1980 langetied et al merger and shareholder risk

8/2/2019 1980 Langetied Et Al Merger and Shareholder Risk

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AND QUANTITATIVE ANALYSIS. 3, September 1980

MERGER AND STOCKHOLDEK RISK

Terence C. Langetieg, Robert A. Haugen, and Dean W. Michern*

I. IntroductionIn a world characterized by perfect and complete capital markets, the suc-(or failure) of a merger is judged by the merger's impact on stockholder

th. With completeness, the merger's impact on the probability distributionstockholder returns is unimportant. The perfect market assumption

tees that the stockholder not satisfied with the consolidated firm's re-

merger's impact on wealth. However, if wethe existence of commissions, taxes, and other frictions, or if

are not complete, the merger's impact on the stockholder return distri-n becomes relevant. In this study we will analyze 149 mergers involving

S.E. firms. We will examine four different hypotheses related to themerger on attributes of the stockholder return distribution. We

iance, and several other risk-related attributes. In a companion, merger's impact on wealth is calculated for the same sample but will not

The literature provides four major hypotheses concerning merger and risk,to the four hypotheses as: (1) the "portfolio effect"; (2) the

game"; (3) the "risk-reducing effect"; and (4) the "leverage effect." Thet" is simply an application of portfolio theory. The merger

o a portfolio. Assuming that the merger produces nothing that an in-on his own, the consolidated or merger firm should ex

the same risk attributes as a market-value weighted portfolio of theThe "market-value weights" are determined


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time of the merger. Diversification, if any, must be consistent with that im-plied by this portfolio. The major support for this hypothesis comes fromHaugen and Langetieg [13] and Firth [8]. Although both studies indicate thatsome merged firms exhibit a significant change in risk from market-value weighportfolio of the acquired and acquiring firms' stock prior to merger, the num-ber of instances in which there was such a change is not significantly differ-ent from the number associated with a control group of firms that did not mergeThus, the observed changes are attributed, not to merger, but to the generalinstability associated with the risk variable. However, Mandelker [18, 19],who examines merger-associated changes in systematic risk via a moving averagebeta, rejects the "portfolio effect" hypothesis and concludes that the direc-tion of change in risk is unpredictable. However, since Mandelker does not em-ploy a control group in his analysis, it is difficult to assess the extent towhich one may attribute these results to general instability in the risk varieior to the impact of the merger.

The second hypothesis, the "P/E game," is explained by Steiner [26] as thmarket's unwitting use of the acquiring firm's pre-merger P/E to value the consolidated firm's earnings. Of course, this results in instant gains if theacquiring firm's P/E is higher than the acquired firm's, thereby providing areason for merger through the "P/E game." To the best of our knowledge, no onhas seriously advanced this hypothesis. However, the hypothesis would be sup-ported if we found that the consolidated firm takes on the risk attributes (other attributes relevant to determining the P/E) of the acquiring firm. The"portfolio effect" and the "P/E game" are generally competing hypotheses, butare identical for beta if the betas of the acquiring and acquired firms areequal, or if the acquiring firm is large relative to the acquired firm. Thehypotheses are also identical for the variance of returns if the variances ofthe acquired and acquiring firms are equal and the returns of the acquiring anacquired firms are perfectly correlated. Hence, it may not always be possibleto empirically differentiate between these two hypotheses. The empirical workof Lev and Mandelker [16] shows that the beta of the consolidated firm is, onaverage, insignificantly different than that of the acquired firm, a resultconsistent with the "P/E game."

A third hypothesis comes from Lewellen [17], Alberts [1], Steiner [26],and others who propose that some mergers are motivated due to "risk-reducing


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e "portfolio effect." Lev and Mandelker's study [16]above) is inconsistent with the risk-reducing hypothesis. Smith and

[25) find that the level of diversification in conglomerates is in-of mutual funds. This suggests that merger's "risk-reducing

anti-A foiirth hypothesis concerns the change in risk caused by a merger-related

e. Following Hamada [12] we hypothesize that mergers in-induce an increase in risk. Note that the

rage effect" is jointly present with either the "portfolio effect," theE game," or the "risk-reducing effect." If the "portfolio effect" (or "P/E

market-value weightolio (or acquiring firm). If the merger has some "risk-reducing effects,"

rger also involves an increase in leverage, the net impact is of in-nt sign unless we also have a theory for predicting the exact magni-

e of the "leverage effect" or the "risk-reducing effect." While there aretwo ways to model the change in risk due to leverage, the analysisdata that were not available at the time of the study. The possi-

Therefore, we restrict our attention to amergers involving exchange of only common stock and presumably no

However, Section VI will provide limited results for mer-involving the "leverage effect."we summarize hypotheses concerning the "portfolio effect," the "P/E game,"

cing effect" and the "leverage effect" in Table 1 for beta. Hypo-rning industry risk (defined in Section III) are similar, and

beta of an unlevered firm, by the ratio of the value

j t i e r e l a t i v e l y


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TABLE 1HYPOTHESES FOR BETA (b)

PortfolioEffect

P/E CSame

Risk-ReducingEffect

LeverageEffect

PortfolioEffect

b = bc p

Consistentonly ifW^ Wj

Consistentonly ifb = b= and P

b > bc P

P/E Game

-

b = b^

Inconsistent

b > b.c 2

Risk-ReducingEffect

-

-

^c ^^^2

Indeterminantchange in ris>

LeverageEffect

-

-

-

Testableonly asa JointL Hypothesis

c = consolidated firm,

p = total market-value weighted portfolio of (pre-merger) acquiringand acquired firms,1 = acquired firm, and -2 = acquiring firm. .


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hypotheses concerning variances and level of diversification are similar withthe exception of an additional requirement for the consistency of the "port-folio effect" and "P/E game" hypotheses, (i.e., perfect correlation in the returns of the acquired and acquiring firms is also required).

Finally, we put forth the alternative hypothesis which is defined as thecase where change in risk is not explained by any of the preceding hypothesesMandelker [18, 19] reports that the direction of the change in risk is unpre-dictable, a result suggesting this alternative hypothesis. The results of thstudy also support this alternative hypothesis but, unlike Mandelker, we findthe merger accompanied by an (unhypothesized) increase in risk.

II. The Sample ProfileThe total sample consists of 149 mergers taken from the period 1929

through 1969, with the majority, 61.8 percent, of the sample from the 1960s,25.8 percent from the 1950s, and 12.4 percent before 1950. We focus our attetion on a subsample of 82 mergers involving an all common exchange to avoidcomplications that arise if a merger is accompanied by a change in leverage(see Section I ) . The total sample encompasses all mergers on the Center forResearch in Security Prices (CRSP) data file which meet the following screenicriteria:

1. The firms must have at least 36 months of readable data in theperiod surrounding the merger.

2. For each merger included in the sample, both firms must not havemerged more than once in the three-year period before and afterthe merger date.

The use of the CRSP tapes and the screening criteria unavoidably limitsthe sample to successful mergers between large, infrequently-merging firms.The first screening requirement is necessary to insure a minimum amount of dafor analysis, but it also screens out some unsuccessful mergers (i.e., delistfirms). The second screen eliminates frequently-merging firms in order tofocus on the impact of a single merger. The use of the CRSP data file limitsthe sample to mergers between N.Y.S.E. firms, which are typically very largecompanies. We caution the reader that the results of this study may not begeneralizable to the class of all mergers.


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consumer sector (21, 26) coming in a distant third. The petroleum (18, 14)transportation (15, 15), and wholesale sectors (7, 10) have a modest represetation, and there are only a few mergers from the financial (6, 4) and servisectors (2, 2). Seventy-nine mergers involve two industries, while 70 invola single industry. Looking at the type of consolidation as defined by the F[7], we find 22 percent horizontal mergers, 12 percent vertical mergers, 12percent market-extension mergers, 38 percent product-extension mergers, and percent pure-conglomerate mergers. In this sample, 72 percent of the mergeroccurred in a rising or peak stock market, and nearly 80 percent of the mergoccurred during periods that could be considered as having a higher than norlevel of merger activity in the economy. The average acquired firm was 39 pcent the size of the acquiring firm with respect to t:otal market value of oustanding common stock, and 26 percent the size of the acquiring firm with respect to product-market share. Nearly 55 percent of the mergers involved anontaxable exchange of only common stock, while 20 percent of the mergers wetaxable to some extent.

III. Definition of Risk AttributesAssume, in accord with Jensen's two-factor, "instantaneous horizon,"

return generating model [11], that individual security and industry averagereturns are generated by the following stochastic processes:

wherea = a measure of security j's average-excess return over T time period

(also known as the Jensen performance index [11]),a^ = a measure of industry I's average-excess return over T time period

The empirical evidence of Fama and MacBeth [5], Black-Jensen and Schol[2], Friend and Blume [10], and Pettet and Westerfield [22] indicates a retugenerating process of the following form:

r. - r = b.(r ^ - r ^) + e. ^ , jrt 2,t 3 m,t z,t 3,t


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b = the beta of industry I,

p J r i r ' portfolio of stocks representing industry

" " ' ' ^ " " " ' ' " ^ " " associated with a risk-free asset in period t.and''m,t ^^^ c ontinuous return for the market portfolio in period t.

,t ^^^ identical ly and independently distributed (iid) with2 2zero means and variances a. and o respec tively.

COV(e., (r^ ~ ^p^^ = 0-Final l y, we al so assume that the residual e^ ^ can be expressed as a linea

of the residual e p lus an independent'error.1 , U

where u is iid, CX)V(u,,e_) = 0, and E(u.) = 0. J t j I j

the variable e^^^ represents the influence of al l nonmarket factors. The d e^. represents the influence of security j's industry, and u. repre-the influence of firm-unique events and other factors not already accounte

by the market and the industry.Substituting (3) into (1) yiel ds:

: : "^j.t - ^F,t = ^j * ^ ^^m,t - ^F,t' -


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strengthened. Note also that the industry factor manifests itself only in theex post generating process, not in the determination of the expected rate ofreturn, (i.e., expected rate of return is assumed to be determned according tthe capital asset pricing model E(rJ = ECr^) + B^[E(r^)-E(rp)]).

In this study the market return, r^, is taken to be Fisher's equally-weighted Arithmetic Link Index [9]. This index is broadly based and has beenused in many other merger studies [13, 18, 19], so its use in this study shoulprove valuable for comparative purposes. The three-month treasury bill rate[6] is used as proxy for the risk-free rate.

An equally-weighted industrial index is constructed for each merging fiObviously, the merging firms are not used in the index. To create greater hogeneity among the firms included in the index, an initial, equally-weightedportfolio is constructed of all firms in the merging firm's two-digit industrclassification. The correlation of the residuals for this portfolio and theresiduals for each constituent firm is calculated, and the firms are rank or-dered. The 10 percent of the firms having the lowest correlation coefficientare eliminated, and the index is computed on the basis of the remaining firms

The risk measures relating to the market-value weighted portfolio, theacquired firm, and the acquiring firm are estimated usinq monthly returns ovethe period from 72 months before to 12 months before the merger date. The rimeasures relating to the consolidated firm are estimated in the period from 1months after to 72 months after the merger date. The intervening period arouthe merger date is eliminated on the basis of the possible presence of tempornonstationarity in the coefficients induced by preliminary negotiations, by tannouncement of, or by the preliminary assessment of the merger's results. Nstationarity may still be present in the time intervals used to calculate rismeasures. The use of five years of data in calculating risk measures represea trade-off between using a sufficient amount of data to construct reasonabltight confidence intervals and the use of less data corresponding to shorter

form:The residual, e, is computed on the basis of a regression of the follo

r . = a. + b . r ^ + e . . . . . ,-j . t : D m , t ],t

An alternative index is also employed, and all the results have been


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intervals and greater stationarity. The impact ofnonstationarity ofbetinsome depth byMandelker [18, 19].

in addition tomarket risk andindustry risk weanalyze several additionaof the return distribution:

= variance oftotal returns,VAR(R) = variance of the risk premium (R=r-r ),VAR(u) = residual variance, net ofmarket and industry influence,VAR(e) = diversifiable variance (i.e., residual variance net of onlymarket influence, VAR(e) = d2 VAR(e ) + VAR(u),

VAR(u) iCOR(u) = [1 ] = the coefficient of multiple correlation

VPiR{r-r^} which measures the level of residualvariance relative to risk-premium variancVAR(e) i

COR(e) = [1 - ] = the coefficient ofmultiple correlationVhR{r-r^) which measures the level ofdiversifiable

variance relative torisk-premium variancandMAD(R) = Z I R - RI = mean absolute deviation ofthe risk premium.

IV. Statistical Tests and the Control GroupThree different tests are used toexamine the merger's impact onrisk. The

of the tests isdescribed in the Appendix. Wewill explicitly testhe "portfolio effect" and the "P/E game" hypotheses. Since the "P/E game"

"risk-reducing effect" are mutually exclusive, wecan infer that a "risk-ispresent only ifthe "P/E game" isrejected, andthe rejec-

isaccompanied by a risk reduction. The key test statistic is the "dif-as the hypothesized risk level minus the consolidate

1. There is a test for the magnitude of the "difference." If a hypothe-sis holds, the "difference" should beequal tozero. The "differencesare "standardized" and aggregated. If a hypothesis holds, the aggre-gate of the "standardized differences" should also have a mean equalto zero.

2. There is a test for the percent ofpositive "differences" orrisk


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significant changes to be less than or equal to 5 percent. We alsexainine the number of positive and negative significant "differencby a similar procedure.

Each test statistic has unique advantages and disadvantages. It is quipossible that one test could show that the merger has a significant impactwhile the other tests do not. Ideally we would find all tests indicating a8significant impact, or all tests indicating an insignificant impact.

A control group is employed to serve as a check for sources of systematbias in merger results. The combination of potential bias introduced from mspecification of the return generating model, errors in measuring the indepeent variables, violation of the assumption of normality, and nonstationarityregression coefficients could lead to a false signal of statistical signifi-cance in the tests for changes in stockholder risk. If the bias is introducin a systematic manner, then the bias may also be reflected in a significanctest performed for a nonmerging control group. Hence, the control group seas a check for systematic bias in the statistical tests.

In cases where both the control group and the merging group show signifcant rejection of a hypothesis, we must acknowledge the possibility of a systematic bias. One method for "netting out" systematic bias is to perform apaired-comparison test. Each merger statistic is compared with the corresping control statistic. The difference between the two statistics representthe merger's net impact on risk. If a hypothesis holds, the aggregate of tpaired differences should have an expected value equal to zero.

One control firm is selected for each of the merging firms (both acquiand acquiring). The residuals (as given in footnote 6) of the merging firmare compared to the residuals of each firm in its two-digit SIC industry. firm having the highest residual correlation with the merging firm is selecas the control.

^It should be noted that hypotheses involving regression coefficients


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V. Results: The Effect of Merger on Stockholder Risk(All Common Exchange) ~ ~ ^ ^The results of the tests are presented in Tables 2 and 3. Table 2 pro-

vides the results for tests relating to regression coefficients, and Table 3presents the results for the remaining risk variables. Turning first to thebeta coefficient. Table 2 shows the results of three statistical tests made fthe merging firms, the control group, and the paired comparison. The resultsClearly indicate that the consolidated firms' beta is on average slightly greer than one would expect for the "portfolio effect," the "P/E game," or "therisk-reducing effect." Unlike the merging firms, the control firms exhibit aSignificant reduction in beta. Moreover, the paired-comparison test indicatethere is a statistically significant difference between the change in risk inthe control group and the change in risk in the merger group. The ability ofthe merging finns to maintain their risk levels in the presence of generallyfalling risk levels for closely associated firms might be taken as evidence suorting the presence of a merger-induced risk change in this sample.

one source of systematic bias that is correctable is the tendency of beta"regress toward the mean." Blume [3] has reported that nonstationarity in

ta is systematic because, in general, firms exhibit a propensity to regressward their (cross-sectional) mean value of one. This tendency is correctablthe extent that it is uniform for all securities, by applying Blume's corre

on formula to the post-merger beta. The tests for beta were replicated afteThe results of these

reinforce the conclusion that the consolidated firm experienced an in-in beta not anticipated for by any of the three hypotheses.

Turning now to other aspects of the return-generating process. Table 2

the "P/E game," and the "risk-reducing effect." However, the paired-

ongly significant. This leaves open the possibility that the change in in-

Table 3 provides the result for the remaining risk measures: total vari-


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as measured by the paired-comparison test is still positive and significant.However, both the "portfolio effect" and the "P/E game" are acceptable in thepaired-comparison test for COR{u) and COR(e).

While it appears that the data are inconsistent with all three hypotheseit is interesting to compare the relative explanatory power of the three hypotheses. Examination of Tables 2 and 3 shows that the "portfolio effect" andthe "P/E game" are rejected for most risk measures, and the level of rejectiois highly similar. For some risk measures the "portfolio effect" is acceptabin the paired-comparison tests, but we find that the "P/E game" is also accepable in those cases. In cases where both of these hypotheses are rejected, wgenerally find an increase in risk, which implies that the "risk-reducing ef-fect" is even more strongly rejected. An explanation for the similar resultfor the "portfolio effect" and the "P/E game" is provided by the observationthat the acquired firm and acquiring firm have similar risk levels, particulafor beta. This implies that the levels of risk in the market-weighted port-folio and the acquiring firm are approximately equal; hence it is extremelydifficult to empirically discern the difference between the "portfolio effec9and the "P/E game" in this sample.

To summarize, on the basis of the results thus far, we have been able treject all three hypotheses as adequate explanations for the behavior of therisk variables including beta, VAR(r), VAR(r-r ) , VAR(e), VAR(u), and MAD(R)The "portfolio effect" and the "P/E game" are rejected less strongly (and areven acceptable in the paired-comparison tests) for changes in the industrycoefficients, COR(u) and COR(e). Thus, at this point, the evidence seems tolean in favor of the alternative hypothesis, the rejection of all three hypotheses. In the next section we shift to a consideration of subaggregates anexamine the risk changes for mergers of difference types.

9We would expect that the "portfolio effect" hypothesis (that b = w b+ w b ) , will be equivalent to the "P/E game" hypothesis (that b = b _ ) , whe^ z c z


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^^ The Nature of Merger and the Change in RiskIn this section we try to isolate groups of mergers that are distincti

m terins of their tendency to expe rienc e a change in risk . We then suba ggrgate the total samp le (149 merg ers) to make a rigorou s mea sure ment of thechange in risk for each subagg reg ate . Becau se of the signific ance of beta the theory of finance, and because the results of Section V indicate that snificant deviations from the "portfolio effect " hypothesis occur with respeto bet a, we focus our attention on the "portfolio effect" for bet a.^

A regression procedure is used to screen the total sample for firm andmerger characteristics that may have a significant bearing on the degree ofrisk Change experience d. The depende nt variable is the "difference" which defined as the level of risk in the market value weighted portfolio minus tlevel of risk in the conso lida ted firm, (b^ - t.^). The independent variablare desc ript ive of the nature of the merger and are either conti nuous or dicrete, depending on their natu re.^ ^ Firs t, we employed ordinary least squarregressing the "differen ce" on each of the different independent variable s.Then, a series of step-wise multiple regressions are employed to study theinteractive effect of the independent variables.

10^ ^ " ^ f """ the "P/E game" hypothesis with respect to beta were a

' / ^ ' deviations from the "P/E game" are similar to the deviatsiSL ? for S'^'"r''"/"' '"' explanatory power of exogenous variSlfly. ^ " , ^ypo tl.es es wi th res pec t to the sign ific ance and the

the relationship between the deviation and the exogenous variabEight sets of independent variables are used in the regressions:

(1) The natu re of the securitie s used for compensation in the co nsolida(e.g., only coimnon stock used in exch ang e, othe r sec urit ies use d inchange, nontaxable exchange, taxable exchange)

(2) Dummy var iable s relati ng to the type of merger (horizontal, ver tic aproduct-extension, market-extension, and pure conglomerate)

(3) Dummy var iabl es relati ng to the industries of the acquired and acquiing compa nies . ^(4) The perfor man ce of the stock mark et in the period around the merger (5) The rela tive size of the acquired and acquiring compani es with respe

to total market value of common stock at the time of merger(6) The histo rical time period of merg er, where the time peri ods refe r t

the^fo ur ten-year perio ds and eight five-year perio ds included in th


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Variables identified as having "distinctive" behavior in simple regressioand in step-wise, multiple-regression procedure included: taxable mergers; megers involving exchange of bonds; preferred stocks or assets; pure conglomeratmergers; mergers occurring in the consumer sector; and mergers occurring in thfinancial sector.^^' ^^ Mergers associated with other subaggregates (e.g.,historical time of the merger, relative size of merging firms, etc.) exhibiteda tendency for risk change that was not significantly different from that ofthe total sample.

Variables identified as having a distinctive tendency for risk change inthe regressions are used to subaggregate the total sample, and the more rigorous tests employed in Sections IV and V are applied to the resulting subaggregates. Results are shown in Table 4. All of the subaggregates are seen tohave a greater than average tendency toward a change in risk, which is typi-cally an (unhypothesized) increase in risk that is of even greater magnitudethan the increase in risk experienced by the "all common exchange" subaggregaHence, the results for subaggregates are uniformly consistent with the resultreported for t;he "all common exchange" subaggregate in Section V. Again, weconclude that the "portfolio effect" hypothesis is empirically unsupportable.

Finally, we examine a new sample of mergers involving bonds, preferredstock, or cash in the exchange. Such mergers typically involve an increase ileverage. The results suggest an even greater tendency for these types of megers to be associated with an increase in risk than was found in mergers invoing an all-common exchange. Of course, this is exactly what one would expectsince increasing leverage implies an increase in the risk level [12] . The

We caution the reader against interpreting "distinctive" (i.e., distitive in terms of the tendency to experience a change in risk) as a "statisti-cally significant distinction." The motive for subaggregation is to extend examination of the "portfolio effect" hypothesis for subaggregates. Our re-gressions are merely a "first pass" attempt to identify subaggregates with adistinctive tendency for risk change. A more rigorous treatment of subaggregates is reported below.

^\hile the "all-common exchange" subaggregate is easily justified to etract from the leverage effect, subaggregation with respect to characteristisuch as industry or type of merger needs further theoretical justification.Furthermore, the subaggregation for conglomerate, consumer, and finance mergshould be treated with caution because of the small sample size for these su


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subaggregate experienced an even greater risk increase, which is

, preferred stocks, or cash represent 100 percent of the exchangetaxable mergers in this sample were typically mergers having a very l

verage effect." Since the "leverage effect" seems to be present, a rigor

regate requires the prediction of the magnitude of the "leverage effec(see Section I and footnote 2 ) .

VIX. Summary and ConclusionsThis paper has reported the results of an in-depth study of the changes

The analysis has attempted both to measure and to explain the charisk attributes. The evidence provides some support for the notion that

r has an impact on stockholder risX, but it is generally not of a form thabeen suggested by others in the literature. On the average, we find tha

tends to be associated with an vinexpected increase in the levels of band diversifiable risk for the consolidated firm. This i

ising result, as merger is rarely viewed as risK-increasing. While theature would lead us to believe that some mergers are motivated to reducwe find more may be motivated to increase risk. However, a risk incre

arily inconsistent with stockholder wealth maximization if capi

ncrease in a commensurate amount-To conclude this study we ask, "Why is merger associated with risk in-

reases?" While an increase in leverage may account for part of the risk inrease in some mergers, the risk increase in mergers involving an all-commonexchange is not adequately explained by any of the available sample charactetics. Hence, further research is warranted with respect to the examination additional explanatory variables (see footnote 11). Finally, we suggest thathe increasing risk level may only reflect an aggressive management in theacquiring firm. The fact that many mergers are also accompanied by an increin leverage supports this viewr


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APPENDIXA. Construction of Aggregation Statistics

For the "portfolio effect" and the "P/E game" hypotheses for eachrisk measure, three statistical tests are constructed which involve the aggrgation of : (1) standardized "differences"; (2) positive "differences"; and(3) significant "differences." To illustrate the three tests consider the"portfolio effect" hypothesis expressed for changes in beta. Define d. as "difference" between the hypothesized risk level and the consolidated firm'srisk level. Then, d. = b . - b . for merger i, where b . and b . refer to t

1 pi Cl pi Clbeta of the market-value weighted portfolio and the consolidated firm respetively. According to the "portfolio effect," hypothesis E(d.) = 0 for each ger i.

The first test concerns aggregation of standeirdized "differences." Befthe "differences" are aggregated, they are standardized by dividing each d. its estimated standard deviation, SD(d.). Noting that d. = b . - b ., that

1 1. pi Clb . and b . are calculated from nonoverlapping time intervals, and assumingthat security returns are serially independent [4], it follows that SD(d.) =[VAR(b ^) + VAR(b ^)] (see Table 5 ). Next, define the aggregate average d - 1 "d = - E d :

where n is the sample size, and d! is equal to d./SD{d.). Since n is rela-tively large (82 mergers), we appeal to the central limit theorem and assumethe distribution of d to be approximately normal. According to the "portfoleffect," hypothesis E(d.) = 0 for each i, and this implies that E(d) = 0 , whis the aggregate form of the "portfolio effect" hypothesis. To test E(d) we construct a (1 - 2a) percent confidence interval based on the normality od. Assuming independence of the "difference" across mergers, d has a samplevariance of 1/n. The "portfolio effect" hypothesis is accepted if and only zero is included in the confidence interval.

The second statistical test involves aggregation of the number of mergehaving positive "differences." Assuming the "difference" is approximately smetrically distributed, we would expect an equal number of positive and negtive "differences." Define p as the proportion of positive "differences."


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coefficients since they are approximately normal, but not as strongly justififor the variance risk measures and for the correlation coefficients, which malso be slightly nonsyitimetrical.

The third statistical test involves aggregation of the number of mergershaving a significant "difference" from the hypothesized risk level. Signifi-cance is determined by a 95 percent confidence interval constructed for theindividual "differences." The distribution of the "differences" varies accoring to the risk measure being examined and is as shown in Table 5. It shouldbe noted that the assumption of normally distributed returns is used in deriving distributions for the different risk measures. If the "portfolio effect"hypothesis holds and we conduct a large niomber of independent tests, using a95 percent confidence interval, then we would expect significant departuresfrom the hypothesis in 5 percent (or less) of the tests. Assuming that thetests for significant "differences" are independent across mergers and notingthe sample size is large, the distribution of s, the proportion of significa"differences," will be approximately normal, with an estimated standard devition equal to: [ s(l-s)] . A (1-a) percent critical level for the hypothethat E(s) .05 is determined. The "portfolio effect" hypothesis is accepteonly if .05 is less than or equal to the critical level.

The three statistical tests defined above have unique advantages and diadvantages. The "standardized-difference test" is subject to domination by few mergers having extremely large standardized "differences." The "standardifference test" and the "percent positive test" may fail to pick up significant departures from a hypothesis if "differences" are offsetting (i.e., a snificant positive difference offset by a significant negative difference ofcomparable magnitude). The "percent-positive test" is also dependent on thesymmetry of the distribution of the "differences." The "percent-significanttest" is dependent on the normality of security returns, which has been questioned by Fama [4) and others. In addition, the "percent-significant test"will fail to detect "differences" that are nonzero but too small to be stattically significant. Finally, all tests are subject to the assumption of crsectional independence among the "differences" in the sample. Since no testideal, we employed all three tests in analyzing the merger's impact on risk.B. The Paired-Comparison Test -


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sur es; (2) spe cific atio n error s in the generating process used in calculatioeffi cient s; (3) errors in measuring independent variables in re -

ssio ns; (4) viola tion of ass ump tion s used in forming statistical tests; andcha ra cte ris tics pecu liar to the sample (e.g., the sample involves merger s

ntly m erg ing, established N.Y.S .E. firms in which the merger itotally unsuc ces sfu l in that the consolidat ed firm remains listed.) The

exer ted s yste matic ally on the mergin g and control firms .One way to mode rat e e xterna l, systematic influence is to use the paired-

arison test. Define the "paired difference" D, as: D, = d , - d , where1 1 mi ci

, and d , denote the "difference" for merger i and its control merger respecely. According to the "portfolio effect" hypothesis, E(d ,) = 0 and

ml,) = 0. This implies that E(D,) = 0. We consider the aggregate form of"portfolio effect" hypothesis which implies that E{D) = 0, where Z D,/SD(D,); that is, 5 is the sample average of the standardized D, .

y distributed with SD(D) = n , and a (l-2a) percent confidence intervalcan be constructed. To conpute SD(D,) used in standardization, we notet VAR(D,) = VAR(d ,) + VAR(d ,) - 2C0V(d ,,d . ) . We assumed that the lattei mi ci mi ci

rieuice term is negligible. For regression coefficients and the residual

t the residuals (net of market and industry influence) of the merging firmscontrol firms are correlated. In fact, the residual correlation between

l firms was calculated and found to be positive but quitell in magnitude. In only a handful of cases was the correlation significan

the assurption of a zero covariance seems justified in the case of theon coefficients and the residual variance. However, it is acknowledge

at this assumption is violated to some extent in other risk measures. A

in the two groups. Let P = p^^ - P ,. where p^ and p^ denote the pro-positive "differences" in the merger group and control group. Agai

ed with VAR(P) = VAR(p^) + VAR(p^) = [i^P^d-P^^) + " ^c^^'^c^ ^ "^^^


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REFERENCES[1] Alberts, William W. "The Profitability of Growth by Merger." In The

Corporate Merger, ed. by William W. Alberts and Joel E. Segall. IllinoiUniversity of Chicago Press (1974).

[2] Black, Fischer; Michael C. Jensen; and Myron Scholes. "The Capital AssePricing Model: Some Empirical Tests." In Studies in the Theory of Capital Markets, ed. by Michael C. Jensen. New York: Praeger Publishers (

[3] Blume, Marshall. "On the Assessment of Risk." Journal of Finance (Marc1971), pp. 1-10.

[4] Fama, Eugene F. "The Behavior of Stock Market Prices." Journal of Business (January 1966), pp. 34-105.[5] Fama, Eugene F., and James D. MacBeth. "Risk, Return, and Equilibrium:Empirical Tests." Journal of Political Economy (May-June 1973), pp. 607

636.(6] Federal Reserve Monthly Bulletin, published by the Board of Governors ofthe Federal Reserve System (1929-1969).[7] Federal Trade Commission. Statistical Report on Mergers and AcquisitiReport No. 6-15-18 (October 1973).18] Firth, Michael. "Synergism in Mergers: Some British Results." Journalof Finance (May 1978), pp. 670-672.[9] Fischer, Lawrence. "Some New Stock Market Indexes." Journai of Busines(January 1966), pp. 191-225.[10] Friend, Irwin, and Marshall Blume. "Measurement of Portfolio Performanc

under Uncertainty." American Economic Review (March 1970), pp. 561-575.[11] Jensen, Michael C. "Risk, the Pricing of Capital Assets, and the Evaluation of Investment Portfolios." Journai of Business (April 1969), pp. 1247.

[12] Hamada, Robert S. "The Effect of the Firm's Capital Structure on the Sytematic Risk of Common Stock." Journal of Finance (March 1969), pp. 13-[13] Haugen, Robert A., and Terence C. Langetieg. "An Empirical Test for Syn

gism in Merger." Journal of Finance (September 1975), pp. 1003-1013.[14] Langetieg, Terence C. Merger and Stockholder Welfare. Unpublished Ph.D.

dissertation, Graudate School of Business, University of Wisconsin-Madi(June 1977) .An Application of a Three-Factor Model to Measure Stockhol

" Journai of Financial Economics (December 1978), pp


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of Some Recent PlnSiri,,." m jtuijer te t, , ,d. by Mchael C. Jen.en. .. vork:

" ' * r ; o ^ K , " - ; . S f w r t ; S ^ f " ^ .2] Pettet, R. Richardson, and Randolph Westerfield. "Using the Capital As

P r i c i n g M o d e l a n d t h M k t d l^, n Randolph Westerfield. Using the Cap

Pricing Model and the Market Model to Predict Security Returns " l o ^of Financial and Quantitative Analysis (September 1974), pp. 579-606.3] Reid, Richardson S. Mergers, Managers, and the Economy. New York-McGraw-Hill, Inc. (1968).

Roll, Richard. "Bias in Fitting the Sharpe Model to Time Series Data "Journal of Financial and Quantitative Analysis (March 1969), pp. 271-28

5] Smith, Keith V., and John C. Schreiner. "A Portfolio Analysis of Congloate Diversification." Journal of Finance (June 1969), pp. 413-427.

' "^^^^'"^- ' '^ '"'^''' "'= university of Michigan Pr

Inc" "" ' "^"^^' ^""^-^P^e^ o^ Econometrics. New York: John Wiley s Sons


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1980 langetied et al merger and shareholder risk

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