Journal of Financial Economics 22 (1988) 355-385. North-
. Universir): of Texus at Austin, Austin, TX 78712, CrSA
University of Arizona, Twon, A 2 85721, USA
Seha
University of Texas at Austin, Austin, TX 7$712, USA
Received July 1987, final version received August 1988
This paper develops and tests the uncertain information hypothesis as a means of explaining the response of rational, risk-avesr a -- investors to the arrival of unanticipated ;cfc~~~ion. The theory pr&icfs that foiiowing news of a dramatic financial event, both the risk and eqzcted rcttum of the affected companies increase systematically, and that prices react more strongly to bad ne?Js than good. An empirical investigation of over 9@X marketwide and firm-specific events produces results consistent with these predictions. We conclude that the market reacts to uncertain information in an efficient, if not instantaneous, manner.
Rationality in financial markets implies avtilable information in establishing security
that investors correctly use all prices. natural consequence of this definition is that researchers concerned with how stock returns are aenerated mllct firct consider how market participants deterlmine and assimi- ----r-Y- a-1” &te the relevant data in their decision aking. In its more refined for
where the costs of producing nized, the efficient market hyp
at any point is a noisy estimate of t
*Earlier versions of the paper were presented at the 1988 meetings of the Westet-n Finance Association, European Finance Association, and at the Finance S osium of thz Texas A University. We benefited from the comments of
the referee, Rex Thompson, and the editors, extrenely helpful comments and su
356 K.C. Brown et al., &certain information and market eficiency
lenks of its risky future 4XSh flOWS., l Beyond this, the EMH also assumes that investors learn to make correct inferences about the impact of new informa- tion on the probability distribution of potential stock returns - that is, they form rational expectations about the future.
hat the us& definitions of rationality do not imply, however, is that security prices react to major informational surprises instantaneously. For n when an event clearly conveys good or bad news about a firm’s
t’s prospects, the full extent of its eventual impaek on stock prices be uncertain. Thus, with incomplete information, the best that investors may be able to do is to estimate the paramekers of a conditional probability distribution summarizing the various potential outcomes.
n this paper we present a somewhat richer version of the EMH based on quite general and completely rational decision rules for investors. The model, which we refer to as the uncertain information hypothesis (UIH), begins with the assumption that investors often set stock prices before the full ramifica- tions of a drarrakic financial event are known. The UIH then predicts that in the aftermath of new informati(on, both the risk and khe expected return of the affected companies increase in a systematic fashion. More precisely, we demenstrate that in addition to increasing measurable risk, a noisy piece of favorable or unfavorable news immediately causes a market comprisirlg risk- averse investors to sek stock prices significantly below their conditional ex- pected values. As khe uncertainty over the eventual outcome is resolved, subsequent price changes tend to be positive on average, regardless of the nature of the catalyzing event. Further, if investors’ preferences exhibii de- creasing absolute risk aversion the UIH pre4fc t. &at the average price change 6 will be larger following bad news than good.
Although no other study tests the risk and expected return predictions of directly, the empirical Lterakttre does provide indications of their validity. For example, French, Schwert, and Skambaugh (1987) demonstrate that the ex ante risk premium on common stocks is positively related to the anticipated volatility of rekums. Also, there is some evidence that the arrival of informaticn increases stock-return variability. In particular, Bower and Bower (1983) document that the residual variances of stocks around the time of dividend-omission announcement e twice as large as their variances during nonevent periods. Beaver (1968), tell and ?Volfson (19791, Christie (1983) alay and Lowens,tein (1985) all report that struck returns are more
around regularly scheduled announcements. It seems reasonable, e, that surprises impart even greater uncertainty. There is also a substantial bocly of work that quantifies how stock prices react ko qualitative
‘The ccnventional definition of EMH, which claims that security prices impound all availakle inform&ion, requires that information is costless. Grossman and Stiglitz (1980) develop a fuller and E-ore interesting version of the EM
by knowledgeable investors who incur
in which prices reveal m.ost of the information produced
K.C. Browr et al., Uncertain information and market eficienq 351
financial events. t the l:wo extrer study, which shows that large followed by large, randomly vat
and Thaler (II 985), which demonstrates that investors chroni news and must therefore
though most of the collected rese than to the latter, price behavior is very much an open
En this paper, we p
measure market reactions to th.e arrival of good an proposition that maj
expected I ttums on
support the alternati ntly overreact to new
information. The p
raain theory and its testable implications. Sect
&sign and the test methods. The results for the ns anges are presen section 4 and section 5 examines the exact nature of the postevent price responses. Section 6 considers the link between risk and return; while section 7 contains a summary and our conclusions.
2.1. The uncertain information hypothesis (
To develop the lJI somewhat more specifically, we assume that: ( investors are rational in the von Neumann- rgenstern sense (i.e., they maximize expected utility) and they form rati expectations; (ii) they are risk-averse; (iii) the stock market incorporates all available information in security prices quickly; and (iv) major surprises can be identified as good or bad news, but the full extent of their impuII iiii a~+ fin -market prices is uncertain. However, investors can form conditional probability distributions of returns given good and bad news.
With these assumptions it is relatively straightfor3vard to de rational investors’ reactions to unfavorable surpris
pattern of price changes that will superticially res is, the initial decline in stock prices will be followed, increase. ith favorable surprises, the pattern
appearance of an underreaction: i.e., the initial followed by further price increases.
*More precisely, the overreaction h extreme movements in equity prices are followe Such behavior implies that investors do evaluation of new information.
358 KC. Brown et al., Uncertain information and market eficiency
These propositions are demonstrated graphically in fig.
1. For
purposes of comparison, panel A shows the adjustment of stock prices to bad news whichleaves the nondiversifiable risks of the securities unaltered. Arrival of bad news on the event day (t = 0) drives the preevent value of the security, P, down to _?B7 and there is no price response after the evcrii. In this case, the present value of the certainty equivalents of the stock’s risky cash flows is reduced to PB rapidly because the event discloses a definite decrease in the stock’s expected future cash-flow stream. Priced at Ps, the postevent expected return of the stock would be exactly equal to its preevent expected rate of return.
in contrast, panel B shows the pattern of price changes that would be caused by unfavorable surprises that not only decrease the expected cash flows of the security but also increase their systematic risks. With the additional uncertainty, the present value of the certainty equivalents of the risky cash flows is PJ which would be strictly less than Ps in a stock market dominated by risk-averse investors. However, after the uncertainty imparted bv the surprise is resolved in day i = k after the event, the price increases frc,il P$
to FB. In other words, investors price the stock at Pg so that it would yield a
higher expected rate of return to compensate for the increase in its systematic risk that is induced by the bad news.
The impact of favorable surprises on the values of securities is shown in panels C and D. When the full extent of the good news is certain, the price of the stock increases from P to PG. The adjustment is completed on the event day and there is no abnormal price response after the event. On the other hand, when good news increases the security’s systematic risk as well as its expected future cash flows the price rises from P to P$. Eventually, when the uncertainpj induced by the news is completely resolved on day t = k, the price of the security further increases from P$ to PG. As in the case of uncertain bad news, this price reaction after the event is caused by rational risk-averse investors’ demand for higher expected returns to compensate them for the increased uncertainty induced by the surprise.
Although the preceding discussion is couched in terms of favorable and unfavorable surprises that affect the systematic risks of individual stocks, the uI[W is equally r&v~nt to marketwidc ~,,l~~-pr&s that &ect the vabtcs of broad14 based stock indexes. The UIH :Jaims that major favorable and unfavorable surprises about the economy will typically increase the risks of holding common stocks in general. Thus, the returns on bro;idly based stock indexes following the events will also exhibit the asymmetric pp.ttems shown in panels B and D of fig. 1. Moreover, the UIH implies that, when investors’ preferences exhibit decreasing absolute risk aversion and broadly diversified portfolios of equities constitute very large fractions of investors’ wealth, the price reaction to major unfavorable marketwide surprises will be more pro- nounced than the reaction to equally sngnificam. favorable surprises. The important point here is ihat the portfolios are priced rationally in both
KC. Brown et al., Uncertain informtim and market eficieny
/
e \ e
360 K.C. Brown et al., Uticertain information and market eficiency
situations, and there are no ex ante arbitrage opportunities that can lead to an increase in the expected utility of the investors. Whc~ samples of only bad or good informatinnal events are analyzed using ex post data, however, the results may create the illusion that investors consistently overreact to bad and under-react to good news.
2.2. Testidle i~~li~~ti~ns of the theory
ts the following testable following the anno
ositions: (i) stock return
than for favorable events if
investors can expect to be this is what should ealth, our discussion
wever, enables us to are the quantities of rtfolios and are their market e stock in the portfolio. Thus, the values of large-firm stocks are te cne return patterns predicted by our theory.
to the same specifications, we gat analogous
reactions for the 200 largest firms in the S 500 index as of t
of the data base.
3.2. Be$ning the set of events
to a single index return-generatin
where
Rj, = return for job day t,
R mf = return to the C ly-wei ex
aj, bj = regression parameters of t
base and define
companies. Using this t
362 K.C. Brown et al., Uncertaiu information and market eficiency
mean daily return for a 60.day preevent period (- 60, - 1). Prospective events es are defined in terms of residuals that are at least 1% in e. This selection method leaves a sample of 75 price change proxy, 39 decreases and 36 increases? The second ose events in which the absolute value of the residual was greater than equal to 2.5%. Two important points should be noted about tion process. First, sample of events with residuals that were at least solute value was very small; only 30 for the CRSP
a meanasa
market return is at so defined
events in terms of the entire 1962-1985 period (over th the sample of individual events, this modification identi-
number of events with equivalent character&&.
Two tial cornmezts must be made about +&e way we have defined our price-change ~.zvents. In creating the event samples, we make no attempt io link the price, reactions to any particular financial announcement about the firm or market. The advantage of defining events numerically is that the UIH can be tested without the introduction of biases about what type of announcement should cause investors to respond. Also, we chose the size of the Grms included in the an&lysis, as well as the minimum levels for the residual price-change samples (2.5% for the 200 individual S&P companies,
market proxy), so as to exclude spurious events caused price differentials that can result with thinly traded ~~riiiti.
Table 1 p;=nts a descriptive summary of tht: events associated with both the individual and marketwide samples. Along with the mean, standard deviation, minimum and maximum values for the residual price changes on the event day itself, the display also lists the maximum cumulative average residual from the subsequent M-day period. Roth the CRSP index and individual-firm samples are qualitatively compiirable in that the events are roughly equally divided between positive and negative values. They differ widely, however, in their degrees of dispersion. For instance., the sample of 1 events for the CRSP index has a range (in absolute terms) of 1.02% to 3.47%, while the individual-firm sample varies between 2.50% and 30.63% in absolute value. Further, the coefficients of variation for the same marketwide sample are 0.299 and -0.331 for positive and negative events, respectively, while the analogous sKistics for the individual-firm events are 0.466 and - 0.441. Of course, these differences are to be expected when comparing the price move-
‘The empirical ana!yses were also replicated with the S&P 500 index. The same procedure using the S&P 500 index as the market proxy produced a sample of 42 dec?ines and 39 inc~ar.ec dutin_r 1962-1985 measurement period. The results of the statistical tests based on the S&P 500 returns are very simikr to those obtained with the CRSP equally-weighted index. To conserve space, on@ the tests based on the CRSP equally-weighted index are reported in the paper. The results of the analyses on the S&P 500 index are available from the authors.
K.C. Brown et al., Uncertain information and market eficienqp 365
Table 1 Descriptivlr: statktics for residual returns on
day
pliCe=&alI 2-1985.
twit days and in the f&wing 60
Pie
Sample .
(i) Positive events @mo
2.5% events
(ii) Negative events (aho
4,317 -4.06 1.79 - 2.50 - 30.63 0.62
a* %Imximm CXJimh during the 60 days event.
bDefined as the CRSP index of aU NYSE st lewzls indicate the minimrlm abso>me residual value nwssary to be in&&d in the sample.
%efined SC the ti-spedfic 2.540 events for the largest 200 stocks in the S&P 500 index aM@ed im%GJ~~y.
ments of a well diver5i.M portfolio with those of 200 large, but sepzxate, fhms. What is more important for asseSz4g the validity of tZle U
is that regardless of the direction or de5ition cf event sample, the maximum cumulative response is akzy~ positive. 5ding is strongly consistent with the predictions of our thesis about the m
uncertain information is resokd, a 5 gment must be re a more detailed analysis.
364
erating process. To test for the po4Aity that the event itself may have altered the risks if the slxurities, we calculate the postevent residual responses using the parameters estimated in a 200-day interval following the 600day response
might alter both the systematic and unsystematic subsequently provides
Finally, to avoid the
ay interval following the
population excluding all event-related
below.
The initial prediction of e UIH is that, on average, news announcements that surprise the mar&, will itd 80 an increase in stock return variability. We
ways. First, using the collection of marketwide e CRSP index, we compare the estimated daily return
the postevent (+ I, +60) and nonevent inter- in this comparison. Second, for the sample of firm events, we assess the significance of the structural change in the parameters of the market model implicit in eq. (1). These coefficients are measured in three nczoyer!apping periods: preevent (- 200, - l), postevent ( + I, + 60), and subsquent days (+ 61, + 261). Segmenting the analysis of the market-model parameters in this &&ion makes it possible to test the temporal nature of 3ny s in uncertainty induced by the Iunanticipated event. That is, although th predicts that risk will increase following an informatio4 shock there is no Q priori reason to conclude that the change will be
arisons of the risk p eters from the postevent other two intervals such an analysis.
6Bar-Yosef and Brown (19771, for example, document that systematic risks of common stocks exhibit significant, but temporary, changes around stock-split announcements.
KC. Brown et al., Uncertain injortmtion and market eficiency 365 3.5. halua !ing posteuent returns
The second testable i return will rise concod
stevent exces
ter both favorable and en the increases
AR,, = ‘: . t = +I,..., +
i2)
The subscript 9
of observations then be defined as
CARS, =
CAR,,,,+
t =
+a,...,
-+6W
where the value for CAR, is equal to AR,. test statistic is [T - stat], = [CAR,,] + [VU( R,,)]‘/*, t = +I,..., +
the average resi be correlated across event days, s mod%
methodology is used to calculate the variance in (4):
where the variance and the covariance terms are computed using the residuals from the return-generating modeL7 The statistic in (4), which has a Student-t distribution under the present assumptions, forms the basis for the p l
test of the directional prediction of the
Although the standard CAR test o above can assess the aver sample-wide response to a fimancial event by design, it c
‘There is some confusioh about the apppriate mHhod for amputing the cowariancc maW.k for the average residual. Ruback
distribution with a stable mean individual US, exist, the variance
Amy @EC days czm be calculated directly. It is also po
A&+,,)=O. ‘We used & .kee methods to generate the statistic in (5). results, however, 0x2~ the Ruback statistic is reported in the next section.
366 KC. Brown et al., Uncertain information and market eflciency
presence of event-specific effects. In terms of examining the UIII, this inflexi- bility represents the loss of potentially valuable information, since the collec- tion of price-change events in question is defined in terms of both direction
third empirical proposition of the tude of the response to a given residual eve tude of the initial event and is greater for
sition, a Final test of the U
where
jt = the cumulative residu e jth event [i.e., (C,V,, }) for ten&, t, aftertheevent (t = +P ,..., +60),
q = day 0 residual ($) if negative, 0 otherwise,
l.$* = day 0 residual f$) if positive, 0 otherwise.
he variables L$ and L$* are defined so as to separate the reactions following negative and positive events, rss&vely, while maintaining the magnitude and direction of day 0 price change.
rized by nly for-the sample of generated by the 20 largest s ‘the variability in the res al-event magnitudes of the ma&-t i-dcx zs-& 2 not large. This lack of variability does not a&t the results of the CM test outlined earlier, however, since for that statistic only the average response is required.
As characterized by (a), the UI predicts a sigiii&~~‘;ly negative coefficient for PI ositive co&Sent &. The hypothesis tests are one-sided. The cumulative residual for a particular Grm should, on average, be zero in the aLence of any event large enough to trigger a reaction. Thus, the intercept of (6) is hypothesized to be zero.
‘To guard against the possibility that the regression results are unduly influenced by ItfLe day-of-the-week effect documented by French (1980). we estimated another version of the regression equation that includes dummy variables for Monday and Friday events. Because the coefficients of the dummy variables were not significantly different from zero at conventional probability levels {t = 0.51 and t = 0.59, resyective:y), only the results of the simple model are presented.
KC. drown et al., Uncertain information and market e@cienc?) 367
Comparison of event and nonevent Peturn variances for m t-index samples, 19624985. Daily return variances of the CRSP equally-weight& market-index samples, 1%2-1985. arate variance estimates are calculated for the set of all postevent days (the 60 days fofiowmg an
abnormal price-change event) and set of all other n: neveEt days.
Event days on Event days on
Fb Nonevent days Postevent days: 3, 0. 1.24= 1,336 9. 5 2.2w d-) After (abno increase) 2, 0. 515 P l.Jr, 92c 1,020 3. 5 2.33’ 1.30’ .28’
‘PI represents the number of da!, i w =Wms used to e&mate the statistical variance, a*.
bStandard F-test for the equality of the d stevent a~! a?nevent intervals. %ignifxant at the 0.1% critical level.
4.1. rketwide events
To test the piGpGSitiW. that major surprises are typically follow &repcpA uncer&&q, ~6 Grst compare the daily return variances
market index - the CRS equally-weighted index - during ostevent (+ I, -MO) and nonevent interv r the 1% price change events, nonevent period variances of th
from a sample of 1,936 daily re es a!9 evtint-day and p&event-
368 KC. &own et al., Uncertain information and market @ich-y
conclusion. n fact, the volatility increase on days following bigger price
swings tends to be considerablv more pronounced. The variance of the
equally-weighted index on days following 2.5% or larger price changes i s variance on a typical uneventful day.
To guard against the possibility that these results ue driven by relatively few events, we also estimate the variance of the index after each individual
event with data from the 60 daily returns in the postevent interval. In sample of negative events, 20 of the 39 (51%) postevent variances are consider- ably larger than the return varhe during the nonevent period. SimilarP~, the
aily return varhmxs after 16 of *the 36 positive events are greater than the nonevent period. Not surprisingly, the sample of reduces ~ry similsrr rest&s. The postevent variance CRSP index is larger than its nonevent-period ~ariancx after
negative and 69 of the positive surprises. Thus, the da*: support
claim that major surprises tend to be followed by increased uncertainty in the stock market.
e dso investigate the effects of favorable unfavorable surprises on the rtainty about postevent returns for the largest S&P companies.
As
mentioned earlier, we riced to take into account the possibility that an event itself can substantially change the nature of the subsequent expected returns. Consequently, any method that ignores this possibility and estimates the postevent r preevent market-model coefficients runs the risk of misstating cc of the event-price responses. To establish the validity of this concern, &lc 3 reports the overall incidence of Darametric shifts for the 9,105 individual-firm events includ in our a&y& of the (Jlay lists the cross-sectional average positive partitions of the event
ta coe&ients (bj) for sample. e coefficient of system- ws a significant increase followin negative and positive
erpge postevent is 5.32% large s value in the preeyent
larger following positive surprises. e average beta coefficients in the
K.C. Bmwn et al., Uncertain imf” tim and m&et eficiency 369 Table 3
Changes in systematic risks of individual fi s 2.5% in absolute val
induced by abnormal price &aga of at test the event day, 1962-1985.
One-factor analysis of variance for testing
ad subsequent ~~e~~ p&&s for 4&e
in the mean risk parameters over
calculated according to the single-index marke event periods (listed in
(-200, -1) (*I, -t-40) (961, +263j F-statist?
C”) (2) (3) (l)-(2) w-(3) (2)-(3)
Negative Events (abnormal price decrease ok event day is at least equal to - 2.5
Mean beta
coefficient (9) 1.00875 1.07257 1.03285 31.87” 6ABb 12.34b
Fmitive Events (abnormal price iiwease on event day is at least equal to 2.5
Mean beta
coefficient (bj) 1 1.05615 1.02472 22.74’ .w 8.42”
‘F-statistics test the equality of p st-, ad subsequent event ), (2), and (3), respectively.
critical level. at the 5% critical level.
postevent intervals indicate that the differences are statistic signifimt in both partitions of the samp
postevent return variances and the resid
pattern. After negative events, the average return variance increze by 11.3%
return variance and the resid
1 in the interval following positive surprises.
rest&s in table 3 also indicate that a considerable portion of t iu~nease in the systematic risk of the stocks following major s
transitory. The average bi during the interv +61, i-261) is larger than the bj in the preevent period, ( - l), but it is
smaller than the mean coefficient estimated for the ediate postevent interval, ( + 1, + 60). The same pattern appears to hold
the positive events. Transitory risk increax is, of course, co notion that major inf~rmatiowal su rises create m uncert prospects that requires time to resolve.
370 et al., Uncertain information and market eficiency
Postevent cumulative ave
le 4 five ents M=39 0. 2. 2. 2. L8sO 2.w 2.6F 2.51= 2.46= 2.23’ itive Events N=36 OX 0.81 Iv=17 0.781 1.773 1.851 1.955 1 A&Q *.““# 1. i. 1. 2.302 3.258 3.669 .286 Iv=13 -n ?In \p.J1/ - 0.829 - 0.850 - 0.571 -0. -0. -0353 1.7@ 2.75’ 1.36’ LS8d l.Btd 1.86 1 .Uld 1.57 1.26 1.29 1.10 d d 2.2w - 0.88 - 1.77 - L.54 - 0.88 - 0.89 - 0.57 - 0.34 -0. - 0.69 - 0.71 0.27 0.08 0.20 0.73 0.86
stat! on event - 1 42 "b3 "% -I- 5 + + +8 +9 4-10 +20 + + 4-m +60 0.339 8. 6. 0. 0.281 *--? 3.5 ii
B. Pasitiue bents (abnod
price
here4-l +2 +3 d-4 +5 +6 0.077 +3 4-8 +9 4-10 +20 +30 +50 +60
372 K.C. Brown 44’ al., Uncertain irlpi mation aatd market efJiciency
as to separate the reactions to negative and positive initial even
ividual firms is straightfo s on the market index
37 + 0.38519 RCRsP . t_lT
(7)
(T= 2.53) (T= 18.12) .
where (t) is the set of nonevent days. Thus, the atmom& return on day t
C. Brown et al., ihcertairo i tion and market ciency Panel A. leaf 1% nts) Panel B. CRSP (Sample of 2.5 0.05 0.04 0.03 0.02 0.01 bitive Events ostevent rumula
Pattern of cumulative average residuals
crease) and positive (abno
374 KC. Brown et al., Uncertain information and market eficiency
0.006
45 50 55 60
q,_ -
) ‘. Postevent cmtiative average resid-ds for -firm sample.
Pattern of cumulative average r&duals the 60 days following abnormal prime events for the 200 largest firms in the S&P 1%2-1985. CARS are nxasti as market modei- itdjusted daily returns using data from with the fesponscs foRowing negative
(abnormal price decrease of at rmal price increase of at least
impart a positive bias to the that follow propitious
C. wn et al., Wncemin infomation and .~a~~et eficiency 375
dictiea about kow
376 KC’. hwn et al, Uncertain inform&on and market esfciency Table 6
Relationship between cumulative average responses and the abnormal price change on the ev;nt day for the individual-firm sample.
Estimated coefficients of the regression between cumulative average residuals on various postevent days and the size of the abnormal event-day price change using the model CR,, = 8, + &L$ -b #3&’ + Uj. Uj and Uj* represent the ma@ude QT the pti~e chqe for the jth individual firm on the event day for negative and pozitive changes respectively. Test statistics are based on 9,105
observations (4,788 positive events; 4,317 negative events) during the period 1962-1985. Dependent variable: cRjt Cumukuve residual from event day to day t=l t== 5 Pi0 t==20 t=30 t-40 pa P60 -0.ooo4 0.54 0.70 i.31 - 0.20 -1.40 - %.98= - 1.52 - 1.55 - 0.0145 _ 0 3x3 -0.W7i -0.0680 - 0.1249 - 0.2136 - 0.2129 - 0.2406 - 0.98 0.0104 - l.!xb - 0.0082 - 1.23 -0.8444 - 1.27 0.0248 - a.!Mb -2.77b 0.1885 - 2.45’ 0.1365 - 2.52a 0.14% 0.74 O.oool - 0.30 O.NlO - i.20 0.0016 1.69b 0.0011 2sa 0.0019 1.65b 0.0012 1.54 o.OG17 0.48 5.20a 5.5Sa 1.02 1.88 4.14a 3.!13a 3.27’
~Si@icant at the 1 critical level usinq a one-taii test.
. Significant at the 5% critical level using a one-tail test ‘Significant at the 10% critical level using a two-tail test.
3
point is
ther corro*boraIed by t&e fat: -&a_; iihe intercept term in theregiessions is virtually always equal to zero. Of course, these are exactly hat H would predict for an effic:!ent stock market.
the gs of the previous section, the results of the regressions in table 6 suggest that investors price securities in a manner consistent with t rational evdaation of uncertain information.
g anaiysls, all thee of the testable implications of the esis receive substantial empirical support. In
K.C. Browtt c: al., Uttcerht ittformatimt ovtd market eyJkiettq 377
$he postever. s- return
interest rate remain
returns to variance is 1.577 for the C
larger than the observed increases in ret NthougL the resul
capital assets and their re variance rate is stochastic.
Table 7 Relationship betwe~a event-induced Inca iu risk and return for market-index samples. A comparison of increases in return and return variance for the 60 days following events for the CRSP equally-weighted market-index sampks. Changes measured as percentage increases in relation to all nonevent days during the period 1962-1985. (1) Percentage increase (2) Percestage inmemt ia daily re1ums Awi!I$ in daily wriamx during postevent interval (days + 1, +60) poste:uent interval (days + 1, + 60) Ratio of (l)/( 2) 1% events 2.5% events l!& events 2.5% events 1% events 2.5% events CRSP Equally- Weighted/ index Negative a positive WeGts pooled Only negative c:cisnts (abnormal price decrease on event day is at ieast equal to stated s) Only positive events (abnormal p&e increase on event day is at least equal iu stated 5&j 41.838% 152.891% ‘;!6.523% 119.656% 1.577 1.278 46.538 132.161 33.998 133.419 1.369 0.991 _. 49.393 133.015 30.440 128.375 1.623 1.036
K.C. Brown et al., Uncertain information and market eficiency 379
events:
a*(Rj)
=aO+alUjO+ Wj,a*(
ej) = a0 + CrlUj* + &j,(9)
00)
where bj, 0 *( Rj), and a*( ej) are the beta coefficient, daily return variance, and the residual variance, respectively, of stock j during the postevent interval (+ 1, +60); and q0 is the abnormal return of the stock on day 0 (i.e., q0 < 0 for negative events and L$, > 0 for positive eventsj.
The estimated coeffici~lfs of the r&qIression equations are reported in table
8. In general, the rezultz lz~5d~ s*Sistical support for the proposition that postevent uncertainty is an increasing function of the size of the unexpected price change - whether positive or negative - on the event day. The data also indicate that the choice of risk measure - i.e., total variance, beta, or diversi- fiable risk - has virtually no impact on the conchision. Regardless of how risk is measur& the postevent uncertainty tends to be larger for stocks that experience big price drops or increases, These results would seem to explain whi the magnitudes of postevent price swings tend to be related to the size of the initial price declines caused by bad news. When the relationship between the initial price decline and the subsequent increase in uncertainty is ignored, the postevent price swings may give the deceiving impression of investor overreaction to bad news.
Although the results presented in table 8 are consistent with the UIH, it might also be argued that the increases in postevent b&a coefficients are not large enough to account for the cumulative abnormal returns reported in table 6. If we use the mean daily return of 0.07536% on the CRSI? equally-weighted
index during 19624985 and a daily risk-free rate of O%, an increase of
0.06382 in the average beta ~~~~~~~-* uuwurrl..~c f&~wi~g unfavorable news wo’31d translate into an app;ox.imateiy 0.C&%% per day increase in postevent ex- pected returns. lo Similarly, the increase in the estimated expected returns following favorable news should be approximately 0.0038% per day. Obvi- ously, these numbers are not large enough to account fully for the CARS of 0.39’1% and O.i50% that trail negative and positive events, respectively. But do they compel rejection of the UIH? This question cannot be answered ‘yes’ unless one is wiihng to piace a very tight prior on the empiricai validity of the CAPM. Recen! tests of the CAPM, however, do not provide strong justifica-
‘“This estimate of thz expwted returu is based on the capital asset pricing model (CH?M). According to the CAPM, LE( 5) = A$ E( rM j, Here 5 and rM are the excess returns of stock j and the market portfolio, respectively.
the subsequent 60 days for 1962-1985. The risk me@
ndent variable
Estimated coefficient
cue a1 A2 F-stat.
. Negative Events (abnormal on event day is at least - 2.5
4 0.9250 - 3.6352 0.012 S3.20a
(41.86) ( - 7.29)
!Mm 351.V
U’(cej) a078 363.43’
price increase on event day is at
Isp 3.8333 0.013 65.58” (8.10) G2iRJ) 0.059 .35” 0.059 (13.62) (17.39) ‘Si
382 K.C. Brown et al., Uncertain information and market eflciency
Table 9
Cross-sectional analysis of event-induced risk changes for tke individual&m sample. Ratios of total return variance, beta, and residual variance estimates on various days surrounding abnormal price change events in relation to the preevent period ( - 60, - 6) during the period 1962-1985. Risk estimates are calculated from separate cross-sectional regressions of the market
model on a daily basis
pay t Return variance ondaytasaratio of average return variance during days ( - 60, - 6)” Beta coefficient on day t as a ratio of average beta - coefficient during days(-60, -6) Variance of estimated beta coefficient on day t
as a ratio of its average duringdays(-60,~6) (-60 to -6) 1.000 MI0000 1.000 -5 1.139 1.03532 0.980 -4 1.111 1.02629 0.848 -3 :.rc7 1.04263 0.920 -2 1.250 1.00264 0.903 -1 1.583 1.07018 0.985 : 0 1.222 0.99878 0.627 +l 1.639 0.80313 1.223 +2 1.306 0.87214 1.148 +3 1.278 0.97549 1.241 +4 1.250 1.01473 1.058 +5 1.222 l.OlSO9 1.156 (+6 to +60) 1.111 l.OIW I .w?
Ir. Yontrve Events (abn rice Increase on event day is a? Ieast equal to 2.5% j, IV = 4,788
(-60 to -6) l.ooQoo l.OKl -5 0.98498 0.860 -4 1.029 1.01646 0.875 -3 1.l47 1.08037 0.932 -2 1.412 1.10968 1.054 -1 1.912 1.28219 1.066 0 1.353 1.11726 0.658 +l ? .676 1.02731 1.327 +2 1.412 1.06153 1.127 +3 1.205 0.99801 0.988 +4 1.20s 0.92855 1.002 +5 1.176 1.03853 1.032 (+6to+60) l.i93 1.03766 1.078
‘During days ( - 60, - 6) average return variance, average beta coefficient, and the average variance of the e
iqative events
beta coefficient are O.ooO36, 0.98767, and 0.00305, respectively, for 4,0.95437, and 0.00094 for positive events.
K.C. Brown et al., Wncertain information and market eflciemy 383 The data in th
uncertainty in the variance of t than its value
increase in the variance of parameter is almost 3 event. The estimation ris
samples.
Despite the puzzling behavior of
regression mode!, taken as a whole, major surprises are typically accompani stock market. Al
measures - estimat
the grounds that the in in expected returns is more (or less) t
commensurate with the prediction of the asset pricing model.
7. ims
EfRciency in securities markets is b able to incorporate relevant info unbiased fashion. In this p require that the information the presence of imperfect in respond by initially setting overreactions to bad news
se that investors are
rims in a rapid an
se investors willi
which we referred to as the uncertain information hypothesb, ~U~&CS &&
when relatively large samples of favorable or unfavorab’lc events are analyz separately, the immediate pri changes induced by these events will followed by positive ii%WES &khg the postevent period.
claims that this pattern of ex post stock returns is illusory, since impnssibie to predict the direcoic9 and the magnitude of the tr for inGiividual events on an ex ante basis.
us’ing data on an equaiiv-we%ltti C ual stocks in the S&P 500; we &-XL PIS
foiiowing both favorable and unfavorable events cant’ly positive. owever, the correlations between
384 KC. Brown et al., Uncertain information and market e@cienqy
implies that the responses following individual events are random. we present evidence that these increases in expected ret
to increases in stock variability induced by the events t rns the number of
pattern in stock returns follo particular, our
overreact to substantive news of any nat though the findings in
tial news announcements does not reveal
our analysis does not capture. SAlthough this possibility cannot be rejected out of hand, we argue that examinin g stock returns over longer horizons is less likely to provide a more powerful test of the WI3 unless expected rates of return remain stationary over long intervals. Analyses based on long postevent horizons would therefore require tests of joint hypotheses about the stock and the validity of a particular model that desmibes the raaes Of lw*Ja~ fiQ’IP%“= s -\I-.. vvwa 4&cx. EVCR ti the joint hypotheses were rejected, the results would again leave us guessing about the rationality of e stock market. In any case. until we accumulate compe?ling evidence that stock prices consistently under- or overestimate their underlying fundamentals in tJte long run, discarding models based on rational investor behavior would seem to he unwarranted.
C.B. and Stephen J. Brown, 1985, Differential informa”’ *Aurn and security market equilibrium, Jo~rrnal of Financial and Quantitative Analysis 20,407-422.
Bar-Yosef, S. and L.D. Brown, 1977, A reexaminati~~~ of stock splits using moving betas, Journal of Finance 32.1069-1080.
Beavq W.H., 1968, The information content of annual earn&s ~nounceme~ts, in: Empirical reearch in accounting: Selected studies, Suppiemeni to the Journal of Accounting Research 6, 67-92.
I1 Eec~se of their empirical design, DeBondt and ‘Whaler never present a direct test of the separate reactions to favorable and ur+=~~* I,.,,able events. Theu ultimate conclusion of overreaction is based large?y on tbe si
types of events.
cance of the di-gerence % I_, ti-e cttmulativ? average reactions to the two
result 4r&hg bee
condude that the reiponses are hi@y asymmetric, with the final rrmined by the negative event sample. Further, it is diffcult to assess the hpact d event-induced changes in return n their findings, since
K.C. Brown et al., Uncertain information and market eficiency 385
Bower, D.H. and R.S. BOWU, 1983, Dividend omissions: Consojidated Edison may really -be &fferent, Unpublished working paper ( OS TM& School of Business Administration,
et overreaction: Magnitude and intensity, Journal of
paye, ~~raduat~ School of Cornell, B. and R. Roll, 1981,
Bell JotVVrat of Ecolkomics DeBondt, W. and R. Thaler,
7930II05
ts and organizations,
overreaction Fiuanci
e case of dividend
UUlOlZIlCe~nts, d lrsconomics 14,
Merton, R.C., 19E10 exploratory investiga-
Patell, J.M. and MA. Wolfson, 1979, Anticipated information releases reflected in call option prices, Journal of Accounting and Economics 1; 117-140.
Rothschild, M. and J. Stiglitz, 1970, Increasing risk I: A definition, Journal of Economic meory 2, 225-243.
Ruback, R., 1982, The effects of discriminatory price co&o!! d-czz_- e ‘cinns on equity values, Journal of Financial Ec0nom.i~ 10,83-105.
Samuelson, P.A., 1977, Proof that properly discounted present values of assets vibrate randon@
in. PI. Nagatani and K Crowiey, eds., Collected scientific papers of Paul A. SamuebDn, vol.
1984, Risk and return: January vs. the rest of the year, humd of Tinic, SM. and R.R. West, 1986, Risk, return, and equilibrium: A revisit, SOW& of
Economy 94,126-147.
van Neumann, J. and 0. Morgenstern, 1947, Theoq of games and econontic bebatior (
University Press, Princeton, NJ).
Warner, LB., 1977, Bankruptcy, absolute s, Jo
