Construction of market-implied measures of diversification

measures do not accurately account for the dissimilarities of products because they assume equal distances between SIC codes.²⁴⁶ Also, using segment data may cause distorted results due to strategic accounting: To avoid detailed information disclosures on separate segments in the presence of competitors, a firm may group multiple former independent business segments so that they appear to perform more poorly than single segment firms in the same industry.²⁴⁷ Alternatively, large reporting units may be created after an acquisition to reduce the danger of future goodwill write-offs.²⁴⁸

II.3.3. CONSTRUCTION OF MARKET-IMPLIED MEASURES OF

implied diversification measures employ a set of ten STOXX® EUROPE 600 sector indices to obtain information on the extent to which equity risks are diversifiable.

Barnea and Logue (1973), instead, use a broad market portfolio.

The starting point for constructing the market-implied diversification measures is a multivariate regression model: Let 𝑟_𝑖 denote the equity return of firm i in year t and let 𝑟_𝑖 be a linear function of the multivariate return series of ten STOXX® EUROPE 600 sector indices during the period commencing 250 days before and ending on the last trading day prior to the individual firm’s fiscal year end:

𝑟_𝑖 = 𝛿_𝑖𝑆_𝑗+ 𝜖_𝑖 (13)

where:

r_𝑖 = stock price return of asset i,

𝑆_𝑗 = multivariate return series of STOXX® EUROPE 600 sector indices,

𝛿_𝑖 = vector of regression parameters, and 𝜖_𝑖 = error term.

The first and most straightforward form of the market-implied diversification measures then involves numerically counting the number of significant regression coefficients in 𝛿_𝑖. MCOUNT takes a value of one if the number of significant coefficients exceeds one and is zero otherwise:

MCOUNT = {1, N_𝛿 > 1

0, N_𝛿 ≤ 1 (14)

where:

MCOUNT = degree of market diversification based on numerical count, and

N_𝛿 = number of significant regression coefficients.

To avoid distortions induced by insignificant regression coefficients, equation (13) is estimated using a forward stepwise regression procedure. The boundaries for the removal and the addition of a sector index are p ≥ .1 and p ≤ .05, respectively. Whenever R² is used, statistical inferences are based on Huber- White standard errors to correct for heteroscedastic residuals.²⁵¹

251 Cp. Huber, 1967, p. 221ff.; White, 1980, p. 817ff.

The index is the easiest to calculate among all market-implied diversification measures but falls short in taking into consideration differences in the size distribution and the relative importance of the various industry involvements. In order not to exaggerate the overall significance of diversification by merely counting the significant sector indices, this thesis proposes two more comprehensive diversification measures, MHDIV and MDIV, that reflect the relative strength of each STOXX® EUROPE 600 sector index.

The second measure is an application of the Berry-Herfindahl index and measures the extent of diversity as the inverse of the sum of the squares of each standardised regression coefficient divided by the squared sum of the absolute regression coefficients

𝑀𝐻𝐷𝐼𝑉 = 1 − ∑ 𝛿_𝑗²∗ 1 Δ_𝐽²

N_𝛿

𝑗=1

(15)

where:

𝑀𝐻𝐷𝐼𝑉 = degree of market diversification based on Herfindahl weighting scheme,

N_𝛿 = number of significant regression coefficients, Δ_𝐽 = sum of the absolute regression coefficients, and 𝛿_𝑗 = vector of regression parameters.

MHDIV assumes a value of zero for single-business firms and approaches towards one as the number of significant regression coefficients increases. Relying on the market’s view about the interrelationships between various industry sectors, MHDIV is robust against distortions resulting from the inherent hierarchy of industry classification systems such as the SIC system.²⁵² A major disadvantage of MHDIV is that it does not take account of the extent to which equity risks are diversifiable in external capital markets, thereby likely overestimating the level of corporate diversification. For instance, consider the case of three significant indices with homogenous beta-coefficients which according to equation (15) would mean a mid-degree of diversification (66%). Nevertheless, R² could be relatively small indicating that the portfolio uses the diversification benefits offered by equity capital markets only to a limited extent.

252 For a discussion of the limitations of the SIC system as an information source, instead of many, see Robins & Wiersema, 1995, p. 281f.

The third measure integrates the number of significant industry sectors, their relative importance, and the proportion of explained variance into a single diversification measure. More specifically, MDIV is the minimum of the proportion of explained variance (R²) and the inverse of a Herfindahl index based on standardised regression coefficients resulting from yearly forward stepwise regressions of equation (13):

𝑀𝐷𝐼𝑉 = min (𝑅²; 1 − ∑ 𝛿_𝑗²∗ 1 Δ_𝐽²

N_𝛿

𝑗

) (16)

where:

𝑀𝐷𝐼𝑉 = degree of market implied diversification 𝑅² = coefficient of determination,

N_𝛿 = number of significant regression coefficients, Δ_𝐽 = sum of the absolute regression coefficients, and 𝛿_𝑗 = vector of regression parameters.

In this equation, the left-hand side of the minimum function refers to the level of explained variance in the regression model. R² determines the extent to which the corporate portfolio makes use of diversification effects offered by external capital markets. The second element of the minimum function equals MHDIV.

Analogous to MHDIV, MDIV converges towards one as the firm becomes less focused.

The following example of BASF SE illustrates how the various market- implied measures can be used to obtain the level of corporate diversification. BASF SE is a German multi-national chemical organisation and, is amongst the most abundant chemical producer in the world. The corporate umbrella comprises subsidiaries and joint ventures around the world offering a broad range of products across the business sectors chemicals, plastics, performance products, crop protection products, and oil and gas. According to the market-implied diversification measures, BASF SE is diversified across the industries “Basic Materials” and “Industrials”; thereby making less use of diversification benefits offered by the capital market as indicated by low values of MHDIV and MDIV.

Table 4: Regression results for BASF and fiscal year 2017²⁵³

Linear, stepwise regression

VARIABLES Coef. Std. Err. t P>|t|

STOXX® EUROPE 600 INDUSTRIALS 0.334 0.072 4.650 0.000

STOXX® EUROPE 600 BASIC MATERIALS 0.454 0.073 6.240 0.000

OBSERVATIONS 256

R-SQUARED. 0.546

F TEST 116.76***

MCOUNT = 2

𝑀𝐻𝐷𝐼𝑉 = 1 −0.334²+ 0.454² (0.334 + 0.454)²= 0.489 𝑀𝐷𝐼𝑉 = min(0.546; 0.489) = 0.489

The estimates of the degree of diversification based on the traditional business count measures show that BASF SE is diversified across industry segments, but, except for one business segment, remains within the industry group chemicals (SIC codes beginning with 28XX). The two approaches therefore lead to different assessments of the portfolio configuration of BASF SE (e.g. MHDIV: 49%

<< H4DIV: 74%). This can have far-reaching implications for the analysis of the value contribution of diversification as contained in chapter IV.

Table 5: BASF SE reported sales per business unit and fiscal year 2017²⁵⁴

Segment description SIC Sales Sales^2

Functional Solutions 2851 20,745,000 430,355,025,000,000

Chemicals 2891 16,331,000 266,701,561,000,000

Performance Products 2865 16,217,000 262,991,089,000,000

Agricultural Products 2879 5,696,000 32,444,416,000,000

Oil & Gas 6221 3,244,000 10,523,536,000,000

Total n/a 62,233,000 1,003,015,627,000,000

𝐵𝐷𝐼𝑉4 = 5 BDIV2 = 2

𝐻4𝐷𝐼𝑉 = 1 −1,003,015,627,000,000 62,233,000² = 0.741 𝐻2𝐷𝐼𝑉 = 1 −58,989,000²+ 3,244,000²

62,233,000² = 0.100

253 Source: Own representation.

254 Source: Worldscope database by Thomson Reuters.

II.4. EMPIRICAL FINDINGS AND EXPLANATORY APPROACHES ON THE