of hisarticle are a model of caution in inter-preting startling new findings. Notingthat “the size effect exists but it is not at all clear why,” he suggests that itmay be a proxy for other “true butunknown factors correlated with size.”He also invokes Klein and Bawa (1977),who suggest that securities for whichlittle information is available will beunderpriced and offer superior returns;small firms may fit this categorization.Finally, Banz comments that “given thelongevity [of the effect], it is not likelythat it is due to a market inefficiencybut it is rather evidence of a pricingmodel misspecification,” a view thatprefigures the work of Fama and Frenchmany years later and that conforms to a position we take later in this paper.

Marc Reinganum is sometimes con-sidered the co-discoverer of the small-stock effect. Actually, Reinganum (1981)takes the existence of a small-firm effectas a given (citing Banz’s 1978 PhD dis-sertation) and attempts to disentanglethe size effect from the P/E effect.4

Because of the need for earnings as wellas price and capitalization data, his

Discovery and measurement of the small-stock premium

4


study covers only 1963–1977.Reinganum concludes that the sizeeffect subsumes or dominates the P/E(or E/P) effect:

After controlling returns for any E/Peffect, a strong firm size effect stillemerged. But, after controllingreturns for any [size] effect, a sepa-rate E/P effect was not found. Whilean E/P anomaly and a [size] anoma-ly exist when each variable is consid-ered separately, the two anomaliesseem to be related to the same set ofmissing factors, and these factorsappear to be more closely associatedwith firm size than E/P ratios.

Ibbotson and Sinquefield (1982)extended the measurement of returnson stocks of all capitalization categoriesand also measured their risk (standarddeviation). Taking a “just the facts”approach, they note:

Over the entire [1926–1981] period,the arithmetic mean of the annualreturns was 18.1% for small stocks…[and]…11.4% for [large] stocks.…Small stock returns were morevolatile.… The standard deviation of small stock annual returns was37.0% [compared to 21.7% for largestocks], while the returns rangedfrom 142.9% in 1933 to -58.0% in1937.

Applying a simple test, then, thegreater returns of small stocks were notout of proportion to their greater risk.As other researchers had pointed out,

however, this risk did not show up inthe beta as it was then being measured.In Thread 2 of this paper we address theissue of measuring the beta of smallstocks more precisely.

Ibbotson and Sinquefield (1982) alsoidentify, apparently for the first time,the long waves of small-stock outperfor-mance and underperformance that wecover at greater length in Thread 8 ofthis paper:

From 1926 to 1931, the compoundannual rate of return for [the premi-um of the smallest NYSE stocks overthe largest ones] was -17.0%, and thepremium was negative in every year.From 1932 to 1945 the premium hada compound…return of 16.6% andwas positive in 12 of the 14 years.From 1946 to 1957, the compound…return was -4.4%.… Finally, the smallstock premium returned 7.6% per yearfrom 1958 to 1981. Most of the1958–1981 gain occurred in the lasteight years of the period, in which thecompound [relative] rate of returnwas 18.5% and the premium was pos-itive in each year.

Ibbotson and Sinquefield (1982) extended the mea-

surement of returns on stocks of all capitalization

categories and also measured their risk (standard

deviation).…They also identify, apparently for the

first time, the long waves of small-stock outperfor-

mance and underperformance.

15


We would add that 18.5% is a veryhigh annual rate of outperformanceindeed, and it is little surprise that asmall-stock effect might be discoveredafter such a period. Interestingly, thenext downward-trending period beganalmost as soon as the small-stock effectwas discovered. From 1984 to 1990,small stocks underperformed at a com-pound annual rate of -10.5%, and the pre-mium was negative in all but one year.Starting in 1991, the small-stock effecthas been mixed, with good performancein 1991–1994 and poor performancethereafter.5

The works of Banz, Reinganum, andIbbotson and Sinquefield were occasion-ally criticized as representing a sector of

stocks too small to be representative ofsmall-stock investing as actually prac-ticed. (As of year-end 1997, the indexused by Ibbotson and Sinquefield to represent small stocks had a weighted-average capitalization of $161 million.)To remedy this, Ibbotson Associates(1998), updating the work of Ibbotsonand Sinquefield, also constructs a span-ning set of size-decile portfolios of theNYSE6 (see Table 1).

Notably, both the arithmetic-meanreturn and risk of the portfolios increasemonotonically7 as one moves from largerto smaller stocks. The 15 years of subparperformance of small stocks has notundone the effect accumulated over theperiod that started in 1926.

6


The fact that small stocks have muchmore risk than large stocks promptedmany researchers to speculate thateither (1) small stocks have higher betasthan large stocks, but the betas werenot being properly measured by themethods of Banz, Reinganum, andIbbotson and Sinquefield; or (2) smallstocks have risk that is unrelated tobeta but that is compensable in themarket.

2a The premium is a payoff

for risk that is captured by properly

measured beta

Unlike large stocks that are tradedmany times per day, many small stocksare traded infrequently. As a result,their betas are understated by the ordi-nary-least-squares (OLS) regressiontechnique.8 Scholes and Williams (1977)and Dimson (1979) pointed out that bysumming the betas from led, contempo-raneous, and lagged regressions of dailystock returns on daily market returns,betas can be estimated more accuratelyfor stocks that do not trade every day.Further adjustments are also possible.Richard Roll (1981) speculated thatinfrequent trading might cause themeasured betas of small stocks to bemuch too low, and conducted a simpletest suggesting the conjecture wasright. He compared an equally-weightedportfolio of all NYSE- and AmericanStock Exchange-listed stocks (in whichsmall stocks have a large weight) with the value-weighted S&P 500 Index,using returns of different time frequencies:

[N]otice that when weekly, bi-weekly,monthly, bi-monthly, quarterly, andsemi-annual returns are employed,the correlation coefficient of returnsstays about the same. In contrast, thebeta and the ratio of total variancesincreases uniformly and materially.

Remarkably, the ratio of variancesrises more than threefold, so that aninvestor with a long time horizon wouldregard the equally weighted portfolio asmore than three times as risky as theS&P 500. This contrasts with the OLSbeta, which suggests that the equallyweighted portfolio is less than 1.5 timesas risky as the S&P 500. Clearly there is a risk factor for smaller stocks that isnot being captured by beta.

The reason that small-stock portfo-lios are riskier as one lengthens thereturn measurement period is simple:their returns are autocorrelated.(Autocorrelation measures the extent towhich one period’s return influencesthe next period’s return; in a highlyautocorrelated return series, one down-turn is likely to be followed by others,creating a risk that is not present when

The small-stock premiumas a payoff for taking risk

T H R E A D 2

Scholes and Williams (1977) and Dimson (1979)

pointed out that by summing the betas from led,

contemporaneous, and lagged regressions of daily

stock returns on daily market returns, betas can

be estimated more accurately for stocks that do

not trade every day.

7


returns are independent across time. Ina highly autocorrelated series, then, goodand bad returns tend to have “runs.”9)Roll, relying on his initial conjecture,blames infrequent trading for theappearance of autocorrelation in small-stock returns, and concludes:

At first, one might think there is aknotty theoretical question of howrisk is related to the investment

“horizon.” A moment’s reflection, how-ever, reveals that no such problem ispresent. The true riskiness is exactlythe same for all data intervals; it issimply underestimated for the shorterones.

This is true, however, only if theautocorrelation is an illusion caused byinfrequent trading or other measure-ment problems. If, however, small-stockreturns are truly autocorrelated (that is,if a perfect measurement existed andsmall-stock returns were still found tobe autocorrelated), then the true riski-ness is not the same for all data inter-vals. The risk is that low returns willlead to more low returns, resulting in asignificant erosion of investor wealthover time. Returns measured over wholeyears tend (it is hoped) to eliminate bias-es from infrequent trading. The autocor-relation of annual small-stock returns inexcess of S&P 500 returns, from IbbotsonAssociates (1998), is 0.38, with a stan-dard error of 0.12, indicating strong sta-tistical significance (as though Ibbotson’snarrative about long periods of over-and underperformance were notenough). Clearly, the long-run autocor-relation of small-stock excess returnsposes a risk to the investor that returns

2might have a run of underperformanceduring the investor’s horizon—for whichhe might demand to be compensated.

In 1982, Reinganum authored a“direct test of Roll’s conjecture,” usingDimson’s (1979) method of measuringbeta for stocks that trade infrequently.Roll had been correct in guessing thatmeasured betas would rise if the methodwere changed to account for infrequenttrading. To cite an extreme example, thebeta for the smallest decile of NYSE andAMEX stocks measured over 1964–1978rises from 0.75 using the OLS method to1.69 using the Dimson method. Evenwith the much higher beta estimates,the returns of small stocks substantiallyexceed that which is predicted by theCAPM. (Note that the overall return onthe market in excess of Treasury billswas flat over the period studied, so thatbeta risk went unrewarded in that par-ticular time frame.) Reinganum’s testdid not, however, consider the possibili-ty that long-run autocorrelation in the underlying data poses a risk to theinvestor that is unrelated to beta.

In adjusting the betas of smallstocks to capture their true risks,Ibbotson, Kaplan, and Peterson (1997)also build on the work of Dimson.Unlike Reinganum (1982), however, theyadjust for “cross-autocorrelation,” whichis the correlation of one time series with

Roll, relying on his initial conjecture,

blames infrequent trading for the

appearance of autocorrelation in

small-stock returns.


the “led” or “lagged” version of a differ-ent time series. By introducing autocor-relation into the analysis, they con-struct a beta that captures some of therisk of repeated underperformance towhich we referred in the discussion ofRoll (1981).10 They find that the adjustedbetas partially explain the size effect.

2b The premium is a payoff

for risk that is not captured in beta

If one has made all reasonable adjust-ments to beta and that factor still doesnot explain the high returns on smallstocks, then perhaps the small-stockpremium is a payoff for a risk that isunrelated to beta. Such a findingwould, of course, overturn the CapitalAsset Pricing Model.11

Chan, Chen and Hsieh (1985) useArbitrage Pricing Theory (APT)12 toestimate the returns expected by small-stock investors, and determine that thefive macroeconomic APT factors theyuse are sufficient to explain the addi-tional returns of small stocks. The factors are industrial production, unan-ticipated inflation, changes in expectedinflation, the realized excess return ofTreasury bonds over short-term bills,and the realized risk premium on low-

8

grade corporate bonds over Treasuries.They use the market factor, identical tothe CAPM beta, as a sixth explanatoryvariable.

If these APT factors explain the“return to size,” then transaction andinformation costs need not be invokedas a reason why small-stock investorsappear to earn high returns before sub-tracting these costs. However, in theAPT model, the small-firm effect is stilla payoff for risk, and there is no freelunch in small-stock investing, even ifall costs can be avoided. Moreover, wefind the arguments relating small-stockreturns to various types of costs to bevery compelling (see Thread 3).

Friend and Lang (1988) take a cre-ative turn in using Standard and Poor’sstock ratings, which are constructed by security analysts, to measure therisk of stocks. They find that these rat-ings are extremely powerful in predict-ing differential returns and that they in essence subsume the small-stockpremium as well as the CAPM beta.Friend and Lang’s method is intuitivelysensible in that if stocks have a type of systematic risk that is not reflected inthe beta, security analysts might beable to find it using traditional financialanalysis. By reading the description ofthe analyst’s methods, it seems thattheir concept of risk is closely alignedwith standard deviation, because theyare evaluating each stock on its ownmerits, not calculating the marginalcontribution of the stock to portfoliorisk (which is what beta does). This isnoteworthy in light of our comments on standard deviation in our discussion of Ibbotson Associates (1998).

Friend and Lang (1988) find

that S&P stock ratings are

extremely powerful in predict-

ing differential returns and

that they in essence subsume

the small-stock premium as

well as the CAPM beta.

29


Unfortunately, there is (at leastpotentially) an element of circularity inFriend and Lang’s approach. If securityanalysts know that a stock has a smallmarket capitalization, and if they areaware that an expected-return premiumattaches to small stocks, they may modifythe risk rating of the stock accordingly.Thus, if there is a risk premium specifi-cally for smallness, it will be reflected insecurity analysts’ ratings, and these rat-ings may appear statistically to subsumeor dominate the small-stock effect whenall they are doing is mirroring it.

The work in the 1980s of Chan, Chenand Hsieh, and of Friend and Lang, pre-figures the later literature on the inade-quacy of beta as a predictor of cross-sectional differences in stock returns.This literature came into its own withEugene Fama and Kenneth French’slandmark 1992 article, The cross-sectionof expected stock returns. Fama andFrench found that over 1963–1990, thereward for taking the risk of high-betarather than low-beta stocks was almostexactly zero.13 (Much earlier, FischerBlack [1972] predicted that if investorsface restrictions on borrowing or selling

short, the CAPM line will be flatter thanpredicted by the original theory, but it is a stretch to read Fama and French’scompletely-flat CAPM line into Black’sprediction.) Fama and French’s resultslend support to APT rather than theCAPM and bolsters the idea that thesmall-stock premium is a reward for tak-ing risks that are unrelated to beta.

The debate in response to Fama andFrench on whether beta is “dead” is out-side the scope of this paper, except tothe extent that it sheds additional lighton the small-stock premium. Most note-worthy is an article by Kothari,Shanken, and Sloan (1995), in whichthey use annual data to obtain estimatesof small-stock beta that are not taintedby infrequent trading. They find thatbeta risk was rewarded over the sameperiod as that tested by Fama andFrench, but that there is still a sizeeffect. The authors also caution that allstudies of stock-market “effects” tend tobe tainted by data-snooping and hiddenbiases,14 so that one should not jump toconclusions.15

2c An argument that one would

observe some small-stock premium

even if small stocks are fairly priced

A different tack is taken by JonathanBerk, a young University of Washingtonprofessor who came over to economicsfrom the hard sciences and is thus un-tainted by years of indoctrination. Hepoints out that if markets discount riski-er securities at higher discount rates,then firms of identical “physical size”

Fama and French’s results

lend support to APT rather

than the CAPM and bolsters

the idea that the small-stock

premium is a reward for

taking risks that are unrelated

to beta.

10


but differing risk will have differingmarket capitalizations, with the smallerfirms offering higher returns eventhough they are fairly priced:

Imagine an economy in which allfirms are the same size (i.e., have the same value of assets in place).…Assume that all firms, because theyhave the same size, also have thesame expected cash flows. Of course,[that] is not the same as having thesame cash flows. Because somefirms’ cash flows are likely to beriskier than others, [their] discountrates will differ.… Consequently, thediscounted value of a riskier firm(i.e., its market value) will be lowerthan the discounted value of a lessrisky firm’s cash flows.

A firm’s expected return is defined tobe its expected cash flows divided byits market value. The assumptionthat all firms have the same expectedcash flows implies that (risky) firmswith low market values have highexpected returns and vice versa.Thus, even though I have explicitlyassumed that all firms have the samesize, the so-called “size enigma”exists in this economy—market valueis inversely related to return.

Thus, even if small-cap stocks arefairly priced, one would observe a small-stock “effect” that has no implicationsfor investment management. In other

words, the higher returns on small-capare not really an effect; they simply mirror the market mechanism workingto price riskier companies more cheaplythan safe companies.

Market capitalization, then, is not apure measure of a firm’s size; it simulta-neously measures size and the discountrate. (The discount rate on a security isalso the expected return from holdingthe security.) To measure a firm’s sizealone, Berk uses two admittedly imper-fect measures—sales and book value. He finds that the size effect is nonexis-tent when firms are ranked by these

variables. In other words, “the size enig-ma results from the part of market valuethat measures the firm’s discount rateand not from a relation between the sizeof firms and returns.” When stocks aresorted by these nonmarket measures ofsize, then, the results are completelyconsistent with the CAPM, and greaterreturn and greater risk are associatedwith each other, with nothing left overfor capitalization to explain.

Berk concludes that (1) because the size (market-

capitalization) effect is theoretically predicted, we

would be surprised not to find it in the data; and (2)

we cannot use the market–capitalization effect to

earn higher risk–adjusted returns, because the size

premium is in reality a premium for risk, not for size.

11


2off to the investor for being forced topay transaction and information costs.Perhaps behavioral factors (that is,irrationality) are required to explainthe small-stock premium. Perhaps, asBerk suggests, a small-size effect isimplicit in the mechanism that mar-kets use to price assets and we shouldbe surprised not to find it. Finally, per-haps the premium is a type of freelunch or permanent arbitrage opportu-nity—a true capital-market anomaly.We explore these possibilities in thefollowing sections.

Berk concludes that (1) because thesize (market-capitalization) effect istheoretically predicted, we would besurprised not to find it in the data; and(2) we cannot use the market-capital-ization effect to earn higher risk-adjusted returns, because the size pre-mium is in reality a premium for risk,not for size. While Berk’s contentionthat small stocks are fairly priced ishardly unique, his contribution is totake the small-stock effect out of therealm of anomalies. It is simply to beexpected from the way markets areorganized. The real anomaly, in Berk’sview, would be if a small-stock premi-um were not observed.

Conclusion

The preponderance of the evidencesuggests that at least part of the small-stock effect cannot be explained bybeta, no matter how accurately beta ismeasured. The best statistical explana-tion may be a risk premium for smallsize (independent of beta) in the styleof Fama and French. This is somewhatunsatisfying: at some level, Fama andFrench have merely attributed to somesort of generalized “risk” the part ofthe return that beta cannot explain.Perhaps the small-stock effect is a pay-

The preponderance of the evidence suggests that

at least part of the small-stock effect cannot be

explained by beta, no matter how accurately beta

is measured. The best statistical explanation may

be a risk premium for small size (independent of

beta) in the style of Fama and French.

12


The idea that the small-stock premiummight be a form of compensation fortransaction costs is simple, and wasunderstandably raised quite early, byHans Stoll and Robert Whaley in 1981.They write,

A simple explanation of [the small-stock premium] is that an investortaking a small-firm portfolio positionfaces higher transaction costs thanhe does when he takes an otherwisesimilar large-firm position. The mar-ket maker’s spread on a proportionalbasis is generally higher for smallfirms because of their infrequenttrading activity and risk; and the bro-ker’s commission rate is, amongother things, an inverse function ofthe price per share, a variable corre-lated with the total market value ofthe stock. In addition, there areother, less-explicit costs such as thecost of investigating and monitoringa firm that may be higher for smallfirms.… [Our study suggests thatwhile] small firms find it more costlyto attract investment funds, unjusti-fied discrimination against smallfirms is not necessarily present.16

Unjustified discrimination againstsmall firms is, of course, the prerequi-site for the finding of a true small-capanomaly. If the premium is merely com-pensation for the higher costs thatinvestors pay to maintain small-firmportfolios, and after-cost returns onsmall firms are unexceptional, then themarket is arguably efficient and theCAPM correct.

Stoll and Whaley go on to demon-strate that, over 1960–1979, if one hadsold all the stocks in a small-firm port-folio at the end of each month and thenbought the stocks in the newly consti-tuted portfolio, the transaction cost(including brokerage commissions andbid-asked spreads) would have been so onerous as to reverse the small-firmeffect. That is, large-firm portfolioswon.17 This is unsurprising becauseturning over the whole portfolio month-ly is a profoundly irrational way for aninvestor facing transaction costs tobehave. Apparently anticipating thiscriticism, Stoll and Whaley lengthenthe holding period to two, three, four,

six, and 12 months. They find that fourmonths is the break-even holding peri-od, and that the smallest-firm portfoliohad positive abnormal returns aftertransaction costs for all holding periodsof six months or longer. At a holdingperiod of 12 months, the abnormalreturn is huge (4.53% per month).

While Stoll and Whaley contendthat transaction costs at least partlyoverturn the size effect, that is not nec-essarily the case over the time periodthey studied. Even the most activeinvestors are unlikely to turn over theirwhole portfolios monthly, so the rever-sal of the small-firm effect for investorshaving a one-month holding period is astraw man. Moreover, the results sug-gest that a buy-and-hold approach tosmall stock investing (with, say, rebal-ancing every 12 months) would havebeen very profitable over 1960–1979.Note that buying and holding is differ-

Transaction, information, and other investor costs

T H R E A D 3

313


ent from indexing; because small-stockprices fluctuate a lot, substantial turnoveris required to track changes in a size-decile index. If small-stock investingwere always as profitable before transac-tion costs as it was over 1960–1979,investors could reap abnormal returnsby holding small-firm portfolios and lim-iting their turnover. (We will argue laterthat transaction costs go a long waytowards negating the small-stock effectfor all practical purposes, but Stoll andWhaley did not get that far.)

Schultz (1983) points out many ofthese problems with Stoll and Whaley’sapproach, and in addition takes note ofsome aspects of the size effect that can-not be explained by transaction costs.Most important, the small-stock premi-um was sharply and persistently nega-

tive over 1926–1931, 1946–1957, and1984–1990. Transaction costs were obvi-ously not negative in these periods.Moreover, as Schultz indicates, small-stock returns have been much higher inJanuary (until recently) than in othermonths of the year. On a per-transaction

basis, transaction costs are not higherin January than at other times.However, there may be more transac-tions in January due to tax-loss sellingand other rebalancing behaviors.

Roll (1983) and Blume andStambaugh (1983) advance an argu-ment quite similar to that of Stoll andWhaley, although they frame it (some-what confusingly) in terms of a “biasin mean return calculation.” Rolldraws a distinction between arith-metic-mean and buy-and-hold methodsof computing mean returns. The arith-metic-mean method is the one used inmost academic studies of the small-stock effect, and (though it is rarelyadmitted) assumes costless rebalanc-ing at the same time interval as thedata-sampling frequency. That is, if

actual daily stock-return data for asmall stock indexare averaged overtime using thearithmetic-meanmethod, the resultis an average of aseries that is rebal-anced regularly tothe index designcriteria, and thusthe averages takenfrom this series

implicitly assume daily rebalancing.The buy-and-hold method, in contrast,assumes no rebalancing. Realisticrebalancing rules (that is, somewherebetween daily and never) can be incor-porated by changing the method ofmean-return calculation.

Stoll and Whaley go on to demonstrate that,

over 1960–1979, if one had sold all the stocks in a

small-firm portfolio at the end of each month and

then bought the stocks in the newly-constituted

portfolio, the transaction cost (including broker-

age commissions and bid-asked spreads) would

have been so onerous as to reverse the small-firm

effect. That is, large-firm portfolios won.

14


Roll’s empirical work shows that the size premium is cut in half (from14.9% per year to 7.45% per year over1963–1981) if the buy-and-hold methodis used instead of the arithmetic-meanmethod.18 Blume and Stambaugh arriveat a similar result. The explanationseems to be that it would have beenimpossible to transact at the closingprices used to construct the returnseries that implies daily rebalancing.One would have paid the ask andreceived the bid, and incurred commis-sions. Thus, the buy-and-hold methodgives a more realistic estimate of theprofits that can actually be earned bysmall-stock investing.

A 7.45% annual small-stock premi-um is still substantial. Moreover, Rolladmits that:

Papers with monthly returns are…much less subject to mean returnestimation problems.… The well-known paper by Banz (1981) usedmonthly data.… Thus, it seemsunlikely that the results… will bemuch affected by the problem investi-gated here. In a more recent paper,Reinganum (1983) used the buy-and-hold method and found results closeto those reported above.

However, the cost of one full turn ofa small-stock portfolio has been report-ed at as much as 4%. Typical turnoverfor actively managed small-stock portfo-lios is around 100% (one full turn) peryear (it varies greatly), so that the 7.45%annual premium may fall by more thanhalf—and this premium was measuredin a period when small stocks outper-formed by a healthy margin. They do

not always do so. The effect of any real-istic transaction-cost estimate on thesmall-stock premium is profound whenturnover rates typical of active manage-ment are considered. Only an indexedor other low-turnover strategy can miti-gate these costs in an effort to capturethe larger portion of the premium.

Costs other than those related totransacting have received less attentionfrom researchers, although they are noless important. Perhaps this is becausedata on transaction costs are more read-ily measured. Lustig and Leinbach(1983) sensibly assert, without present-

ing evidence, that the cost of obtainingand updating information on smallfirms is differentially greater and thatinvestors may be demanding andreceiving a premium in the before-costreturn to compensate them for this bur-den. Barry and Brown (1983) present atheoretical framework in which theimpact of differential information aboutstocks on their returns can be evaluat-ed, but find the data too scarce to sup-port a strong conclusion.

An interesting discussion of allthese issues can be found in Ibbotson,Diermeier, and Siegel (1984). Theseauthors argue that investors demandand, in equilibrium, expect to receivecompensation (that is, a higher before-cost expected return) for all investor

Ibbotson, Diermeier, and Siegel (1984) argue that

investors demand and, in equilibrium, expect to

receive compensation (that is, a higher before-

cost expected return) for all investor costs.

15


3costs. These costs include risks(including but not limited to beta risk),transaction and information costs,taxes, and other costs not enumeratedin the article. After subtracting thecosts faced by the marginal investorfrom the market return, markets maybe observed to be efficient. However,investors who can be “off the margin”with respect to these costs can earnabove-market returns. In the small-stock sector, an index fund has thebest chance of earning the superiorreturns that small stocks appear tooffer on a before-cost basis, particular-ly for index managers who have theability to “cross” trades internally.

Because all the investor-cost articles cited thus far are quite old, an update is in order. Wagner andEdwards (1993) point out that the costof illiquidity is not limited to the ex-plicit cost of trading (consisting of market impact plus commissionsand/or spreads). There is also theopportunity cost of not trading:

[Delay] cost [is] the price move priorto being able to trade; it can bethought of as the cost of seeking liquidity…[and]…is defined asprice movements between the initialsubmission to the trade desk andthe exposure of that order, mostly ineasily digested pieces, to the broker.

[Missed-trade] cost [is] the cost offailing to find the liquidity to completethe trade. We define opportunity costas the price change on unexecutedshares from the time of submission tothe trade desk until cancellation [bythe manager, due to an excessive risein the market price].19

From their firm’s study of variousinstitutional portfolios, Wagner andEdwards find that the missed-tradecost for stocks over $1 billion in mar-ket capitalization was 1.03%, while itwas 3.93% for stocks under $1 billionin market capitalization. (Theseamounts are per one-way trade; doublethem for a round turn.) This differencecompares with the 1.7% spread ofsmall-stock geometric mean returnsover large stocks in the 1926–1997period studied by Ibbotson Associates.If a small-stock portfolio is subjected to50% turnover per year, it is legitimateto directly compare these two num-bers. Extrapolating (somewhat hero-ically) Wagner and Edwards’ result to1926–1997, then, more than all of thesmall-firm premium is confirmed byopportunity cost alone.

In an update of Wagner andEdwards’ work, Plexus Group (1998)estimates the “implementation cost”—the total of commission, impact, delay,and missed-trade costs—to be 1.01%for stocks over $1 billion, and a tower-ing 4.49% for stocks under $1 billion.(Double these amounts for a roundturn.) However, an indexed manage-ment style keeps turnover low, andimpact costs can be minimizedthrough internal crossing and othertechniques available by exemption tocertain informationless trades. Onlythen might the expected return premi-um from investing in small stocks besufficient to overcome the cost disad-vantage of trading them.

16


This section focuses on arguments thatthe small stock premium is unreliable,nonexistent, or a proxy for some othereffect. We start with the observationthat much of the historical small-stockpremium was earned in a single periodfrom 1974 to 1983.

4a Arguments that the small-

stock premium derives from a singleobservation or one-time repricing of

these stocks

One of the most damning criticisms ofthe idea that one can win by buyingsmall stocks was enunciated by JeremySiegel (1994) in his best-selling book,Stocks for the Long Run:

[I]f the period from 1974 to 1983 iseliminated, the total accumulationin small stocks falls nearly 25%below that in large stocks. Even forthe long-term investor… , if youdon’t catch the small-stock wave,you miss the boat!20

If the entire small-stock premiumas measured over 1926 to the presentcan be explained by a single, continu-ous 10-year period (what statisticianscall a single observation, even thoughmeasured over multiple periods), thenone cannot rely on the premium. Thebest one can do is to try to time theweight of small stocks in the portfolioto correspond with upward relativemoves in that sector (see Thread 8).

What would cause small stocks toexperience a tremendous upwardmove in the 1970s and early 1980s?One explanation is that these neglectedand poorly regarded “secondaries”were underpriced (see Thread 3) atthe start of the period, when they soldat a P/E ratio some 50% lower thanthat of the S&P 500. Then, as the biginvestment houses became interestedin this underpriced sector, they “insti-tutionalized” the process of gatheringinformation about these companiesand made massive purchases of them,driving up prices. By 1983, smallstocks were selling at a 20% P/E-ratiopremium compared to the S&P 500. Ofcourse, this 140% upward revaluationof the P/E multiple is insufficient

to explain the 344% relative return on small stocks (as measured by the Ibbotson index) over 1974–1983.Earnings of smaller companies alsoboomed. In a period of relatively poorperformance by large-corporateAmerica, and in a political climate ofderegulation, it was relatively easy forenterprising small companies (as well

Evidence that the small-stock premiumis unreliable or does not exist

T H R E A D 4

What would cause small stocks to experience

a tremendous upward move in the 1970s and early

1980s? One explanation is that these neglected

and poorly regarded “secondaries” were under-

priced at the start of the period.

417


as foreign companies) to chip away atoligopolies in businesses as diverse asairlines and financial services. Thistrend has been sharply reversed, andUS industry is now about as concen-trated as it has ever been. The currentcondition may augur well for smallstocks in the near future.

Jensen, Johnson, and Mercer (1996,1997) report a contrasting result.Constructing equally weighted ratherthan value-weighted portfolios, andcontrolling for beta so as to isolate thepure stock effect, they find smallstocks outperformed in every “decade”(1963–1969, 1970–1979, 1980–1989,and 1990–1995). However, it is difficultfor investors to bet on this pure factorreturn; equally-weighted portfolios donot stay that way, and require costlyrebalancing; and if decades weredefined in some other way, the premi-um might not be positive in all of them.We believe that Jeremy Siegel’s argu-ment (echoed by many other authors,before and since) regarding the single-observation character of the small-stock premium casts substantial doubton the reliability of the premium in thefuture—even before transaction costs.

4b Arguments that the mall-

stock effect is a really a proxy forother effects such as low P/EThe existence of a small-firm effect(whether at all times or only some-times, and whether or not it survivestransaction costs) does not mean thereis necessarily something unique or

mysterious about small stocks thatcauses them to have high returns.Perhaps the small-firm effect is aproxy for some other effect or combi-nation of effects.

Other than Reinganum (1981),whose work has already beenreviewed, Basu (1983) was the first toseriously evaluate this possibility.Basu’s results contrast with those ofReinganum (whom he criticizes ongrounds of statistical method), andimply that the P/E and size effectswere closely related over 1963–1979.He writes,

This E/P effect…is clearly signifi-cant even after experimental con-trol was exercised over differencesin firm size.… On the other hand… ,the size effect virtually disappearswhen returns are controlled for differences in risk and E/P ratios.…While neither E/P nor size can be considered to cause expectedreturns… , most likely, both vari-ables are just proxies for more fun-damental determinants of expectedreturns for common stocks.21

This opened a can of worms thatcould only be contained with a muchlarger can. More than a dozen otherarticles by major authors attempt todisentangle the size effect from otheridentified or suspected effects such asP/E, price-to-book (P/B), and neglect(that is, lack of coverage by brokeragehouse research staffs). We review themvery briefly in chronological order

18


4(some have already been mentionedelsewhere herein).

Cook and Rozeff (1984), in contrastto several other authors cited above,found that size and P/E are two sepa-rate effects.22 Lakonishok and Shapiro(1984) contend that the size effectswamps both beta and variance (totalrisk) as explainers of the differences instock returns; they did not look at P/Eor other measures of “cheapness.”Dowen and Bauman (1986) find thatsize dominates P/E, although not com-pletely; but that size fully explains the“neglect” effect. Zivney and Thompson(1987) arrive at the startling conclusion(never since confirmed) that “a stock’srelative price ratio, the ratio of the cur-rent price to the average of the highestand lowest prices over some holdingperiod, is a better predictor of futurestock returns than firm size.” If this istrue, then the small-stock effect is aproxy for cheapness and has no inde-pendent existence. Keim (1990), using alonger data period than other authors,23

finds that P/E and size effects are bothsignificant, but that the size effect dis-appears if one removes data fromJanuary of each year (see Thread 7).

Fama and French (1992, 1995) find thatsize and P/B (a kind of cheapness) inde-pendently explain returns, and theysurely have not had the last word on thesubject.

What we get out of all this is thatsize and “cheapness” are deeply inter-twined. Stocks have earned excessreturns because they are low-priced inmany dimensions—price per unit ofbook value, earnings, or cash flow; priceper share; price relative to their own historical price series, as in Zivney andThompson; and price-times-shares-outstanding, which is the small-stockeffect. When statistical analysis revealsthat the small-cap effect is at least par-tially independent of other effects, thatfinding can be interpreted to mean that“cheap” firms (those bargain-priced bythe market) can be identified to someextent by choosing the small ones. Ofcourse, such a procedure will turn upsome emerging growth companies thatare not cheap by valuation measures, butthese do not appear to dominate thesmall-firm universe.

When statistical analysis reveals that the small-cap

effect is at least partially independent of other

effects, that finding can be interpreted to mean that

“cheap” firms (those bargain-priced by the market)

can be identified to some extent by choosing the

small ones. Of course, such a procedure will turn

up some emerging growth companies that are not

cheap by valuation measures, but these do not

appear to dominate the small-firm universe.

19


5If small-cap, low P/E, and other “buycheap” investment strategies work withany degree of consistency, then a behav-ioral explanation is in order. Behavioralfinance is the branch of finance thatrejects (or sets aside for the sake of ex-ploration) the assumption that all economic agents are rational. Instead,behavioral finance says, investorsengage in all sorts of activity that is irrational from the standpoint of net-present-value (dollar) maximization,although it may be rational in the senseof maximizing psychological utility.24

Because capital-market efficiency relieson investor rationality, behavioralapproaches to finance may help explaininefficiencies.

Behavioral finance has been appliedto the small-stock question by severalauthors, of whom the most noteworthyare Lakonishok, Shleifer, and Vishny(1994). They propose that the small-stock effect is a value effect caused bythe preference of investors for safe, well-known companies. As Lakonishok andhis colleagues argue, a large fraction of investors has historically disdainedrisky, unprofitable, poorly capitalized,or otherwise troubled companies. Byfailing to buy these stocks for their port-folios, these investors have caused theprices of “unloved” stocks to be lowerthan their fair value, and (because ofthis low pricing) to be lower in capital-ization ranking than the stocks wouldotherwise be. Then, as the unloved com-panies become loved or at least acceptedin the mainstream of institutionalinvesting, a correlated return-to-value

and return-to-small-size emerges. Manyauthors have speculated along theselines, but it is difficult to devise empiri-cal tests for love and disdain, so theargument has remained mainly concep-tual.

A related (and more testable) idea,supported by some empirical evidence,is that firms neglected by brokerage-house researchers have higher returnsbecause they are initially underpriced.We have already (in Thread 4b) seenDowen and Bauman’s finding that theneglect effect is subsumed by the sizeeffect. Beard and Sias (1997) confirmthis. These works still do not addressthe question of whether neglect causesthe size effect. Along with risk andtransaction costs, it very well may.Today, few small firms are as neglectedas they used to be—small-cap portfoliosare part of practically every broker’sand money manager’s repertoire—andthis may dampen the small-stock effectin the future.

Not all small stocks are valuestocks. In fact, most investors probablycare more about small companies fortheir growth potential. Emerging-growth companies, particularly in tech-nology fields, have had exceptional performance in recent years, takingattention away from “fallen angel” andother value-oriented styles of small-capinvesting. However, high earningsgrowth rates do not have a significantrole in the research literature on thecauses of historical excess returns inthe small-stock universe.

Behavioral explanations for the small-stock effect

T H R E A D 5

20


Perhaps because academic journalsrarely publish articles that fail to findan explanation for something, the liter-ature suggesting that the small-stockeffect is a true anomaly or profit oppor-tunity is relatively sparse. A couple ofnotable articles, however, appear to beclassifiable only by invoking thisthread.

The first is a review article by G.William Schwert (1983) in the Journalof Finance issue that focused exclusive-ly on questions of small-stock behav-ior. Because of the burst of activity thatimmediately followed the discovery ofthe size effect in 1979–1981, a surpris-ingly large number of the explanationswith which we are familiar today hadalready been suggested. At that time,Schwert writes, all had been foundinadequate:

The search for an explanation ofthis anomaly has been unsuccess-ful. Almost all authors of papers onthe ‘size effect’ agree that it is evi-dence of misspecification of the[CAPM], rather than evidence ofefficient capital markets. On theother hand, none of the attempts tomodify the CAPM to account fortaxes, transaction costs, skewnesspreference, and so forth have beensuccessful at discovering the ‘miss-ing factor’ for which size is a proxy.Thus, our understanding of the…causes of the apparently high aver-age returns to small firms’ stocks isincomplete. It seems unlikely thatthe ‘size effect’ will be used to mea-

The small-stock effect as a true market anomaly

T H R E A D 6

sure the opportunity cost of riskycapital in the same way as theCAPM is used because it is hard tounderstand why the opportunity costof capital should be substantiallyhigher for small firms than for largefirms.… Therefore, it is unlikely thatthe ‘size effect’ will be taken intoaccount in teaching capital budget-ing or performance evaluation forinvestment portfolios.25

Schwert, of course, could not pre-dict the emergence of the Fama-Frenchthree-factor model (in which size is a risk factor). By saying that the sizefactor would be unlikely to be used todevelop cost of capital estimates inapplications requiring an estimate ofrisk, Schwert reveals his view that thefactor is unrelated to risk, and that the size effect is a market anomaly.

Writing in 1987 about the arcanetopic of parameter preference,26 Boothand Smith argue that, all other thingsbeing equal, investors should preferassets which have return distributionsthat are skewed to the right (that is,having more outlying positive observa-tions than predicted by the normal orlognormal distribution). Small stockshave positive skewness, while medium

Booth and Smith’s elaborate statistical test

rejects the hypothesis that the small-stock

effect is caused by a preference for assets

with positively skewed return distributions.

21


6and large-cap stocks have zero or nega-tive skewness. Whether a preference forpositive skewness explains the small-stock effect is a testable proposition.

Booth and Smith’s elaborate statisti-cal test27 rejects the hypothesis that thesmall-stock effect is caused by a prefer-ence for assets with positively skewedreturn distributions. They write,

This is an extremely strong conclu-sion for the following reasons: First,returns are measured monthly sothat…problems…with nonsyn-chronous trading… are minimized.Second, the conclusion is in no waydependent on specification of a…market portfolio, and, thus, bench-mark error in the market portfolio[or]… in the risk-free rate is not anissue. Third… , the small-firm effectpersists even when January returnsare excluded.… Fourth… , the findingof a small-firm effect by third-degreestochastic dominance means that noutility function that exhibits skew-ness preference will account for theeffect. These findings strongly sug-gest that the resolution of the…paradox will be found in comprehen-sive analysis of the… institutionalfactors that affect asset value.

This powerful and overlooked arti-cle, then, falls squarely into the groupthat advises us to look at the small-firmeffect as a market inefficiency, perhapscaused by institutional behavior.Another possibility that Booth and Smithdo not mention is transaction costs.

We earlier reviewed a class of arti-cles that indicate the small-stock effectexists and is not a reward for takingrisk. Banz (1981), the originating articlefor this topic, is the most illustriousexample. These articles may be inter-preted as part of the true-anomaly liter-ature, but that would be a little mis-leading. Tests of the Banz (1981) typeare joint tests of (1) market efficiencyand (2) a specific model of investorbehavior toward risk (say, the CAPM).Thus, one cannot reject market effi-ciency at the general level—and con-clude that a permanent arbitrageopportunity exists—purely on the find-ing of a small-stock premium unrelatedto risk as specified by that particularmodel. Maybe—likely—the behavioralmodel is simply inadequate to the task.To conclude that there is a permanentarbitrage, one has to find that smallstocks beat other stocks fairly consis-tently over time, after all risks andcosts have been accounted for, and fora large class of investors (not just, say,those who have a seat on the stockexchange). Such a conclusion is diffi-cult to support in light of the accumu-lated evidence to date.

22


One of the most puzzling findingsabout small stocks is that their returnsin excess of large-stock returns areusually concentrated in January of eachyear, and (some studies find) in thefirst few days of January. Such a “sea-sonality” is entirely inconsistent withefficient-market theory, for if a regularpattern of returns becomes known, itshould be quickly eliminated by arbi-trageurs. As early as 1925, Owens andHardy had written, “Seasonal varia-tions are impossible.…If a seasonalvariation in stock prices did exist, gen-eral knowledge of its existence wouldput an end to it.”28 Yet the Januarysmall-stock seasonality has been wide-ly written about since 1983 at the latest, and it continues to persist. Thisis very odd.

Because this paper is directed tolong-term investors, an explanation ofthe January effect and a forecastregarding its reliability or continuedexistence is of secondary interest.Therefore, we keep the review of the lit-erature relatively brief.

The January effect was discoveredby Keim (1983). He found that over1963–1979, a period of high perfor-mance for small stocks, about 50% ofthe extra return was earned in Januaryof each year. Moreover, 10% of theannual size effect for an average year

was earned in the first trading day ofthe year, and 26% was earned in thefirst five trading days.29 Keim suggeststhat tax-loss selling30 or the release ofinformation may explain the effect. Healso allows for the possibility that thereis a data error or bias.

Reinganum (1983) tests for a tax-loss selling effect. First, he identifies“loser” small-cap stocks that are mostlikely to have been sold to realize taxlosses. He compares the January andearly-January returns on losers to thoseof winners, and finds that the losers did

spring back with unusual vigor afterthe turn of the year. However, small-cap stocks that had been winners overthe previous year, and unlikely to havebeen sold for tax loss reasons, also out-performed large issues in January.Thus, the tax-loss hypothesis does notexplain the entire January effect.

If tax-motivated behavior helps toexplain the January effect in the UnitedStates, then one should find it on differ-ent dates in countries with a different

Short-term timing of the small-stock effect (the January effect, etc.)

T H R E A D 7

The January effect was discovered by Keim (1983).

He found that over 1963–1979, a period of high

performance for small stocks, about 50% of the

extra return was earned in January of each year.

23


7tax year. In Australia, where the tax yearends on June 30, Brown, Keim, Kleidon,and Marsh (1983) find a substantial Julypremium—and a January premiumwhich may be caused by Americaninvestors. However, the authors pointout that:

The tax-loss selling hypothesis itselfrelies on an absence of arbitragefrom those not forced to sell a particu-lar security for tax purposes. It seemsdifficult to reconcile an integratedcapital market, that functions so wellthat a US tax-induced January sea-sonal shows up in even penny stocksin Australia, with simultaneous mis-pricing of securities to create the orig-inal US January seasonal.31

This comment suggests that even fourfinance professors can occasionally forcetheir views to bow to common sense.

Some researchers have hypothesizedthat the January effect is a payoff forhigher risk levels in January, but theresults are unconvincing.32 Another gen-erally unproductive thread associatesthe January effect with institutionalrebalancing and “window dressing” ofportfolios at year end.33 Taking a differ-ent tack, Lakonishok and Smidt (1986)find that most, but not all, of the profitsfrom a trading strategy designed toexploit the January effect for small firmswould be consumed by transaction costs.They do not, however, find any evidencethat transaction costs cause the effect toexist in the first place.

Some observers believe that thesmall-stock January effect has been dis-appearing. Addressing this question,Haugen and Jorion (1996) find that “theJanuary effect is still going strong 17years after its discovery.” Riepe (1997),however, finds this conclusion is appli-cable only to the very smallest stocks,where transaction costs are highest.Riepe writes,

The January effect has weakened.…Almost no January effect occurs formany deciles [of all US stocks sortedby market capitalization] over thelast four years [1994–1997].…[F]or deciles 5 to 8, there is virtuallyno effect at all.34… The January effect is still there for the smallestcompanies.

Institutional investors with substan-tial assets under management, however,will probably have a difficult timeexploiting the January phenomenongoing forward.

24


The seminal work on predicting long-term trends in the small-stock effectcame later than that on other threads.Reinganum (1992) attributes the delayto a view among academics, prevalentin the wake of the efficient-markethypothesis, that predictable trends inthe stock market were impossible andthus not worth looking for. Whateverthe reason, little follow-up was done onIbbotson and Sinquefield’s (1982)observation that the small-stock premi-um was highly autocorrelated and thussomewhat predictable. As noted earlierin this paper, Ibbotson and Sinquefieldrecorded periods of small-stock over-and underperformance lasting manyyears, and having a large magnitude interms of differential return. This sug-gests timing approaches basing nextperiod’s forecast on last period’sreturn.

Jacobs and Levy (1989) introduceda macroeconomic model relating small-stock returns to six APT-type factors.35

They isolated the “pure” returns tosize; that is, the returns which remainafter removing other effects such asP/E and price-per-share. This makesthe forecast signals too weak to makemuch profit from using the signals.Then, Reinganum (1992, 1993) pro-posed a simple overreaction model inwhich small-stock underperformancein a given year is predictive of outper-formance about five to six years later.The model worked remarkably well:

[H]istory suggests that the first halfof the 1990s should be a boom peri-od for small cap stocks.… By themid-1990s, however, this researchsuggests that the small-cap advan-tage will diminish or perhaps eventurn negative.

We thus have a true out-of-sampletest, for Reinganum’s article was com-pleted before the end of 1990. Over1991–1994, the Ibbotson Associatessmall-stock index rose by 42% inexcess of the S&P 500 return. Then,over 1995–1997, it fell by 14% relativeto the S&P 500.36

The overreaction model was betterat predicting rebounds after periods ofpoor small-stock performance than itwas at the opposite. When small stocksare proxied by decile 2, 6, or 10 of theNYSE ranked by capitalization (wheredecile 1 contains the largest stocks,and decile 10 contains the smallest), afive-year period of small-stock under-performance was followed by a five-year period of outperformance everytime over 1926–1989.37 (When smallstocks are proxied by other deciles, theregularity is very much there, but it is

Long-term timing of the small-stock effect

T H R E A D 8

Reinganum (1992, 1993) proposed a simple

overreaction model in which small-stock

underperformance in a given year is predictive

of outperformance about five to six years later.

825


less perfect.) However, periods of out-performance do not predict periods of underperformance nearly as accu-rately. For example, outperformanceover 1974–1978 might be interpretedas predicting underperformance in1979–1983. This second period wasone of the best in history for smallstocks, and the overreaction modelwould have caused investors to miss it (or, much worse, sell small stocksshort during the period).

A five-year reversal is less frequentthan the signals usually preferred bytactical asset allocators, although thatis not to say that it would not be valu-able. Macedo (1993), in contrast, haspresented a model that relates small-stock relative performance to changesin macroeconomic variables, and thatgives much more frequent signals.

Macedo’s model identifies five eco-nomic variables—the equity risk pre-mium, market volatility, Treasury billyields, the trend of leading economicindicators, and exchange rate volatility—that are correlated to subsequent rel-ative returns of the S&P 500, small-capvalue stocks, and small-cap growthstocks.38 The variables are said to workas follows:

A high equity risk premium favorsportfolios perceived as more risky,so small cap is indicated over largewhen the equity risk premium ishigh. After a period of high [stockmarket] volatility, small-cap stockscan be expected to outperformlarge, since small cap tends to be

oversold during the “flight to quali-ty” that occurs during turbulentmarkets. Rising Treasury bill yieldsfavor large cap over small cap.Small companies outperform largeat the beginning of a recovery; afterthere is evidence of a healthiereconomy, such as a strong year-over-year rise in the leading indica-tor, large tends to outperform small.Large stocks are more leveraged tooverseas earnings growth thansmall stocks; consequently, largestocks are penalized when theexchange rate is highly volatile.

The model was backtested over1981–1992, and 100% of the portfoliowas allocated to the most attractiveasset (from among the S&P 500, theWilshire small value index, and theWilshire small growth index). Anallowance of 2% round-trip was madefor small-cap transaction costs; for theS&P 500 the allowance was 0.5%round-trip. Forecasts were updatedmonthly, but allocations were changedonly when the expected difference inreturns exceeded transaction costs.The benchmark portfolio consisted of50% in the small value index and 50%in the small growth index.

The results indicate a 6.0% annualreturn advantage to the timing model,with very modest turnover (19% annu-ally). However, there is an element ofretrofitting in this analysis. It isunlikely that the correct variablescould have been identified by econom-ic reasoning at the beginning of theperiod. Because the author had access

826


(at least subconsciously) to informa-tion about how markets behaved dur-ing the study period, a model could be constructed that was highly effec-tive in-sample. Future researchers can determine how models such asMacedo’s work out-of-sample.

Finally, Jensen, Johnson, andMercer (1997) identify a number ofcandidate variables for explaining dif-ferences between small- and large-stockreturns, and conclude that monetarypolicy is the critical factor. Specifically,

We find significant and consistentsmall-firm and low price-to-bookeffects only during expansive mone-tary policy periods. In restrictiveperiods, neither size nor price-to-book ratio is significantly or consistently related to returns.

However, when two closely corre-lated variables (in this case, real eco-nomic activity and monetary policy)are subjected to the type of analysisperformed by Jensen, Johnson, andMercer, the variable with the slightlystronger statistical effect appears to

dominate completely. As Kaplan (1997)notes, monetary policy over the pasttwo decades has been conducted in amanner that is highly correlated withreal economic activity, but the causalrelationship between easy money anda growing economy is dubious. Thus,monetary policy may be an importantfactor in determining small-stock rela-tive returns, or it may be serving as a proxy for economic growth.

It is worthwhile to note that, forreasons made clearer in Grinold andKahn (1995), tactical asset allocationacross large- and small-capitalizationstocks is difficult. There is simply notenough cross-sectional diversificationacross just two investment alternativeswith relatively few independent invest-ment signals during the course of theyear, causing the residual risk to belarge relative to the expected alpha ofthe signal.39 This problem is, of course,general to all problems of choicebetween two assets, not specific tothese two particular assets.

As Kaplan (1997) notes, monetary policy over the

past two decades has been conducted in a manner

that is highly correlated with real economic activity,

but the causal relationship between easy money

and a growing economy is dubious. Thus, monetary

policy may be an important factor in determining

small-stock relative returns, or it may be serving as

a proxy for economic growth.

927


So far, this discussion has beenfocused on the United States becauseresearchers have been motivated bythe superabundance of data to studythat market closely. Non-US markets,however, are just as important (moreso if total market capitalization is thecriterion), so investors can benefit fromknowing whether the size effectapplies in other countries. The litera-ture on the small-stock effect outsidethe US is focused primarily on what wereferred to as Thread 1—identificationand measurement of the effect.

A summary of small- and large-stock returns in developed marketsaround the world, from Bruce andLeahy (1993), is shown in Table 2.

Bruce and Leahy compare returns onthe bottom 20% (sorted by market capi-talization) of the stocks in the MorganStanley Capital International (MSCI)country indices with returns on the top80% of the stocks in the same indices.40

The comparison is over the brief 41

13-year period from 1978 to 1991.Small-cap stocks outperform in 14 ofthe 18 countries. Excess returns ofsmall over large issues range from acompound annual rate of 22% in NewZealand to -5% in the Netherlands. Notethat portfolios are rebalanced annuallyand transaction costs are not deducted;because the bottom quintile of an MSCIcountry index is subject to considerableturnover while the top 80% has muchless turnover, transaction costs wouldbe much larger for the small-stock port-folios.

We now review academic literatureon the international small-cap effect,country by country. Unfortunately, dueto data limitations, the periods coveredby most of the studies are even shorterthan the 13 years studied by Bruce andLeahy. Thus, it may be better to gener-alize from US results than to draw distinctions among countries based on these short-period studies. There isno particular reason to expect that thesmall-cap effect should be differentfrom country to country. Therefore, wemay do as good a job at estimating it in any particular country by generaliz-ing from what we have learned fromlong data series in the US as by relyingon much shorter data series from thatcountry. The standard error of the estimate from short-period studies isnecessarily quite high.

The small-stock effect around the world

T H R E A D 9

28


Japan

Probably the most thorough investiga-tion of a small-stock effect in countriesoutside the US is that of Hamao andIbbotson (1989). Following the methodof Ibbotson and Sinquefield, Hamao andIbbotson measure monthly, capitaliza-tion-weighted returns on Tokyo StockExchange (TSE) sections I and II stocks,and on the fifth quintile of the TSE sec-tion I. (The authors describe section I asconsisting of “large, mature firms” andsection II as consisting of “small, young,or troubled firms.” The fifth quintile ofsection I corresponds more closely tothe fifth quintile of the NYSE, contain-ing a good number of fallen angels thathad once been large but that becamesmaller.) The study covers 1971–1988.The shortness of the period and the factthat it essentially covers only risingmarkets creates problems in interpret-ing the results, but the authors had lim-ited data with which to work.

They found that the fifth (smallest)quintile of TSE section I beat largerissues at a compound rate of 4.3%.Moreover, the yearly excess returns ofsmall stocks are highly autocorrelated(follow long waves of good and bad per-formance), as in the US, and are higherin January than in other months, as in the US.

Rao, Aggarwal, and Hiraki (1992)study a slightly more recent period, andalso found a “significant” size effect, aswell as a seasonal anomaly. They specu-lated, “The fact that these anomaliesbehave in a fashion similar to thatobserved in the United States is sugges-

tive of either an integrated global capi-tal market or the omission of commonelements in the pricing process used, or both.”

United Kingdom

In 1988, Mario Levis found a substantialsize effect in the UK over 1966–1982.The smallest stocks outperformed thelargest by an arithmetic mean of 6.8%per year. Interestingly, small stockswere less risky (had lower standarddeviations of quarterly returns) thanlarge stocks. Small stocks also hadlower OLS betas, but these are subjectto our earlier comments on infrequenttrading and autocorrelation.

Only a year later, Levis (1989) com-mented that size effect was present butnot strikingly important: “[I]nvestmentstrategies based on dividend yield,price-earnings ratios, and share pricesappear as profitable [as], if not more[than], a strategy concentrating on firmsize.… [T]here is a large degree of inter-dependency between all four effects.”By 1997, Jonathan Fletcher found nosize effect at all. This contrasts with thework of Bruce and Leahy (1993), whosedata ended in 1991.

The Netherlands

Corhay and Rad (1993) investigated 50firms comprising most of the capitaliza-tion of the Dutch stock market usingdaily returns over 1987–1992.42 Whiletheir work focuses on the effect ofreturn-measurement frequency on mea-sured beta in the style of Stoll andWhaley, they noted that “the size effectis reduced when the interval length is

29


9increased, although it remains statisti-cally significant.” The contrast betweenthis finding and Bruce and Leahy’sobservation of a negative size effect in the Netherlands over 1978–1991shows that any such short period studyis very sensitive to the choice of a data period, which is consistent withour expectation based on statisticalnotions.

Canada

Calvet and Lefoll (1989) and Elfakhani(1993) both found a small-stock effectin Canada, although the conclusions inthe first article are hedged. Calvet andLefoll find a size effect using the CAPMover 1963–1982, but “[w]ith a multi-parameter model…, size is no longerpriced.… Non-systematic risk and sizeappear highly correlated, and we can-not reject the hypothesis that the non-systematic risk could be, at least inpart, behind the size effect.” Elfakhani,who found that P/E, beta, and sizeeffects are all related, assures us that“[t]he results show support for the firmsize effect, even after proper adjust-ment for risk.”

Mexico

Over the extremely brief period1987–1992, Mexican small stocks out-performed larger issues, according toHerrera and Lockwood (1994). In addi-tion, there was a beta effect (high-betafirms had higher returns), and beta andsize were priced separately.

Korea

Lee and Chang (1988) found that thefirm-size effect and a January effectexist in Korean stock-market data col-lected over January 1976 to June 1985,

even after adjusting for biases suggest-ed by various hypotheses. Cheung,Leung, and Wong (1994), using datafrom 1982–1988, reported similarresults and, in addition, a P/E effect.The Korean market was completelyclosed to foreign investors for the dura-tion of these studies, so these findingshave limited application to the currentinvestment environment.

Various emerging markets

The International Finance Corporation’sEmerging Markets Data Base containsstock-by-stock return data on 20 devel-oping markets, with differing startingdates for different countries. Studyingtheir returns, Claessens, Dasgupta, andGlen (1995) find “limited evidence” ofsmall-firm and turn-of-the-year effects.

International small stocks:

conclusion

In none of the countries studied do thedata approach the 70-plus years of theUS studies. However, taken as a whole,the non-US results tend toward thesame conclusion as the US results;namely, that small stocks outperformlarge ones before adjusting for risksand costs. It is probably safe to general-ize that the “first principles” that govern the relative performance ofsmall- and large-capitalization stockswithin the US probably also governthem similarly outside the US.

30


Having toiled through such a largequantity of material, the reader nodoubt expects some wisdom to emergeto provide guidance for investmentdecisions. What strikes us most vividly,however, is the lack of agreementamong researchers on many of the mostbasic concepts: whether the small-stockeffect exists, whether it was a one-timeevent, whether it is a payoff for risksand investor costs, and so forth.

Obviously, the attraction to small-capitalization stocks arises becausethey have historically offered a grossreturn higher than that of large stocksby an amount sufficient to generatesubstantial and ongoing investor inter-est. However, there are several reasonswhy one should be cautious withrespect to actually being able to achievelarge exceptional small-cap results in aportfolio:

• More than all of the historical excessreturn was earned in one ten-yearperiod, 1974–1983, under conditionsunlikely to be repeated.

• To the extent small stocks haveearned higher returns, the premiumis at least partly a payoff for takingmore beta risk, and likely for takingother risks that are not captured bythe beta (but that are potentially iden-tified by Arbitrage Pricing Theory).Thus, the premium is smaller than itfirst appears or may not exist at all.

• Transaction and information costs,which are likely to be higher for smallstocks, have not been subtracted fromthe returns of either the small- or

large-stock indices. These costs alsosubstantially diminish the achievablesmall-capitalization premium in prac-tice.

So what guidance comes out of allthis? Let’s look at a few issues:

Active versus Passive

The active versus passive decision forsmall stocks tilts in favor of passive.Index funds and other low-turnoverstrategies will avoid many of the trans-action costs that are blamed for dimin-ishing the small-capitalization premiumin practice, giving this category offunds a better return rate with respectto the premium than active funds.Further, those index-fund investmentmanagement firms having the legal abil-ity to cross trades internally (certainbank collective funds having regulatoryapproval) will avoid most transactioncosts entirely, maximizing the achieve-ment of whatever small-capitalizationpremium might be available.

The active versus passive decisionis best made using recently developedapproaches for optimizing managerstructure, such that the expected alphais maximized at some acceptable levelof residual risk (tracking error). In such

Summary and conclusions

What strikes us most vividly is the lack of agree-

ment among researchers on many of the

most basic concepts: whether the small-stock

effect exists, whether it was a one-time event,

whether it is a payoff for risks and investor

costs, and so forth.

31


an approach, described by Waring andCastille (1998), active and passive arebalanced according to their relativecontributions to the expected alpha(after fees and costs) and the residualrisk of the portfolio. The substantialcost advantage of passive over activein the small-capitalization sectormeans that an active managementfirm has a higher hurdle to get overbefore successfully persuading theoptimizer that it should be held in theportfolio based on its net expectedalpha. While we believe there areactive small-capitalization managersthat have positive expected alphas,the proportion of the manager popula-tion that is in that category in theexpectancy is probably smaller in thesmall-capitalization sector than inother sectors.

As always, active managers shouldnever be used merely because theyare active, but only if they are expect-ed to create a worthwhile positivealpha after fees and costs. Investorswho lack confidence in their ability toidentify investment managers withstrong positive net alphas willimprove their results by allocatingmore to passive management.

Are small stocks an asset class?

How investors allocate between smalland large stocks depends, first, onwhether one views small stocks as atrue asset class or, more modestly, astyle of equity investing.

Ideally, an asset class is a set ofsecurities that are highly correlatedwith each other, but that are less high-

ly correlated with securities not in theset. Of course, no asset class in reallife fits this description neatly.

Small stocks certainly met thisstringent qualification for an assetclass over the historical period studiedby Banz, Reinganum, and Ibbotsonand Sinquefield. Acting under theseauthors’ influence, many investorsadopted a “barbell” approach thatinvolved buying the largest and thesmallest stocks (the latter held in aproportion larger than their marketcapitalization), to accentuate thesmall-cap effect (Table 1, p. 5).

This is still the most common con-figuration. On the active side, more-over, small-stock managers arethought to have skills and industrycontacts different from those of large-stock managers, so that a managersearch is done separately for the twocategories.

As institutions have brought smallstocks into the investment main-stream, these securities have becomesteadily less different from otherstocks, giving rise to the contentionthat they form an investment stylewithin the asset class of all US stocks,rather than a separate asset class. Ifthis is the appropriate way to look atsmall stocks, then market-cap weightsshould be held (at least as a base case)across the whole range of capitaliza-tion from smallest to largest. A sub-stantial minority of institutionalinvestors acts on this view, using abroad equity benchmark such as theWilshire 5000 or Russell 3000 indices.

32


Which decision framework—smallstocks as asset class or style—shouldbe used? Certainly the very differentreturn, risk, and correlation behaviorof small stocks, and especially the highautocorrelation of that sector, lend sup-port to the asset-class view. The returnpremium may be less than oncethought, but small stocks remain aneffective diversifier.

On the other hand, there is a con-tinuum between small, mid-cap andlarge stocks, and many managersselect from these sectors at will, blur-ring the distinctions among them.Moreover, the smaller one believes thesmall-stock premium to be, the morejustified one is in regarding all capital-izations as belonging to the same assetclass. At any rate, it is not a matter ofgreat importance whether one regardssmall stocks as an asset class or style,because any resulting misallocation islikely to be minor if the small-cap pre-mium is kept at modest levels.

Expected return assumptions for

strategic asset allocation

To the extent that the premium forholding small-capitalization stocks issmaller than indicated in the raw data,the expected return premia of 3% to 6% sometimes used in asset allocationstudies are too high. Much smaller premia, perhaps in the range of 0.5% to 2%, are more consistent with theresearch. A true small-capitalizationpremium skeptic might well put thepremium at zero. However, some pre-mium should probably be included

particularly for investors using indexfunds or other low-turnover invest-ment strategies in the small-capitaliza-tion sector.

International small stocks

Anything an investor might do withUS small stocks, including holding

broad capitalization exposure, is prob-ably equally sensible in the interna-tional arena. International small-capinvestment products are not availablein wide variety. (MSCI only recentlyestablished a developed-country,small-capitalization benchmark;Salomon Smith Barney’s benchmark,the oldest in existence, is reconstruct-ed only to 1989.) However, the catego-ry is becoming investable as moreinvestment managers provide usableproducts designed to serve this sector.

Market timing and tactical asset

allocation

The research results from both tacticalasset allocation and market-timingapproaches are encouraging at firstglance. While the return advantage ofsmall stocks over large ones is modeston average over time, it is very sub-

To the extent that the premium for holding small-

capitalization stocks is smaller than indicated in the

raw data, the expected return premia of 3% to 6%

sometimes used in asset allocation studies are too

high. Much smaller premia, perhaps in the range of

0.5% to 2%, are more consistent with the research.

33


stantial when small stocks are in an up trend, and investors may be able totake advantage of this. Of course, theperfection of the five-year down-to-upreversal signal for some deciles mustbe regarded as a coincidence. However,overreaction in the relative valuationof small versus large stocks appears tobe a fact, and long-term tactical assetallocators can act on this information.With three years of small-stock under-performance behind us, it is possiblethat investors will soon have an oppor-tunity to profitably increase their allocations to small stocks.

A more aggressive market-timingapproach is fruitful in a back-test, butinvestors should make a realisticallowance for trading costs, andarrangements for their minimizationmust be made before deciding to trans-act. Because the superior return ofsmall-capitalization stocks over large-capitalization stocks, and vice versa,appears to run in long secular waves,there is a strong need to be correctwhen the calls are (infrequently)made. In this situation, residual riskcan be cumulatively bad as well ascumulatively good.

Any timing approach based onthese ideas should probably be justone aspect of a more complete tacticalasset allocation framework. With moreasset classes, acceptable signal-to-noiseratios (information ratios) can be generated because there is adequatecross-sectional diversification.

Final word

Small-capitalization stocks should defi-nitely be held. The investor, however,should probably not expect to achievethe same small-capitalization premiumin the future as the index returns sug-gest might have been achieved in thepast. Regardless of the size of the pre-mium, there are clear diversificationgains to be had. At a minimum, small-capitalization stocks should be held ina weight proportionate to their repre-sentation in the market portfolio; mod-est levels above that remain defensi-ble. But the allocations justified by riskpremia of 2% or more, which havegrown to be common in recent years,are likely to be overly aggressive forstrategic asset allocation.

Small-capitalization stocks should definitely be

held. The investor, however, should probably not

expect to achieve the same small-capitalization

premium in the future as the index returns suggest

might have been achieved in the past.

34


Endnotes

1 See, for example, Owens and Hardy (1925).

2 An anomaly with respect to a theory is an occurrence in nature (or in theeconomy) that is contrary to what the theory predicts. For example, if it ispossible to make money (earn excess risk-adjusted returns) consistently bybuying a particular set of stocks, then that sector of the market is not effi-cient, and that set of stocks is considered to be anomalous with respect to theefficient market theory.

3 The CAPM is true if one accepts the assumptions required to derive it, butmany of these assumptions are unrealistic in practice.

4 Like Banz, Reinganum attributes the discovery of the P/E effect to Basu(1977). Properly, our review of Reinganum (1981a) belongs in the thread (4b)on disentangling the various effects, but because of the influence thatReinganum’s article had in establishing the existence of a small-stock effect,we cover it here instead. Reinganum (1981b) is a précis of the parts ofReinganum (1981a) that deal with the small-firm effect, and is written inpractitioner’s language.

Reinganum’s claim to be the co-discoverer of the small-firm effect would bemore widely accepted if he had not generously referred to Banz’s dissertationin a footnote, and if his paper had been more clearly focused on demonstrat-ing the existence of a small-firm effect rather than on separating it from apurported price/earnings anomaly.

5 Data in this paragraph are from Ibbotson Associates (1998), in which thesmall-stock index is proxied by the actual return of the Dimensional FundAdvisors (DFA) Small Company 9/10 (for ninth and tenth deciles) fund. Thefund is composed of American Stock Exchange and NASDAQ stocks as wellas ninth- and tenth-decile NYSE stocks. To reduce trading costs, the fund ismanaged somewhat differently from a pure index fund.

6 Moreover, Ibbotson Associates uses names for the sectors—mid-cap (NYSEdeciles 3-5), low-cap (deciles 6-8), and micro-cap (deciles 9-10)—that corre-spond more closely to current portfolio management practice.

7 Counting nonnegative, rather than strictly positive, changes in arithmetic-mean return; that is, the fifth and sixth decile have the same return, so themonotonic relation holds.

8 The ordinary-least-squares regression technique produces a line that “fits”a scatter-plot of data so as to minimize the sum of the squares of the dis-tances of the data points above and below the line. When the term “regres-sion” is used without modification in economic or financial literature, OLSregression is usually meant.

9 Autocorrelation is sometimes called serial correlation or serial dependence.It is measured by calculating the correlation of a series of returns with thesame series “lagged” (time-shifted) by one or more periods.

10 We wish they had captured more of the autocorrelation risk. The risk ofrepeated underperformance can develop over many years, while Ibbotson,Kaplan, and Peterson’s (1997) method examines only the one-month lag.

11 To overturn the CAPM one would have to find that there was an expectedreturn (not just a realized one) associated with the non-beta factor. WhetherFama and French (1992) found an expected return, as they claimed, or just arealized return is the subject of amusing debate (see Davis [1994]).

12 APT asserts, contrary to the CAPM, that there can be multiple risk factorsthat are “priced” in the sense that investors can expect higher returns if theytake these risks. Some critics of APT contend that it merely breaks up beta(CAPM) risk into its constituent parts, and that APT therefore offers nothingnew. We tend to regard APT as having substance, and if the cross-section ofexpected stock returns can be better explained with APT factors than withthe CAPM beta, then the CAPM has been shown to be incomplete.

13 Over this period, the market return in excess of Treasury bills was sub-stantially positive, so that if the CAPM is correct then beta risk should havebeen rewarded.

14 Data snooping is the practice of looking at all the variables that mightconceivably explain a particular phenomenon and choosing the ones that pro-vide the best statistical fit. When the variables are themselves related (forexample, P/E, price-to-book, size, beta, and price-per-share), classical mea-sures of statistical significance will overstate the true economic significanceof the variables that “win” in this process of elimination.

15 While this might seem like a natural place to review the rest of the litera-ture on disentangling size, low P/E, and other non-beta effects (or effectsappearing to be non-beta effects), this discussion is deferred to Thread 4b,which deals with the possibility that the size effect is a proxy for otherattributes that convey “cheapness.” The question is important because, if the size and (for example) low P/E effect are one and the same, the investorcan earn small-stock-like profits by buying low P/E large stocks.

16 “Unjustified”: our emphasis.

17 The portfolios formed by Stoll and Whaley are “arbitrage” portfolios thathold a long position in an equally-weighted portfolio representing a particu-lar decile of the NYSE ranked by market capitalization, and a short positionin the equally-weighted NYSE index. This wrinkle does not change the inter-pretation of their findings.

18 Roll does not form size fractiles. Instead, to proxy the small-firm effect, he compares returns on the AMEX index with those of the NYSE, which listsmuch larger stocks on average.

19 Delay cost is called timing cost in the original; and missed-trade cost iscalled opportunity cost in the original. The new wording is from the PlexusGroup’s (1998) update of Wagner and Edwards. Both types of costs are oppor-tunity costs in the ordinary sense, necessitating a change in the wording.

20 Emphasis on “below” and exclamation point in the original.

21 The E/P effect is the same as the P/E effect (because the P/E ratio is theinverse of the E/P ratio). Because stocks do not sell at zero or negative prices,the E/P ratio is more amenable to mathematical analysis.

22 This view, while unconfirmed by most researchers before or since, sur-vives in consultants’ “style maps” that show size and valuation to be separateeffects.

23 Earnings data are less easily obtained for distant historical periods thanprice, return, and market-capitalization data.

24 A primer on behavioral finance can be found in Wood (1995).

25 “Causes”: our emphasis.

26 The first four “parameters” or “moments” of a distribution of observationsare (1) mean, (2) variance, (3) skewness, and (4) kurtosis. The discussion upto this point has been concerned with mean and various measures (includingstandard deviation, beta and correlation) that are related to variance.

27 Too complex to describe here.

28 Owens and Hardy (1925), quoted in Riepe (1997).

29 In a later paper, Keim (1987) also notes that 63% of the small-stock premi-um was realized on Fridays.

30 Tax-loss selling is the selling of securities by taxable investors at a pricebelow the investor’s cost, to realize a loss that can be offset against realizedgains in other securities for the purpose of calculating income subject to per-sonal income tax. This practice is widespread in non-US markets as well asin the United States.

31 Emphasis on “seasonal” in the original.

32 See Rogalski and Tinic (1986).

35


33 Window dressing refers to the practice of money managers selling stocksperceived to be risky or undesirable from the client’s point of view, andreplacing them with safe stocks, just before portfolio contents are reported tothe client at quarter end or year end. This could contribute to year-end under-pricing of small-capitalization issues.

34 As Riepe notes, deciles 6 to 8 correspond roughly to the Russell 2000Index.

35 Unexpected changes in (1) the Baa corporate bond rate, (2) the Treasurybond rate, (3) the Treasury bill rate, (4) the S&P 500 return, (5) the ConsumerPrice Index, and (6) industrial production.

36 There is a hidden bias here, which is that we would probably not haveselected Reinganum’s articles for review if his out-of-sample predictionsturned out to be wrong.

37 The five-year periods include overlapping years; that is, underperfor-mance in 1969-1973 and in 1970-1974 count as separate observations.

38 While Macedo’s explanatory variables resemble those of Jacobs and Levy(1989), her model provides stronger forecasts because she is forecasting the

“naive” returns to size (that is, the difference between small- and large-stockreturns) while Jacobs and Levy are forecasting the “pure” returns to size(with the effect of all related factors, such as P/E, price-per-share, earningssurprise, etc. removed).

39 Cross-sectional diversification is the extent to which different asset class-es have different returns in the same time period.

40 The smallest stocks in these markets are not in the MSCI indices at all; asBruce and Leahy note, the Salomon Extended Market Indices must be used toaccess these returns. However, the distinction between bottom-quintile MSCIstocks and the top 80% is sharp enough to test the small-stock effect with rea-sonable accuracy. Nevertheless, MSCI indices need to be evaluated for bias.For each country, MSCI creates a stratified sample of stocks, diversified byindustry, that sums to approximately 60% of the total capitalization of thecountry’s market.

41 By comparison, the Ibbotson data for the US now spans 72 years, a muchmore robust statistical sample.

42 To be exact, they studied data from October 28, 1987 to March 1, 1992.

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