1-s2.0-S0304405X98000075-main

*Corresponding author. Tel.: #1 540 231 4316; fax: #1 540 231 3155; e-mail: [email protected] versions of this paper were entitled, Bidask spreads, holding periods, and realized

transaction costs. We are grateful for many helpful comments from Yakov Amihud, JenniferConrad, Larry Dann, Diane Del Guercio, Dave Denis, Diane Denis, Craig Dunbar, Ed Dyl, RogerEdelen, Rob Hansen, Mark Huson, Raman Kumar, Chris Lamoureux, John McConnell, WayneMikkelson, Megan Partch, Henri Servaes, Vijay Singal, Mike Weisbach, Marc Zenner, and ananonymous referee. In addition, we appreciate the comments from seminar participants at the 1997American Finance Association meetings, the University of Arizona, Kansas State University, theUniversity of North Carolina, the 1996 Pacific Northwest Finance Conference, Virginia PolytechnicInstitute, and the University of Wisconsin. This work has been partially supported by a summerresearch grant from the Pamplin College of Business.

Journal of Financial Economics 48 (1998) 159188

An empirical examination of the amortized spread1

John M.R. Chalmers!, Gregory B. Kadlec",*! Lundquist College of Business, University of Oregon, Eugene, OR 97403, USA

" Pamplin College of Business, Virginia Polytechnic Institute, Blacksburg, VA 24061, USA

Received 9 September 1996; received in revised form 29 September 1997

Abstract

Theories of asset pricing suggest that the amortized cost of the spread is relevant toinvestors required returns. The amortized spread measures the spreads cost overinvestors holding periods and is approximately equal to the spread times share turnover.We examine amortized spreads for Amex and NYSE stocks over the period 19831992.We find that stocks with similar spreads can have vastly different share turnover, andthus, a stocks amortized spread cannot be predicted reliably by its spread alone.Consistent with theories of transaction costs, we find stronger evidence that amortizedspreads are priced than we find for unamortized spreads. ( 1998 Elsevier Science S.A.All rights reserved.

JEL classification: G10

Keywords: Transaction costs; Bidask spread; Share turnover

0304-405X/98/$19.00 ( 1998 Elsevier Science S.A. All rights reservedPII S 0 3 0 4 - 4 0 5 X ( 9 7 ) 0 0 0 0 7 - 5

2For other theories of optimal investment policy and asset pricing under transaction costs see, i.e.,Brennan (1975), Goldsmith (1976), Levy (1978), Milne and Smith (1980), Mayshar (1981), Aiyagariand Gertler (1991), and Vayanos and Vila (1995).

1. Introduction

While the role of transaction costs in asset pricing remains the subject ofdebate, few would argue with the basic premise that transaction costs affect anindividuals required return. For example, an individuals required return ona stock will equal his required return in the absence of a bidask spread, plus thepercentage bidask spread amortized over the individuals expected holdingperiod. The theoretical debate over the importance of transaction costs in assetpricing arises primarily from differing assumptions regarding investors holdingperiods. Amihud and Mendelson (1986) assume that individuals trade forliquidity purposes with an average holding period of 1.6 years. Under thisassumption, spreads are amortized over relatively short holding periods, andthus, the amortized cost of transacting is large. As a result, Amihud andMendelsons model predicts that bidask spreads have a significant effect onasset returns. Alternatively, Constantinides (1986) assumes that individualstrade only to rebalance their portfolios. Under this assumption, spreads areamortized over relatively long holding periods, and thus, the amortized cost oftransacting is small. Consequently, Constantinides model predicts that bidaskspreads have only a second-order effect on asset returns.2

Empirical studies of the relation between stock returns and bidask spreadshave not resolved this debate. Amihud and Mendelson (1986) find a significantpositive relation between stock returns and bidask spreads, while Chen andKan (1989) find an insignificant relation and Eleswarapu and Reinganum (1993)find that the relation between stock returns and bidask spreads is significantonly in the month of January. However, these studies focus solely on themagnitude of the spread without consideration of the length of the holdingperiod over which spreads are amortized. For example, Amihud and Mendelson(1986), Chen and Kan (1989), and Eleswarapu and Reinganum (1993) all useclosing bidask spreads as a proxy for the expected cost of the spread. If stockswith similar spreads trade with different frequency, the magnitude of the spreadis not a sufficient proxy for the amortized cost of the spread.

We examine amortized spreads, which explicitly capture both the magnitudeof the spread and the length of investors holding periods. We define theamortized spread as the product of the effective spread and the number of sharestraded summed over all trades for each day and expressed as an annualizedfraction of equity value. Intuitively, the amortized spread measures the an-nualized cost of the spread to investors and is approximately equal to theeffective spread times share turnover. We compute amortized spreads for the

160 J.M.R. Chalmers, G.B. Kadlec/Journal of Financial Economics 48 (1998) 159188

universe of U.S. domiciled common stocks listed on either the Amex or NYSE atany time during the period 19831992.

We find that, while the average round-trip effective spread of Amex/NYSEstocks is 2.2% of equity value, the average annual amortized spread is only 0.5%of equity value. More importantly, because stocks with similar spreads can havevastly different share turnover, a stocks amortized spread cannot be predictedreliably by its spread alone. For example, transportation stocks have lowereffective spreads than stocks of firms in consumer goods, financial, capital goods,and basic goods. However, due to their higher share turnover, transportationstocks have higher amortized spreads than stocks in any of these industries.

Our analysis of the determinants of the amortized spread reveals that a stocksamortized spread is strongly related to its return volatility, a variable that ispositively related to both spreads and share turnover. For example, utilitystocks, which have relatively low return volatility, have both low spreads andlow share turnover, and thus, low amortized spreads. By contrast, technologystocks, which have relatively high return volatility, have both high spreads andhigh share turnover, and thus, high amortized spreads.

We argue that, in the context of asset pricing, the amortized spread is a morerelevant measure of transaction costs than the spread. Consistent with this view,we find stronger evidence that amortized spreads are priced than we find forspreads. However, we interpret these asset pricing results with caution due to thelimited sample period (19831992) over which the tests are conducted. Given thecurrent interest in market value of equity and book-to-market as factors insecurity returns, we also examine the relation between amortized spreads andthese two variables. Although amortized spreads are negatively related tomarket value of equity and positively related to book-to-market, multivariateasset pricing tests show that the explanatory power of the amortized spread isnot subsumed by market value of equity or market-to-book.

The remainder of the paper is organized as follows. Section 2 defines ourmeasure of the amortized spread and describes the data that are used tocalculate it. Section 3 reports cross-sectional and time-series descriptive statis-tics of amortized spreads. In Section 4, we examine determinants of the amor-tized spread. In Section 5, we estimate the relation between stock returns andtwo alternative measures of spread-related transaction costs, amortized spreadsand unamortized spreads. Section 6 summarizes our findings and discusses theirimplications. The Appendix provides details concerning the methodology usedin the asset pricing tests.

2. Amortized spreads

In this section we formally define our measure of the amortized spread anddescribe the data that we use to calculate the amortized spread.

J.M.R. Chalmers, G.B. Kadlec/Journal of Financial Economics 48 (1998) 159188 161

2.1. Calculating amortized spreads

To calculate amortized spreads, we first measure the total dollar amountexpended on bidask spreads for each sample stock on each trading day.Following Blume and Goldstein (1992) and Lee (1993), define P

tas the transac-

tion price and Mtas the midpoint of the prevailing bidask quote. A stocks

daily dollar spread is defined as the sum, over all trades, t"1, . . . , , of theproduct of the absolute value of the effective spread, DP

t!M

tD, and the number

of shares traded, t. The daily amortized spread for day is equal to the daily

dollar spread scaled by the firms market value of equity at the end of day (P

Tx SharesOut

T),

AST"+Tt/1DPt!MtD )t

PT)SharesOut

T

. (1)

For expositional purposes, we annualize daily amortized spreads by multiplyingthe daily amortized spread by 252 trading days per year. The calculation of dailyamortized spreads involves an average of 50 transactions per day for 2000 firmsover 2520 trading days or roughly 250 million transactions. To keep our datasets manageable, we work with monthly averages of the annualized dailyamortized spreads.

Eq. (1) is related to Amihud and Mendelsons (1986) spread-adjustmentfactor kS, where 1/k is the expected holding period and S is the relative spread.From Eq. (1), a stocks amortized spread is approximately equal to the effectivespread times share turnover,

AS+DP!MDP

)

SharesOut, (2)

which is also the effective spread divided by the average holding period (1/turn-over). Thus, a stock which has an effective spread of 4% and annual turnover of50% would have an annual amortized spread of 2%. If expected gross returnsinclude reimbursement for expected transaction costs, cross-sectional differencesin amortized spreads provide a benchmark for assessing the potential impact ofbidask spread-related transaction costs on security returns.

The amortized spread in Eq. (1) has several important features as a measure oftransaction costs. First, it is calculated with effective spreads rather than quotedspreads. Theoretical models of the bidask spread, such as Amihud and Mendel-son (1980), Ho and Stoll (1981), and Glosten and Milgrom (1985) typicallyanalyze the specialists quoted spread. However, it is the effective spread atwhich investors conduct trades, and thus is the more relevant measure for


3The effective spread measure as defined by Blume and Goldstein (1992) and Lee (1993) and usedhere to compute amortized spreads has at least two limitations as a measure of the cost of the spread.First, to the extent that the specialists quotes lie asymmetrically about the true price the effectivespread measure, which compares transaction prices to the midpoint of the bidask quote, may eitherunderstate or overstate the true spread. Though, there is no reason to believe that this source of errorresults in biased estimates. Second, if a market order is matched directly with another market orderthe effective spread measure will overstate the actual cost of the spread (which on average is zero).However, Hasbrouck (1988) suggests that such occurrences are rare.

computing transaction costs.3 Blume and Goldstein (1992), Lee (1993), andPetersen and Fialkowski (1994) find that the effective spread is approximately5070% of the specialists quoted spread. More importantly, Petersen andFialkowski (1994) report that the cross-sectional correlation between the effec-tive spread and the quoted spread is less than 0.31.

Second, Eq. (1) incorporates investors holding periods since it is calculatedfrom actual trades. The length of investors expected holding periods determinesthe spreads impact on required returns. For example, Barclay and Smith (1988)show that an individuals required return on a stock can be expressed as therequired rate of return in the absence of a spread plus the percentage bidaskspread amortized over the investors expected holding period. Thus, the shorterthe expected holding period, the greater the impact of the bidask spread on anindividuals required return.

Third, our measure of the amortized spread implicitly incorporates the depthof the spread quote. Lee et al. (1993) argue that no measure of the spread is trulymeaningful without information concerning its depth. Eq. (1) incorporates theconstraint imposed by the depth of quote because it measures the cost ofcompleted trades.

There are some potential limitations of our measure. First, the amortizedspread reflects only transaction costs associated with the bidask spread. Othercosts of transacting may also be priced, such as brokerage fees, commissions,and price movement. Second, while the impact of bidask spreads on requiredreturns is determined by expected holding periods, our measure of the amortizedspread reflects realized holding periods. This limitation is important if a stocksamortized spread is driven largely by unanticipated shocks to turnover. Toaddress this concern, we provide evidence which suggests that a stocks amor-tized spread is relatively stable over time. Finally, our measure of the amortizedspread reflects the average holding period of all investors. If a large portion ofa firms stock is held by an individual with an unusually long holding period, ourmeasure may understate the amortized spread for the marginal investor. Not-withstanding these important qualifications, we believe that, in the context ofasset pricing, our measure of the amortized spread is a more relevant measure oftransaction costs than the simple magnitude of the spread.


2.2. The data

Our sample includes the universe of U.S. domiciled common stocks listed oneither the Amex or the NYSE at any time during the period 19831992. Data forcomputing effective spreads and amortized spreads are obtained from theInstitute for the Study of Security Markets (ISSM) transactions files. We useonly Best Bid/Offer (BBO) eligible quotations and exclude certain quotes andtransactions that are identified by ISSM as erroneous. In addition, ISSMidentifies quotations and transactions that are atypical. We exclude all quotesidentified as pre-opening indications, trading halts and non-firm quotations andall trades that are identified as either batched, executed as part of a basket trade,or reported out of sequence. In addition to the filters provided by ISSM, weapply additional filters to remove observations that may be subject to data entryerrors. Following Keim (1989) and Blume and Goldstein (1992), we eliminateany bidask quote that is greater than 20% of the stock price for stocks pricedover $10 dollars and greater than $2 for stocks priced under $10. We alsoeliminate transactions that occur following a quotation that was eliminated andprior to a new quote. As Lee and Ready (1991) suggest, we adjust for errors inthe time stamp of quotations. The time stamp adjustments are necessary due tothe differential delays in the reporting of quotes and transactions. Finally, weeliminate Berkshire Hathaway and Capital Cities because of their unwieldystock prices. Collectively, these screens eliminate less than 10% of all trades byvolume. Data for computing market value of equity and share turnover aretaken from the Center for Research in Security Prices (CRSP) daily return files.We exclude observations in which daily share turnover is greater than 20% ofthe firms outstanding shares to avoid large errors in share turnover due todelays in updating shares outstanding following stock splits and stock issues.This screen eliminates fewer than 0.01% of the total observations.

3. Characteristics of the amortized spread

In this section, we examine cross-sectional and time-series characteristics ofannualized amortized spreads calculated using Eq. (1).

3.1. Cross-sectional properties

Table 1 reports pooled cross-sectional time-series descriptive statistics of theamortized spread, and its two components, the effective spread and shareturnover. In panel A, stocks are assigned to deciles on the basis of their averagemonthly amortized spread rank. In panel B, stocks are assigned to deciles on thebasis of their average monthly effective spread rank. In panel C, stocks areassigned to deciles on the basis of their average monthly share turnover rank.


Tab

le1

Ave

rage

amort

ized

spre

ads,

effec

tive

spre

ads,

and

shar

etu

rnov

er

Pan

elsA

,Ban

dC

pres

entcr

oss

-sec

tiona

land

tim

e-se

ries

aver

ages

oft

he

amort

ized

spre

adan

ditsco

mpon

ents

,the

effec

tive

spre

adan

dsh

aretu

rnov

erfo

ral

lU.S

.bas

edst

ock

str

aded

on

theA

mex

orN

YSE

atan

ytim

eduring

theper

iod

from

1983

199

2.A

stock

sam

ort

ized

spre

adis

thepr

oduct

ofth

eeff

ective

spre

adan

dth

enu

mbe

rof

shar

estr

aded

sum

med

over

allt

rades

and

expr

esse

das

anan

nua

lper

centofe

quity

valu

e.T

heeff

ective

spre

adis

the

differ

ence

betw

een

thetr

ansa

ctio

nprice

and

them

idpo

into

fthepr

evai

ling

bida

skqu

ote

.Shar

etu

rnov

eris

equa

lto

thean

nual

shar

evo

lum

ediv

ided

by

thenum

ber

ofsh

ares

outs

tand

ing.

Inpan

elA

,sto

cksar

eas

sign

edto

deci

lesbas

edupo

nth

eirav

erag

em

ont

hly

amort

ized

spre

adra

nk.I

npa

nel

B,s

tock

sar

eas

sign

edba

sed

upo

nth

eirav

erag

em

ont

hly

effec

tive

spre

adra

nk.I

npa

nel

C,s

tock

sar

eas

sign

edbas

edupo

nth

eirav

erag

em

onth

lysh

are

turn

ove

rra

nk.I

nea

chca

se,dec

ile1

refe

rsto

the

low

estva

lues

ofth

era

nki

ng

variab

lean

dde

cile

10ar

est

ock

sth

atex

hibit

the

larg

est

valu

esfo

rth

era

nkin

gva

riab

le.

Dec

ileLow

23

45

67

89

Hig

hA

vg.

Pan

elA

:D

ecile

sfo

rmed

byam

ortize

dsp

read

Am

ort

ized

spre

ad0.

09%

0.15

%0.

21%

0.28

%0.

34%

0.44

%0.

56%

0.78

%0.

99%

1.76

%0.

51%

Effec

tive

spre

ad0.

51%

0.56

%0.

67%

0.74

%0.

84%

1.00

%1.

20%

1.62

%1.

92%

2.81

%1.

11%

Sha

retu

rnov

er0.

230.

370.

460.

530.

600.

680.

730.

780.

841.

030.

60

Pan

elB

:D

ecile

sfo

rmed

byeff

ective

spre

adA

mort

ized

spre

ad0.

19%

0.24

%0.

29%

0.34

%0.

42%

0.50

%0.

56%

0.71

%0.

88%

1.17

%0.

51%

Effec

tive

spre

ad0.

25%

0.35

%0.

43%

0.53

%0.

66%

0.80

%0.

98%

1.43

%2.

26%

4.16

%1.

11%

Sha

retu

rnov

er0.

730.

660.

670.

630.

630.

640.

600.

540.

470.

370.

60

Pan

elC

:D

ecile

sfo

rmed

bysh

are

turn

over

Am

ortize

dsp

read

0.21

%0.

30%

0.44

%0.

44%

0.51

%0.

58%

0.59

%0.

60%

0.63

%0.

82%

0.51

%Effec

tive

spre

ad1.

84%

1.50

%1.

46%

1.22

%1.

09%

0.98

%0.

91%

0.77

%0.

65%

0.59

%1.

11%

Sha

retu

rnov

er0.

130.

230.

330.

410.

510.

610.

710.

811.

021.

480.

60


For example, to construct panel A, we assign each stock an amortized spreadrank for each month of the sample period for which at least 10 days of data areavailable for that stock. We then assign each stock to an amortized spread decileon the basis of the stocks average monthly rank during the stocks sampleperiod. We use this approach for two reasons. First, assigning stocks to decileson the basis of their average rank as opposed to the average value of the rankingvariable mitigates potential misclassifications due to time series variation in thelevel of the ranking variable. This is necessary because many stocks are notpresent for the entire sample period. Second, assigning firms to deciles ona one-time basis as opposed to yearly or monthly allows for a more straightfor-ward interpretation of the results, i.e., deciles contain stocks as opposed tostock-years or stock-months. However, our conclusions are not sensitive to thechoice of the ranking procedure.

Table 1 documents several facts. First, in contrast to the magnitude of theround-trip spread, the amortized spread is quite small. From panel A, theaverage round-trip effective spread for our sample stocks is 2.2% of equity value,twice the average one-way effective spread, while the average annual amortizedspread is only 0.5% of equity value. Furthermore, 88% of all sample stocks haveamortized spreads of less than 1%. Thus, if a primary component of securityreturns is reimbursement for transaction costs, one would expect to find lessthan a 1% difference among the annual returns of most Amex/NYSE stocks anda 1.7% difference between the annual returns of stocks in deciles one and ten.The distribution of amortized spreads differs somewhat across the two ex-changes. The average amortized spread is 0.67% for Amex stocks and 0.46% forNYSE stocks. The t-statistic for a test of equal means for the amortized spreadsof Amex versus NYSE stocks is 8.8 with a p-value less than 0.0001. Thestatistically significant difference in mean amortized spreads between Amex andNYSE stocks is not due to a few extreme values. A large proportion of Amexfirms are found in the high amortized spread deciles. For example, while Amexstocks represent 33% of the sample, they account for 47% of the stocks indeciles nine and ten. The s2 statistic, against the null that Amex stocks aredistributed uniformly across the amortized spread deciles, is 56 (p(0.0001).

Second, much of the cross-sectional variation in amortized spreads is lostwhen effective spreads are used as a proxy for the amortized spread. Forexample, the interdecile range of amortized spreads drops from 1.7%, whenstocks are sorted by the amortized spread (panel A), to less than 1% when stocksare sorted by the effective spread (panel B). Though not reported in Table 1, theinterdecile range of amortized spreads is less than 0.9% when stocks are sorted bytheir average closing quoted spread. While a 0.9% difference in annual returns iscertainly of economic importance, it is unlikely that current asset pricing tests canreliably detect it. In other words, the lack of variation in amortized spreadscoupled with the use of a limited proxy, i.e., quoted spreads, may explain therather weak evidence of a spread effect in the returns of Amex/NYSE stocks.


To more formally assess the relation between amortized spreads and effectivespreads, we estimate the Pearson and Spearman correlation between amortizedspreads and effective spreads. The cross-sectional correlations between averageamortized spreads and average effective spreads are 0.54 (Pearson) and 0.59(Spearman). The imperfect correlation between amortized spreads and effectivespreads is due to the fact that not all stocks with the same spread trade with thesame frequency. In Amihud and Mendelsons (1986) framework, there is a per-fect correlation between spreads and amortized spreads because all stocks withthe same spread trade with the same frequency. This feature of Amihud andMendelsons (1986) model is not supported by the data in Table 1. If all stockswith the same spread traded with the same frequency, deciles formed by spread(panel B) would be the exact inverse of deciles formed by turnover (panel C).This is not the case. For example, the average spread of the highest spread decile(panel B) is 4.16%, while the average spread of the lowest share turnover decile(panel C) is 1.84%.

Finally, it is interesting to note that stocks with high amortized spreads haveboth high effective spreads and high share turnover, while stocks with lowamortized spreads have both low effective spreads and low share turnover.From panel A, stocks in the highest amortized spread decile have averageeffective spreads of 2.8% and average share turnover of 103%, while stocks inthe lowest amortized spread decile have average effective spreads of 0.5% andaverage share turnover of 23%. The positive association between spread andshare turnover in panel A is in contrast to Amihud and Mendelsons (1986)clientele effect, whereby stocks with higher spreads are held for longer periodsthan stocks with lower spreads.

Fig. 1 provides a more detailed view of the surface of amortized spreads in thedimensions of the effective spread and share turnover. Panel A displays theaverage amortized spread for stocks falling into the various spread ranks (frompanel B of Table 1) and share turnover ranks (from panel C of Table 1). Thenumber of stocks in each cell is presented in panel B of Fig. 1. As previouslynoted, there is little variation in amortized spreads across most stocks. Note thatthe only stocks with markedly different amortized spreads are found in the highspread/high turnover region of Fig. 1A. Fig. 1B reveals that few stocks fall intothis category. Furthermore, stocks with similar spreads can have vastly differentamortized spreads because of differences in share turnover. For example, inspread rank ten, the average effective spread is 4.16%, yet these stocks averageamortized spreads range from 0.5% to 3.5%. Likewise, due to differences inturnover, stocks with vastly different spreads can have similar amortizedspreads. For example, in spread rank ten, turnover rank one, we find 92 stockswith average amortized spreads of 0.50%, and in spread rank one, turnover rankten, we find 57 stocks with average amortized spreads of 0.37%. Table 1 andFig. 1 provide evidence that stocks with similar spreads can exhibit vastlydifferent amortized spreads and stocks with vastly different spreads can exhibit


Fig. 1. The surface of amortized spreads. A stocks amortized spread is the product of the effectivespread and the number of shares traded summed over all trades and expressed as an annualizedpercent of equity value. The effective spread is the difference between the transaction price and theprevailing bidask midpoint. Share turnover is equal to the annualized volume of shares tradeddivided by the number of shares outstanding. In panels A and B, stocks are assigned to effectivespread/share turnover cells based upon their average monthly effective spread rank and theiraverage monthly share turnover rank. The sample includes U.S. based stocks traded on either theAmex or NYSE from 19831992. In each case, decile 1 refers to the lowest values of the rankingvariable and decile 10 includes stocks that exhibit the largest values for the ranking variable.


4 In 1983, decile 1 includes a maximum of 214 firms and finishes the 10 year period with 139 firms.Likewise, decile 10 includes a maximum of 219 firms in 1983 and finishes the 10 year period with 85firms. The monthly average amortized spread is calculated from an average of 1988 stocks.

similar amortized spreads. This is why one cannot infer the amortized cost oftransacting on the basis of the spread alone.

3.2. Time-series properties

The ranking procedure we use to form the deciles in Table 1 is designed tocapture a stocks long run amortized spread. However, this ranking method willobscure variation in the amortized spreads of individual stocks over time.A natural question concerns the stability of a stocks amortized spread overtime. To address this question, we provide several pieces of evidence.

Fig. 2 plots the time-series of monthly amortized spreads for stocks assignedto deciles on the basis of their amortized spread rank in 1983. For clarity, wefocus on amortized spread deciles one and ten. We compare the amortizedspread of deciles one and ten to the average amortized spread of all stocks ineach sample month. The relative stability of a stocks amortized spread isimmediately apparent. In particular, the amortized spreads for deciles one andten never revert to the average amortized spread over the ensuing nine yearperiod.4 This simple experiment shows that, even over a protracted period oftime, a stocks amortized spread is relatively stable.

To more formally assess the stability of a stocks amortized spread over time,we estimate the correlation between a stocks average amortized spread in yeart and its average amortized spread in year t!1. Over the 10 year period from1983 to 1992, the average of the nine correlation coefficients is 0.56. The averagecorrelation between a stocks amortized spread rank in year t and its amortizedspread rank in year t!1 is 0.81. To determine whether the stability of theamortized spread is due to the stability of the effective spread or the stability ofa stocks share turnover, we repeat the above analysis for the effective spreadand share turnover. The average of the nine correlation coefficients betweena stocks average effective spread in year t and its average effective spread in yeart!1 is 0.75. The average correlation between a stocks effective spread rank inyear t and its effective spread rank in year t!1 is 0.93. The average of the ninecorrelation coefficients between a stocks average share turnover in year t and itsaverage share turnover in year t!1 is 0.65. The average correlation betweena stocks share turnover rank in year t and its share turnover rank in year t!1is 0.79.

Finally, we examine the correlation of a stocks amortized spread, effectivespread, and share turnover between two five year sub-periods (19831987 and19881992). The correlation coefficient for a stocks average amortized spread,


Fig

.2.

Stab

ility

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read

isplo

tted

forth

esu

rviv

ing

firm

sfrom

deci

lesone

and

ten

over

the

entire

120

mont

hper

iod,

with

the

firs

ttw

elve

mont

hs

bei

ng

the

ranki

ng

per

iod.

The

aver

age

amort

ized

spre

adfo

ral

lsa

mpl

efirm

sin

each

month

ispr

esen

ted

forre

fere

nce.

Theav

erag

enu

mber

offirm

suse

din

the

calc

ulat

ion

oft

heav

erag

eam

ort

ized

spre

adis

1976

.Dec

ile1

incl

udes

am

axim

um

of2

14fir

msin

1983

and

finishe

sth

e10

year

period

with

139

firm

s.D

ecile

10in

clud

esa

max

imum

of2

19fir

msin

1983

and

finishe

sth

e10

year

per

iod

with

85fir

ms.


5For theories of the bidask spread see Demsetz (1968), Treynor (1971), Amihud and Mendelson(1980), Ho and Stoll (1981), Glosten and Milgrom (1985). For empirical evidence see Bensten andHaggerman (1974), Stoll (1989), Glosten and Harris (1988), and George et al. (1991).

6For theories of trade see Constantinides and Ingersoll (1984), Kyle (1985), Karpoff (1986),Constantinides (1986) and Harris and Raviv (1993). For empirical evidence see Atkins and Dyl(1997a), Bessembinder et al. (1996).

effective spread, and share turnover between these two periods are 0.52, 0.55 and0.51, respectively. The correlation for a stocks amortized spread rank, effectivespread rank, and share turnover rank between these two periods are 0.78, 0.86,and 0.74, respectively. These results suggest that there are persistent factorswhich influence a stocks amortized spread.

4. Determinants of the amortized spread

Researchers have examined the determinants of the bidask spread anddeterminants of trade separately. The theoretical literature on bidask spreadshas identified order processing, inventory control, and adverse selection costs asthree primary components to the spread. The general empirical implications ofthese theories are that bidask spreads are negatively related to share turnoverand share price and positively related to stock return variance.5 The theoreticalliterature on trading volume has examined a number of motives for trade,including liquidity, portfolio rebalancing, tax-loss selling, asymmetric informa-tion, and differences of opinion. According to theories of trade, frequency oftrade is negatively related to the bidask spread and positively related to stockreturn variance.6 Because the amortized spread is determined by the interactionof the spread and frequency of trade, the net effect of these factors on theamortized spread is unclear.

Table 2 reports coefficient estimates for cross-sectional regressions of effectivespreads, share turnover, and the amortized spread on the determinants ofspreads and share turnover. Panel A reports coefficient estimates from regres-sions of the effective spread on stock price, stock return variance and shareturnover. Panel B reports coefficient estimates from regressions of share turn-over on stock return variance and the effective spread. Panel C reports coeffic-ient estimates from regressions of the amortized spread on stock price and stockreturn variance. We use time-series means of stock prices, share turnover,effective spreads, and amortized spreads, and calculate return variance frommonthly returns over each stocks available sample period. We use logarithmictransformations of these variables to eliminate skewness that is present in theraw data.


Table 2Determinants of spreads, turnover, and amortized spreads

Table 2 reports coefficient estimates for cross-sectional regressions of effective spreads, shareturnover, and the amortized spread on share price, return volatility, and spreads or share turnoverwhere applicable. Panel A reports coefficient estimates from regressions of the effective spread onstock price, stock return variance and share turnover. Panel B reports coefficient estimates fromregressions of share turnover on stock return variance and the effective spread. Panel C reportscoefficient estimates from regressions of the amortized spread on stock price, and stock returnvariance. For each cross-sectional observation, we use time-series means of stock prices, shareturnover, effective spreads, and amortized spreads, and calculate return variance from monthlyreturns over each stocks available sample period. We use logarithmic transformations of thevariables. Standard errors are presented in parentheses. Each of the coefficient estimates has anassociated p-value less than 0.01.

Panel A: Dependent variable effective spread

Intercept Turnover Price Return variance Adj-R2 N

!2.06 !0.14 !0.70 0.24 0.91 3366(0.02) (0.01) (0.01) (0.01)

Panel B: Dependent variable share turnover

Intercept Effective spread Return variance Adj-R2 N

!1.58 !0.71 0.60 0.28 3366(0.07) (0.02) (0.02)

Panel C: Dependent variable amortized spread

Intercept Price Return variance Adj-R2 N

!2.59 !0.24 0.56 0.48 3366(0.06) (0.02) (0.02)

We begin with the cross-sectional relation between effective spreads and stockprice, stock return variance, and share turnover. The coefficients reported inpanel A are consistent with prior studies of the determinants of the spread. Inparticular, the coefficient of stock price is negative (!0.70) and significant(p-value(0.0001), the coefficient of stock return variance is positive (0.24) andsignificant (p-value(0.0001) and the coefficient of share turnover is negative(!0.14) and significant (p-value(0.0001). Though not reported in Table 2,coefficient estimates from regressions of quoted bidask spreads on share price,volatility, and share turnover are nearly identical to those reported in panel A.


7Given the fact that the spread and turnover are functions of one another, the regressions ofpanels A and B have an endogeneity problem. We do not attempt to resolve this issue. We report theresults of regression that are similar to prior studies.

Panel B reports coefficient estimates from regressions of share turnover onstock return variance and spread. The coefficients reported in panel B areconsistent with prior studies of the determinants of trade. In particular, thecoefficient of stock return variance is positive (0.60) and significant(p-value(0.0001) and the coefficient of the spread is negative (!0.71) andsignificant (p-value(0.0001).

Having examined the determinants of effective spreads and share turnoverseparately, we now turn to the cross-sectional relation between amortizedspreads and the determinants of spread and share turnover. Because amortizedspreads are an explicit function of both spread and share turnover, we do notinclude either of these as independent variables in the regressions.7 PanelC reports coefficient estimates for regressions of amortized spreads on stockprice and stock return variance. Because stock price appears only in theregression for spread and has a negative coefficient, we expect a negative relationbetween amortized spreads and stock price. The expected relation betweenamortized spreads and return volatility is unclear. Since both spread and shareturnover are positively related to return volatility, one might expect to observea positive relation between amortized spreads and return volatility. However,because of the negative relation between spread and turnover, the expectedassociation between return volatility and the amortized spread is ambiguous.

From panel C, the coefficient of stock price is negative (!0.24) and signifi-cant (p-value(0.0001) as expected. The coefficient of return volatility is positive(0.56) and significant (p-value(0.0001). The positive coefficient of return volatility suggests that the positive effect that volatility has on spread and share turnoveroutweighs the negative effect that spread and turnover have on each other.

Table 3 provides additional information concerning the relation betweenamortized spreads and return volatility by reporting the distributions of amor-tized spreads for stocks assigned to deciles on the basis of their return volatility.More specifically, for each volatility decile we report the number of stocks thatfall into each of the amortized spread deciles of Table 1.

The relation between amortized spreads and volatility in Table 3 is striking.For example, 63% of stocks in the lowest volatility decile fall into the lowest twoamortized spread deciles, while 58% of stocks in the highest volatility decile fallinto the highest two amortized spread deciles. In fact, return volatility appearsto be a better proxy for the amortized spread than the effective spread. Theinterdecile range of amortized spreads across volatility deciles is 1.2%, whileTable 1 panel B shows that the interdecile range of amortized spreads acrosseffective spread deciles is less than 1.0%.


Tab

le3

Ret

urn

vola

tilit

yan

dth

eam

ortize

dsp

read

Forth

est

ock

sin

each

vola

tilit

yde

cile

,we

repor

tth

epe

rcen

tage

sth

atar

efo

und

inea

chofth

eam

ort

ized

spre

addec

iles

defi

ned

inTab

le1.

Inad

dition,

mea

nam

ortize

dsp

read

s,eff

ective

spre

ads,

shar

etu

rnov

eran

dst

andar

dde

viat

ion

ofm

onth

lyre

turn

sar

ere

por

ted

for

each

vola

tilit

yde

cile

.Ast

ock

sam

ort

ized

spre

adis

the

prod

uct

ofth

eeff

ective

spre

adan

dth

enum

ber

ofsh

ares

trad

edsu

mm

edov

eral

ltr

ades

and

expre

ssed

asan

annu

alpe

rcen

tof

equi

tyva

lue.

Am

ort

ized

spre

adde

cile

Vol

atili

tydec

ile

Low

vola

tilit

y2

34

56

78

9H

igh

vola

tilit

y

Low

38%

21%

10%

10%

7%5%

2%3%

1%1%

225

%21

%17

%11

%10

%6%

4%1%

1%2%

317

%18

%18

%12

%10

%9%

7%4%

2%2%

49%

16%

20%

13%

15%

8%6%

6%3%

3%5

5%12

%18

%17

%13

%11

%8%

6%4%

6%6

2%6%

9%14

%19

%17

%11

%11

%6%

6%7

3%4%

6%12

%12

%16

%19

%11

%10

%7%

80%

1%2%

6%9%

18%

14%

16%

20%

15%

91%

0%1%

3%5%

7%18

%21

%22

%24

%H

igh

0%0%

1%1%

2%3%

11%

19%

30%

34%

Dec

ilem

ean:

Am

ort

ized

spre

ads

0.17

%0.

20%

0.26

%0.

33%

0.38

%0.

45%

0.60

%0.

78%

1.04

%1.

40%

Effec

tive

spre

ad0.

38%

0.45

%0.

51%

0.61

%0.

76%

0.85

%1.

08%

1.62

%2.

25%

3.50

%Turn

over

0.45

0.53

0.62

0.65

0.65

0.71

0.78

0.73

0.76

0.68

Stan

dard

dev

iation

ofre

turn

5.96

%7.

89%

9.03

%10

.08%

11.1

7%12

.39%

13.8

8%15

.80%

18.7

8%27

.84%


Table 4Industry profiles of the amortized spread

For each industry, we report the percentage of stocks within that industry that fall into each of theamortized spread deciles defined in Table 1. The industry classification scheme is based upon Roll(1992) with the exception of technology, which Roll (1992) does not define. In addition, meanamortized spreads, effective spreads, share turnover and standard deviation of monthly returns arereported for each industrial classification. A stocks amortized spread is the product of the effectivespread and the number of shares traded summed over all trades and expressed as an annual percentof equity value. The number of firms within each industrial classification is reported directly belowthe classification label.

Amortized Industry classification (number of firms)spread decile

Technology Transport Consumer Financial Capital Basics Utilities Energy(271) (85) (1129) (494) (359) (717) (282) (32)

Low 3% 6% 8% 16% 5% 10% 21% 28%2 4% 2% 10% 10% 7% 10% 20% 16%3 4% 11% 9% 10% 12% 10% 17% 13%4 7% 6% 9% 13% 9% 10% 13% 16%5 7% 6% 10% 10% 12% 11% 7% 13%6 10% 7% 10% 9% 10% 13% 6% 3%7 10% 15% 11% 8% 14% 10% 5% 9%8 14% 19% 11% 9% 11% 10% 4% 0%9 21% 13% 10% 9% 9% 9% 4% 0%High 20% 15% 11% 7% 10% 8% 5% 3%

Industry mean:Amortizedspreads

0.73% 0.67% 0.59% 0.55% 0.55% 0.53% 0.34% 0.26%

Effective spread 1.28% 1.02% 1.19% 1.15% 1.15% 1.36% 0.61% 0.50%Turnover 0.86 0.91 0.68 0.62 0.68 0.58 0.55 0.53Standard devi-ation of return

0.16 0.13 0.14 0.13 0.13 0.14 0.09 0.09

Table 3 also highlights how a stocks return volatility can dominatethe negative relation between spread and turnover. In particular, both spreadand turnover increase as one moves across volatility deciles. For example,the lowest volatility decile contains stocks with an average effective spread of0.4% and average share turnover of 45%, while the highest volatility decilecontains stocks with an average effective spread of 3.4% and average shareturnover of 68%.

A less direct, yet more intuitive, way to characterize a stocks return volatilityis by the assets of the issuing firm. Table 4 reports distributions of amortizedspreads for the stocks of different industries. Our industry classifications arebased on Roll (1992) and include: capital goods, basic goods, consumer goods,


8Roll (1992), defines seven industry categories: capital goods, basis goods, utilities, energy,transportation, and financial. We assign technology stocks to their own category, and thus, haveeight industry categories. We define technologies to be stocks in firms whose primary lines ofbusiness include: computer and office equipment, communications equipment, electronic compo-nents, electronic measurement and navigational instruments, and computer software.

utilities, energy, transportation, financial, and technology.8 For each industry,we report the percent of stocks within that industry that fall into each of theamortized spread deciles of Table 1.

In Table 4, we find evidence that a firms assets influence both spreads andfrequency of trade, and thus, the amortized cost of transacting. For example,utilities which are characterized by relatively stable cash flows and substantialassets in place have both low spreads and low share turnover. By contrast,technologies, which are characterized by relatively volatile cash flows andsubstantial growth opportunities, have both high spreads and high turnover.From Table 4, utility stocks have an average monthly standard deviation ofreturn of 9%, average effective spreads of 0.6%, and average share turnover of55%, while technology stocks have an average monthly standard deviationof return of 16%, average effective spreads of 1.3%, and average share turnoverof 86%. The positive relation between spread and turnover in Tables 3 and 4 isinconsistent with Amihud and Mendelsons clientele effect. These results suggestthat return volatility and the characteristics of a firms assets are good proxiesfor, and perhaps important determinants of, amortized spreads.

Table 4 also illustrates that a stocks amortized spread cannot be predictedreliably by its spread alone. For example, transportation stocks have lowereffective spreads than stocks of firms in basic goods. However, due to theirhigher share turnover, transportation stocks have higher amortized spreadsthan basic goods stocks. From Table 4, the average effective spread for trans-portation stocks and basic goods stocks are 1.0% and 1.4% (t-statistic fordifference in means is 2.37), while the average annual amortized spread fortransportation stocks and basic goods stocks are 0.67% and 0.53% (t-statisticfor difference in means is 2.10) A number of similar examples can also be foundin Table 4.

5. Stock returns and the amortized spread

The empirical results in Sections 3 and 4 show that the magnitude of thespread is not always a reliable proxy for the amortized cost of the spread. In thissection we compare the relative merits of amortized spreads and unamortizedspreads in the context of asset pricing. First, we examine the relation betweenamortized spreads and market value of equity and book-to-market, two vari-ables which are currently important in empirical studies of asset pricing.


5.1. Amortized spreads, market value of equity, and book-to-market

Banz (1981) and Reinganum (1981) find that stock returns are negativelyrelated to market value of equity, while Stattman (1980) and Rosenberg et al.(1985) find that stock returns are positively related to book-to-market. Famaand French (1992) argue that market value of equity and book-to-market maybe related to risk factors that are not captured by a stocks beta. Alternatively,Amihud and Mendelson (1986) and Kothari et al. (1995) argue that thesevariables may be related to a stocks liquidity premium. Because the amortizedspread is a direct measure of a stocks liquidity, it is interesting to examine therelations between amortized spreads, market value of equity and book-to-market.

Table 5 reports the distribution of amortized spreads across market value ofequity deciles and Table 6 reports the distribution of amortized spreads acrossbook-to-market deciles. From Table 5, we find a negative relation between theamortized spread and market value of equity. For example, the average amor-tized spread for stocks in the lowest market value decile is 1%, while the averageamortized spread for stocks in the highest market value decile is 0.20%. Thecross-sectional correlation between amortized spread and market value ofequity is !0.20 (Pearson) and !0.43 (Spearman).

From Table 6, we find a positive relation between amortized spread andbook-to-market. For example, the average amortized spread for stocks in thelowest book-to-market decile is 0.48%, while the average amortized spread forstocks in the highest book-to-market decile is 0.63%. The cross-sectional cor-relation between a stocks amortized spread and book-to-market are 0.15(Pearson) and 0.16 (Spearman). These results indicate that amortized spreadsare related to both market value of equity and book-to-market. However, therelatively low correlation between these variables suggests that market value ofequity and book-to-market are unlikely to be proxies for the amortized spread.

5.2. Cross-sectional regressions

To estimate the relation between stock returns and our two alternativemeasures of transactions costs, we use the cross-sectional regression approach ofFama and MacBeth (1973). For each year, t, we estimate variants of thefollowing cross-sectional regression:

rjt"c

0t#c

1tbj#c

2tME

j,t~1#c

3t(B/M)

j,t~1#c

4tpj,t~1

#c5tC

j,t~1#e

j,t, (3)

where rjt

is the excess return of security j over the one-year Treasury bill, bjis the

market risk of security j, MEj,t~1

is the natural log of market value of equity ofsecurity j measure in the year t!1, (B/M)

j,t~1is equal to the ratio of the end of


Tab

le5

Mar

ket

valu

eofeq

uity

and

the

amort

ized

spre

ad

For

the

stock

sin

each

size

dec

ile,w

ere

por

tth

epe

rcen

tage

sofst

ock

sin

the

size

deci

leth

atar

efo

und

inea

chof

the

amort

ized

spre

adde

cile

sde

fine

din

Tab

le1.

Inad

ditio

n,m

ean

amort

ized

spre

ads,

effec

tive

spre

ads,

shar

etu

rnove

ran

dm

arke

tva

lue

(inm

illio

ns)

are

report

edfo

rea

chsize

dec

ile.A

stock

sam

ort

ized

spre

adis

the

pro

duc

tof

the

effec

tive

spre

adan

dth

enum

ber

ofsh

ares

trad

edsu

mm

edove

ral

ltr

ades

and

expre

ssed

asan

annu

alpe

rcen

tof

equi

tyva

lue.

Am

ort

ized

Size

dec

ilesp

read

dec

ileSm

allfirm

s2

34

56

78

9Lar

gefirm

s

Low

2%4%

5%10

%11

%10

%10

%15

%11

%21

%2

3%7%

8%7%

8%11

%11

%15

%12

%19

%3

4%8%

6%10

%9%

8%9%

10%

16%

20%

45%

9%10

%7%

8%9%

11%

10%

13%

17%

58%

11%

6%11

%6%

10%

9%13

%14

%12

%6

10%

7%7%

7%12

%15

%12

%9%

15%

6%7

9%11

%16

%9%

8%11

%13

%11

%9%

3%8

15%

10%

15%

16%

13%

10%

9%6%

6%1%

918

%17

%13

%12

%10

%11

%9%

8%3%

0%H

igh

26%

16%

14%

10%

15%

7%7%

3%2%

0%

Dec

ile

mea

n:A

mort

ized

spre

ads

1.00

%0.

77%

0.76

%0.

62%

0.57

%0.

49%

0.49

%0.

35%

0.30

%0.

20%

Effec

tive

spre

ad3.

41%

2.07

%1.

72%

1.20

%0.

90%

0.73

%0.

61%

0.56

%0.

39%

0.29

%Turn

over

0.39

0.48

0.55

0.60

0.71

0.72

0.84

0.76

0.80

0.71

Mar

ket

valu

e(m

illio

ns)

922

4273

124

199

337

610

1203

5319


Tab

le6

Book-

to-m

arket

and

the

amort

ized

spre

ad

Forth

est

ock

sin

each

boo

k-to-m

arket

deci

le,w

ere

port

the

perc

enta

geofth

ose

stoc

ksth

atar

efo

und

inea

chofth

eam

ort

ized

spre

addec

iles

defi

ned

inTab

le1.

Inad

dition,m

ean

amort

ized

spre

ads,

effec

tive

spre

ads,

shar

etu

rnove

ran

dbo

ok-t

o-m

arket

are

repor

ted

for

each

boo

k-to-m

arket

deci

le.

Obse

rvat

ions

for

whi

chB

/Mis

neg

ativ

ear

enot

incl

uded

inth

esa

mple

use

dto

const

ruct

this

table

.A

stock

sam

ort

ized

spre

adis

the

product

ofth

eeff

ective

spre

adan

dth

enum

ber

ofsh

ares

trad

edsu

mm

edov

eral

ltr

ades

and

expre

ssed

asan

annua

lper

cent

ofeq

uity

valu

e.

Am

ort

ized

spre

adde

cile

Book-

to-m

arket

deci

le

Low

B/M

23

45

67

89

Hig

hB

/M

Low

12%

12%

12%

13%

10%

10%

13%

10%

5%4%

211

%12

%9%

10%

14%

8%11

%8%

9%9%

314

%10

%10

%10

%11

%16

%9%

6%8%

4%4

14%

8%10

%8%

15%

10%

8%11

%9%

7%5

5%12

%14

%10

%9%

8%10

%13

%12

%7%

67%

11%

8%10

%10

%11

%12

%10

%10

%10

%7

10%

11%

7%8%

8%9%

10%

11%

10%

16%

86%

8%10

%8%

8%6%

11%

13%

13%

16%

97%

10%

9%12

%8%

11%

8%14

%10

%11

%H

igh

12%

7%10

%10

%7%

11%

8%6%

14%

16%

Dec

ile

mea

n:A

mort

ized

spre

ad0.

48%

0.42

%0.

51%

0.46

%0.

44%

0.48

%0.

46%

0.54

%0.

54%

0.63

%Effec

tive

spre

ad0.

86%

0.79

%0.

81%

0.88

%0.

92%

1.02

%1.

03%

1.25

%1.

14%

1.63

%Turn

over

0.71

0.66

0.67

0.66

0.62

0.59

0.54

0.55

0.60

0.55

Book-

to-m

arket

0.22

0.39

0.50

0.61

0.70

0.82

0.90

1.06

1.29

2.18


the previous years book value of equity to market value of equity if B/M ispositive, and zero if B/M is negative, p

j,t~1is the standard deviation of monthly

returns estimated with three to five years of data, as available, prior to the testyear, and C

j,t~1measures expected transaction costs with either the expected

effective spread or the expected amortized spread of security j. Returns aremeasured from July 1 to June 30 of the following year. We use annual returnsrather than monthly returns in an attempt to sidestep the statistical problemsthat arise from the seasonality and measurement biases found in stock returnsduring the month of January. For example, Bhardwaj and Brooks (1992) andHuson (1995) find that bidask bounce causes the relations between stockreturns and market value of equity and stock returns and bidask spread to beoverstated during the month of January. Details concerning the estimation ofthe independent variables in the above cross-sectional regressions are discussedin the appendix.

Table 7 reports coefficient estimates from cross-sectional regressions of stockreturns on beta, market value of equity, book-to-market, standard deviation ofreturn and our two alternative measures of transaction costs. Before discussingthe results we raise two caveats. First, given data availability constraints (ISSMdata is available only from 1983 to 1992), we are able to conduct our assetpricing tests using only nine years of data. Prior empirical studies whichexamine the relation between stock returns and bidask spread related transac-tion costs utilize 20 or more years of data. However, these studies use year-endclosing bidask quotes as a proxy for costs incurred from the bidask spread. Toour knowledge, this study is the first to test the relation between stock returnsand the effective spread as opposed to the quoted spread.

Second, from Table 1 we know that the cross-sectional variation in amortizedspreads for Amex/NYSE stocks is relatively small. The variation in our esti-mates of expected amortized spreads is even smaller. For example, while theinterdecile range of amortized spreads is 1.7% (Table 1), the interdecile range ofour estimates of expected amortized spreads is 1%. Thus, it is possible that theamortized cost of transacting is important, yet the variation in amortizedspreads for our sample stocks is not great enough to allow detection. One way toaddress this issue would be to conduct our asset pricing tests using securitieswith greater variation in amortized spreads, say NASDAQ stocks. Unfortunate-ly, reported volume for NASDAQ stocks is highly inflated due to interdealertrading and there is no systematic way to correct for differences in the overstate-ment across stocks (see Atkins and Dyl, 1997b).

We begin with the cross-sectional relation between stock returns and amor-tized spreads. From panel A of Table 7, we find weak support for a cross-sectional relation between stock returns and amortized spreads. In particular,the time-series average coefficient of the amortized spread is positive withtwo-tailed p-values ranging from 0.02 to 0.18 for the alternative regressionspecifications. Furthermore, the coefficient of the amortized spread is insensitive


Table 7The relation between stock returns and amortized spreads

Asset pricing tests are conducted in the spirit of Fama and MacBeth (1973). Using OLS, we estimatethe cross-sectional relation between each stocks annual return in excess of the one-year treasuryyield and b, the log of the market value of equity, the book-to-market ratio in year t!1, thestandard deviation of monthly returns, and, in panel A, the amortized spread, and, in panel B, theeffective spread. Annual returns are measured from July 1 of each year through June 30 of thefollowing year. Betas are estimated using a two-stage procedure similar to Kothari et al. (1995).Market value of equity is estimated immediately prior to each test year. Standard deviation of returnis the standard deviation of monthly returns estimated with three to five years of data, as available,prior to the test year. A stocks spread is the average effective spread over the preceding twelvemonths. Amortized spreads are estimated as the product of the effective spread estimate and theaverage level of share turnover for each firm over the stocks entire sample period. Panels A andB contain time-series averages of the nine cross-sectional regression coefficients. Standard errors arepresented in parentheses. p-values for a two-tailed t-test are provided in square brackets.

Panel A: Returns and amortized spreads

rj,t"c

0,t#c

1,tbj#c

2,tME

j,t~1#c

3,t(B/M)

j,t~1#c

4,tpj,t~1

#c5,t

Amortized Spreadj,t~1

#ej,t

Dependent variable: Return in excess of 1 year t-bill yield for firm j

Intercept bj

MEj,t~1

(B/M)j,t~1

pj,t~1

AmortizedSpread

i,t~1

Mean coefficient 0.13 !0.08 4.12(std err) (0.04) (0.02) (2.82)[p-value] [0.01] [0.00] [0.18]Mean coefficient !0.03 !0.07 0.01 4.62(std err) (0.12) (0.01) (0.01) (2.58)[p-value] [0.78] [0.00] [0.19] [0.11]Mean coefficient !0.07 !0.07 0.01 0.01 4.54(std err) (0.10) (0.01) (0.01) (0.02) (2.58)[p-value] [0.54] [0.00] [0.11] [0.45] [0.12]Mean coefficient 0.20 !0.02 0.00 0.00 !1.35 7.89(std err) (0.13) (0.02) (0.01) (0.02) (0.48) (2.87)[p-value] [0.16] [0.42] [0.99] [0.79] [0.02] [0.02]

Panel B: Returns and effective spreads

rj,t"c

0,t#c

1,tbj#c

2,tME

j,t~1#c

3,t(B/M)

j,t~1#c

4,tpj,t~1

#c5,t

EffectiveSpreadj,t~1

#ej,t


Intercept bj

MEj,t~1

(B/M)j,t~1

pj,t~1

EffectiveSpread

i,t~1

Mean coefficient 0.12 !0.07 0.43(std err) (0.04) (0.02) (2.12)[p-value] [0.01] [0.01] [0.84]


Table 7 (Continued)

Panel B: Returns and effective spreads

rj,t"c

0,t#c

1,tbj#c

2,tME

j,t~1#c

3,t(B/M)

j,t~1#c

4,tpj,t~1

#c5,t

Effective Spreadj,t~1

#ej,t


Intercept bj

MEj,t~1

(B/M)j,t~1

pj,t~1

EffectiveSpread

i,t~1

Mean coefficient !0.12 !0.06 0.02 2.04(std err) (0.14) (0.02) (0.01) (2.77)[p-value] [0.43] [0.01] [0.11] [0.48]Mean coefficient !0.15 !0.06 0.02 0.01 1.91(std err) (0.14) (0.02) (0.01) (0.02) (2.76)[p-value] [0.33] [0.00] [0.08] [0.42] [0.51]Mean coefficient 0.05 !0.00 0.01 0.00 !1.37 3.64(std err) (0.15) (0.02) (0.01) (0.02) (0.36) (2.64)[p-value] [0.73] [0.81] [0.32] [0.77] [0.00] [0.20]

to the inclusion of either market value of equity or book-to-market. Forexample, the time-series average coefficient of the amortized spread is 4.1(t-statistic 1.49) when accompanied by beta, 4.6 (t-statistic 1.79) when accom-panied by beta and market value of equity, and 4.5 (t-statistic 1.76) whenaccompanied by beta, market value of equity, and book-to-market. Theseresults suggest that the amortized spread effect is distinct from either the sizeeffect or book-to-market effect. While we focus on the coefficients estimates forthe amortized spread, it is important to note that the unusual negative coeffic-ient on beta and positive coefficient on size are consistent with the results inEleswarapu and Reinganum (1993) over a similar time period.

Panel B of Table 7 reports coefficient estimates from regressions of stockreturns on beta, market value of equity, book-to-market, standard deviation ofreturn, and effective spreads. We find no support for a cross-sectional relationbetween stock returns and effective spreads. In particular, while the time-seriesaverage coefficient of the effective spread is positive, two-tailed p-values rangefrom 0.20 to 0.84 in the alternative regression specifications.

The results of panel B differ from those of Amihud and Mendelson (1986),who find a positive and significant relation between stock returns and bidaskspreads. There are a number of possible reasons for this finding. First, Amihudand Mendelson use quoted bidask spreads to proxy for transaction costs whilewe use effective spreads. Second, Amihud and Mendelson use monthly returnsdata while we use annual returns data. Finally, Amihud and Mendelson usea pooled cross-sectional time series approach, as opposed to the cross-sectionalapproach of Fama and MacBeth (1973), and conduct their tests over a differenttime period (19611980). The results of panel B are, however, consistent with


9As a practical matter, it is important to note that neither the amortized effective spread nor theamortized quoted spread are priced when a single end-of-period observation is used to estimate thespread. For example, using periods from July 1 to June 30, if for each stock the amortizd spread iscalculated from a single spread observation on June 30th and multiplied by the average turnover,this measure of the amortized spread is not significant in Fama and MacBeth-type regressions.

those of Eleswarapu and Reinganum (1993), who use the Fama and MacBeth(1973) methodology over a similar time period.

The strong contemporaneous association between the amortized spread andreturn volatility observed in Table 3 raises the question of whether return volatil-ity is a viable proxy for the amortized spread. Prior studies find a weak andinconsistent cross-sectional relation between stock returns and historical standarddeviation of returns (i.e., Fama and MacBeth, 1973). Nevertheless, it is interestingto examine whether the inclusion of standard deviation of returns in the regressionof Eq. (3) has any impact on the coefficient of the amortized spread. If, in fact,standard deviation of returns is a viable proxy for the amortized spread, onewould expect to observe a positive coefficient for the standard deviation of returnsand, because of their high correlation, a less significant coefficient for the amor-tized spread. We estimate Eq. (3) with the addition of each stocks standarddeviation of monthly returns estimated over three to five years preceding each testyear, as available. Surprisingly, the coefficient for standard deviation of returns isnegative, !1.35, and significant (t-statistic !2.81, p-value(0.05), while thecoefficient for the amortized spread is now larger (7.9) and significant (t-statistic2.75, p-value(0.05). The negative coefficient estimate for return volatility ap-pears to be related to the negative risk premium over this period. In particular, thecoefficient estimate for beta is insignificant with the inclusion of standard devi-ation of return in the regression. Coefficient estimates for market value of equityand book-to-market in this regression are insignificantly different from zero.Thus, it appears that, if there is a relation between stock returns and standarddeviation of returns, it is distinct from that of the amortized spread. However, aswith all of our asset pricing results, we interpret these with caution due to thelimited and unique period over which the tests are conducted.

Finally, because data on quoted spreads are more readily available than dataon effective spreads, we repeat the regressions from panel A of Table 7 usingquoted spreads to calculate amortized spreads. The coefficient estimates for theamortized quoted spread are similar to those for the amortized effective spreadreported in panel A. For example, the time-series average coefficient of theamortized quoted spread is positive (3.1; t-statistic 1.37) when accompanied bybeta, market value of equity, and book-to-market. The coefficient estimates forthe unamortized quoted spread are similar to those for the unamortized effectivespread reported in panel B. For example, the time-series average coefficient ofthe quoted spread is 0.94 (t-statistic"0.36) when accompanied by beta, marketvalue of equity, and book-to-market.9 These results do, however, suggest thatthe effective spread conveys more information than the quoted spread.


10Fowler and Rorke (1983) show that the equally weighted sum betas of Dimson (1979) are biasedwhen the market retun is autocorrelated. The 1st order autocorrelation of the quarly returns of theequally weighted Amex/NYSE CRSP index over our sample period is 0.0005 (p"0.97). Thus, wemake no attempt to correct for this bias here.

Although these asset pricing results are by no means conclusive, we believethat they are consistent with the intuitive notion that transaction costs that areimpounded in asset returns are related to the amortized cost of the spread.

6. Summary and conclusions

Empirical studies of the importance of bidask spreads in asset pricing havefocused on the magnitude of the spread as opposed to its amortized cost. Weempirically examine the reliability of using the magnitude of the spread as a proxyfor the amortized cost of the spread. We find that, in contrast to the spread, theamortized cost of the spread is quite small. Furthermore, the distinction betweenspreads and amortized spreads yields new information. For example, transpor-tation stocks have lower average spreads than stocks in basics goods, yet,because of their higher share turnover, transportation stocks have higher aver-age amortized spreads than stocks in basic goods. One implication of this resultis that tests of the relation between bidask spreads and security returns whichrely solely on the magnitude of the spread are misspecified. We find thatamortized spreads are positively related to return volatility, a variable which ispositively related to both the magnitude of the spread and share turnover.Finally, consistent with theories of transaction costs and asset pricing, we findstronger evidence that amortized spreads are priced than we find for spreads.

Appendix A. Details of the asset pricing tests

As in Fama and French (1992), our approach is to estimate betas for port-folios and then assign a portfolio beta to each stock. This allows us to useindividual stock data for market value of equity, book-to-market, effectivespread, and amortized spread in the Fama and MacBeth (1973) style assetpricing tests.

A.1. Estimating betas

We first estimate each stocks rank-period beta over the three to five years (asavailable) prior to each test year, t. A stocks rank-period beta is the sum of thecoefficients in the regression of the stocks return on the contemporaneous andlagged return of the CRSP equally weighted index.10 We use quarterly returns


data and include both contemporaneous and lagged market returns in anattempt to mitigate the effects of non-synchronous trading and price-adjustmentdelays on our estimates of beta. Nonsynchronous trading and price adjustmentdelays induce systematic cross-temporal covariance in short-interval returnsthat do not appear to be present in longer interval returns data (see Cohen et al.,1983). The implications of this intervalling effect for asset pricing tests is welldocumented (see Handa et al., 1989; Jagannathan and Wang, 1996; Kothari,Shanken and Sloan, 1995). This issue is particularly important for the currentstudy as biases in beta estimates caused by nonsynchronous trading and price-adjustment delays are likely to be related to market value of equity (Handa et al.,1989), bidask spreads (Huson, 1995), and share turnover (Denis and Kadlec,1994). Stocks are then assigned to one of 20 portfolios on the basis of theirrank-period beta. Following Kothari et al. (1995), test-period betas are thenestimated by regressing annual equally weighted portfolio returns on the con-temporaneous CRSP equally weighted Amex/NYSE index return over theperiod 19801994.

As is always the case for CAPM based asset pricing tests involving factors inaddition to beta, it could be that the additional factors capture errors in a stocksbeta estimate. In this study, we took precautions to mitigate this potentialproblem by employing long-interval returns data to estimate beta (Kothariet al., 1995). Furthermore, we believe that the amortized spread is less likely tobe correlated with errors in beta estimates because the amortized spread ispositively related to both spreads and share turnover. These variables haveopposing associations with estimation errors caused by nonsynchronous trad-ing and price-adjustment delays.

A.2. Estimating transaction costs

The primary purpose of our asset pricing tests is to compare the relative meritsof two alternative measures of spread-related transaction costs, spreads andamortized spreads. In this section we discuss our estimation of these two proxies.

We use each stocks average effective spread in year t!1 as our estimate of itsexpected effective spread in year t. We use all of the previous years data asopposed to the most recent observation (i.e. last trading day of December) toavoid a potential seasonal bias in our spread estimate. Clark et al. (1992) showthat there are seasonalities in the spread and that spreads during the month ofDecember are significantly greater than those during other months of the year.Thus, spread estimates taken from the month of December will be upwardlybiased estimates of the spread throughout the year.

Our approach to estimating the expected amortized spread makes use of theapproximation of Eq. (2) that the amortized spread is approximately equal tothe effective spread times share turnover. We use this simplification and estimateeach stocks effective spread and expected turnover separately and then combine


them to form an estimate of the stocks expected amortized spread. As before, weuse each stocks average effective spread in year t!1 as our estimate of itsexpected spread in year t. A stocks expected turnover is taken to be the stocksaverage annual turnover during the sample period for that stock. Finally,a stocks expected amortized spread for year t is taken to be the product of itsaverage effective spread in year t!1 and its average turnover during the sampleperiod. While our estimates of expected turnover include both historical andfuture turnover data, we emphasize that we are not proposing a trading strategy,but rather testing whether stock returns are related to expected trading costs.For our purposes, the best estimate of a stocks expected turnover is the averageturnover over the available sample period as opposed to a purely historicalmeasure. Furthermore, it does not appear that our estimate of expected turnoveris driving the results in Table 7. In a regression of stock returns on beta, marketvalue of equity, book-to-market, effective spread, and the estimate of expectedturnover, we find that the coefficient on expected turnover is insignificantlydifferent from zero (p-value of 0.53). Thus, while it is possible that stock returnsare related to future turnover, it is unlikely that the results of Table 7 are drivenby this relation. This is not the case when estimating asset pricing factors such assize, book-to-market, P/E ratio, and spread which are explicit functions of stockprice, and thus, directly related to future stock returns.

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