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The seasonal behavior of the liquidity premium in asset pricing
.lournal of Financial lkooomics 34 (1993) 373~3%.
asonal behavior m in asset prici t R. Eleswarapu huhan Institute of Management. Bangaore. India
Marc R. Reinganum University of Iowa, ima City, IA 52242, USA Received October 1992, fina! version recz.ved February 1993
This paper empirically investigates the seasonal behavior of the liquidity premium in asset pricing The evidence suggests a strong seasonal component. In the 1961-1990 period, the liquidity premium is reliably positive only during the month of January. For the non-January months, c le cannot detect a positive liquidity premium. The impact of the relative bid-ask spreads on asset pricing in nonJanuary months cannot be reliably distinguished from zero. In contrast to An&d and Mendelson (1986), howclver, our evidence sugges,s that the size effect is signi&ant, even after controlling for spreads. Key words: Bid-ask spreads; Asset pncing tiasonality;
Liquidity premium
1 htmduetion 1)
An imp Jrtant link between asset pricing and market microstructure is developed by Amihud and Mendelson (1986). In their model, rational investors price securities in such a Yriaythat the expected return is higher (firm value is lower) for stocks with larger bid-ask qreads.’ Amihud and Mendelson Grrespondence fo: Marc R. Reinganum, Qepartment of Finance/CB& University of Iowa, 565 Philhps Hall, Iowa City, IA, 52242, USA. *We wish to thank Paul Fellows, Narayana Kocherlakota, Paul Schultz, Richa.i-d Stevenson, Susan Watts, Bill Schwert (the editor), and Eugene F. Fanma(the referee) for their hsipful comments and suggestions. We would like to thank Hans Stoll ancl Robert Whalev for providing us with their spread data. We gratefully acknowledge the secretarial support of __._,a Herring and finan&_: support from the Financial Markets Research Institutt: at the University of lowa. Any remaining errors are ours. ‘Numerous researchers have adclressecl thti issue of ‘how the market maker sets the spread and what determines the level of spreads. For example, see Demsetz (i 968%Ragehot (1971), Tinic ( f 9721, Tinic and West (1972), Benston and Hagerman (1974), Garman (1976), Stoll(1978), Amihud and Mendelson (1980), Ho and Stoll(198 I)* Copeland and Galai (1983), Glosten and Milgrom (i985), O’Hara and Oldfield (19 t Er&y and G’Hara (1987j,, and Glosten and Harris (1988). 0304-405X/93,306.
sevier Science Publishers B.V. All rights deserved
374
V I,?‘.Eleswarapu cAndM. R. Reinganwz. Seasona&* of liquidit v pwmiumz
Mj provide empirrcal sup c nmdei in tests using portfolios of New York Stock Exch;r*?ge(NYSE) stocks during the ?961-80 period. They find a positive association between annual portfolio returns and bid-ask spreads.2 The design of their empirical tests, however, does not per& the explortition of potential monthly seasonality in the relation between expected returns and bid-ask spreads. The purpose of this paper is twofold: 1, to investigate the relation bs-:.tween average returns and bid-ask spreads in January and in non-January months, and 2) to determine if A&M’s empirical resufts are sensitive to ,heir restrictive portfolio selection criteria. Previous research documsnts January effects [e.g., Rozeff and Kinney (1976), Meim (1983), Reinganum ( 1983j, and Roll (198311.Tinic and West (1984, 1986) find that beta risk in the capital asset pricing model is priced only in the month of January. Chang and Pinegar (1988) report that the market return is reliably greater than the return on one-month Treasury bills only during January. This paper explores whether such seasonality also characterizes the behavior of liquidity premiums. In addition, this paper explores whether the restrictive portfolio selection technique of Amihud and Mendelson could lead to spurious empirical conclusions. The paper is organized as follows. Section 2 describes the data (which are updated through 1990) and t?ileportfolio formation method. Section 3 presents the empirical results, which suggest a strong January component in liquidity premiums. However, unlike Amihud and IVIendelson (1986), the results also suggest a significant size effect, even after accounting for the liquidity premium. The final section offers some conclusions.
2. Data and iuitial portfolio formation technique The cross-sectional relation between monthly returns, betas, and the relative bid-ask spread is tested over the 1961-98 period using NYSE firms. Monthly NYSE stock returns are obtained from tapes provided by the Center for Research in Security Prices. The relative spread of a stock is the callar t&-ask spread divided by the average of the bid and ask grices. As in A&G/J,the average spread for stock i in year n, Sin, is the average of the br;ginning and end-of-year relative spreads in the preceding year n - 1. For 1960-79, the relative spread data are those used in Stoll and Whaley (1983);3 ,Fbr;;lle 1980-89 period, the year-end spread data are obtained from Fitch Investors Service, Inc. h 2There is some disagreement about the existence of this liquidity premium. ConstivnGnides (1986), in an inte:temporal portColio selection model, show tlzat transactions costs should have only very small effects on the expected returns. Empiricaliy, Reinganum (1990) concluder that t%eNASDAQ provides better liquidity than the NYSE for small stocks using the A&M model, although Loughran (1992), 91Jec.!ons . t’ the magnitude of this effect. 3Stoll and Whaley kindly provided us with these data.
V.R. Elewarapu and M R. Reinganm, Seasonalityof liquiditypremium
375
The return-spread relation is initially tested using 49 equally-weighted portfolios formed using the criteria of A&M. Stocks are olaced inta portfolios based L on their spread and estimated beta. The exact fcmaticc r;ro&ure requires eleven years of complete return data for a stock. In an iniGa1 6ve-year period, betas of individual stocks are estimated using market model regressions base on monthly rebams: Rjt =
ai +
Mnt
+
&it
9
t=1,...,60,
where Ri, and R,,,? are the month t excess returns (over the correspondhg one-month Treasury bill return) on stock i and on the rngz=k zt index, respectively [following Amihud and Mendelson (1986) and Fama and Macbeth (1973), the market index is the equally-weighted portfolio of all NYSE stocks]. Stocks are ranked and divided into seven equal groups based on their average spread, &, in the last year of the second five-year period (see paragraph below). Each of these seven groups is divided further into seven equal subgroups by ranking the stocks according to their estimated beta ‘coefficients. There are thus 49 test portfolios with approximately equal numbers of stocks. [Sorting by size and beta, instead of the spread and beta, yields similar results (available on request). The potential impact of portfolio formation techniques is nicely discussed by Jegadeesh (1992).] In the second five-year period, ihe betas of the 45 portfolios are estimated using the market model regression ;snd monthly portfolio returns. The average spread &,,) of a portfolio is computed by averaging the spreads of all the stocks in portfolio p in the last year of this five-year period. For example, for the test-period year 1961, the initial estimation period is 1951-55 and portfolio betas are estimated in the 1956-60 period. The spreads used in the test period would be from 1960. Thus, for each portfolio p (p = 1, . . . ,49) and each year n (n = 1, . . . ,30), there is an estimated beta, &,,, and an average spread, SPn. These estimated betas and average spreads are compared against excess portfolio returns during the following year. For a stock to be included in the analysis, it needs eleven years of return data and a relative spread in the last year of the second five-year period. This estimation and ranking procedure is repeated each year, resulting in 30 test-year periods (1961-90). The number of firms included in each test period ranges from 654 to 929. Table 1 presents descriptive statistics for the 49 portfolios formed on the basis of spreads and estimated betas using the A&M criteria. Each cell of the table contains the value of the variable averaged over the 30 periods. Average portfolio relative spreads range from 0.454% to 3.530%. The average portfolio betas range between 0.517 and 1.470.The average market value of equity in each of these portfolios is also presented. Average equity values, calculated each year by averaging the equity valuec across all the stocks in that portfolio at the end of
V.R. Eleswarapuand MR. Rebaganum,Seasonalrtyof liquiditypremiww
376
Table 1 relative bid-ask spread (in percent), betas, and rzarket va!ne clfequity (in millions of dollars) for the d9 portfolios of NYSE firms based 0~ , _ Aruihud and Mendelson (1986) sample selection criteria, requiring return data for ten years preceding each test year, 1961-90.
Averqe
The portfolios are formed each year preceding the test year by ranking the stocks into seven equal groups, based on their spread, and then dividing them into seven equal subgroups according to their estimated beta coefficients. The number of firms included in each test year ranges from 654 to 929. Each cell contains three entries. The top number is the relative bid-ask spread of the portfolio in percent. The purtfolio spread is Pe average spread of the stocks in the year preceding the test year. The second number is the portfolio txtsr, estimated over the five years preceding the test-period year. The bottom number is the market value oithe equity in millions of dollars, where the equity value of the firm is computed at the end of the year prt+ing the test year. Each entry is averaged over the 30 years of this study, 1961-90. Spread, [Beta), (Equity value) Beta group Spread group
Lowest
2
3
0.4541 [O.S57] (5167)
0.4536 [0.701] (7328)
0.4572 iO.760) (5730)
2
0.7077 [0.570] (1492)
0.7089 [0.?17] (1816)
0.7127 CO.8 191 (1713)
3
0.9030 co.5393 (1120)
0.9006
0.9029 co.7991 (984) 1.1044 CO.8451 (579) 1.3562 CO.85 13 (374) 1.7568 CO.8881 (204) 3.2513 [ 1.0353 (81) 1.3630 [0.857] (1381)
Lowest
4
5
6
f%i&
Mean
SF
CO.6773 (1044) 1.1@45 1.1036 [o.son] CO.6631 (607) (771) 1.3564 1.3470 [0.564-J [0.704-J (392) (456) 1.7407 1.7319 CO.5691 CO.7281 (215) (228) 2.9874 3.1041 L3.739-j LO.9353 (214) (91) 1.3220 1.3360 CO.5861 CO.7321 (1315) (1676) --
4
5
6
Highest
0.4681 0.4555 0.4638 0.4665 [0.806-J CO.8721 LO.9951 [1.104] (1470) (2879) (2811) (453) 0.7079 0.7090 0.7126 0.7110 CO.8861 CO.9361 [ 1.0303 [1,241] (1108) (1304) (662) (1402) 0.9003 0.9002 0.8994 0.9004 [0.908] [ 1.2291 CO.9761 [1.043] (1352) (757) (531) (622) 1.1040 co.9341 (526) 1.3517 CO.9691 (305) 1.7554 co.9733 (204) 3.2458 Cl.1351 (81) 1.3600 co.9451 (1118)
1.1027 1.1019 CO.9961 [ 1.088] (435) (448) fi-3537 1.1512 [1X3] [Cl433 (266) (317) 1.7541 1.7593 Cl.1023 Cl.1543 (133) (162) 3.4191 3.4209 F1.3313 [ 1.232) (60) (71) 1.3874 1.3864 [ 1.0223 [l.lOS] (859) (780)
1.1010 Cl.2531 (322) 1.3580 Cl.3211 (207) 1.7331 [ 1.325) (125) 3.5304 [ 1.4703 (55) 1.4057 [ 1.2771 (482)
Mean 0.4600
CO.8221 (4205) 0.7100 CO.8861 (1357) 0.9010 CO.8821 (916) 1.1032 [0.9&] (527) 1.3535 [0.941] (331) 1.7530 CO.9631 (181) 3.2799 [1.125] (93) 1.3660 CO.9321 (1087) -
the last year of the second five-year period, range between $55 million and $7.328 billion. Spreads, betas, and market value of equity are not independent. Low-spread stocks tend to be low-beta stocks, and vice versa. Spreads and market value of equity tend to be inversely related - the smaller the spread, the larger the firm value.
V.R. Eleswarapuand M.R. Reinganm, Seamnalir)?of liquiditypremiums
377
3. Empirlcsl results 3.1. A&M portfolio formation technique The test-period data comes from 1961-90, extending the original A&M sample by ten years. Data from the 1980s can be viewed as a validation period for the seasonJ effects investigated in this paper, since it roughly postdates the Keim (1983) evide ce on the January effect. What is the liquidity premium in January and i non-January months during the entire 1961-90 period? As a starting point, fig. 1 depicts the average January and non-January returns of the 49 NYSE portfolios classified by spread and beta. The graphs are dramatic. In January, as one moves from low-spread to high-spread securities, the average returns increase, which is consistent with a positive liquidity premium. On the other hand, the average non-January returns do not exhibit any such relation. The relation between average returns and spread appears virtually flat in the non-January months. The formal empirical tests bv Amihud and Mendelson (1986) are based on the pooled cross-section and time:series methodology. Chen and Kan (1989) raise concerns with this methodology; they argue that since it constrains the market
Fig. la. Average January returns. Average portfolio returns for the 49 portfolios of NYSE firms based on the Anrihud and Mendelson portfolio technique, requiring return data for ten years preceding each test ysar, 1961-90. The portfolios are formed each year preceding the test year by ranking the stocks into seven equal groups, based on their spread, and then dividing them into seven equal subgroups according to their estimated beta coeficients. The number of firms included in each test year ranges from 654 ice929. The portfolio return is the arithmetic average of the monthly returns on the stocks in the portfolio in excess of that month’s Treasury bill return.
378
V. R. Eleswarapu and M. R. Rhganum,
SeasngvmlityoJriiquidity premiums
Fig. lb. Average non-January returns. Average portfolio returns for the -%9 portfo!ios of ‘NYSE firms based on the Amihud and Mendelson portfolio technique, requn.+c A..0 return data for ten years preceding each test yea;. 1961-90. The portfolios are formed each year preceding the test year by ranking the stocks into, seven equal groups, based on their spread, and then dividing them into seven equal subgroups acccrding to their estimated beta coefficients. The number of firms included in each test year ranges from 654 to 929. The portfolio return is the arithmetic average of the monthly returns on the stocks in the portfolio in excess of that month’s Treasurv bill return.
risk premium to be constant over the SO-year period, it may induce a spurious spread effect. Chen and Kan recommend the use of cross-section regressions as in Fama and MacBeth (1973). Therefore, in this paper, only results from these monthly cross-section regressions are reported.4 The liquidity premiums estimated in a Fama--Macbeth fra. rework are presented in table 2. The returns of the 49 portfolios are regre: sed each month against beta, spread, and size. The time-series averages of the m nthiy regression coefficients are reported in table 2. When all months from the 1961-90 period are lumped together (panel A of table 2), the liquidity premium coefficient of the spread variable) is positive but less than two standard errs rs from zero in regressions that include beta. When only the January months are considered, however, the liquidity premium and beta-risk premium are &imated io ‘cw’: positive and reliably different from zero. Thus, in January both reta and spread seem to be priced. IIowever, size does not anpear to be priced ir, January in the 1. presence of spread and beta, By contrast, in the non-January months, the point estimates of the liquidity premium are negative, although within two standard errors of zero. In fact, none ‘For the sake of completeness, we also use the A&M pooled cross-section and t%e-series regression methodology (available on request). We look at their 1961-80 time period, the overall test period of 1961-90, and the subperiod 1981-90. We investigate possible seasonality in the liquidity premium using January dummies. We find that the liquidity premium is reliably positive only in the month of January.
Table 2 Estimates of coefficients for Fama-Macbeth type regressions of excess returns for the portfolios of NYSE firms based on Amihud and Mendelson (1986) sample selection criterk, requiring reun data for ten years preceding each test year. Standard errors in parentheses. (A):
R, = a0 + ad& + ep
0%
R, = bo + b&
(C):
R, = co + c&g -I- c&
+ @pc
(W:
&f = do + dl iog(Si3)
+ e,
(E):
R, = tfo + eJ.&, + e-S, + ejLog(Size) + e,
+ eFt
There is one obse+v _ .s t’:m for each month of a test-period year for WC%e.3’the 49 portfolios. As in Amihud and Mcndelson (1986), a stock is required to have eleven years of complete return data for inclusion in a portfolio. Excess return (R,,,) is the average excess return (over the corresponding orre-month Treasury bill return) for portfolio p in month t. The cross-sectional regression is fit in each month t of the test-period years. The coefficients are the time-series means with corresponding standard errors. Regression Variable
(A)
(B)
(C)
(D)
(E)
Panel A: Test period 1961-90 All months Beta
0.0063 (0.0032)
Spread
0.1424 (0.0741)
0.0053 (0.003 1)
0.0048 (0.0028)
0.0659 (0.0647)
0.0458 (0.0665)
Log (Size) - 0.0011
(0.0005) N
360
360
360
360
- 0.0003 (0.0005) 360
January Beta
0.0643 (0.0143) 2.306 (0.3540)
Spread
0.0374 (O.iH33j
0.0333 (0.0139)
1.8816 (0.3460)
1.617 (0.2400) - 0.0026 (0.002 1)
Log (Size) N
30
30
30
30
Non-January Beta
0.0024 (0.03 1)
0.0010 (0.0032) - 0.0542 (0.0642)
Spread
- 0.099 (0,055)
Log (Size) N
-----
330
33Q
330
.._
- 0.0026 (0.002!) 30
380
V.R. Eleswatapuand M. R. Reiriganum,Seasonalityofliquiditypremi?zFm Table 2 (mntinued)
--
--
_- Regression Variable
(A)
(W
(C)
(B)
(El
Panel B: Test period 1981-W
Beta
*
‘- 0.0045 (O.OOS3)
All months - 0.0050 (0.005 1)
- c.oo60
0.0017 (O.1063)
- 0.0524 (0.1157)
- 0.0366 (O.lW73
Spread
(0.0052)
0.0005
Log (Size)
(O,ooo8, N
120
120
1211)
120
- - 0.0003
(0.0007) 120
January Beta
0.0202 (im66) f.4233 (0.4696)
Spread
0.002 1 (O.!ml)
0.0020 (0.0194)
1.4250 (O.S!72)
1.5486 (0.3783) - 0.0077 (0.0033)
Log(Size) N
10
10
10
10
0.0014 (0.0035) 10
Non-Jahuary Beta
- 0.0067 (0.0055) - 0.1693 (0.1049)
Spread
- 0.0057 (0.0054)
- 0.0067 (0.0054)
- 0.1277 (0.0906]
- 0.1980 (“3.1121)
Log (Size) N
110
of the prem_ium estimates in ihe
110
110
0.0012 (0.0008)
- omO5 (OMIOS)
110
110
reliably diflerent from zero. Thus, using the A&M sample selection criteria, the liquidity premium appears to be reiiably positive only in the month of January during 1961-90. [Of course, the magnitude of the liquidity preinium in January months may be overstated; Keim (1989) documents that the observed January returns are biased upwards for stocks with high spreads due to the trading patterns at the end of the year.] Panel B of table 2 reports the results for the subperiod 1981-90, which post-da@ the original A&M sample period. In this subperiod, the liquidity premium is still positive’and more than two standard errors from zero in January. In regressions with beta, spread, and size, only spread appears to be statistically significant in January. The liquidity premium in non-January months is negative. Ann-January
n~~&s
FR
V.R. Eleswarapu and MR. Reingantm, Seasona/ity of liquidity pemiwns
381
Unlike the overall 1961-90 period, however, the point estimate of the liquidity premium in this subperiod is negative for all months combined. 3.2. Mod@ed portfolio ‘
formation technique
The stringent data requirements of the A&&I selection criteria raise the possibility that the results are an art&&a& ;rnnt of'a limited sample rather than the manifestation of a true effect. For example, in the &WI framazork, the size variable does not appear to matter, even in January: after coatrollrng for spread. Yet the requirement that there be eleven years of return data may systematically exclude smaller filrmsfrom the sample and: hence, bias the resu!ts against finding a size effect. The restrictive A&M criteria are not necessary to test the cross-set: .nal relation between returns and spreads, In this section, portfolios are formed using just three years of return data. (Similar results are obtained with portfolios requiring five years of prefomation data instead of three.) Assignment afa stock to a particular beta/spread portfolio in a given test year depends on two criteria* 1) the stock’s spread in the previous year and 2) the stock’s ordinary leastsquares beta estimated with 36 montils of preceding returns. Thus, only three years of preformation returns are needed for inclusion in the tests. Also, in contrast to the previous section, firms can be delisted in the middle of a test year, avoiding a potential survivorship bias. For the test period, stocks are again ranked into seven equal groups based on their spread in the previous year, as in A&M. They are further divided into seven equal subgroups by ranking the stocks according to their estimated beta coefficients, computed with the preceding ‘4 monthly returns. The average portfolio excess returns in the test year a r~ obtained by averaging the excess returns of the stocks in each of the 49 portfolios. This procedure is repeated in each of the 30 test-year periods, 1961-90. The portfolio formation technique dramatically increases the number of stocks included in the analysis. For example, the average number of firms in a year increases by 45 %, from 795 to b,I 53. The average market capitalization of a firm in the enlarged sample is 16% smaller than that of the restricted sample. In this analysis, the number of firms included in each test period ranges from 895 to 1,346 (versus a range of 654 to 929 for the restricted sample). Another change from the A&M framework is that unconditional g~rrfolio Betsy are used in the cross-sectional regressions. The unconditional portfolio betas are computed using the monthly portfolio returns during the test-period years. In other words, portfolio betab are computed with 360 months of portfolio return data (1961-90). Table 3 presents the descriptive statistics for the 49 pdolios form using the modified portfolio technique. In general, they have the same characteristics as those formed using the A&M portfolio formation techniqtte. However, the portfolios now have smaller-size Grms with larger average bid-ask spreads.
382
VA Eleswarapuand MR. Reinganum, Seasonality
of liquidity premiums
Table 3 Average relative bid-ask spread (in percent), betas, and market value of equity (in millions of dollars) tfolio formation technique, requiring for the 49 portfolios of NYSE firms based on modified test year, 1961-90. return data for three years preceding e king the stocks into seven equal The portfolios are formed each year preceding t ual subgroups according to their groups, based on their spread, and then dividing year ranges from 895 to 1,346. estimated beta coefficients.The mu asP .read of the portfolio in Each cell contains three entries. Th plea, Treceding the test year. percent. The portfolio spread is the a wrth c 41 months of portfolio return The second number is the estimated eqway in millions of dollars, where the data (1961-90).The bottom number i ece~o~,~the test year. Portfolio spread equity value of the firm is compute and market value of equity are averaged over the 30 yetrs ct this study, 1961-90. Spread, [Beta], (Equity value) Beta group Spread group Lowest
2
3
4
5
6
Highest
Mean
Lowest
2
3
5
6
Highest
Mean
0.5064
0.4904 CO.8171 (3705)
0.5066 0.4930 0.4973 l] CO.8063 CO.8451 CO.98 (1958) (2737) (2291)
[1.141] (1347)
0.7654 0.7651 CO.9581 Cl.0761 (9301) (946) 6.9749 8.976C 0.9714 0.9710 0.9738 [1.058] CO.69 l] CO.8473 CQ.9491 [0.979] (612) (869) (788) (574) (547) 1.2035 1.1983 1.1962 1.1994 1.1986 [l.llO] CO.9381 [l.OlOl co.7513 [0.853] $39) (394) (411) (36 (465) 1.4783 1.4767 1.483; 1.4832 1.4832 co.7411 CO.8981 P.~l [ 1.0871 Cl.1433 (351) (233) (226) (197) (283) 1.92OC 1.9298 1.9288 1.9401 1.9296 [0.833-j [0.954] [1.188] [ 1.2391 rt.o60] - (146) (179) (119) (172) (133) 3.5985 3.3452 3.5429 3.6285 3.7800 Cl.0321 Cl.1831 [1.204-J [ 1.3671 [ 1.437) (99) (74) (54) (54) (64) 1.4490 1.4812 1.4939 1.4932 1.5212 CO.7781 CO.8941 co.9743 [ 1.0621 Cl.1493 (1619) (1101) (657) (765) (594)
0.7663 [ 1.2481 (674) 0 9z.W [ 1:234] (387) 1.2017 Cl.3103 (262) 1.4906 Cl.3811 (161) 1.9627 [1.407] (118) 3.9154 [r,ssl] (53) 1.5462 Cl.3241 (429)
0.4814 IO.5353 (5785)
0.4781 0.4700 CO.6831 co.7311 (4739) (7081)
0.7621 [0.561] (1062) 0.9733 co.5773 (673) 1.2015 CO.565 ] (459)
0.7605 co.7131 (2345)
1.4880 co.5951 (267) 1.9184 co.5941 (130) 3.5117 [0.818-J 1(3W 1.4770 [0.607] (1240)
4
0.7617 [0.790-J (1189)
0.7602 CO.85 13 (1169)
0.7631 [0.885] (1188) 0.9?44 [0.905] $36) 1 1999 [Cr.9341 (388) 1.4834 co.9793 (245) 1.9328
Cl*0403 (142) 3.6175 [ 1.227) (100) 1.4950 [0.970] (915)
The cross-sectional regression is fit in each aaronth of the test-period years using three independent variables: 1) unconditional portfolio betas, 2) average spread, and 3) size. The estimates of these ( -Macbeth) coefficients and standard errors are reported in table 4. The toe ts are the time-series means with corresponding standard errors.
W?. Eleswarapu and M. R Reinganum, Seasonality of liquidity premiums
383
Table 4 Estimates of Fama-Macbeth coefficients obtained with unconditional betas and modified portfolio formation technique, requiring return data for three years preceding each test year. Standard errors in parentheses. (A): (B):
R, = a0 + a~& + ept R, = b0 + b,S, + ept
(C):
R, = co + Cl&M+
0%:
R, = do + &Log(Size)
(E):
R, = e. + e,S,, + e2Spr + e3 Log (Size) -+ epl
c2
Sp? +ept + ep
Assignment of a stock to a particular beta/spread portfolio in a given test year depends on two criteria: (1) the spread in the previous year and (2) a stock’s OLS beta estimated with 36 months of preceding returns. In the cross-sectional regression, the portfoiio beta is the unconditional beta; that is, the beta is computed using the monthly portfolio returns from all of the test-period years. The cross-sectional regression is fit in each month t of the test-peeod years. The coefficients are the time-series means with corresponding standard errors. -
Regression Variable
(A)
(B)
(C)
(D)
(E)
Panel A: Test period i961-90 All months Beta
0.0024 (0.0035) 0.1339 (0.0689)
Spread
- 0.0012 (0.0036)
- 0.0001 (0.0035) 0.1477 (0.0636)
0.0875 (0.0626)
Log (Size) - 0.0011 N
360
360
360
(O-000@ 360
- 0.0008 (O.Ooos) 360
January Beta
0.0642 (0.0161) 2.0964 (0.3415)
Spread
0.0319 (0.0149)
0.0247 (0.0151)
i .7023 (0.3477)
1.3072 (0.28 14) - 0.0158 (0.0032)
Log (Size) 30
N
30
30
30
- 0.050 (0.0020) 30
Non-January - 0.0032 (0.0034)
Beta
- 0.0445 (0.0596)
Spread
- 0.0029 (0.0035)
- 0.0036 (0.0036)
0.0063 (0.0557)
- 0.0234 (0.0599) o.WO3 (0.0005)
Log (Size) N _.-_.-
-
330
330
330
330
- 0.0004 (0.W) 330
384
V. R. Eleswarapu and M. R. Reinganum, Seasonality of L#iity
premiums
Table 4 (continued) Regression Vqri?51e --
(A)
(B)
D)
C)
--.
_--
(E)
-
Panel B: Test period 1981-90 AfI months - 0.0075 (0.005 51 - 0.0914 (0.097 1)
Spread
- 0.0759 (0.0916)
ti.0375 (0.0918) 0.0 08 (OSM07)
Log (Size) lv
- O.Q’I78 (O.GOSS:,
-- 9.CO68 (CLASS)
120
120
120
121
- 0.0003 (O.rn) t20
January
B&a
1.1940 (0.4165)
Spread
1.1903 (0.4654)
Log, Size) N
- wOO3 (e.0238)
0.0019 (0.023 1)
0.0125 (0.02 14)
1.0584 (0.42 18) - 0.0071 (0.0030)
10
10
10
10
- 0.0014 (0.0027) 10
Non-January
Beta
- 0.0094 (0.0057) - 0.2085 (0.092 1)
Spread
- 0.0075 (0.0056)
- 0.0085 (@.Om)
- 0.1491 (0.082 3)
- 9.1790 (0.@865)
Log (Si2 2) IJ
110
110
110
0.0016 (0.0007)
- 0.0002 (O.OOOw
110
110
Pane1 A of table 4 shows the results for the 1961-90 period. Overall, the basic result that the liquidity premium is present only in January still appears to hold. However, the size eflrectis now very much present. In fact, over all the months taken together, size is the only variable which appears to be significant in the presence of the other two variables. This conclusion differs from the inferences drawn based on the restricted A&M sample. With the enlarged sample, the evidence for a positive beta-risk premium is diminished and perhaps nonexistent. The beta-risk premium is not significant in the presence of spread and size, ever in January. (Using Dimson’s aggregatedcoefficiems betas with one monthly 1td.d and one monthly lag yields the same result.) Th,2se results on he pricing of beta risk seem consistent with Fama and French (1992). Apparently, requiring only three years of data mstead of eleven
CIR. Eleswarapu and M. R. Reinganm. Seasma/@ qf liquidiry premiums
385
years makes a difference for inferences about the pricing ti! beta risk as well. The pricing of beta nsk may also be &ected by the relaxing t>fth? requirement that firms survive for the whole test-period year following the portfolio formation. Panel B of table 4 shows the results for the subperiod l%I-90. The point estimates of the liquidity premium are ncgctive for all t& months combined. In non-January months, the liquidity pne.miumis negative and about two standard errors below zero In January, ti=o@~, the liquidity premium is still reliably positive. Thus, the predictions of t&e .A&M model are confirmed for January but not for the non-January months. Of course, in the non-January m<.n*hsfor the overall period 1961-90, none of the variables seem to be reliably 2; iceal.
4. Summary and conclusions
This paper empirically investigates the season21 b&~&r of the liquidity premium as modeled by Amihud and Mendelson (1986). The evidence suggests a strong seasonal component. In the 1961-90 period, the liquidity premium is reliably positive only during the month of January. For the non-January months, one cannot detect a positive liquidity premium. That is, the impact of the relative bid-ask spread on asset priciug in non-January months cannot be reliably distinguished from zero. Unlike the original A&M study, the evidence in this paper suggests a significant size effect even after controlling for spreads and beta. The restrictive sampie selection criteria of A&M tend to systematically exclude smaller fims and hence bias the results against finding a size effect. By modifying the portfolio formation technique, the number of firms included in the analysis increases by 45%. The evidence reveals a positive relation between bid-ask spreads and average returns, but only during the month of January. The lack of such a positive relation between spreads and average returns outside of January may well be part of a broader puzzle. Tinic and West (1984) report that beta risk is reliably priced only during January. The broader issue may well be why the empirical representations of asset pricing models work well only in January* Apart from January, the empirical support for asset pricing mo&ls seems tenuous at best, as documented by the evidence in this paper for the model of A&M (1986). While liquidity may very well be a determinant of asset pricing, the reason that its effect on asset pricing seems limited to January is not clear.
References Amihud, Yakov and Haim M ndelson, 1980, Dealership market: Market-making with inventory, Journal of Financial Economics 8, 31 -53. Amihud, Yakov and Haim Mendelson, 1986, Asset pricing and the bid-ask spread, Journal of Financial Economics 17, 223-249. Bagehot, Walter, 1971, The only game in town, Financial Analysts Journal, March-April, 12-14.
386
V. R. Eleswarapuand M. R. Reinganum, Seasonniityof iiquidilypremiums
Benston, George J. and Robert il. HagermaG, 1974, Peterminants of the bid-ask spi-eads m t!x over-the-counter market, Journal of Financial Economics 1. 353-364. Chang, Eric C. an f Michael J. Pinegar, 1988, A fuudamental study oi the seasonal risk-return relationship: A note, Journal of Fmance 43, 10351039. Chen, Nai-fu and Raymond Kan, 1989, Expected return and the bid-ask spre&d, Working paper (University of Chicago, Chicago, IL). Constantinides, George, 1986, Capita! market equrlibrium with transaction costs, Journal of Poiiticat Economy 94,842-862. Copeland, Thomas E. and Dan Galai, 1983,Information effects on the bid-ask spread, Journal of
Finance 38, 1457-1469. Demsetz, Harold, 1968, The cost of transacting, Quarterly Journal of Economics 82,33-53. Dimson, Elroy, 1979, Risk measurement when shares are subject to infrequent trading, Journal of Financial Economics 7, 197-226. EasIey, David and Maureen Q’Hara, 1987, Price, trade size, and information in securities markets, Journal of Financial Ecc-comics 19, 69-90. Fama, Eugene F. and Kenneth French. 1992, Cross-section of expected stock returns, Journal of Finance 47.429-465. Fama, Eugene F. and James D. Macbeth, 1973, Risk, return, and equilibrium: Empirical tests, Journal of Po!itical Economy 71, 607-636. Garman, Mark B., 9976, Market microstructure, Journal of Financial Economics 3,257-275. Gioste&a, Lawrence R. and Lawrence E. Harris, 1988, Estimating the components of the bid/ask spread, Journal of Financial Economics 21, 123-142. Glosten, -Lawrence R. and Paul R. Milgrom, 1985, Bid, ask and transaction prices in a specialist market with heterogeneously informed traders, Journal of Financial Economics 14, 71-100. Ho, Thomas and Hans R. Stall, 13’21, ??;:>.& dealer pricing under transpctions and return uncertainty, Journal of Financial Economics 9,47-73. Jegadeesh, Narasimhan, 1992, Does market risk really explain the size &ect?, Journal ot Financial and Qualltitative Analysis 27, 337-351. Keim, Don&id B., l983, Size related ::n~*tl?&cs and stock return seasonality: Further empirical evidence, Journal of Financial Economics 12, 13-32. Keim, Donald B., 1989, Trading patterns, bid-ask spreads and estimated scurity returns: The case of common stocks at calender turnin;; points, Journal of Financial Economics 25, 75-97. Loughran, Tim, 1993, NYSE vs. NASDAQ returns: Market microstructure or the poor performance of initial public offerings?, jGurna1 of Financial EsfJEcmics 33, 241-260. Ci’Hara, Maureen and Geohge Qldficid, 1986. The iuicro economics of market making, Journal of Financial and Quantitative Analysis 21, 3831-37‘6. Reinganum, Marc R., 1983, The anomaious stock market behavior of small firms in January: Jmwnal 12, 89-~Q4 f nr tau-iclss &i?ig, Empirical . .I”.” +PC+c L1. - 1-_-m_. nf v. *Gnaw-;-j r.u.drr‘U Econs;nics Reinganum, Marc R.: 1990,Market microstructure and asset pricing: An empirical investigation of NYSE and NASDAQ securilies, Journai of Financial Economics 28, 127-147. Roll, Richard, 1983, Vas ist das? The turn of the year e&ct and the return: premium of smail firms, Journal of Portfolio Management 9, 18-28. Rozeff, Michael S. and William R. Kinney, Jr., 1976, Capital market seastsnaiity. T:ae ceaseof stock returns. Jou~na! of Financial Economics 3, 379-402. Str~i?,Hans R., l978, T’hc pricing of security dealer services: A.n empirical stud! oCNASDAQ stocks, ~oussisl cf Finance 33, 1153-1172. St01l. Ham and Robert Whaley, 9983, ‘L’ransaction costs and the small firm effect, Journal of Financial Economics 12, 57-80. Tinic, Sehz M., 1972, The economics of liquidity services, Quarterly Journal of Economics 86,79-93. Tinic, Seha M. and Richard R. West, 1972, Competition and the pricing of dealer service in the over-the-counter stock market, Journal of Financial and Quantitative Analysis 7, 1707-1727. Tinic, Seha M. and Richard R. West, 1984, Risk 2nd return: January vs. the rest of the year, Journal of Financial Economics 13, 561-574. Tinic, Seha M. and Richard R. West, 1986, Risk, return and equilibrium: A revisit, Journal of Political Economy 94, 126- 147. l
asonal behavior m in asset prici t R. Eleswarapu huhan Institute of Management. Bangaore. India
Marc R. Reinganum University of Iowa, ima City, IA 52242, USA Received October 1992, fina! version recz.ved February 1993
This paper empirically investigates the seasonal behavior of the liquidity premium in asset pricing The evidence suggests a strong seasonal component. In the 1961-1990 period, the liquidity premium is reliably positive only during the month of January. For the non-January months, c le cannot detect a positive liquidity premium. The impact of the relative bid-ask spreads on asset pricing in nonJanuary months cannot be reliably distinguished from zero. In contrast to An&d and Mendelson (1986), howclver, our evidence sugges,s that the size effect is signi&ant, even after controlling for spreads. Key words: Bid-ask spreads; Asset pncing tiasonality;
Liquidity premium
1 htmduetion 1)
An imp Jrtant link between asset pricing and market microstructure is developed by Amihud and Mendelson (1986). In their model, rational investors price securities in such a Yriaythat the expected return is higher (firm value is lower) for stocks with larger bid-ask qreads.’ Amihud and Mendelson Grrespondence fo: Marc R. Reinganum, Qepartment of Finance/CB& University of Iowa, 565 Philhps Hall, Iowa City, IA, 52242, USA. *We wish to thank Paul Fellows, Narayana Kocherlakota, Paul Schultz, Richa.i-d Stevenson, Susan Watts, Bill Schwert (the editor), and Eugene F. Fanma(the referee) for their hsipful comments and suggestions. We would like to thank Hans Stoll ancl Robert Whalev for providing us with their spread data. We gratefully acknowledge the secretarial support of __._,a Herring and finan&_: support from the Financial Markets Research Institutt: at the University of lowa. Any remaining errors are ours. ‘Numerous researchers have adclressecl thti issue of ‘how the market maker sets the spread and what determines the level of spreads. For example, see Demsetz (i 968%Ragehot (1971), Tinic ( f 9721, Tinic and West (1972), Benston and Hagerman (1974), Garman (1976), Stoll(1978), Amihud and Mendelson (1980), Ho and Stoll(198 I)* Copeland and Galai (1983), Glosten and Milgrom (i985), O’Hara and Oldfield (19 t Er&y and G’Hara (1987j,, and Glosten and Harris (1988). 0304-405X/93,306.
sevier Science Publishers B.V. All rights deserved
374
V I,?‘.Eleswarapu cAndM. R. Reinganwz. Seasona&* of liquidit v pwmiumz
Mj provide empirrcal sup c nmdei in tests using portfolios of New York Stock Exch;r*?ge(NYSE) stocks during the ?961-80 period. They find a positive association between annual portfolio returns and bid-ask spreads.2 The design of their empirical tests, however, does not per& the explortition of potential monthly seasonality in the relation between expected returns and bid-ask spreads. The purpose of this paper is twofold: 1, to investigate the relation bs-:.tween average returns and bid-ask spreads in January and in non-January months, and 2) to determine if A&M’s empirical resufts are sensitive to ,heir restrictive portfolio selection criteria. Previous research documsnts January effects [e.g., Rozeff and Kinney (1976), Meim (1983), Reinganum ( 1983j, and Roll (198311.Tinic and West (1984, 1986) find that beta risk in the capital asset pricing model is priced only in the month of January. Chang and Pinegar (1988) report that the market return is reliably greater than the return on one-month Treasury bills only during January. This paper explores whether such seasonality also characterizes the behavior of liquidity premiums. In addition, this paper explores whether the restrictive portfolio selection technique of Amihud and Mendelson could lead to spurious empirical conclusions. The paper is organized as follows. Section 2 describes the data (which are updated through 1990) and t?ileportfolio formation method. Section 3 presents the empirical results, which suggest a strong January component in liquidity premiums. However, unlike Amihud and IVIendelson (1986), the results also suggest a significant size effect, even after accounting for the liquidity premium. The final section offers some conclusions.
2. Data and iuitial portfolio formation technique The cross-sectional relation between monthly returns, betas, and the relative bid-ask spread is tested over the 1961-98 period using NYSE firms. Monthly NYSE stock returns are obtained from tapes provided by the Center for Research in Security Prices. The relative spread of a stock is the callar t&-ask spread divided by the average of the bid and ask grices. As in A&G/J,the average spread for stock i in year n, Sin, is the average of the br;ginning and end-of-year relative spreads in the preceding year n - 1. For 1960-79, the relative spread data are those used in Stoll and Whaley (1983);3 ,Fbr;;lle 1980-89 period, the year-end spread data are obtained from Fitch Investors Service, Inc. h 2There is some disagreement about the existence of this liquidity premium. ConstivnGnides (1986), in an inte:temporal portColio selection model, show tlzat transactions costs should have only very small effects on the expected returns. Empiricaliy, Reinganum (1990) concluder that t%eNASDAQ provides better liquidity than the NYSE for small stocks using the A&M model, although Loughran (1992), 91Jec.!ons . t’ the magnitude of this effect. 3Stoll and Whaley kindly provided us with these data.
V.R. Elewarapu and M R. Reinganm, Seasonalityof liquiditypremium
375
The return-spread relation is initially tested using 49 equally-weighted portfolios formed using the criteria of A&M. Stocks are olaced inta portfolios based L on their spread and estimated beta. The exact fcmaticc r;ro&ure requires eleven years of complete return data for a stock. In an iniGa1 6ve-year period, betas of individual stocks are estimated using market model regressions base on monthly rebams: Rjt =
ai +
Mnt
+
&it
9
t=1,...,60,
where Ri, and R,,,? are the month t excess returns (over the correspondhg one-month Treasury bill return) on stock i and on the rngz=k zt index, respectively [following Amihud and Mendelson (1986) and Fama and Macbeth (1973), the market index is the equally-weighted portfolio of all NYSE stocks]. Stocks are ranked and divided into seven equal groups based on their average spread, &, in the last year of the second five-year period (see paragraph below). Each of these seven groups is divided further into seven equal subgroups by ranking the stocks according to their estimated beta ‘coefficients. There are thus 49 test portfolios with approximately equal numbers of stocks. [Sorting by size and beta, instead of the spread and beta, yields similar results (available on request). The potential impact of portfolio formation techniques is nicely discussed by Jegadeesh (1992).] In the second five-year period, ihe betas of the 45 portfolios are estimated using the market model regression ;snd monthly portfolio returns. The average spread &,,) of a portfolio is computed by averaging the spreads of all the stocks in portfolio p in the last year of this five-year period. For example, for the test-period year 1961, the initial estimation period is 1951-55 and portfolio betas are estimated in the 1956-60 period. The spreads used in the test period would be from 1960. Thus, for each portfolio p (p = 1, . . . ,49) and each year n (n = 1, . . . ,30), there is an estimated beta, &,,, and an average spread, SPn. These estimated betas and average spreads are compared against excess portfolio returns during the following year. For a stock to be included in the analysis, it needs eleven years of return data and a relative spread in the last year of the second five-year period. This estimation and ranking procedure is repeated each year, resulting in 30 test-year periods (1961-90). The number of firms included in each test period ranges from 654 to 929. Table 1 presents descriptive statistics for the 49 portfolios formed on the basis of spreads and estimated betas using the A&M criteria. Each cell of the table contains the value of the variable averaged over the 30 periods. Average portfolio relative spreads range from 0.454% to 3.530%. The average portfolio betas range between 0.517 and 1.470.The average market value of equity in each of these portfolios is also presented. Average equity values, calculated each year by averaging the equity valuec across all the stocks in that portfolio at the end of
V.R. Eleswarapuand MR. Rebaganum,Seasonalrtyof liquiditypremiww
376
Table 1 relative bid-ask spread (in percent), betas, and rzarket va!ne clfequity (in millions of dollars) for the d9 portfolios of NYSE firms based 0~ , _ Aruihud and Mendelson (1986) sample selection criteria, requiring return data for ten years preceding each test year, 1961-90.
Averqe
The portfolios are formed each year preceding the test year by ranking the stocks into seven equal groups, based on their spread, and then dividing them into seven equal subgroups according to their estimated beta coefficients. The number of firms included in each test year ranges from 654 to 929. Each cell contains three entries. The top number is the relative bid-ask spread of the portfolio in percent. The purtfolio spread is Pe average spread of the stocks in the year preceding the test year. The second number is the portfolio txtsr, estimated over the five years preceding the test-period year. The bottom number is the market value oithe equity in millions of dollars, where the equity value of the firm is computed at the end of the year prt+ing the test year. Each entry is averaged over the 30 years of this study, 1961-90. Spread, [Beta), (Equity value) Beta group Spread group
Lowest
2
3
0.4541 [O.S57] (5167)
0.4536 [0.701] (7328)
0.4572 iO.760) (5730)
2
0.7077 [0.570] (1492)
0.7089 [0.?17] (1816)
0.7127 CO.8 191 (1713)
3
0.9030 co.5393 (1120)
0.9006
0.9029 co.7991 (984) 1.1044 CO.8451 (579) 1.3562 CO.85 13 (374) 1.7568 CO.8881 (204) 3.2513 [ 1.0353 (81) 1.3630 [0.857] (1381)
Lowest
4
5
6
f%i&
Mean
SF
CO.6773 (1044) 1.1@45 1.1036 [o.son] CO.6631 (607) (771) 1.3564 1.3470 [0.564-J [0.704-J (392) (456) 1.7407 1.7319 CO.5691 CO.7281 (215) (228) 2.9874 3.1041 L3.739-j LO.9353 (214) (91) 1.3220 1.3360 CO.5861 CO.7321 (1315) (1676) --
4
5
6
Highest
0.4681 0.4555 0.4638 0.4665 [0.806-J CO.8721 LO.9951 [1.104] (1470) (2879) (2811) (453) 0.7079 0.7090 0.7126 0.7110 CO.8861 CO.9361 [ 1.0303 [1,241] (1108) (1304) (662) (1402) 0.9003 0.9002 0.8994 0.9004 [0.908] [ 1.2291 CO.9761 [1.043] (1352) (757) (531) (622) 1.1040 co.9341 (526) 1.3517 CO.9691 (305) 1.7554 co.9733 (204) 3.2458 Cl.1351 (81) 1.3600 co.9451 (1118)
1.1027 1.1019 CO.9961 [ 1.088] (435) (448) fi-3537 1.1512 [1X3] [Cl433 (266) (317) 1.7541 1.7593 Cl.1023 Cl.1543 (133) (162) 3.4191 3.4209 F1.3313 [ 1.232) (60) (71) 1.3874 1.3864 [ 1.0223 [l.lOS] (859) (780)
1.1010 Cl.2531 (322) 1.3580 Cl.3211 (207) 1.7331 [ 1.325) (125) 3.5304 [ 1.4703 (55) 1.4057 [ 1.2771 (482)
Mean 0.4600
CO.8221 (4205) 0.7100 CO.8861 (1357) 0.9010 CO.8821 (916) 1.1032 [0.9&] (527) 1.3535 [0.941] (331) 1.7530 CO.9631 (181) 3.2799 [1.125] (93) 1.3660 CO.9321 (1087) -
the last year of the second five-year period, range between $55 million and $7.328 billion. Spreads, betas, and market value of equity are not independent. Low-spread stocks tend to be low-beta stocks, and vice versa. Spreads and market value of equity tend to be inversely related - the smaller the spread, the larger the firm value.
V.R. Eleswarapuand M.R. Reinganm, Seamnalir)?of liquiditypremiums
377
3. Empirlcsl results 3.1. A&M portfolio formation technique The test-period data comes from 1961-90, extending the original A&M sample by ten years. Data from the 1980s can be viewed as a validation period for the seasonJ effects investigated in this paper, since it roughly postdates the Keim (1983) evide ce on the January effect. What is the liquidity premium in January and i non-January months during the entire 1961-90 period? As a starting point, fig. 1 depicts the average January and non-January returns of the 49 NYSE portfolios classified by spread and beta. The graphs are dramatic. In January, as one moves from low-spread to high-spread securities, the average returns increase, which is consistent with a positive liquidity premium. On the other hand, the average non-January returns do not exhibit any such relation. The relation between average returns and spread appears virtually flat in the non-January months. The formal empirical tests bv Amihud and Mendelson (1986) are based on the pooled cross-section and time:series methodology. Chen and Kan (1989) raise concerns with this methodology; they argue that since it constrains the market
Fig. la. Average January returns. Average portfolio returns for the 49 portfolios of NYSE firms based on the Anrihud and Mendelson portfolio technique, requiring return data for ten years preceding each test ysar, 1961-90. The portfolios are formed each year preceding the test year by ranking the stocks into seven equal groups, based on their spread, and then dividing them into seven equal subgroups according to their estimated beta coeficients. The number of firms included in each test year ranges from 654 ice929. The portfolio return is the arithmetic average of the monthly returns on the stocks in the portfolio in excess of that month’s Treasury bill return.
378
V. R. Eleswarapu and M. R. Rhganum,
SeasngvmlityoJriiquidity premiums
Fig. lb. Average non-January returns. Average portfolio returns for the -%9 portfo!ios of ‘NYSE firms based on the Amihud and Mendelson portfolio technique, requn.+c A..0 return data for ten years preceding each test yea;. 1961-90. The portfolios are formed each year preceding the test year by ranking the stocks into, seven equal groups, based on their spread, and then dividing them into seven equal subgroups acccrding to their estimated beta coefficients. The number of firms included in each test year ranges from 654 to 929. The portfolio return is the arithmetic average of the monthly returns on the stocks in the portfolio in excess of that month’s Treasurv bill return.
risk premium to be constant over the SO-year period, it may induce a spurious spread effect. Chen and Kan recommend the use of cross-section regressions as in Fama and MacBeth (1973). Therefore, in this paper, only results from these monthly cross-section regressions are reported.4 The liquidity premiums estimated in a Fama--Macbeth fra. rework are presented in table 2. The returns of the 49 portfolios are regre: sed each month against beta, spread, and size. The time-series averages of the m nthiy regression coefficients are reported in table 2. When all months from the 1961-90 period are lumped together (panel A of table 2), the liquidity premium coefficient of the spread variable) is positive but less than two standard errs rs from zero in regressions that include beta. When only the January months are considered, however, the liquidity premium and beta-risk premium are &imated io ‘cw’: positive and reliably different from zero. Thus, in January both reta and spread seem to be priced. IIowever, size does not anpear to be priced ir, January in the 1. presence of spread and beta, By contrast, in the non-January months, the point estimates of the liquidity premium are negative, although within two standard errors of zero. In fact, none ‘For the sake of completeness, we also use the A&M pooled cross-section and t%e-series regression methodology (available on request). We look at their 1961-80 time period, the overall test period of 1961-90, and the subperiod 1981-90. We investigate possible seasonality in the liquidity premium using January dummies. We find that the liquidity premium is reliably positive only in the month of January.
Table 2 Estimates of coefficients for Fama-Macbeth type regressions of excess returns for the portfolios of NYSE firms based on Amihud and Mendelson (1986) sample selection criterk, requiring reun data for ten years preceding each test year. Standard errors in parentheses. (A):
R, = a0 + ad& + ep
0%
R, = bo + b&
(C):
R, = co + c&g -I- c&
+ @pc
(W:
&f = do + dl iog(Si3)
+ e,
(E):
R, = tfo + eJ.&, + e-S, + ejLog(Size) + e,
+ eFt
There is one obse+v _ .s t’:m for each month of a test-period year for WC%e.3’the 49 portfolios. As in Amihud and Mcndelson (1986), a stock is required to have eleven years of complete return data for inclusion in a portfolio. Excess return (R,,,) is the average excess return (over the corresponding orre-month Treasury bill return) for portfolio p in month t. The cross-sectional regression is fit in each month t of the test-period years. The coefficients are the time-series means with corresponding standard errors. Regression Variable
(A)
(B)
(C)
(D)
(E)
Panel A: Test period 1961-90 All months Beta
0.0063 (0.0032)
Spread
0.1424 (0.0741)
0.0053 (0.003 1)
0.0048 (0.0028)
0.0659 (0.0647)
0.0458 (0.0665)
Log (Size) - 0.0011
(0.0005) N
360
360
360
360
- 0.0003 (0.0005) 360
January Beta
0.0643 (0.0143) 2.306 (0.3540)
Spread
0.0374 (O.iH33j
0.0333 (0.0139)
1.8816 (0.3460)
1.617 (0.2400) - 0.0026 (0.002 1)
Log (Size) N
30
30
30
30
Non-January Beta
0.0024 (0.03 1)
0.0010 (0.0032) - 0.0542 (0.0642)
Spread
- 0.099 (0,055)
Log (Size) N
-----
330
33Q
330
.._
- 0.0026 (0.002!) 30
380
V.R. Eleswatapuand M. R. Reiriganum,Seasonalityofliquiditypremi?zFm Table 2 (mntinued)
--
--
_- Regression Variable
(A)
(W
(C)
(B)
(El
Panel B: Test period 1981-W
Beta
*
‘- 0.0045 (O.OOS3)
All months - 0.0050 (0.005 1)
- c.oo60
0.0017 (O.1063)
- 0.0524 (0.1157)
- 0.0366 (O.lW73
Spread
(0.0052)
0.0005
Log (Size)
(O,ooo8, N
120
120
1211)
120
- - 0.0003
(0.0007) 120
January Beta
0.0202 (im66) f.4233 (0.4696)
Spread
0.002 1 (O.!ml)
0.0020 (0.0194)
1.4250 (O.S!72)
1.5486 (0.3783) - 0.0077 (0.0033)
Log(Size) N
10
10
10
10
0.0014 (0.0035) 10
Non-Jahuary Beta
- 0.0067 (0.0055) - 0.1693 (0.1049)
Spread
- 0.0057 (0.0054)
- 0.0067 (0.0054)
- 0.1277 (0.0906]
- 0.1980 (“3.1121)
Log (Size) N
110
of the prem_ium estimates in ihe
110
110
0.0012 (0.0008)
- omO5 (OMIOS)
110
110
reliably diflerent from zero. Thus, using the A&M sample selection criteria, the liquidity premium appears to be reiiably positive only in the month of January during 1961-90. [Of course, the magnitude of the liquidity preinium in January months may be overstated; Keim (1989) documents that the observed January returns are biased upwards for stocks with high spreads due to the trading patterns at the end of the year.] Panel B of table 2 reports the results for the subperiod 1981-90, which post-da@ the original A&M sample period. In this subperiod, the liquidity premium is still positive’and more than two standard errors from zero in January. In regressions with beta, spread, and size, only spread appears to be statistically significant in January. The liquidity premium in non-January months is negative. Ann-January
n~~&s
FR
V.R. Eleswarapu and MR. Reingantm, Seasona/ity of liquidity pemiwns
381
Unlike the overall 1961-90 period, however, the point estimate of the liquidity premium in this subperiod is negative for all months combined. 3.2. Mod@ed portfolio ‘
formation technique
The stringent data requirements of the A&&I selection criteria raise the possibility that the results are an art&&a& ;rnnt of'a limited sample rather than the manifestation of a true effect. For example, in the &WI framazork, the size variable does not appear to matter, even in January: after coatrollrng for spread. Yet the requirement that there be eleven years of return data may systematically exclude smaller filrmsfrom the sample and: hence, bias the resu!ts against finding a size effect. The restrictive A&M criteria are not necessary to test the cross-set: .nal relation between returns and spreads, In this section, portfolios are formed using just three years of return data. (Similar results are obtained with portfolios requiring five years of prefomation data instead of three.) Assignment afa stock to a particular beta/spread portfolio in a given test year depends on two criteria* 1) the stock’s spread in the previous year and 2) the stock’s ordinary leastsquares beta estimated with 36 montils of preceding returns. Thus, only three years of preformation returns are needed for inclusion in the tests. Also, in contrast to the previous section, firms can be delisted in the middle of a test year, avoiding a potential survivorship bias. For the test period, stocks are again ranked into seven equal groups based on their spread in the previous year, as in A&M. They are further divided into seven equal subgroups by ranking the stocks according to their estimated beta coefficients, computed with the preceding ‘4 monthly returns. The average portfolio excess returns in the test year a r~ obtained by averaging the excess returns of the stocks in each of the 49 portfolios. This procedure is repeated in each of the 30 test-year periods, 1961-90. The portfolio formation technique dramatically increases the number of stocks included in the analysis. For example, the average number of firms in a year increases by 45 %, from 795 to b,I 53. The average market capitalization of a firm in the enlarged sample is 16% smaller than that of the restricted sample. In this analysis, the number of firms included in each test period ranges from 895 to 1,346 (versus a range of 654 to 929 for the restricted sample). Another change from the A&M framework is that unconditional g~rrfolio Betsy are used in the cross-sectional regressions. The unconditional portfolio betas are computed using the monthly portfolio returns during the test-period years. In other words, portfolio betab are computed with 360 months of portfolio return data (1961-90). Table 3 presents the descriptive statistics for the 49 pdolios form using the modified portfolio technique. In general, they have the same characteristics as those formed using the A&M portfolio formation techniqtte. However, the portfolios now have smaller-size Grms with larger average bid-ask spreads.
382
VA Eleswarapuand MR. Reinganum, Seasonality
of liquidity premiums
Table 3 Average relative bid-ask spread (in percent), betas, and market value of equity (in millions of dollars) tfolio formation technique, requiring for the 49 portfolios of NYSE firms based on modified test year, 1961-90. return data for three years preceding e king the stocks into seven equal The portfolios are formed each year preceding t ual subgroups according to their groups, based on their spread, and then dividing year ranges from 895 to 1,346. estimated beta coefficients.The mu asP .read of the portfolio in Each cell contains three entries. Th plea, Treceding the test year. percent. The portfolio spread is the a wrth c 41 months of portfolio return The second number is the estimated eqway in millions of dollars, where the data (1961-90).The bottom number i ece~o~,~the test year. Portfolio spread equity value of the firm is compute and market value of equity are averaged over the 30 yetrs ct this study, 1961-90. Spread, [Beta], (Equity value) Beta group Spread group Lowest
2
3
4
5
6
Highest
Mean
Lowest
2
3
5
6
Highest
Mean
0.5064
0.4904 CO.8171 (3705)
0.5066 0.4930 0.4973 l] CO.8063 CO.8451 CO.98 (1958) (2737) (2291)
[1.141] (1347)
0.7654 0.7651 CO.9581 Cl.0761 (9301) (946) 6.9749 8.976C 0.9714 0.9710 0.9738 [1.058] CO.69 l] CO.8473 CQ.9491 [0.979] (612) (869) (788) (574) (547) 1.2035 1.1983 1.1962 1.1994 1.1986 [l.llO] CO.9381 [l.OlOl co.7513 [0.853] $39) (394) (411) (36 (465) 1.4783 1.4767 1.483; 1.4832 1.4832 co.7411 CO.8981 P.~l [ 1.0871 Cl.1433 (351) (233) (226) (197) (283) 1.92OC 1.9298 1.9288 1.9401 1.9296 [0.833-j [0.954] [1.188] [ 1.2391 rt.o60] - (146) (179) (119) (172) (133) 3.5985 3.3452 3.5429 3.6285 3.7800 Cl.0321 Cl.1831 [1.204-J [ 1.3671 [ 1.437) (99) (74) (54) (54) (64) 1.4490 1.4812 1.4939 1.4932 1.5212 CO.7781 CO.8941 co.9743 [ 1.0621 Cl.1493 (1619) (1101) (657) (765) (594)
0.7663 [ 1.2481 (674) 0 9z.W [ 1:234] (387) 1.2017 Cl.3103 (262) 1.4906 Cl.3811 (161) 1.9627 [1.407] (118) 3.9154 [r,ssl] (53) 1.5462 Cl.3241 (429)
0.4814 IO.5353 (5785)
0.4781 0.4700 CO.6831 co.7311 (4739) (7081)
0.7621 [0.561] (1062) 0.9733 co.5773 (673) 1.2015 CO.565 ] (459)
0.7605 co.7131 (2345)
1.4880 co.5951 (267) 1.9184 co.5941 (130) 3.5117 [0.818-J 1(3W 1.4770 [0.607] (1240)
4
0.7617 [0.790-J (1189)
0.7602 CO.85 13 (1169)
0.7631 [0.885] (1188) 0.9?44 [0.905] $36) 1 1999 [Cr.9341 (388) 1.4834 co.9793 (245) 1.9328
Cl*0403 (142) 3.6175 [ 1.227) (100) 1.4950 [0.970] (915)
The cross-sectional regression is fit in each aaronth of the test-period years using three independent variables: 1) unconditional portfolio betas, 2) average spread, and 3) size. The estimates of these ( -Macbeth) coefficients and standard errors are reported in table 4. The toe ts are the time-series means with corresponding standard errors.
W?. Eleswarapu and M. R Reinganum, Seasonality of liquidity premiums
383
Table 4 Estimates of Fama-Macbeth coefficients obtained with unconditional betas and modified portfolio formation technique, requiring return data for three years preceding each test year. Standard errors in parentheses. (A): (B):
R, = a0 + a~& + ept R, = b0 + b,S, + ept
(C):
R, = co + Cl&M+
0%:
R, = do + &Log(Size)
(E):
R, = e. + e,S,, + e2Spr + e3 Log (Size) -+ epl
c2
Sp? +ept + ep
Assignment of a stock to a particular beta/spread portfolio in a given test year depends on two criteria: (1) the spread in the previous year and (2) a stock’s OLS beta estimated with 36 months of preceding returns. In the cross-sectional regression, the portfoiio beta is the unconditional beta; that is, the beta is computed using the monthly portfolio returns from all of the test-period years. The cross-sectional regression is fit in each month t of the test-peeod years. The coefficients are the time-series means with corresponding standard errors. -
Regression Variable
(A)
(B)
(C)
(D)
(E)
Panel A: Test period i961-90 All months Beta
0.0024 (0.0035) 0.1339 (0.0689)
Spread
- 0.0012 (0.0036)
- 0.0001 (0.0035) 0.1477 (0.0636)
0.0875 (0.0626)
Log (Size) - 0.0011 N
360
360
360
(O-000@ 360
- 0.0008 (O.Ooos) 360
January Beta
0.0642 (0.0161) 2.0964 (0.3415)
Spread
0.0319 (0.0149)
0.0247 (0.0151)
i .7023 (0.3477)
1.3072 (0.28 14) - 0.0158 (0.0032)
Log (Size) 30
N
30
30
30
- 0.050 (0.0020) 30
Non-January - 0.0032 (0.0034)
Beta
- 0.0445 (0.0596)
Spread
- 0.0029 (0.0035)
- 0.0036 (0.0036)
0.0063 (0.0557)
- 0.0234 (0.0599) o.WO3 (0.0005)
Log (Size) N _.-_.-
-
330
330
330
330
- 0.0004 (0.W) 330
384
V. R. Eleswarapu and M. R. Reinganum, Seasonality of L#iity
premiums
Table 4 (continued) Regression Vqri?51e --
(A)
(B)
D)
C)
--.
_--
(E)
-
Panel B: Test period 1981-90 AfI months - 0.0075 (0.005 51 - 0.0914 (0.097 1)
Spread
- 0.0759 (0.0916)
ti.0375 (0.0918) 0.0 08 (OSM07)
Log (Size) lv
- O.Q’I78 (O.GOSS:,
-- 9.CO68 (CLASS)
120
120
120
121
- 0.0003 (O.rn) t20
January
B&a
1.1940 (0.4165)
Spread
1.1903 (0.4654)
Log, Size) N
- wOO3 (e.0238)
0.0019 (0.023 1)
0.0125 (0.02 14)
1.0584 (0.42 18) - 0.0071 (0.0030)
10
10
10
10
- 0.0014 (0.0027) 10
Non-January
Beta
- 0.0094 (0.0057) - 0.2085 (0.092 1)
Spread
- 0.0075 (0.0056)
- 0.0085 (@.Om)
- 0.1491 (0.082 3)
- 9.1790 (0.@865)
Log (Si2 2) IJ
110
110
110
0.0016 (0.0007)
- 0.0002 (O.OOOw
110
110
Pane1 A of table 4 shows the results for the 1961-90 period. Overall, the basic result that the liquidity premium is present only in January still appears to hold. However, the size eflrectis now very much present. In fact, over all the months taken together, size is the only variable which appears to be significant in the presence of the other two variables. This conclusion differs from the inferences drawn based on the restricted A&M sample. With the enlarged sample, the evidence for a positive beta-risk premium is diminished and perhaps nonexistent. The beta-risk premium is not significant in the presence of spread and size, ever in January. (Using Dimson’s aggregatedcoefficiems betas with one monthly 1td.d and one monthly lag yields the same result.) Th,2se results on he pricing of beta risk seem consistent with Fama and French (1992). Apparently, requiring only three years of data mstead of eleven
CIR. Eleswarapu and M. R. Reinganm. Seasma/@ qf liquidiry premiums
385
years makes a difference for inferences about the pricing ti! beta risk as well. The pricing of beta nsk may also be &ected by the relaxing t>fth? requirement that firms survive for the whole test-period year following the portfolio formation. Panel B of table 4 shows the results for the subperiod l%I-90. The point estimates of the liquidity premium are ncgctive for all t& months combined. In non-January months, the liquidity pne.miumis negative and about two standard errors below zero In January, ti=o@~, the liquidity premium is still reliably positive. Thus, the predictions of t&e .A&M model are confirmed for January but not for the non-January months. Of course, in the non-January m<.n*hsfor the overall period 1961-90, none of the variables seem to be reliably 2; iceal.
4. Summary and conclusions
This paper empirically investigates the season21 b&~&r of the liquidity premium as modeled by Amihud and Mendelson (1986). The evidence suggests a strong seasonal component. In the 1961-90 period, the liquidity premium is reliably positive only during the month of January. For the non-January months, one cannot detect a positive liquidity premium. That is, the impact of the relative bid-ask spread on asset priciug in non-January months cannot be reliably distinguished from zero. Unlike the original A&M study, the evidence in this paper suggests a significant size effect even after controlling for spreads and beta. The restrictive sampie selection criteria of A&M tend to systematically exclude smaller fims and hence bias the results against finding a size effect. By modifying the portfolio formation technique, the number of firms included in the analysis increases by 45%. The evidence reveals a positive relation between bid-ask spreads and average returns, but only during the month of January. The lack of such a positive relation between spreads and average returns outside of January may well be part of a broader puzzle. Tinic and West (1984) report that beta risk is reliably priced only during January. The broader issue may well be why the empirical representations of asset pricing models work well only in January* Apart from January, the empirical support for asset pricing mo&ls seems tenuous at best, as documented by the evidence in this paper for the model of A&M (1986). While liquidity may very well be a determinant of asset pricing, the reason that its effect on asset pricing seems limited to January is not clear.
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386
V. R. Eleswarapuand M. R. Reinganum, Seasonniityof iiquidilypremiums
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