by E>onald B. Keim

The CAPM and Equity ReturnRegulaPities

Differential returns on dividend and capital gains income, systematic abnormal returnssurrounding ex-dividend dates, excess returns on small versus large capitalimtion stocks,excess returns on low versus high price-earnings ratio stocks—these are among the recentfindings that cast doubt on the traditional Capital Asset Pricing Model and tease investorswith the promise of systematic excess returns.

Some of these effects are undoubtedly related. Tests indicate, for example, that the higher aportfolio's price to book ratio, the higher the corresponding values of market capitalization,P/E and stock price. Furthermore, P/E, dividend yield, price and P/E effects all experiencesignificant January seasonals. What has not been conclusively determined is whether theeffects are additive. So far, it appears that the dividend yield and size effects are not mutuallyexclusive. Investors may want to use a strategy employing several of these characteristics,rather than one.

Efforts to explain the size effect have focused on January, because the effect is concentratedin that month. The most common hypothesis attributes this to year-end tax-loss selling, butthe evidence is less than conclusive. Evidence strongly suggests, however, that, among smallfirms, those with the largest abnormal returns tend to be the firms that have recently becamesmall, that either don't pay dividends or have higher dividend yields, and that have lowerprices and low P/E ratios.

THE CAPITAL ASSET Pricing Model Rz = rate of return on the riskiess asset;^

(CAPM) has occupied a central position E(RM) = the expected rate of return on thein finandal economics since its introduc- market portfolio of all marketable as-

tion over 20 years ago.' The CAPM states that, sets; andunder certain simplifying assumptions, the rate j8j = the asset's sensitivity to market move-of return on any asset may be expected to equal ments (beta),the rate of return on a riskiess asset plus a If the model is correct, and security markets arepremium that is proportional to the asset's risk efficient, security return will on average con-relative to the market.^ This is expressed mathe- form to the above relation.* Persistent depar-matically as follows: hires from the expected relation, however, may

x2rD \ — D _L rc/D \ r> 1 o indicate that the CAPM and/or the EfficientE(Ri) - Rz + [E(RM) - Rz]A, j ^ j ^ g j Hypothesis are incorrect.^

^ " ^ ^ The strict set of assumptions underlying theE(Ri) = the expected rate of return on asset i; C A P M has prompted numerous criticisms. But

1. footnotes appear at end of article. any nuxiel proposes a Simplified view of theDmdd Keim is Assistant Professor (^ Finance at the '^°^^' *«* ^ "o* sufficient grounds for rejec-Wharton School of tkeUnwersittft^Pennsiflvmia. *«>«• Rejection or acceptance should rest on

The author tfeinfe Wayne Fmon, AUan Kkidon, Craig sdentific evidence. The Univereity of Chicago'sMacKinla^, Terry Mrn^, Kri^ria Ramasmmy and Jay creation of a computerized datel^se of stockRitterfor their helpful comments. prices and distiibutiicms in the 19^)s made such

FINANCIAL ANALYSTS JOURNAL / MAY-JUNE l^te O 1 9

testing possible. This artide reviews brieflysome of tite results of these tests arui discussesin some detail more recettt evidence that rai%s%rious questikms about the validity of theCAFM.

Early EvidenceNumerous studies in the early 1970s generallysupported the CAPM, although finding thecoefficient on beta (representing an estimate ofthe market risk premium) to be cmly marginallyimporbmt in explaining cross-sectional differ-ences in avera^ security returns.* In 1977,hovsrever. Roll raised some legitimate questionsabout the validity of these tests.^ Briefly, Rollargued that tests performed with any marketportfolio otiier than the true niarket portfolioare not tests of the CAPM, and that tests of theCAPM may be extremely sensitive to the choiceof market proxy. He also pointed out that someof the early tests' need to specify an alternativemodel to the CAPM may have led to faultyinferences. For instance, Fama and MacBethhad tested whether residual variance or betasquared help explain returns; thus the CAPMmay be false, but if residual variance or betasquared do not capture the violation, the testwill not rqect the model.*

In response to Roll's first poirit, Stambaughconstructed broader market indexes that includ-ed bonds and real estate and found that suchtests did not seem to be very sensitive to thechoke of market proxy.' Gibbons, Stambaughand others have addressed Roll's second pointby using multivariate tests that do not requirethe specification of an alternative asset pridngmodel."* The^ multivariate tests have not con-clusively proved or disproved the validity of theCAPM.

Researchers have meanwhile formulated al-ternative models, ntany of which relax some ofthe CAPM assumptions. Mayers, for example,allowed for nonmarketable assets such as hu-man capital; feennan and litzenbeiger and Ra-maswamy rdaxed the no-tax assumption."Otiiere, in the spirit of Fama and MacBettt, haveexamined ad hoc alternatives to the CAPM.Among this group, Banz examirved the impor-tarux of market value of common equity, andBasu investigated the imp(»rtanc£ of pritx-eam-ings ratios in explaining risk-adjusted returns. 'The r ^ t of &m artide discuses sudi aitema-thn^ to the CAFM and ttie implications of dieassodated evidence im ptxtifolk) management.

After-Tax EffecteifecBuse in fte U.S. dividend income is sul^ectto a higher marginal tax rate than capital gains,iayskhke investors should rationally prefer a dol-lar of pretax capital gain to a dollar of dividends. ^&ennan and litzenbei^er and Ramaswamy ex-tended the CAPM to indude an extra factor—dividend 3deld. They hypothesized that, thehigher a stock's dividend yield, holding riskconstant, the higher the pretax ietum a taxableinvestor vdll require in order to compensate forttie tax liability incurred.

There are, of course, coimter arguments.Miller and Scholes argued that the tax codepermits investors to transform dividend incomeinto capital gains." If the marginal investors areusing ttiese or other effective shelters, then thepretax rate on dividend-pa)dng stocks may notdiffer from the rate on stocks that do not paydividends. The tax differential has neverthelessprompted some tax-exempt institutions to "tilt"their portfolios toward higher-yielding securi-ties, with the hope of capturing the benefits ofthe supposedly higher pretax returns.

The effectiveness of such a strategy, ofcourse, hinges on how well after-tax modelsconform to reality. An after-tax CAPM has thefollowing general form:

E(Ri) = ao + a, j8i H- (2)

where dj equals the dividend yield for security iand a2 represents an implidt tax coefficient thatis independent of the level of the dividendyield. The question is whether a2 is reliablypositive and consistent with realistic tax rates.

Empirical tests of the hypothesis that a2equals zero face several difficulties. Becauseasset pridng models are cast in terms of exf>ec-tations, the researcher needs to arrive at asuitable ex ante dividend yield measure. Fur-ther, he must ask whether the teix effects thatmotivate the model ocair at a single point intime (i.e., the ex-dividend date), or whetherthey are spread over a longer period. Finally,most researdiers have assumed a linear relationbetween dividend yields and returns, but therelation might be more complicated.

Studies have employed a variety of defini-tions of divkiend yieM and metiiods. In theinterest erf laevity, we forgo discussion of themethodolc^cal subdeties and simply summa-rize the major result. Table I leporte estimatesof tihe dividend yield c(»IBctent a^.' In eachinstance, the estimate of a2 is positive; holding

HNANC3AL ANALYSIS K)Vie<iAL / MAY-JUNE 1986 O 20

Table I Summary ^ Impted Tax Rates ftom Studies ofdie Relation between Dividend Yields and StockReturns

Author(sj and Dateof Study

Black and Scholes(1974)

Bluine (1980)

Gordon and Bradford(1980)

Litzenberger andRamaswamy (1979)

Litzenberger andRamaswamy (1982)

Miller and Scholes(1982)

Morgan (1982)

Rosenbeig andMarathe (1979)

Stone and Barter(1979)

Test Period andReturn Interval

1936-1966, Monttiiy

1936-1976, Quarteriy

1926-1978, Monthly

1^6-1977, Monthly

1940-1^0, Monthly

1940-1978, Monthly

1936-1977, Monthly

1931-1966, Mon*ly

1947-19ra, Monthly

ImpliedPercentageTax Hue

(t-Statistic)

22(0.9)52

(2.1)18

(8.5)24

(8.6)14-23

(4.4-8.8)4

(1.1)21

(11.0)40

(1.9)56

(2.0)

beta risk constant, the higher the dividendyield, the higher the pretax rate of return oncommon stocks. Although not all the coeffi-cients are significantly different from zero, andnot all authors attribute the positive coefficientsto taxes, the evidence from many of the studiesappears to be consistent with the after-tax mod-els.*'

The truth may not be as simple as the after-taxmodels of Brerman and Litzenberger and Ra-maswamy suggest, however. Blume and a laterstudy by Litzenberger and Ramaswamy foundthat the yield-return relation is not linear forsome definitions of dividend yield. '* The aver-age return on non-dividend-paying firms ishigher than the return on many dividend-pay-ing firms. Furthermore, Keim foxmd that thisnon-linear relation stems largely from the exag-^rated occurrence of the effect in January.Figure A gives little visual evidence of a yield-return relation outside January.

This latter finding is not entirely conastentwith the simple tax-related models and sugg^tsdie possible manifestation of otha: anomalouseffecte, such as the size effect (discussed below).CM onirse, it does not mean that the docu-mented relation between yields and returns hasno value in a fsactical portfolk) amtext. Addi-tiond yieM-related e^cteKS su^es ts ijtere issoQ^ maiginal vahie in ^ e use of dividendyieki, even after iakii^ accotint of firm

Ex-Dividend Price BehaviorBecause the ownership claim to a dividend

expires at the dose of trading before the ex-dividend day, the price of a dividend-payingstock should drop on ttie ex-dividend day. Inthe absence of effective taxes (or of a tax differ-ential between dividends and capital gains),transaction costs and information effects, theprice drop should equal the value of the divi-dend. If, as in the U.S., dividend income istaxed at a higher rate than capital gains income,the price should drop less than the value of thedividend. But if short-term traders or tax-ex-empt institutions dominate the market, then thetax-induced differential will be eliminated. '*

Numerous studies have found that the fall inprire on the ex-dividend day is, on average, lessthan the value of the dividend." For example,Kalay found that, from April 1966 to Mardi1967, the ratio of the dosing price on the lastcum-dividend day minus the ex-day dosingprice to the dividend was 0.734. He conduded,however, that transaction costs would negateany "short-term profit potential for a typicalnorunember investor."^" The evidence sug-gests, in effect, that the magrutude of the ex-dayeffect is related to the ntiarginal transaction costsof short-term traders and may have little to dowith taxes.^'

Further studies of ex-day price behaviorfound abnormal returns over several days sur-rounding the "ex" day. ' The pattern is one ofsignificantly positive abnormal retums for thesix-day period up to and induding the ex date,followed by significantly negative abnormal re-turns in the subsequent five trading days. Grun-dy has a i ^ e d that this pattern of price adjust-ments conforms to models of optimal stocktrading based on tax minimization in the pres-ence of current U.S. tax laws and recognizingcosts of delajring or accelerating stock trades.

Fir>ally, other studies have found evidence ofabnormal return behavior surrounding the exdates of non-taxable stock dividends and splits.^Grinblatt, Masulis artd Titman report a five-dayabnormal return of 2 per cent surrounding theex date for a sample of 1,740 stock dividendsand splits over the l%7-76 period. Their resultsare based on post-announcement returns,hence s t ^ e s t trading strategies based on an-runmcsmertte of st»dk dividends and splits. Butbecause their results <annot ^sily be explainedi ^ tax-related ai^uments, the autiun^ suggest"a tsuxx cautious interpretation of ex-date re-

HNANOAL ANALireXS JOUMMAI. / MAY-JUNE 1986 Q 21

Rebtiofi Betwe«i Average Monthly Returns and EHvkknd Yield for Januaryand All Other Months, 1931-1978

ID

9

8

7

6

5

4

3

2

1 -February to December

JZero Lowest Highest

CHvidend Yield Portfolio*

*Dividencl ykkl in month t is defined as the sum of dividends paid in the previous 12 months divided by the stock price in month t-13.The six dividend yieW portfolios are constructed from firms on the NYSE.

turns for cash dividends than is currently foundin the literature."^^

Size EffectsBoth the finandal and the academic communi-ties have been intrigued by evidence of a signifi-cant relation between common stock returnsand the market value of common equity—com-monly referred to as the "size effect." Otherthings equal, the smaller a firm's size is, thelai^er its expected return. Banz, the first todocument this phenomenon, estimated a modelover the 1931-75 period of the following I

plays the average abnormal returns for portfo-licMi comprising the 10 dedles of size for NYSEand AMEX firms. The difference in abnormalreturns between the smallest and largest firmsamounte to about 30 per cent annually.. Blumeand Stambaugh demonstrated, however, thatthe portfolio strategy implicit in Reinganum'spaper (requiring daily rebalancing of the portfo-lio to eqtial weights) produces upward-biasedestimates of small-firm portfolio returns becauseof a "bid-ask" bias that is inversely related tosize; they showed that the size-related premiumis halved in portfolio strategies that avoid this

E{Ri) = ao + a, ft + (3)

where Si is a measure of the relative marketcapitalization (size) of firm i. Banz found anegative statistical association between retuimsand ^ze of approximately the same magnitudeas tfiat between returns and Iweta.

Rein^num, using a different method em-jrfoying daily data ewer tiie 1963-77 period,found that p^tfolios of small finns had sutetan-tiaBy h i ^ e r risk-^dfusted returns, on average,than portfolic» of ha^ firms. ^' Figure B dis-

Portfolio managers normally have two reser-vations about implementing "small firm" strate-gies—(1) the maiket for the smallest capitaliza-tion firms is illiquid and (2) the firms in thismarket do not meet minimiun capitalizationr^juiremente for many institutional investors.Figure B illtratrates that such potential con-straints m&y not be binding, becau^ the abnor-mal letmn opportunities are not confined to tliwvefy smaHest and teast ]«]uid stocks. Portfoliosof security wi& successive smafler firm val-

HNANCSAt ANALYSTS | m « N A L / MAY-JUNE 19M O 22

TTieSi^Efect (NYSE and AMEX ferns, 1963-1979)

0.09

0.07

0.05

0.01

0

-0.01

-0.03

1.1

0.9

0.7

0.3

0.1

SmaO 4 S 6

Dedfe of Maiicet Value

Laige

lies yield sucressively larger risk-adjusted re- Mtnilarly to the S&P 5(X). Hus suggests theturm. the tM»3 largest fwrtfoUos (9 and 10), with existenos ol a wide array of po^>le portfoliosmedian market opi^lizations raz^iz^ bom vdHt h%her a erage returns— in «7me rases,$433 million to $1.09 hiBkm, tend to behave st^tani^dlyhi^ierretums—^thanttieS&P500.

FINANOAt ANAtYSTS JCaJSNAL / MAY-JUNE li«6 D 23

Size Effect by Day of the Wedc (NYSE aid AMEX finns, 1963-1979)

0.4 - I

0.3 -

0.2 -

0.1 -

-0.1 -

-0.2Small Large

Much subsequent research on the size effecthas attempted to provide a more complete char-acterization of the phenomenon. We now knowthat, among the firms that academic researchersconsider "small" (in 1980, the smallest sizequintile for the NYSE represented firms withmarket capitalizations of less than about $50million), those with the largest abnormal re-turns tend to be firms that have recently becomesmall (or that have recently declined in price),that either do not pay a dividend or have highdividend yields, that have low prices, and thathave low price-earnings ratios.*

Seasimal Size EffectsReseard:Mrs have also ecamined the time-

iekted patterns of pmtf olio letums stratified bymarket capitalization. Brown, Kleidon andMarsh found that, when averaged over allmonths, the size effect reverses itself for sus-tained periods; in many periods there is a con-sfetent premium for small size, whereas in otiier(fewer) periods tJtere is a discxnmt.'* In someperiods (1969-73, for example), a small capital-izi^on strategy would have underperformedthe market on a beta-<adfusted i

The magnitude of the size effect also seems todiffer across days of the week and months of theyear. Keim and Stambaugh found that the sizeeffect becomes more pronounced as the weekprogresses and is most pronounced on Friday.^^Figure C shows that the negative relation be-tween returns and size fot' the 19^3-79 periodbecomes most pronounced at the end of theweek.

The most dramatic seasonal pattern, howev-er, involves the turn of the year. Keim foundthat the size effect is concentrated in January:Approximately 50 per cent of the return differ-ence detected by Reinganum is concentrated inJemuary.'^ Figure D shows the extent to whichthis January seasonal alfects the month-by-montii behaviof of the size effect. Keim alsofound that 50 per cent of this January effect isamcentrated in Ae first five trading days of they«ir. This tum-of-the-year behavior was alsodetected by Roll, who noted abnormally largereturns for smdl firms on the last trading day inDecember.'*

Researd^rs have sAso looked to internationaldata to see whettter the January seasonal pat-tern in the mze eftect tiKat pe r^ t s at Ute turn of

HNANC3AL ANALYSTS pUF»iAL / MAY-JUNE 1986 D 24

D The Relation Between A v e r ^ Daily Abnormal Returns and Market Value for Each MtH>th, 1963-1979*

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0,3

-0.4

Fdmiary- dirough

December

1 I I

Smallest 4 5 6

Decile of Market Value

Largest

•The 10 market value portfolios (dedles) are constructed from firms on the NYSE and AMEX. Abnormal returns are provided by CRSP.

the tax year in the U.S.—and purportedly dueto "tax-loss selling" activity—ocrurs in marketswhere the tax year-end is not December.'^ TableII reports the results of the analysis of stockreturns on four major exchanges—Australia,Canada, Japan and ihe United Kingdom. It isdifficult to compare the magnitude of the sizeeffect across the four countries because of differ-ing time periods and research design (e.g.,some studies use size qtiintiles, others use dec-iles). Nevertheless, each country exhibits aninverse relation between stock returns and mar-ket capitalization.

Infonnation about the existence of size andother effects on foreign stock exchanges is valu-able for portfolio managers who concentrate insmall capitalization stocks but wish to preserveadequate diversification via foreign seauities.The ability to implement such strategies on aninternational basis will become increasingly im-portant as institutional presence in the smallcapitalization (and low P/E) markete expands.

The Frice-Eaiiii^s EffectEamn^-rekted s t ra^ ies have a long traditionitt the investment commumty. The mcmt popu-

lar—buying stocks that sell at low multiples ofearnings—can be traced at least to Graham andDodd, who proposed that "a necessary but nota sufficient condition" for investing in a com-mon stock is "a reasonable ratio of market priceto average earnings."^* They advocated that aprudent investor never pay as much as 20 timesearnings and a suitable multiplier should be 12or less.

Nicholson published the first extensive studyof the relation between P/E multiples and subse-quent total returns, which showed that low P/Estocks consistently provided returns greaterthan the average stocks.^' Basu introduced thenotion that P/E ratios may explain violations ofihe CAPM and found that, for his sample ofNYSE firms, there was a distinct negative rela-tion between P/E ratios and average returns inexcess of those predicted by the CAPM.** If aninvestor had followed his strategy of buying thequintile of smallest P/E stocks and selling shortthe quintile of largest P/E stocks over the 1957-71 period, he would have realized an averageannual abnormal return of 6.75 per rent (beforecommissiiHts and other transaction costs).''

Some have argued tfiat, because firms in the

HNANOAL ANALYSTS K>URNAL / MAY-JUNE 1986 D 25

Table D The Firm Size Efiect: International Evidence

Australia (1

SizePortfolio

Smallest

2

3

4

5

6

7

8

9

Largest

% Return(std. error)

6.75(0.64)2.23

(0.39)1.74

(0.31)1.32

(0.27)1.48

(0.24)1.27

(0.24)1.15

(0.24)1.22

(0.24)1.18

(0.2S)1.02

(0.29)

Gmada (1951-1'.

SizePortfolio

Smallest

2

3

4

Largest

f80/'

% Return(std.

1951-1972

2.02(0.27)1.48

(0.22)1.14

(0.22)0.99

(0.23)0.90(0.23)

error)1973-1980

1.67(0.58)1.66

(0.56)1.41

(0.59)1.39

(0.56)1.23

(0.58)

Japm n966-1983/'

SizePortfolio

Smallest

2

3

4

I-argest

% Return(std. error)

2.03(0.35)1.50

(0.32)I.M

(0.29)1.17

(0.27)1.14

(0.27)

United Kingdom ^956-1980/'

SizePortfolio

Smallest

2

Largest

% Return

(std. error)1956-1965 1966-19^

1.27 l.OO

1.18 0.89

0.98 0.84

a. P. Brown, D. B. Keim, A. W. IQeidon and T. A. Marsh, "Stock Return Seasonalities and the Tax Loss Selling Hypothesis: Analysis of theArguments and Australian Evidence," Jourml of Fimndai Economics, 1983, pp. 105-127.

b. A. Beiges, J. J. McConnell and G. G. Schlarbaum, "The Tum-of-the-Year in Carwda," Journal of Timnce, 1984, pp. 185-192.c. T. Nakamura and N. Terada, "The Size ESfect and Seasonality in Japanese Stock Returns" (Nomura Research Institute, 1984).d. M. R. Reinganum and A. Shapiro, "Taxes and Stock Return Seasonality: EviderKe from the London Stock Exchange" (University of

Southern California, ^3)

same industry tend to have similar P/E ratios, aportfolio strategy that concentrates on low P/Estocks may indeed benefit from higher thanaverage returns, but at a cost of reduced diversi-fication. These arguments also suggest that theP/E effect n«y in fact be an industry effect.Goodman and Peavy examined the P/E ratio of astodc relative to its industry P/E (PER) andfound a distinct negative relation between PERsand abnormal returns over the 1970-80 period.'**'A portfolio that bought the quintile of lowestPER stocks and sold short the highest PERquintile would have yielded an annualized ab-normal return of 20.S) per cent over the period.These resuits, in conjtmction with the findingsof Basu and Reinganum, suggest that the P/Eratio—or an underi5dng and perhaps more ftm-damentai variable for which P/E is a proxy— iscapable of expbining a considerable pc^on ofthe variation in cross-sectional security returns.

The Value Line Eni^nafavvestawnt advisory services often base their

rea>mmendations on earrangs-related informa-tion. The lai^est and most consistently s u a « ^ -ful advisory service is the Value Line Itwestor

Survey. Value Line forecasts the prospectiveperformance of approximately 1,700 commonstocks on a weekly basis, separating the stocksinto five categories of expected return based onhistorical and forecast information such as earn-ings momentum and P/E ratio.

The success of tiie Value line system hasbeen bome out by ^veral academic studies.*'All found that, after adjusting for beta risk,investors can obtain abnormal performance by,for example, buying group 1 securities andselling short group 5 securities. Stickel foundthat investors can earn abnormal returns bydevising strategies based on rank changes (e.g.,buying stocks upgraded from group 2 to group

Value Line's successful performance is ptiz-zling for the same reasons that tine size and P/Eeffects are puzzling. It indicates that predeter-mined variables may be used to construct port-folios tluit have abnormal returns relative to theCAPM. It is, of covirse, possible that ValueLine's ranking system has a high degree ofassociation with a sin^^e ranking based on P/Eat size. In feet, the eviitence in Stickeltliat mudv of Valtte line's abnormal

HNAJ«3AL ANALYSTS JOURNAL / MAY-JUNE 1986 Q 26

ance might be attributable to a small firm effect.More research is necessary to sort out theseissues.

Interrelations Between EfiecteResearch has documenteci a strong cross-sec--tional relation between abnormal returns andmarket capitalization, P/E ratios and dividendyields. Other effects have also been noted, per-haps most notably the relation between risk-adjusted returns and the ratio of price per shareto book value per share (P/B). Few wouldargue that these separate findings are entirelyindependent phenomena; after all, market capi-talization, P/E and P/B are computed using acommon variable—price per share of the com-mon stock. Furthermore, other evidence indi-cates a cross-sectional association between priceper share and average returns.'*^

Table III gives the average values of P/B,market capitalization, E/P and price for 10 port-folios of NYSE firms constructed on the basis ofincreasing values of P/B. The portfolios wererebalanced annually over the 1964-82 period. Itis apparent that the higher the average P/B ofthe firms in a portfolio, the higher the corre-sponding average values of market capitaliza-tion, P/E and stock price.*^ Further evidence ofsome common underljdng factor are the signifi-cant January seasonals in the P/E, dividendyield, and price and P/E effects.'**

In practice, the portfolio manager's objectiveis to isolate and use in a portfolio strategy thecharacteristics that will result in the highest risk-adjtisted returns. That is, the manager is lessinterested in the conjecture that all these effectsare somehow related than in finding the rank-ing characteristics that work best. Recent stud-ies have addressed this issue by trying to an-swer the following question: If a portfoliomanager screens first on characteristic X (say,P/E), can he improve risk-adjusted portfolio per-formance further by adding a screen based oncharacteristic Y (say, market capitalization)?

Several studies have addressed the interrela-tion between the P/E and market capitalizationeffects, with less than conclusive results. Rein-ganum aigued that the size effect subsumes theP/E effect (i.e., there is no marginal value to P/Eafter first ranking on size).'*' Basu a i ^ e d justthe opposite.'** Peavy and Gtxximan and Cookeand Roz^ , after perfonmng meticulous replica-tions and extensions of the methods of Basu andReir^anum, reached surprisangly different con-

Table ni Average Values of Price/Book (P/B), MarketValue, EtP and Price for 10 Portfolios of NYSEFirms Cortstnicted on ihe Basis of IncreasingPrice/Book Values (1964-1982)*

Prux/BookPortfolio

Lowest23456789

Highest

AvengeP/B

Ratio

0.520,831.001,141,291,471.712,072.807.01

AverageMarket Value

($ma)217.1402.5498.6604,7680,2695,6888,9872.6

1099.21964.3

AverageE/P

0.060,110,110.110.100.100.090.090.070,05

AveragePrice(SJ

20,0922,9725.m27,7928,9731,5536.0737.8444.8060,09

* Portfolios are rebalanced at March 31; December 31 fiscal closersonly.

elusions. Peavy and Goodman's results agreedwith Basu's.^' Cooke and Rozeff concluded,however, that "it does not appear that eithermarket value subsumes earnings/price ratio orthe earnings/price ratio subsumes market valueas has been daimed."'"

If an investor constructs a portfolio based onlow P/E stocks, he may still add some value byconsidering the additional dimension of firmsize (or vice versa). One interpretation is thatboth market capitalization and P/E (as weU asother variables mentioned above) may be im-perfect surrogates for an underlying and morefundamental "factor" missing from the CAPM.^'A possible solution for investors is to use astrategy that employs several characteristics,rather than one variable. Analysis of the interre-lation between dividend yield and size effect,for example, indicates that the two effects arenot mutually exclusive and, furthermore, thatsmall capitalization firms that pay no dividends(or that have higher dividend yields) have expe-rienced the largest abnormal returns over the1931-78

Explaiituig the Size EffectThe lion's share of efforts to explain the aboveanomalies has been directed to the size effect.Some have argued that alternative asset pricingmodels may explain the cross-sectional associa-tion between risk-adjusted returns and size.Chen and Chan, Chen and Hsieh have arguedttuit most of the abnormal returns associatedwith the s i ^ effect are explained by additionalrisk factors in ihe context of the Arbitrage Pric-ing Theory of Ross.^' Others maintan that

FINANCIAL ANALYSTS JOURNAL / MAY-JUNE 1M6 • 27

market imperfections assumed away by theCAPM are responsible. Stoll and Whaley, forinstance, have argued that round-trip transac-tion costs are sufficient to offset the abnormalreturns associated witii the size effect.** Schultz,however, points out that transaction costswould have to be larger in January to explainthe January seasonal in abnormal returns, andfinds no evidence of seasonally var5mig transac-tion costs.^^

Others have addressed the possibility that thesize effect is merely a statistical artifact. Rollsuggested that large abnormal returns on smallfirms could be due to systematic biases (attribut-able to infrequent or nonsynchronous trading)in these firms' betas, but Reinganum demon-strates that this bias cannot explain the anoma-ly. * Christie and Hertzel argue that the sizeeffect could be due to nonstationarity of beta."A firm whose stock price has recentiy de-clined—i.e., a firm that is becoming "small"—has effectively experienced, other things equal,an increase in leverage and a concomitant in-crease in the risk of its equity. Thus historicalestimates of beta that assume risk is constantover time understate (overstate) the risk andoverstate (understate) the average risk-adjustedreturns of stocks whose market capitalizationshave fadlen (risen). However, Christie and Hert-zel have adjusted for this bias and found thatthe size effexrt is not eliminated. Chan makes asimilar adjustment and finds that "the sizeeffect is reduced to a magnitude whose econom-ic significance is debatable."'* Unfortunately,neither study differentiated between Januaryand non-January returns.

Finally, Blume and Stambaugh demonstratedthat portfolio strategies that require rebalancingof the portfolio to equal weights jrield upward-Inased estin^ates of small firm returns because ofa "bid-ask bias" Aat is inversely related tomarket capitalization.'' Such strategies some-times buy at the implicit bid price and sell at theask price. Portfolio strategies that avoid this biasexhibit significant size effects only in January.

Explaining tite January EffectIn light of titiese last findings, attempts to

explain the size phenoaienon have focused onJanuary. Rather than exploring alternative equi-Ubiium models that may accommodate seasonaleffects, most studies have instead focused onmaiket frictions that violate CAPM assump-tions. The most popular hypothesis attributes

the effect to year-end tax-toss selling. Brown,Keim, Kleidon and Marsh summarize tids hy-pothesis:

"The hypothesis maintains that tax laws in-fluence investors' portfolio dedsions by en-couraging the sale of securities tttat haveexperienced recent price declines so that the(short-term) capital loss can be offset againsttaxable income. Small firm stocks are likelycandidates for tax-loss selling since thesestocks tj^ically have higher veiriances of pricechanges and, therefore, larger probabilities oflarge price declines. Importantly, the tax-lossargument relies on the assumption that inves-tors wait imtil the tax year-end to sell theirconunon stock 'losers.' For example, in theU.S., a combination of liquidity requirementsand eagerness to realize capital losses beforethe new tax year may dictate sale of suchsecurities at year-end. The heavy selling pres-sure during this period supposedly depressesthe prices of small firm stocks. Aiter the taxyear-end, the price pressure disappears andprices rebound to equilibrium levels. Hence,small firm stocks display large returns in thebeginning of the new tax year."*"Although popular on Wall Street, the tax-loss

selling hypothesis has not met an enthusiasticreception in the academic community. Rollcalled the argument "ridiculous."*' Brown et al.maintain that the tax laws in the U.S. do notunambiguously induce the year-end small stockprice behavior predicted by the h5rpothesis.*^Constantinides daims that optimal tax tradingof common stocks should produce a Januaryseasonal pattern in prices only if investors be-have irrationally.^

The evidence on the tax-loss h5qx)thesis isless than condusive. Tests by Reinganum andRoll suggest that part, but not all, of the abnor-mal returns in Jantiary is related to tax-relatedtrading.^ Schultz, however, found no evidenceof a January effect prior to 1917—i.e., before theU.S. income tax as we know it today createdincentives for tax-loss selling.^

The hypothesis predicts a price rebound inthe month of January immediately followingprice declines, but makes no predictions aboutstodc price movements in subsequent tum-of-year periods. Evideiu^ from Chan and DeBondtand Thaler indicMes that "loi^r" finns a>ntinueto expertence abnormal returns in January for aslong as five years after Hieir identification.^Chan identified 'losers" and "winners" and

FINANCIAL ANALYSTS JCRBNM. / MAY-JUNE 1986 O

E January Retting, Tax-Lc^ Portfolios (portfolios formed in Decentbo-, year t)

i1 —

0

Small

12

13

14

1 15 6

Tax-Loffi Portfolio

17

>

18

^ ^

19

\

2JLarge

constructed an "arbitrage" portfolio (long los-ers, short wirmers) within each decile of marketvalue for NYSE firms at December 31 of year tand tracked January abnormal returns in each ofthe following four yeare (t+1 to t+4). Hisrestdts, presented in Figure E, show a persistentJanuary effect in each of the subsequent threeyears. Based ori such evidence, both Chan andDebondt and Thaler conduded that the Januaryseasonal in stock returns may have Uttie to dowith tax-loss selling.

Others have tested the hypothesis by examin-ing the month to month behavior of abnormalreturns in countries with tax codes similar to theU.S. code but with different tax year-ends. Theyhave found seasonals after the tax year-end, butalso in January—a result not predicted by thehypothesis.*' Berges, McConnell and ScWar-baum found a January seasonal in Canadianstock returns prior to 1972—a period whenCanada had no taxes on capital gains.^

The intx)nastent evidence argues for investi-gating otiher possitaUties. One that has receivedattention on Wall Street is the notion that lkjuid-ity constraints on market participants nay influ-&ace security returns in a seasonal feshion. Forescampk, periodic infuakjns of cash into tiie

market as a result of say, institutional transfersfor pension accounts or proceeds from bonusesor profit-sharing plans may affect the market.Some evidence may be interpreted as support-ing this idea.

Kato and Schallheim, examining small firmreturns in Japan, found January and June sea-sonals coinciding with the traditional bonusespaid at the end of December and in June.**Rozeff found a substantial upward shift in theratio of sales to purchases by investors who arenot members of the NYSE coinciding with thedramatic increase in small firm returns in Janu-ary; Rozelf, however, interpreted this as evi-dence of a tax-loss selling effect.™ Ritter docu-mented a similar pattern in the daily sales topurchase ratios for the retail customers of alarge brokerage firm.'' And Ariel noted a pat-tern in daily stock returns in every month butFebruary ttiat parallels precisely the pattern thatoccurs at the turn of the year.'^ It would beeasier to interpret sudi monthly patterns asliquidity or payroll effects than as tax effects.

PattemsRecent studies have documented additional

empirical regularities related to tiie day of the

FINANCIAL ANALYSTS JOVmiM. I MAY-JUNE 1986 D 2 9

F«ure F Monthly Hfect in Stock lietums (vahie^veighted CRSP index, 1963-1^1)

1.6 -

1.4 -

1.2 -

1 -

0.8 -

0.6 -

1 ^•*-1 0 . 2 -1 0 -

" -0.2 -

-0.4 -

-0.6 -

-0.8 -

-1.0 -

Rret Half of Mwth/ nJ n•I U

tilln nn n

j i 11 M tJ i_| 1

• I I I I ~11L'l l H H Last Half of Month

1 1• •1 1 1 1 1 1 1 1 1 1 1

1 2 3 4 5 6 7 8 9 10 1

Month

nJ-L•

1 12

week or tbe time of the montb. Average stockreturns, for example, tend to be bigher onFridays and negative on Mondays—the "week-end" effect. ^ Because research on this effectdocuments negative Monday returns using Fri-day dose to Monday close quotes, we canrwtascertain whether the negative returns stemfrom the weekend nontrading period or fromactive trading on Monday.

Harris, examining intradaily returns on NYSEstocks over the 1981-83 period, and Smirlock andStarks, using Dow Jones 30 stocks over the1963-73 fjeriod, found negative Monday returnsaccrued from Friday close to Monday open, aswell as dviring trading on Monday.^'* Rogalski,however, looking at intradaily data from 1974 to1^4, found that negative Monday returns ac-crued entirely during the weekend nontradingperiod.'^

Keim and Stambaugh, noting results in Gib-bans and Hess that sugg^t Friday returns vaiycross-sectionally with niarket value, found thattlw return differential between small and largefirms increased as the week progressed, beann-ing largest on Friday (see Figure C).'^ In addi-tion, Keim demonstrated that, controllmg forthe large average retunts in January, the "Fri-day"- effect and the "Monday" eSb&± are no

different in January than in other months.' ' Wedo not yet have an explanation of tbe weekendeffect, but we do know it is not likely a result ofmeasurement error in recorded prices, delaybetween trading and settlement due to checkclearing, or specialist trading activity.^^

The monthly effect was detected by .Ariel,who showed that for the 1963-81 period theaverage returns on common stocks on the NYSEand AMEX were positive only for the last day ofthe month and for days during the first half ofthe month.' ' During the latter half of themonth, returns were indistinguishable fromzero. Ariel concluded that, during his sampleperiod, "all of the market's cumulative advanceoccurred aroimd tbe first half of the montb, thesecond half contributing nothing to the cumula-tive increase."

Figure F illustrates the phenomenon for thetotal returns of the CRSP value-weighted indexof NYSE and AMEX stocks. The figure clearlyindicates that returns in the first half of themontiti are consistently larger than second-halfreturns (except in February); in fact, negativeaverage returns oarur only in ttie s«:ond half.The results in Ariel aiso s u r e s t that, with theex(%pticai of Januaiy, tf» diSer&xce betweenfiret-half returns <rf small firms and first-half

FINAhKlAL ANALYSTS VXmiAL I MAY-JUNE 1986 D 30

returns of large firms is not substantial. Ariel isunaUe to explain the effect, but a fK>tentialexplanation involves liquidity constraints.

ImplicationsMany of these findings are inconsistent with aninvestment environment where the CAPM isdescriptive of reaKty and argue for consider-ation of alternative models of asset pricing.Other findings, such as the day of the weekeffect, do not necessarily represent violations ofany particular asset pricing model, yet are stillintriguing because of their regularity.

The bottom line for portfolio managers is theextent to which this information can be translat-ed into improved portfolio performance. Thatstrategies based on this evidence can improveperformance has, in fact, been borne out in"real world" experiments. There are, however,severed caveats regarding implementation ofsuch strategies.

First, diat some effa:ts have persisted for asmany as 50 years in no way guarantees theirpersistence into the future. Second, even if theeffects were to persist, the costs of implement-ing strate^es designed to capture tiiese phe-nomena may be prohibitive. Market iliiquidityand transaction costs may render a small stockstrategy infeasible, for example. Day of theweek and other seasonal effects may have prac-tical value only for those investors who wereplanning to trade (and pay transaction costs) inany event.

Finally, one must be cautious when interpret-ing the magnitudes of "abnormal" returnsfound by the studies. To the extent that alterna-tive models of asset pricing may be more appro-priate than the CAPM, studies that use theCAPM as a benchmcirk may not be adjustingcompletely for relevant risks and costs. Superiorperformance relative to the CAPM may not besuperior once these costs and risks are consi-dered.!

Footnotes1. See W. F. Sharpe, "Capital Asset Prices: A The-

ory of Market Equilibrium under Conditions ofRisk," Joumal of Finance 1964, pp. 425-442; J.Lintner, "The Valuation of Risk Assets and theSelection of Risky Investments in Stock Portfoliosand Capital Budgets," Review of Economics andStatistics 1%5, pp. 13-37; and J. L. Treynor,"Toward a Theory of Market Value of RiskyAssets."

2. The one-period CAPM assumes that (1) investorsare risk-averse and choose "efficient" portfoliosby maximizing expected return for a given levelof risk; (2) there are no taxes or transaction costs;(3) there are identical borrowing and lendingrates; (4) investors are in complete agreementwith regard to expectations about individual se-curities; and (5) security returns have a multivari-ate normal distribution.

3. Rz M the rate erf return on a risk-free asset in theSharpe-Lintner-Treynor CAPM; or the rate ofreturn of an asset with zero correlation with themarket in the extension by F. Black, "CapitalMarket Equilibrium with Restricted Borrowing,"Journal of Business, July 1972, pp. 444-455.

4. See E. Fama, "Efficient Capital Marketer A Re-view of Theory and Empirical Work," Jounud (^Fimnce, May 1970, pp. 383-417.

5. Such persistent de{»trtures are often referred toas "anomalira." The term anomaly, in this con-text, can be tra<^ to Thomas Kuhn in his dassicIxK^ The Siructme Scientific Remlutims (Oika-go: University of Chicago Press, 1970). Kuhn

maintains that research activity in any normalscience will revolve around a central paradigmand that experiments are conducted to test thepredictions of the underl3dng paradigm and toextend the range of the phffliomena it explains.Although research most often supports the un-derlying paradigm, eventually results are foundthat don't conform. Kuhn terms this stage "dis-covery": "Discovery commences with the aware-ness of anomaly, i.e., with the recognition thatnature has somehow violated the paradigm-in-duced expectations that govern normal science"(pp. 52-53, emphasis added).

6. The most prominent early studies are those ofBlack, Jensen and Scholes, "The Capital AssetPricing Model: Some Empirical Evidence," inJensen, ed.. Studies in the Theory of Capital Markets(New York: Praeger, 1972); M. Blume and I.Frif nd, "A New Look at the Capital Asset PricingModel," Joumal of Finance, March 1973, pp. 19-33;and E. Fama and J. MacBeth, "Risk, Return andEquilibrium: Empirical Tests," Joumal of PoliticalEconomy, May/June 1973, pp. 607-636.

7. R. Roll, "A Critique of the Asset Pricing Theory'sTests: Part I: On Past and Potential Testability ofthe Tlieory," Joumal of Pimndal Economics, March1977, pp. 129-176.

8. SeeFamaandMacBeth, "Risk, Return aned Equi-librium," op. dt.

9. R. Stambaugh, "On the E»lusion of Assets fromthe Two-Parameter Model: A Sensitivity Analy-sis," Journal of Financial Economics 1982, pp. 237-268.

FINAJ«aAX. ANALYSTS JOURNAL / MAY-JUNE 1986 D 3 1

10. See M. GiHxms, "Multivariate Tests of HnancialM o d ^ : A New Approadt/' Journal of FinancudEconomks 1982, pp. 3-27, and Stmnbaugh, "CJntiKe Exclusion," op. cit.

11. See D. Mayers, "Nomnarketable Assets and Cap-ital Market Equilibrium wider Uncertainty," inJensen, ed., Studks in Theory (^Capital Markets, opcit.; M. Brennan, "Taxes, Market Valuation andCorporate Finandai Poliq^," Natwnal Tax Journal1970, pp. 417-^7; and R. Utzenberger and K.Ramaswamy, "The Eltects of Peraonal Taxes andDividends on (Capital Asset PriEes: Theory andEmpirical Evidence," Journal (^Financial EcoMomjcs1979, pp. 163-195.

12. See R. W. Banz, "The Relaticmship betweenReturn and Market Value of Common Stock,"Journal of Financial Economics 1981, pp. 3-18, andS. Basu, "Investment Perfonnance of CommonStocks in Relation to their Price/Earnings Ratios:A Test of the Efficient Market Hypothesis," Jour-nal of Finance 1977, pp. 663-682.

13. M. Miller and M. Scholes, "Dividends and Tax-es ," Journal of Financial Economics, December 1978,pp. 333-364.

14. The table is an updated version of one in R.Utzenberger and K. Ramaswamy, "The Effects ofDividends on Common Stock Prices: Tax Effectsor Information Effects," Journal of Finance 1982,pp. 429-433.

15. Coefficients are not significantly different fromzero in findings by F. Black and M. Scholes, "TheEffects of Dividend Yield and Dividend Policy onCommon Stock Prices and Returns," Journal ofFinancial Economics 1974, pp. 1-22 and Miller andScholes, "Dividends and Taxes: Some EmpiricalEvidence," Journal of Political Economy 1%2, pp.1118-1141. M. E. Blume ("Stock Returns andDividend Yields: Some More Evidence," Review ofEconomks and Statistics 19M), pp. 567-577) andR.H. Gordon and D. F. Bradford ("Taxation andthe Stock Market Valuation of Capital Gains andEKvidends: Theory and Empirical Results," Jour-nal of PuMic Economics l%0, pp. 109-136) do notattribute the effects to taxes.

16. See Blume, "Stock Returns and DividendYields," op. dt, and R. litzenberger and K.Ramaswamy, "IMvidends, Short Selling Restric-tions, Tax-Induced Investor Clienteles and Mar-ket Equilibrium," Journal of Finance 1^0, pp.4^-482.

17. See D.B. Keim, "Kvidend Yields and Stock Re-turns: Implications (rf Almormal January Re-turns," Journal of Financial Economics 1 9 ^ , pp.473-^9, and itom "dividends Yields and theJanuary Effect/' Journal of Portfciio ManagenKnt,1%6, pp. 61-65.

18. Except that translation costs may keep the pricefrom fallhtg by tite full mnount of the cfivitiend;

see Miller and S d u ^ s , "Dividends and Taxes:Some Empirical Evidence," op. cit.

19. See, for example, J. Campbell and W. Berenek,"Stock Price Behavior on Ex-Dividend Dates,"Journal of Finance 1953, pp. 425-429 and E. Eltonand M. Gruber, "Marginal Stockholder Tax Ratesand the Clientele Effect," Review of Economics andStatistics 1970, pp. 68-74.

20. A. Kalay, "The Ex-Dividend Day Behavior ofStock Prices: A Re-Examination of the ClienteleEffect," Journal (^ Finance 1982, pp. 1059-1070.

21. For similar arguments, see K.M. Eades, P.J. Hessand E.H. Kim, "On Interpreting Returns Duringthe Ex-Dividend Period," Jourttal of Financial Eco-nomics, March 1984, pp. 3-34. However, M. J.Barday ("Tax Effects with No Taxes? FurtherEvidence on the Ex-Dividend Day Behavior ofCommon Stock Prices" (Department of Econom-ics, Stanford University, September 1984)) findsthat in the period before the institution of thefederal income tax, stock prices fell on their ex-dividend day by the full amount of the dividend.This evidence is suggestive of a tax story.

22. See F. Black and M. Scholes, "The Behavior ofSecurity Returns Around Ex-Dividend Days"(University of Chicago, 1973); Eades, Hess andKim, "On Interpreting Returns," op, cit.; and B.Grundy, 'Trading Volume and Stock Returnsaround Ex-Dividend Dates" (University of Chica-go, 1985).

23. B. Grandy, "Trading Volume," op, cit,24. See, for example, Eades, Hess and Kim, "On

Interpreting Returns," op. dt, and M. S. Grin-blatt, R.W. Masulis and S. Titman, "The ValuationElfects of Stock Splits and Stock Dividends,"Journal of FinaiKial Economics, December 1984, pp.461-490.

25. Grinblatt, Masulis and Titman, "The ValuationEffects," op, dt.

26. Banz, "TTte Relationship Between Return andMarket Value," op, dt,

27. M. R. Reinganum, "Misspedfication of CapitalAsset Pricing: Empirical Anomalies Based onEarnings' Yields and Nfarket Values," Journal ofFinandal Economics 1981, pp. 19-46.

28. M. E. Blume and R. F. Stambaugh, "Biases inComputed Returns: An Application to the SizeEffect," JourruA of Finandal Eamomics, November1983, pp. 371-386.

29. The S&P 500, bdng a value-weighted index ofprimarily hig^-capitalization firms, behaves verymuch Hke a portftdio <rf very large firms.

30. Tlie dividend influence is examined in Keim,"Dividend Yields and the January Effect, op, dt.;see H. R. SfoH and R.E. Whaley, 'TransactionsCosts and fte Snail Rrm Effect," Journal of Finan-dal Economks, June 1983, pp. 57-80 and Bhuneand Stambai^ji, "Biases in Computed Returns,"

FTNANOAL ANALYSTS JOURNAL J MAY-JUNE W86 O 3 2

op. cit., for flK effect (rf price; and Reinganum,"Nfisspedficatkm erf Caistal Asset Pridng," op.cit., for the effect of low P/E.

31. P. Brown, A. W. Kleidon and T. A. Marsh, "NewEvidence on tl»e Nature of Size-Related Anoma-lies in Stock Prices," Jourrud ofFimncM Eanwmics,June 1^3, pp. 33-56.

32. D. B. Keim and R. F. Stambaugh, "A Furflwrinvestigation of the Weekend Effect in StockReturns," foumal cf Finance, July 1984, pp. 819-S35.

33. See D. B. Keim, "Size-Relat«i Anomalies andStock Return Seasonality: Further Empirical Evi-dence," Jourml of Financial Economics, June 1983,

, pp. 13-32.34. R. Roll, "Vas ist das? The Turn of the Year Effect

and the Return Premium of Small Finns," Journalof Portfolio Managmmt, 1983, pp. 18-28.

35. One exception is T. Nakamura and N. Terada("Hie Size Effect and Seasonality in JapaneseStock Returns" (Nomura Research Institute,4984)), who document a P/E effect on the Tokyostock exchange.

36. B. Graham and D. L. Dodd, Security Analysis(New York: McGraw-Hill, 1940), p. 533.

37. S. F. Nidvolson, "Price-Earnings Ratios," Finan-dal Analysts Jourml, July/August 1960.

38. Basu, "Investment Performance of CommonStocks," op. dt.

39. Reinganum ("Misspedfication of Capital AssetPridng," op. dt.), analyzing both NYSE andAMEX firms, confirmed and extended Basu'sfindings using return data to 1975.

40. J. W. Peavy and D. A. Goodman, "Industry-Relative Price-Earnings Ratios as Indicators ofInvestment Returns," Finandal Analysts Journal,July/August 1983.

41. See, for example, F. Black, "Yes, Virginia, Thereis Hope: Tests of the Vahie Line Ranking Sys-tem," Finandal Analysts Journal, September/Octo-ber 1973, pp. 10-14; C. Holloway, "A Note onTesting an Aggressive Investment Strategy UsingValue line Ranks," Journal of Finance, June 1981,pp. 711-719; and T. E. Copebnd and D. Mayers,"Tlie Value Line Enigma (1965-1978): A CaseStudy of Performance Evaluation Issues," Journalof Financial Economics, November 1982, pp. 289-321.

42. S. E. Stickel, "The Effect of Value Line InvestmentSurvey Rank Changes on Ctanmon Stock Prkes,"Joumd of Financial Eamomics 1985, pp. 121-144.

43. Discussed most recently by B. Rosenberg, K.Reid and R. Lanstein, "Persuasive Evidence ofMaricet Ineffidency," Jourml of Portfolio Mamge-mmt, pp. 9-17.

44. See M E. Blume and F. Husic, "Price, Beta and&cduinge listing," Journal of Fimnce 1973, pp.^3-299; StoD and Whaley, "Transactions Costs

and the Snuill Firm Effect," op. cit.; and Blumeand Stambaugji, "Biases in Computed Returns,"op. dt.

45. One excefriion is the lowest P/^ portfolio, whosestocks on average have a low (high) average E/P(P/E). This is attributaWe to the negative earningsfirms that tend to be concentrated there. Notethat firms with negative book values are exchidedfrom the sample.

46. For P/E, see T. J. Cooke and M. S. Rozeff, "Sizeand Earnings/Price Ratio Anomalies: One Effector Two?" Journal of Financial and Quantitative Anal-ysis 1^4, pp. 449-466; for dividend )deld, seeKeim, "Kvidend Yields and Stock Returns," op.dt.; and for price, see J. Jaffe, D. Keim and R.Westerfield, "EMsentangling Earnings/Price, Sizeand Other (related) Anomalies" (University ofPennsylvania, 1985).

47. See Reinganum, "Misspedfication of Capital As-set Pridng," op. cit.

48. S. Basu, "The Relationship Between Earnings'Yields, Market Value and the Returns for NYSEStocks: Further Evidence," Journal of FinandalEconomics, June 1983, pp. 129-156.

49. J. W. Peavy and D. A. Goodman, "A FurtherInquiry into the Market Value and Earnings YieldAnomalies" (Southern Methodist University,1982).

50. Cooke and Rozeff, "Size and Earnings/Price RatioAnomalies," op. dt., p. 464.

51. See for example R. Ball, "Ancwnalies in Relation-ships between Securities' Yields and Yield-Surro-gates," Journal of Finandal Economics 1978, pp.108-126.

52. See Keim, "Dividend Yields and Stock Returns,"op. dt. and "Dividend Yields and the JanuaryEffect," op. dt.

53. N. Chen, "Some Empirical Tests of the Theory ofArbitrage Pridng," Journal of Finance 38, pp.1393-1414; K. C. Chan, N. Chen and D. Hsieh,"An Exploratory Investigation of the Firm SizeEffect," Journal of Finandal Economics 14, pp. 451-472; and S. Ross, "The Arbitrage Theory of Capi-tal Asset Pricing," Journal <^ Economic Theory 1976,pp. 341-360.

54. Stoll and Whaley, 'Transactions Costs and theSmaU Firm Effect," op. dt.

55. P. Schultz, "Transactions Costs and the SmallFirm Effect: A CcMnment," Journal of FinandalEconomics, June 1983, pp. 81-88.

56. R. Roll, "A Possible Explanation of the SmaUFirm Effect," Journal of Fimnce 1981, pp. 8/^888;M. R. Reinganum, "A Direct Test of Roll's Con-jecture on the Firm Size Efect," Journal of Finance1982, pp. 27-35.

57. A. Christie and M. Hertzel, "Capital Asset Pric-ing 'Anomalies': Size and Other Correlations"(University of Rochester, 1981).

HNANOAL ANALYSIS JOURNAL / MAY-JUNE 1986 D 33

58. K. Chan, "Leverage Changs and Size-RelatedAnomalies" (University of Chicago, 1983).

59. Blume and Stambaugh, "Biases in ComputedReturns," op. dt. A ^milar argument is presentedin R. RoU, "On Computing Mean Returns andthe Small Firm Premium," Joumal of FinancialEconomics, November 1983, pp. 371-386.

60. P. Brown, D. B. Keim, A. W. Kleidon and T. A.Marsh, "Stock Return Seasonalities and the Tax-Loss Selling H)'pothesis: Analysis of the Argu-ments and Australian Evidence," Joumal of Finan-cial Economics, June 1983, p. 107.

61. Roll, "Vas ist das?" op. dt.62. Brown et al., "Stock Return Seasonalities/' op.

dt.63. G.M. Constantinides, "Optimal Stock Trading

with Personal Taxes: Implications for Prices andthe Abnormal January Returns," Joumal of Finan-cial Economics, March 1984, pp. 65-90.

64. M. R. Reinganum, "The Anomalous Stock Mar-ket Behavior of Small Firms in January: EmpiricalTests for Tax-Loss Selling Effects," Joumal ofFinancial Economics, June 1983, pp. 89-104 andRoU, "Vas ist das?" op. dt.

65. P. Schultz, "Personal Income Taxes and the Janu-ary Effect: Small Firm Stock Returns Before theWar Revenue Act of 1917: A Note," Joumal ofFinance, March 1985, pp. 333-343.

66. See K. C. Chan, "Can Tax-Loss Selling Explainthe January Seasonal in Stock Returns?" (OhioState University, August 1985) and W. F. M.DeBondt and R. Thaler, "Does the Stock MarketOverreact?" Joumd of Finance, July 1985, pp. 793-806.

67. Brown et al. ("Stock Return Seasonalities," op.dt.) examine Australia, which has a June tax year-end. The U.K. (which has an April tax year-end)is examined in M. R. Reinganum and A. Shapiro,'Taxes and Stock Return Seasonality: Evidencefrom the London Stock Exchange" (Uruversity ofSouthern CaHfomia, 1983).

68. A. Berges, J. McConnell and G. Schlarbaum,"The Tum-of-the-Year iri Canada," Joumal of Fi-nance, March 1984, pp. 185-192.

69. K. Kato and J. S. Sdiallheim, "Seasonal and SizeAnomalies in tf»e Japanese Stodk Market," Joumalof Financial and Quantitative Analysis 1985, pp.107-118.

70. M. S. Ro2«ff, "The Tax-Loss SeUing Hypotitesis:New Evidence from Share SWfts" (Univeraty ofIowa, April 1985).

71. J. R. FUtter, "Tlie Buying and Selling Behavior of

Individual Investors at ttie Turn of the YeanEvidence of Price Pressure Effects" (University ofMidiigan, November 1985).

72. R. A. Arid, "A Monthly Effect in Stock Returns"(Massachusetts Institute of Technology, 1984).

73. F. Cross ("The Behaviw of Stock Prices on Fri-days and Mondays," Financial Analysts Joumal,November/December 1973, pp. 67-69) and K.French ("Stock Returns and the Weekend Effect,"Joumal of Financial Economics, March 1980, pp. 55 -69) document the effect using the S&P compositeindex begriming in 1953. M. Gibbons and P. Hess("Day of the Week Effects and Asset Returns,"Joumal of Business, October 1^1, pp. 579-5%)document it for the Etow Jones industrials indexof 30 stocks for 1962-78. Keim and Stambaugh("A Further Investigation of the Weekend Ef-fect," op. dt.) extend the findings for the S&Pcomposite to include the 1928-82 period and alsofind the effect in actively traded OTC stocks. J.Jaffe and R. Westerfield ("The Week-end Effect inCommon Stock Returns: The Intemational Evi-dence," Joumal of Finance 1985, pp. 433-454) findthe effect on several foreign stock exchanges.

74. L. Harris, "A Transactions Data Study of Weeklyand Intradaily patterns in Stock Returns" (Uni-versity of Southern California, 1985) and M.Smirlock and L. Starks, "Day of the Week Effectsin Stock Returns: Some Intraday Evidence" (Uni-versity of Pennsylvania, 1984).

75. R. Rogalski, "New Findings Regarding Day-of-the-Week Returns over Trading and Non-Trad-ing Periods: A Note," Joumal of Finance, Decem-ber 1984, pp. 1603-1614.

76. Keim and Stambaugh, "A Further Investigationof the Weekend Effect," op. dt.

77. D. B. Keim, "The Relation Between Day of theWeek Effects and Size Effects," Joumal of PortfolioManagement, forthcomirjg.

78. Measurement error is treated in Gibbons andHess, "Day of the Week Effects," op. dt.; Keimand Staml^u^, "A Further Investigation of theWeekend Effect," op. dt.; and Smirlock andStarks, "Day of the Week Effects in Stock Re-turns," op. dt. Trading delays are treated inGibbons and Hess, and in J. Lakonishok and M.Levi, "Weekend Effects on Stock Returns: ANote," Jourml of Finance, June 1982, pp. 883-889.Specialist trading is dealt with in i^im and Stam-baugh.

79. Ariel, "A Monthly BS&A in Stock Returns," op.dt.

FINANCIAL ANALYSTS JOURNAL / MAY-JUNE 1986 D 3 4

by Robert A. Taggart, Jr.

Corporate Rnanclng: Too MuchDobt?

Are U.S. corporations overburdened with debt? Since 1970, internal funds have been takingwider swings as percentages of total funds sources, as comjmred with the 1950s and 1960s.Furthermore, use of debt financing has been consistently higher since the mid-1960s thanduring previous periods throughout the century. And short-term debt has accounted formost of this rise.

After adjustment for inflation, however, the figures indicate that, since 1974, corpora-tions have relied heavily on internal funds and cut their cost of debt financing to levels thatare not high by historical standards. Despite fluctuations in internal funds and increased useof short-term debt, corporations do not appear to have significantly riskier capital structuresthan they've had in the past.

An examination of determinants of the composition of capital structure reveals thatcorporate reliance on debt financing increases as capital expenditures rise relative to availableinternal funds. Use of debt financing is limited, however, by investors' perceptions of theriskiness of the business environment and by relative supplies of federal governmentsecurities. Over long periods, furthermore, the tax system seems to affect the level of debtfinancing; corporate borrowing increases as personal income tax rates rise above corporatelevels.

IN 1984, NEW DEBT accounted for 45 percent of total sources of funds for U.S. nonfi-nancial corporations. Less than one-quarter

of this new debt came from long-term bondsand mortgages; the rest represented short-termdebt from a variety of sources. Moreover, 15 perrent of net funds sources went, not for invest-ment in new plant and equipment, but for therepurchase of outstanding common stock.

Do such developments reflect increasing fi-nancial weakness of U.S. business? Many ob-servers seem to tiiink so. Their fears have beenstimulated by such highly publicized trends asthe levered buyout boom, tfie growth of "junk"bond financing, and the shrinkage of equitybases that often accompanies corporate restruc-

Rt^Krt Tag^rt, Jr. is Profossor of Finance, Boston Univer-sity, and Bxsemk Associate, National Bttreau of EconomicSiesectrdi.

The au^r tiumks the Natimud Bureau of Emtmmkfor partkl financial support of this resairch.

turing. In addition, the current period is onlythe latest in a series of surges in corporate debtfinancing. Previous notable episodes occurredin 19^-69, 1973-74, and 1978-:^.

Each of these surges gave rise to similar fearsover corporations' financial condition. It hasbeen argued that corporations' reliance on debtfinancing, particularly short-term debt, hasmade them increasingly vulnerable to economicshocks. This reliance on debt financing is in turnblamed on a combination of factors, includingthe tax system's favored treatment of debt overeqmty, reduced availability of internally gener-ated funds dudng inflationary peritxis, andunrealistic assessments of business risk by exec-utives, entrepreneurs and corporate raiders.

This article examines more closely these alle-gations of corporate financial weakness 1^ com-paring recent corporate financing patternsagainst long-term trends and by analyzing thelink between these patterns and potential causal£act(HS. n ^ conclusion emerges that, in many

FINANOAL ANALYSTS JOURNAL / MAY-JUNE 1^6 D 3 5