the size distribution of large shareholdings in some leading british companies

THE SIZE DISTRIBUTION OF LARGE SHAREHOLDINGSIN SOME LEADING BRITISH COMPANIES*

By D. COLLETT and G. YARROW

INTRODUCTION

This paper reports the results of fitting Pareto and lognormal probability densityfunctions to the upper tail of the empirical size distribution of shareholdings ineach of a sample of large British manufacturing companies, and examines someof the factors affecting the parameters of the distributions. The major reasonsfor our interest in such an analysis are as follows. Firstly, fitting size distributionscan be a highly efficient way of summarizing data on share ownership, since thewhole distribution can be represented by a small number of parameters. Incontrast, the most commonly used alternative method of presentationthroughconcentration ratiosnormally only gives a single point, or a small number ofpoints, of the distribution. Second, concentration of share ownership is a factorof some importance in theoretical and empirical analysis of firm behaviour. Forexample, managerial theories of the firm predict that the more dispersed is shareownership the greater is likely to be management's ability to follow policies whichare not in accordance with the interests of shareholders. Thus profitability, andhence the functional distribution of income, may be affected by ownership concen-tration 14]. Finally, given the potential impact of share ownership on companybehaviour, it is of interest to explore the effects on shareholding concentration ofthe investment activities of the large institutions which increasingly dominate thestock market.

The study of share ownership has often been neglected in the structure/conduct!performance literature. Compared with the number of articles and data sourcesdealing with product market concentration, and with its determinants and effects,the quantity of material on structural features of capital markets is relativelysmall. We therefore hope that the data and results presented below will be of someuse to those interested in further analysis in this area.

THE SAMPLE

The sample consists of eighty five firms in the engineering, electrical engineering/electronics, food and textile industries, and comprises the companies in thesesectors which appeared in the top four hundred of The Times list of leading Britishcompanies, ranked by sales, for 1970/71 [9]. Some firms in the original sampletaken from The Times list were, however, excluded from the analysis, either becauseof data inavailability at the time of collection or due to errors in data collection

* We would like to thank Alistair Hendry and Paul Jackson, who collected the data onshareholdings analysed in the paper. Thanks also to Prof. Robin Plackett for his help withsome of the estimation problems. Financial support for the project was provided by the Centrefor Industrial, Economic and Business Research, University of Warwick.

249

250 BULLETIN

revealed by subsequent examination. The list of included companies is shownin Table 1.

Eight of the firms in the sample had two separate types of ordinary share. Intwo cases this was the result of recent takeovers, the B' ordinary shares havingbeen issued in exchange for the shares of the victim, and the rights attached to bothtypes of share were identical. The other six cases involved differential votingrights, where the stock split served to maintain control of the company in the handsof a dominant family group. The latter therefore form a rather special categoryof owner-controlled firm.

TABLE 1

The fit of the Pareto distribution to the top fifty shareholdings of each companyCompany x0 â se. (â) C(50)

Northern Dairies 0.328 1.33 0.188 49.71Melbray 0.256 1.18 0.167 41.43Associated Dairies 0.276 1.80 0.255 27.54 ***Smithfield and Zwanenberg 0.239 1.00 0.142 42.97Associated Fisheries 0.321 1.11 0.157 52.70Baker Perkins 0.322 0.99 0.140 59.15 ***Nottingham Manufacturing (A-ord) 0.340 1.22 0.172 60.70Nottingham Manufacturing (Ord) 0.311 1.25 0.177 66.58Drake and Cubitt 0.383 1.23 0.174 56.14Gill and Duffus 0.355 1.25 0.177 72.41Tate and Lyle 0.194 1.37 0.193 26.94Illingworth Morris (A-ord) 0.097 0.60 0.084 79.62 ***Illingworth Morris (Ord) 0.100 0.61 0.087 75.53Woolcombers 0.125 0.86 0.121 61.19Swan Hunter 0.326 1.49 0.211 46.18Cadbury Schweppes 0.226 1.42 0.201 28.30Unigate 0.160 1.33 0.188 20.59Manbre and Garton 0.323 1.27 0.179 44.70Brooke Bond Liebig 0.245 1.67 0.236 27.69E.M.I. 0.245 1.56 0.220 33.67British Electric Traction 0.186 1.52 0.214 22.40British Ropes 0.268 1.25 0.177 38.08Norcros 0.326 1.15 0.162 57.03London Merchant Securities 0.096 0.97 0.137 67.64Associated Engineering 0.346 1.57 0.222 41.82Thomas Ward 0.322 1.33 0.188 40.86Babcock and Wilcox 0.319 1.28 0.181 41.60G.1C.N. 0.184 1.35 0.190 25.29G.E.C. (Ord) 0.252 1.81 0.256 27.39G.E.C. (B-Ord) 0.244 1.20 0.170 43.65English Calico 0.201 1.19 0.169 38.87Renold 0.350 1.57 0.221 41.18William Press 0.313 1.20 0.170 56.43Dowty 0.270 1.40 0.198 32.54Whessoe 0.430 1.15 0.162 64.26 ***Delta Metal 0.253 1.35 0.191 33.05Johnson Matthey 0.345 1.17 0.165 52.37Vickers 0.229 1.32 0.187 31.33George Cohen 0.4 17 1.47 0.208 49.48Birmid Qualcast 0.303 1.37 0.195 39.33John Brown 0.334 1.26 0.178 47.54Reyrolle Parsons 0.384 1.50 0.212 44.16Chubb 0.370 1.83 0.259 35.50Glynwed 0.368 1.55 0.219 43.05Associated Biscuits (A-oid) 0.419 1.22 0.172 61.39Associated Biscuits (Ord) 0.456 1.39 0.161 54.03 ***Duport 0.375 1.14 0.161 58.63

SIZE DISTRIBUTION OF LARGE SHAREHOLDINGS 251

The data on shareholdings were taken from the registers of ordinary share-holders which all firms subject to the British Companies Acts are required to lodgeat the office of the Registrar of Companies. In most cases the list of shareholdersreferred to a date sometime in 1970, although for some companies the date involvedwas in late 1969 or early 1971. For each firm in the sample a subjective truncationpoint was selected and all shareholdings of greater size were recorded. If thisproduced less than one hundred observations a smaller value for the truncationpoint was chosen and the process was repeated until at least a hundred share-holdings were obtained. The number of data points therefore varies from company

TABLE I-ontjnued

Asterisks indicate that the chi-square statistic is significant at the 5% level.

Company x0 â se. (â) C(50)Mann Egerton 0.275 1.13 0.160 52.94Ever Ready 0.260 1.38 0.195 31.44Staveley 0.246 1.16 0.164 38.42Stone Platt 0.316 1.10 0.156 52.98Simon Engineering 0.318 1.17 0.166 45.72Firth Cleveland 0.078 0.67 0.094 89.90Thomas Tilling 0.194 1.26 0.177 27.33Chloride 0.336 1.41 0.199 42.29Burton (A-ord) 0.375 1.52 0.216 43.57Burton (Ord) 0.127 0.69 0.098 73.81Courtaulds 0.152 1.65 0.234 16.47B.I.C.C. 0.145 1.31 0.185 21.22Bovril 0.231 1.26 0.178 34.37Cavenham 0.078 0.72 0.102 81.20Haden 0.395 1.33 0.188 54.47Westinghouse 0.352 1.28 0.181 55.57Bassett 0.308 1.29 0.182 42.75Clarke Chapman 0.383 1.22 0.172 55.23F. H. Lloyd 0.394 1.37 0.193 54.57Fairey 0.122 1.01 0.142 56.20 ***Brockhouse 0.238 0.97 0.137 47.79Powell Duffryn 0.243 1.38 0.195 29.64B.S.A. 0.237 1.35 0.190 34.36Pegler Hattersley 0.383 1.38 0.194 49.52Avery 0.244 1.35 0.190 30.50F.M.C. 0.078 1.16 0.165 49.75Bibby 0.371 1.31 0.185 51.85Express Dairies (A-ord) 0.302 1.41 0.200 38.30Express Dairies (Ord) 0.063 0.86 0.122 96.52 ***j. Lyons (A-ord) 0.225 1.35 0.191 29.56j. Lyons (Ord) 0.185 1.36 0.193 26.21 ***Rank Hovis and McDougall (Ord) 0.236 1.30 0.183 34.97Rank Hovis and McDougall (B-ord) 0.244 1.20 0.169 37.37Fitch Lovell 0.292 1.32 0.187 36.63Thorn Electrical 0.286 1.41 0.193 38.05Hawker Siddeley 0.157 1.37 0.193 21.00Plessey 0.235 1.44 0.203 30.07Carrington Viyella 0.122 1.41 0.199 78.17Cammell Laird 0.222 1.42 0.201 37.79Wrights 0.146 0.70 0.098 62.86B. Elliott 0.301 1.11 0.157 47.29Selincourt 0.213 1.08 0.152 37.37Morgan Crucible 0.323 1.57 0.222 38.14Alfred Herbert 0.257 1.17 0.165 43.20Mather and Platt 0.403 1.65 0.233 45.60Tube Investments 0.173 1.20 0.169 31.47

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to company, with not less than one hundred for each. Attention was focused onlyon the largest shareholdings for two reasons: (a) to reduce the amount of informa-tion that had to be collected and processed, and (b) because they account for such asubstantial proportion of total shareholdings. As an indication of the relativeconcentration of shareholdings in the tail of the distribution, it may be noted thatthe sample average of the percentage of the total number of shares accounted forby the largest fifty holdings was 45.56%.

Although the registers of shareholders are the most accessible source of data onshare ownership in Britain, they do have certain deficiencies. The major problemis that in some cases it is not possible to identify the beneficial owner of sharesfrom information given in the registers, since the person or institution listed maybe a trustee or nominee for another holder and the identity of the beneficial owneris, at the moment, confidential to the nominee. A second and related difficulty isthat sometimes one person or institution is listed against several holdings. Again,it is not possible to discover whether or not this implies trusteeship for others. Inthe absence of further information, the holdings in such cases have been treatedas separate and have not been consolidated. A priori, it is difficult to determinewhether this convention will lead to results which are biased in any particulardirection (that is, whether it will produce results which overstate or understate thedegree of concentration).

III. THE PARETO DISTRIBUTION

Since many studies of income distribution have found that the Pareto densitygives a good fit to the upper ranges of income data, it is of interest to considerwhether or not this function can also usefully be used to describe the pattern oflarge shareholdings within companies. Letting N(x) be the number of share-holdings of size x and above, the hypothesis to be tested is that

(1)

for shareholdings above some lower size limit, say x0, where fi and a are positiveparameters.

Following Cramer [5] the corresponding distribution function of X, the sizeof shareholding, can be derived by first noting that

Consequently, from (I),

F(x)=P(x)=1_)=1_(2)«

Differentiating with respect to x, the probability density function of

ffaxox', for xx0

(x) - O, elsewhere.

(2)

X is given by

)

'

(8)


It is straightforward to show that the mean and variance of are given by

E(X)=axo/(a-1) ifa>1. (5)

V()=ax/(a_1)2(a_2) if a>2 (6)

Since the hypothesis of equation (I) is to be evaluated using the chi-squaregoodness of fit test, parameter estimates have been obtained by maximum likeli-hood procedures on the assumption that x, is known for each firm. If x, weretreated as unknown we would have a two-parameter estimation problem where therange of variation of the random variable depends upon one of the parametersbeing estimated. This represents a much more substantial statistical problemwhich we have chosen to ignore.

The likelihood function for a sample of size n from the Pareto distribution is

L(x;a)=ax8 fI xç'1« (7)1=1

Taking logarithms and maximizing with respect to a in the usual way leads to theequation

&=n log (xi/xo)J-1

Moreover, the asymptotic variance of the estimator is

ff32 log (L)V(â) ba2

so that, for large samples, the standard error of & is given by

s.e. (&)=&//n

The estimated values of a and their standard errors for the case in which x0 is thesize of the 50th largest shareholding are shown in Table 1. Also shown in the tableare the percentage of each firm's shares accounted for by the largest fifty holdings,denoted by C(50), and the value of x0 for each firm. To permit meaningfulcomparisons between companies, the latter is expressed as a percentage of the totalnumber of ordinary shares issued by the firm concerned. The parameters a and x0provide information on the size distribution of shareholdings within the top fifty,whereas C(50) is a measure of the importance of the top fifty within the totalityof the company's shareholdings.

In order to examine the fit of the Pareto distribution, frequency distributionsof the data were first formed for each of the 85 companies under consideration.The expected frequencies in each interval of the empirical distributions for eachcompany were then evaluated using the maximum likelihood estimates and thechi-square goodness of fit statistics calculated.'

1 To be strictly correct, the maximum likelihood estimates of a used in the evaluation of theexpected frequencies for the chi-square test should be derived after the grouping of the observa-tions, rather than from the original data (see [1]). In fact, calculating the statistics from thegrouped data produced results almost identical to those shown in Table 1. Since the alterna-tive procedure involves a rather more complicated equation for the maximum likelihoodestimator, which can only be solved numerically, we have omitted discussion of this rathertechnical aspect of the study from the present paper.

254 BULLETIN

Using the complete set of data available for each company, the null hypothesisthat the Pareto distribution fits the data is rejected in 82 of the 93 cases at a 5%level of significance. When the sample is restricted in each case to the largest onehundred holdings the null hypothesis is rejected in 31 cases, and for the largestfifty holdings in only 8 cases (these 8 companies being indicated by asterisks inTable 1). It may be noted that in three of the eight cases (for two of which thevalue of the chi-square statistic is very high indeed) the shares concerned werevoting stock of companies with split equity. As already explained, these sharesare usually held for control purposes and it is therefore not surprising that thedistributions are rather different in some cases from those of the more typicalcompanies.

Assuming that the null hypothesis is true, at a 5% significance level theexpected number of cases in which the chi-square statistic would appear significantis 4.65. Comparing this with the actual outcome, and taking into account the pointabout stock splits, it would appear that, overall, the Pareto distribution provides areasonably satisfactory description of the largest fifty shareholdings in the samplefirms, although it fails for larger numbers of holdings.

An appreciation of the fit of the distribution to the data can be obtained fromfigure (j) which shows a plot of log (N(x1)) against log (x1) for the fairly typicalcompany Renold, where the x1 are the upper class limits of the frequency distribu-tion. If the null hypothesis is true there should be a linear relationship betweenthese two variables.

One difficulty with the above analysis arises in those cases for which theestimated value of the parameter a is significantly less than unity, since thisimplies that the distribution has an infinite mean (see equation (5)). It is clear thatfor such companies the limiting behaviour of the Pareto distribution as x tends toinfinity is, in some sense, inappropriate to the dataa conclusion which is hardlysurprising in that X must be bounded above by the total number of shares issuedby the company concerned. Fortunately, since the problem does not show upin the value of the chi-square statistic, the divergence between the theoretical andempirical distributions must only occur at very large values of x, and, provided theresults are interpreted with care, the problem can be ignored for practical purposes.

Given the data in Table 1, it is possible to calculate implied concentrationratios for differing numbers of shareholdings. For example, consider the per-centage of a firm's shares accounted for by the largest n holdings, C(n). From (3)we have that

x=(50/n)'1«x0 (11)

Now, since x0 is the percentage of the total shares accounted for by the fiftiethlargest holding, C(n) may be written as2

50C(n)=C(50)_f x05O"«n_' dn

50"x= C(50) a 1

0 [50(«- 1)/a n1 «] (12)

2 C(n) could also be evaluated as the integral of (li) from zero to n, but this would lead toimproper integral problems when a I.

5

4

2


\

o

I 1 I

O I 2 3 4 5 6 7

Log z

Fig. 1. Pareto representation of the sizes of the shareholdings of Renold (using non-normalizeddata for x).

To illustrate the method, implied values of C(20) have been calculated for the twocompanies Renold and Woolcombers. Substituting for cc, x0 and C(50) from Table 1,the predicted values are 27.53% and 55.03% respectively. These may be comparedwith the actual values of 27.48% and 53.98%. The Woolcombers case indicatesthat the method works reasonably well even in cases in which the estimated valueof a is less than unity and there is an improper integral problem. We are thereforeconfident that Table 1 is a satisfactory way of summarizing the sample informationon shareholding concentration.

256 BULLETIN

IV. THE LOGNORMAL DISTRIBUTION

Although it has been shown that the Pareto distribution provides a satis-factory fit to the empirical size distribution of the largest fifty shareholdings in thesample companies, the fact that it fails for larger numbers of holdings suggeststhat alternative hypotheses be tested on the full sets of data available for eachcompany. We therefore now consider whether or not the tail of the lognormaldistribution provides a better description of all the available observations thandid the Pareto distribution.

A random variable X is said to have the lognormal distribution when itsprobability density function is of the form

f(x)= ax\/27rI exp ((log (x)a)2/2a2), for x

0, elsewhere. (13)

Therefore, =log (k) is normally distributed with mean jz and variance a2.Because of the nature of the data our problem is that of fitting a truncated normaldistribution to logarithms of the shareholding sizes. Denoting the logarithm of thepoint of truncation by y0, the specification of the distribution is

0, for yy0P(y)=1F(y

,a2)F(y I, a) fory>y0, (14)

1 - F(y0I

where F(y j ji, a2) is the distribution function of .

The problem of estimating the parameters of a truncated normal distributionhas been widely discussed and there are several methods by which suitable esti-mates can be derived. The one chosen here has been developed by Cohen [3].Letting e = (y0 - ji)Ia be the normalized point of truncation, and abbreviating thedistribution function to F(y), the likelihood function of the sample can be writtenas

L(y;, a2) =[1 G(e)] (a) exp (- (y_ji)2/2a2)n

(15)

where G(.) is the distribution function of the standard normal random variable.Taking logarithms and maximizing with respect to ji and a, the maximum likeli-hood estimating equations are

y0 /L=ae (16)

- ji = aZ (17)

s2+(37ji)2=a2(1+eZ) (18)

where and 2 are the sample mean and variance respectively, and Z(e)=G'(e)/(1 G(e)). The required estimators , & and the auxiliary estimator ê are to befound as simultaneous solutions of equations (16), (17) and (18) in terms of thesample statistics , y0 and 52


After some manipulation, equations (16) to (18) can be replaced by the follow-ing:

a2=s2+O(yo)2 (19)

9(SYo) (20)

1Z(Ze) s2

(Ze)2 (5y)2where 9=ZI(Ze). Cohen provides tables and a graph of 9 as a function of[1 Z(Ze)]/(Ze)2. Since ê is the value of e for which [1 Z(Ze)]/(Ze)2=s2/(y0)2, we can thereby determine direct1y for any given sample as that valueof O which corresponds to the sample statistic s2/(5y0)2.

Having determined & and ji can be calculated immediately from (19) and(20). Finally, ê can then be obtained from ê=(y0ji)/&.

The estimates of jî and &2 were computed for each of the logarithmicallytransformed data sets. Also computed were ê and the implied proportion of thedistribution accounted for by the sample (i.e. P(Yê)=1 G(ê)). For severalcompanies this probability was found to be very small and, as a result, estimatesof p. and a2 were unobtainable by Cohen's method. The values of jI, &2 and

P(Y ê) for each company are shown in Table 2.Estimates of p. and a2 were also derived using an earlier method of Cohen based

on the first three sample moments [2]. In the cases where ¿î and &2 were unobtain-able using the maximum likelihood method, the three-moment estimators producednegative values for 2 Clearly then, the lognormal distribution is inappropriatein such circumstances.

To test the goodness of fit of the distribution, a frequency distribution of thelogarithms of the data was formed and the observed frequencies were comparedwith the corresponding expected frequencies by means of the chi-square statistic.On the basis of the computed chi-square values the null hypothesis, that thedistribution is lognormal, was rejected in 71 of the 93 cases at a five percent levelof significance, where situations in which estimates of p. and a2 were unobtainableare counted as rejections. In addition, the implied probabilities P(Yê) are,in most cases, markedly different from the actual proportions of shares accountedfor by the largest holdings. We conclude, therefore, that, on the whole, the log-normal distribution is an inappropriate description of the full sets of data.

No attempt has been made to fit truncated lognormal distributions to thelargest fifty shareholdings only, since the objective of this section has been todetermine whether or not this distribution could be satisfactorily fitted to data forwhich the Pareto had failed. Clearly, it can not.

V. FACTORS AFFECTING THE CONCENTRATION OF SHAREHOLDINGS

Having established that the top fifty shareholdings in the great majority ofsample companies follow the Pareto distribution, we now consider the effects ofthree factors which might be expected to influence the values of the parametersa and x0. Note that both parameters may be interpreted as measures of the

(21)

Company P(2ê)Northern Dairies 3.42 1.15 0.949Meibray 0.55 4.33 0.150Associated Dairies 2.07 1.49 0.225 ***Smithfield and Zwanenberg 2.26 2.00 0.678 ***Associated Fisheries 2.50 2.67 0.706 ***Baker Perkins 0.34 4.43 0.104Nottingham Manufacturing (A-Ord) 3.34 1.11 0.994 ***Nottingham Manufacturing (Ord) 3.34 1.26 0.956 ***Drake and Cubitt 1.54 3.17 0.329 ***Gill and Duffus 3.41 1.29 0.997 ***Tate and Lyle 4.22 0.72 0.987 ***lllingworth Morris (A-Ord) -1.14 9.23 0.231 ***Illingworth Morris (Ord) 0.91 5.15 0.499 ***Woolcombers - -Swan Hunter 2.84 1.50 0.842 ***Cadbury Schweppes 5.39 0.74 1.000 ***Unigate 4.09 1.32 0.940 ***Manbre and Garton 3.13 1.23 0.987 ***Brooke Bond Liebig 4.70 1.06 0.999 ***E.M.I. 4.39 0.80 1.000 ***British Electric Traction 5.33 0.66 1.000 *British Ropes 4.35 0.97 0.956 ***Norcros 3.18 1.80 0.855 ***London Merchant Securities - - -Associated Engineering - --Thomas Ward 2.14 1.76 0.656Babcock and Wilcox -0.27 4.17 0.104 ***G.K.N. 3.72 0.68 0.990G.E.C. (Ord) - -G.E.C. (B-Ord) 5.33 1.42 0.997 ***English Calico 5.36 1.11 1.000Renold 4.23 0.56 0.989 ***William Press 4.39 1.32 0.965 ***Dowty 4.51 0.66 0.969 ***Whcssoe 1.75 3.24 0.378 ***Delta Metal 5.41 0.66 1.000 ***Johnson Matthey 3.97 0.93 1.000 ***Vickers 4.53 0.80 0.999 ***George Cohen 4.85 0.68 0.968Birmid Qualcast 5.31 0.72 1.000 ***John Brown 3.71 1.07 0.839Reyrolle Parsons 3.38 0.97 0.994 ***Chubb 4.43 0.66 0.887Glynwed - - -Associated Biscuits (A-Ord) -1.49 4.30 0.237 ***Associated Biscuits (B-Ord) 2.15 0.72 0.994Duport 4.20 1.00 0.997 **t

258 BULLETIN

inequality of the distribution. Given x0, the concentration ratios C(n), I n 50,are higher the lower is the value of a, and, given a, the same ratios are higher thelarger is the value of x0. The effects of changes in the two parameters are illustratedin figure (ii) which shows the relationship of equation (1) plotted in logarithmicform. Starting from AB, an increase in x0 produces a parallel shift of the curve toCD, whereas a reduction in a leads to a rotation to AE. Remembering that x, theshareholding size, is being measured as a percentage of the total number of ordinaryshares issued by the company, the diagram shows that in both cases the parameterchanges must increase the concentration ratios.

The three explanatory variables to be used are the size of the company, theindustry to which it belongs, and the relative importance of leading financial

TABLE 2

Estimates of the parameters of the truncated lognormal distribution


institutions among its largest shareholders. Firm size (S) is measured by capitalemployed, in L thousands, as given in The Times list of leading companies for1970/71. Industry effects are tested by means of three dummy variables definedas follows:

D, {lfor firms in the food industry

O otherwise

{1

for firms in the electrical engineering and electronics industry- O otherwise

D3 - {1 for firms in the textile industryO otherwise

TABLE 2-continued

Asterisks indicate that the chi-square statistic is significant at the 5% level.

Company P( ê)Mann Egerton -0.72 5.09 0.119Ever Ready 4.47 0.61 0.993 ***Staveley 2.50 1.52 0.901 ***Stone Platt 4.59 0.95 0.990 ***Simon Engineering 0.83 3.37 0.119Firth Cleveland -1.09 9.75 0.242Tilling 1.67 3.81 0.088Chloride 4.74 0.70 0.966 ***Burton (A-Ord) 3.87 1.35 0.708Burton (Ord) --CourtauldsB.I.C.C. 5.40 0.63 0.999 ***Bovril 0.12 2.66 0.327Cavenham ._ -Haden 2.71 0.94 0.951 ***Westinghouse 2.49 1.73 0.747Bassett 0.51 3.40 0.270 ***Clarke Chapman 3.50 0.96 0.968 ***F. H. Lloyd 2.64 0.72 0.999 ***Fairey -

j. Brockhouse 2.14 1.33 0.975 ***Powell Duffryn 4.09 0.69 0.906 ***B.S.A. 3.25 1.23 0.930 ***Pegler Hattersley -2.32 5.56 0.013Averys 4.02 0.68 0.998 ***F.M.C. -6.38 10.01 0.009 ***Bibby 2.51 1.77 0.831 ***Express Dairies (A-Ord) 4.83 0.87 1.000 ***Express Dairies (Ord) -J. Lyons (A-Ord) 3.16 0.71 0.993 ***J. Lyons (Ord) - -Rank Hovis McDougall (Ord) 4.68 0.92 0.960 ***Rank Hovis McDougall (B-Ord) 3.65 1.11 0.899 ***Fitch Lovell 4.72 0.85 0.940Thorn Electrical 4.74 0.89 0.995 ***Hawker Siddeley 4.13 0.81 0.999 ***Plessey 5.46 0.74 1.000 ***Carrington Viyella 5.01 0.94 0.985 ***Cammel Laird 3.88 1.21 0.790Wrights - -B. Elliott -0.32 4.21 0.100 ***Selincourt 1.10 4.91 0.170Mortan Crucible 4.30 0.86 0.743Alfred Herbert 3.29 1.00 0.993 ***Mather and Platt 4.41 0.69 0.942 ***Tube Investments 3.90 1.10 0.998 ***

zo-J

Log x Log x

Log s

Fig. 2. The effects of changes in the parameters of the Pareto distribution.

The remaining companies in the sample were nearly all engaged in various aspectsof non-electrical engineering. The final explanatory variable, the relative import-ance of leading financial institutions among the largest shareholdings, is measuredby a proxy variable (T) defined as the proportion of the equity of the fifty largestholdings which is registered in the names of insurance companies. That is, if F isthe total number of shares accounted for by the largest fifty holdings and, amongsuch holdings, I is the total number of shares registered in the names of insurancecompanies, then T=I/F.

The relationships between the parameters of the distributions and the variableT may be expected to be rather more complex than for the other explanatoryvariables, since opposing tendencies are likely to be at work. The fact that personalholdings among the top fifty are usually most important (and, therefore, institu-tional holdings least important) in family-controlled firms having highly unequalshare distributions will tend to lead to a negative relationship between share-

<

a >a

260 BULLETIN

B D


holding concentration and T. On the other hand, for firms in which there is noclearly defined family group in control, the sheer size of the investments of largefinancial institutions could well be a factor making for more concentrated shareownership. The latter is obviously an interesting hypothesis to test since, giventhe increasing dominance of UK capital markets by institutional investors, ithas important implications for the future control, and possibly also performance,of large sections of British industry.

The use of a proxy variable to indicate the relative importance of leadinginstitutional holdings was necessitated by the difficulties which sometimes arisewhen trying to identify the beneficial owner of a particular holding from the shareregisters. As mentioned in section II, the registered shareholder can be a nomineefor the true beneficial owner, and in many cases it would have been impossible toidentify the latter without an input of detective work beyond the resources of thepresent study. The problem is illustrated in Table 3 which summarizes some of the

TABLE 3

Divergences between the registered and beneficial ownership of quo/ed ordinary shares in 1963,1969 and 1975

Estimated registered (R) and beneficial (B) ownership as apercentage of the total shares held

Source: Royal Commission on the Distribution of Income and Wealth Report No. 2, Incomefrom Companies and its Distribution, Tables 1, 2 and 6.

results of two surveys undertaken in 1963 and 1969 by members of the Departmentof Applied Economics at Cambridge [6, 8], and a much smaller survey, concerningitself only with very large companies, by the Royal Commission on the Distributionof Income and Wealth in 1975 [7]. Because of the large divergences betweenbeneficial and registered ownership in the cases of pension funds, investmenttrusts and unit trusts3 it was not feasible to measure the proportion of large share-holdings accounted for by all varieties of leading institutional holders.4

The RIB column in Table 3 shows that it is only possible to identify about 50% of theholdings of pension funds and investment trusts directly from the share registers, and that forunit trusts this proportion falls to zero. In contrast, nearly 90% of the holdings of insurancecompanies can be immediately identified from the registers.

Nor would it have been helpful to proceed indirectly by finding the proportion of registeredpersonal shareholdings and using this as an inverse measure of the importance of institutionalinvestment. Although the divergence between registered and beneficial ownership for personalholdings is relatively small in the aggregate, it is almost certainly much higher among thelargest shareholdings where the use of nominees is likely to be concentrated.

Category of ownership R1963

B RIB R1969

B RIB R1975

B RIBinsurance companies 9.2 10.0 0.92 10.6 12.2 0.87 12.7 14.9 0.85T'ension funds 2.9 6.4 0.45 4.9 9.0 0.54 5.6 15.2 0.37investment trusts 3.2 7.4 0.43 4.2 7.6 0.55 2.0 4.7 0.43Unit trusts 0.0 1.3 0.00 0.0 2.9 0,00 0.0 2.0 0.00Banks 0.9 1.3 0.69 1.4 1.7 0.82 2.1 2.1 1.00Other financial instits.

(icnl. stock exchange)2.6 4.0 0.65 1.2 2.5 0.48 0.3 0.6 0.50

Persons, executors andtrustees resident in UK

51.0 54.0 0.94 44.7 47.4 0.94 38.3 42.1 0.91

Nominee companies 19.2 0.0 - 19.8 0.0 25.5 0.0 -()thers 11.0 15.6 0.71 13.2 16.7 0.79 13.5 18.4 0.73

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The proxy variable actually used was chosen for two reasons. First, the Cam-bridge and Royal Commission studies of share ownership indicate that, amongmajor investing institutions, the proportionate divergence between registered andbeneficial ownership is smallest for insurance companies, as can be seen from Table3. Most of the holdings of insurance companies can therefore be easily identifiedfrom the share registers. Second, because of the size of their investments, arelatively high proportion of the largest shareholders tend to be insurance com-panies. For example, while the later Cambridge survey estimated that theirregistered holdings accounted for 10.6% of all quoted ordinary shares in 1969,among the top fifty holdings of the companies included in the regressions belowthey held an average of 30.97% of the shares. Thus, provided there is not a stronginverse correlation between T and the proportion of the equity of the top fifty heldby leading pension funds, investment trusts, unit trusts, etc., the former variablewill provide a reasonable measure of the relative importance of the major financialinstitutions among the largest shareholders. While the investment objectives ofother institutions may lead to portfolios which differ somewhat from those of theinsurance companies, we would not expect these variations to be so important asto invalidate the use of T as a proxy variable, and inspection of the holdings ofthose large pension funds and investment trusts which are easily identifiable lendssupport to this view.

In considering the factors which might influence the values of the parameters,a and x0 have been regarded as being jointly determined by industry, companysize and the ownership variable T, and reduced form equations have been estimatedfor each parameter in turn. Those firms with two types of ordinary share (whichare rather special cases) and companies having significant chi-square statistics inTable I were removed from the sample, leaving a total of 73 observations. Variousspecifications of the equations were tried and, while they all produced significantcoefficients on the size and type of ownership variables, the most satisfactoryresults were given by:

E(a) =0.0778+0.085l log (S)+2.207 T-3.231 T2 (22)(0.0219)* (0.570)* (0.936)*

+0.0311 D1--0.07l7 D2 0.0429 D3(0.0562) (0.0710) (0.0885)

R2=0.376 n=73E(x0) 1.084 - 0.0700 log (S) + 0.346 log (T) (23)

(0.0147)* (0.0969)*

0.0283 log (S) log (T)-0.0l44 D1+0.0060D2(0.0090)* (0.0215) (0.0263)

0.0900 D3(0.0323) *

R2=0.469 n=73The bracketed figures are standard errors and asterisks indicate significance at the1% level. It can be seen that both company size and the institutional investment


variable have highly significant effects on the parameters of the Pareto distributionwhereas, with one exception, the industry variables do not.

Since a is positively, and x0 is negatively, related to firm size (the latter relation-ship being moderated slightly by high levels of institutional ownership), the equa-tions indicate an unambiguous negative correlation between shareholdingconcentration and firm size. That is, large companies tend to have more dispersedownershipa result familiar from the literature on the divorce of ownership andcontrol. However, the more interesting implications of the regressions concern theeffects of the variable T. Equation (22) shows that the expected value of aincreases with T until the latter reaches 0.341 and declines thereafter. Theinitial increasing part of the curve can be explained by the fact, noted earlier,that a few family controlled firms tend to have distributions characterized by lowvalues of both a (due to the highly concentrated ownership) and T (simply becausethey are family firms). The declining part of the curve suggests that where insur-ance companies have a high percentage of the top holdings they could well be afactor tending to produce more concentrated share ownership. It may be notedthat in the sample T ranges from 0.005 to 0.58, with a median of 0.339, so that theturning point occurs well within the interval of sample values. The suggestedrelationship between concentration and the institutional ownership variable isconfirmed by equation (23) which shows x0 increasing with T for firms withcapital employed less than £204.1 millions and x0/aT greater the smaller the sizeof the company. In the sample, capital employed ranges from £4.14 million to£510.475 million, with a median of £35.352 million, and for all but five of theseventy three firms is less than £204.1 million. Taking equations (22) and (23)together, it can therefore be concluded that, for all but the very largest companies,there is an unambiguous positive relationship between shareholding concentrationand the institutional investment variable T at high (i.e. above the same median)values of the latter.

VI. SUMMARY AND CoNcLusIoNs

This paper has examined the size distributions of large sliareholdings in eachof a sample of eighty-five leading UK manufacturing companies and has exploredsome of the factors affecting the parameters of these distributions.

For each company in the sample a list of the largest shareholdings was con-structed. Each list contained, at a minimum, the top one hundred holdings inthat particular company. Using maximum likelihood estimation procedures,Pareto distributions were fitted to the data and their goodness of fit evaluated bymeans of the chi-square statistic. Overall, the Pareto distribution provided areasonably satisfactory description of the empirical size distribution of the largestfifty shareholdings in the sample companies, but failed for larger numbers ofholdings. The results of the estimations and goodness of fit tests, together with thefiuty-shareholding concentration ratio for each company, are given in Table 1.It is shown in the text how estimates of other concentration ratios can be derivedfrom this table.

Since in a large number of cases the Pareto distribution was unsatisfactory

264 BULLETIN

when applied to the full data sets, an attempt was also made to fit lognormaldistributions to the complete range of observations available for each firm. Maxi-mum likelihood estimates of the parameters in this case were derived from thetruncated samples by a method introduced by Cohen. Again using the cu-squaregoodness of fit test, it was found that, overall, the lognormal distribution did notyield an acceptable fit to the data.

In the final section, for the top fifty holdings, the effects on the parameters ofthe Pareto distribution of firm size, industry and the proxy variable T, measuringthe relative importance of the major financial institutions among each company'sleading owners, were examined. It was found that both company size and thevariable T had highly significant effects on the parameters whereas, with oneexception, the industry variables did not. The concentration of shareholdings wasnegatively related to firm size and tended to be a positive function of the institu-tional investment variable at higher values of the latter.

While earlier work on the divorce of ownership and control has laid stress onthe tendency for share ownership to become more dispersed as firm size increases,the results of section V suggest that tile well-documented increase in the proportionof ordinary shares held by the major financial institutions may be having effects inthe opposite direction. It is therefore quite possible that for large sections ofindustry the concentration of share ownership at the firm level, and hence thepower of shareholders in relation to management, may now be on the increase.

Department of Mathematical Statistics, University of Hull.Department of Economics, University of Newcastle upon Tyne.

REFERENCESChernoff, H. and Lehmann, E. L., 'Tile use of maximum likelihood estimates

in chi-square tests for goodness of fit', Ann. Math. Stat., 25, 1954, 579-586.Cohen, A. C., 'On estimating the mean and variance of singly truncated

normal frequency distributions from the first three sample moments', Ann. Inst.Stat. Math., 3, 1951, 37-44.

Cohen, A. C., 'Simplified estimators for the normal distribution whensamples are singly censored or truncated', Technometrics, 1, 1959, 217-237.

Cowling, K. C., 'Oligopoly and the distribution of income', WarwickEconomic Research Paper No. 68, 1975.

[5j Cramer, J. S., Empirical Econometrics, North-Holland 1968.Moyle, J., The Pattern of Ordinary Share Ownership, 1957-19 70, Cambridge

University Press 1971.Royal Commission on the Distribution of Income and Wealth, Report No. 2:

Income from Companies and its Distribution, London: Her Majesty's StationeryOffice 1975.

Stone, R., Reveil, J. and Moyle, J., The Owners of Quoted Ordinary Shares--A Survey for 1963, London: Chapman and Hall 1966.

Times, The Times 1000: Leading Companies in Britain and Overseas1970-71, London: Times Newspapers 1971.

the size distribution of large shareholdings in some leading british companies

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