Do diversified and focused firms have different growth ... · Evidence suggesting a bias in firm valuations between diversified and focused firms due to differing growth options also

Do diversified and focused firms have different growth options?

Evidence from total asset growth

Davin Wang*♦

This version: 20th August 2012

Abstract

_________________________________________________________________________

Do diversified and focused firms have different growth options? Focused firms yield

economically and significantly higher returns than diversified firms in periods of low growth,

with little difference in returns during periods of high growth. The findings are robust to

alternative diversification measures and persistent across portfolio variations. Overall, the

evidence suggests that diversified firms have growth options with lower systematic risk, thus

resulting in lower future returns. Differing growth options between diversified and focused

firms may explain the diversification discount, and more generally, the negative relationship

between total asset growth and stock returns known as the asset growth effect.

JEL Classification: G11, G12, G31, G32 Keywords: Diversification discount, Growth options, Systematic risk. _________________________________________________________________________

*Corresponding author: Department of Accounting & Finance, Monash University

Contacts: Telephone: +61 4 9903 2043, Email: [email protected]

♦I would like to thank my supervisors, Professor Christine Brown and Dr. Philip Gharghori,

for their invaluable support and feedback in the development of this paper. All errors and

omissions are my own.

mailto:[email protected]

ii

PREFACE

Thesis title: Diversification’s Effect on the Growth of Firms

Supervisors: Professor Christine Brown and Dr. Philip Gharghori

A walk down proverbial “Main Street” points one to the observation that diversified

conglomerates continue to increase in number and thrive. Contrary to conventional wisdom

of a diversification discount that suggests corporate diversification is value-destroying, the

continued resilience of the diversified form implies unique advantages over the single-

segment (focused) firm. This thesis seeks to investigate the effect of corporate diversification

in relation to firm growth by examining the following research topics:

1. Differing growth options between diversified and focused firms

New insight on differing growth options between focused and diversified firms

potentially explains the diversification discount and also yields important considerations for

investment portfolios that seek to incorporate the value of growth options in stock returns.

This paper suggests that the diversified firms experience growth with lower systematic risk.

2. Internal capital markets and firm growth

Internal capital markets (ICMs) are often cited as a value-adding channel of capital

allocation in diversified firms. ICMs are valuable because they reduce the constraints of

scarce capital in relation to productive investment. However, ICM characteristics differ

greatly among firms. This chapter will explore the impact of ICMs on firm growth.

3. Information frictions, corporate diversification and growth of the firm

Prior studies have looked at inefficiencies in the information diffusion process from

the external perspective of the investor, by relating the correction of stock prices to the partial

discovery of firm-specific information. In contrast, this study proposes a novel framework to

study the information diffusion process within a diversified firm versus a focused firm by

relating the investment decision to the efficient exercise of growth options.

The thesis will employ a thesis-by-publication format by developing each of the

above three topics into three separate papers for journal submission. To fulfil thesis

submission requirements, accompanying introductory and concluding chapters are included

to provide motivations and summaries for all findings.

1

1. Introduction

Do diversified and focused firms have different growth options? This question has

important relevance to the debate on a documented diversification discount where the shares

of diversified firms sell at a discount relative to single-segment (focused) benchmark firms.1

Growth options are well documented in the literature to constitute an significant portion of

firm value (see Merton and Modigliani (1961), Myers (1977), Myers and Turnbull (1977) and

Majd and Pindyck (1987), among others). In addition, both Kester (1984) and Danbolt, Hirst

and Jones (2002) underscore the significance of growth options by reporting that, on average,

the present value of growth options account for more than 50% of company market values.

Evidence suggesting a bias in firm valuations between diversified and focused firms due to

differing growth options also casts doubt on value destroying agency explanations for the

diversification discount in the corporate finance literature (examples include Amihud and Lev

(1981), Jensen (1988) and May (1995)).

In this paper I provide new evidence that diversified and focused firms have differing

growth options. The main motivation of this study rests in criticism of the basis by which the

diversification discount is established. Several studies such as Berger and Ofek (1995), Lins

and Servaes (1999) and Lamont and Polk (2002) document the diversification discount in the

valuations of diversified firms by comparing constituent business segments with

corresponding single-segment industry medians. 2 However, recent work suggests that this

approach is flawed. Graham, Lemmon and Wolf (2002) argue that failure to account for

systematic differences between the business segments of diversified firms and the focused

firms to which they are benchmarked may lead to incorrect inferences regarding the

diversification discount.3 More recently, Stowe and Xing (2006) suggests that the valuation

of diversified business segments cannot be based on single-segment medians if diversified

and focused firms have different growth options. They suggest that the diversification

1 See Martin and Sayrak (2003) for a complete review of the literature on the diversification discount. 2 The authors decompose diversified conglomerate firms into their constituent industry segments and value these segments separately in comparison with corresponding single-segment industry peers. The comparative valuation of all segments of the diversified conglomerate are then summed and compared with the market valuation. A “diversification discount” is reported when the comparative valuation based on the individual segments of the diversified firm is less than its actual market valuation. 3 The study finds no evidence that diversification destroys value. By analysing a sample of firms diversifying through mergers and acquisitions, the authors show that much of the excess value reduction documented as the diversification discount is due to target units being discounted already before acquisition.

2

discount documented by researchers could then be a manifestation of the difference in the

available growth options between diversified and focused firms.

The proposition that diversified and focused firms have different growth options can

be intuitively linked to firm structure. All things being equal, each firm is inherently endowed

with some measure of investment flexibility limited only by the growth options uniquely

available to it. In a portfolio context, the scope of growth options accessible to a firm is

constrained to the business segments and/or industries that it participates in. Growth options

will also have different levels of systematic risk specific to its business segment and industry.

As such, diversified firms that participate in a cross-section of product segments and/or

industries naturally have a greater number of growth options with more diverse correlations

of systemic risk than focused firms that have growth options concentrated in one business

segment. Assuming that growth options with lower systemic risk are optimal, this also

implies that investment managers in diversified firms are better positioned to select growth

options with lower systemic risk than counterparts in focused firms.

In order to develop testable hypotheses on the relationship between unobservable

growth options and firm value, it is imperative to begin with established theory. In this aspect,

the dynamic model of Berk, Green and Naik (1999) provides guidance. In their model, firm

value is composed of the value of growth options and the value of assets-in-place. Growth

options with low systematic risk are attractive to the firm. When exercised, the average

systematic risk of the firm’s cash flows in subsequent periods is reduced, leading to lower

returns. 4 Specifically, the model predicts that the turnover of assets-in-place has an

explanatory role for firm value because it alters the relative importance of growth options

versus existing assets.

More importantly, the model offers forward-looking empirical predictions that imply

the presence of differing growth options between diversified and focused firms. During times

of low asset turnover (low asset growth), firm value is determined largely by the value of

growth options. Conversely, during times of high asset turnover (high asset growth), firm

value is determined largely by the value of assets-in-place. Assuming that diversified firms

have a greater number of growth options with more diverse correlations of systemic risk than

focused firms, diversified firms should have lower returns than focused firms during periods

4 Similarly, Carlson, Fisher and Giammarino (2004) and Jacquier, Titman and YalçIn (2010) argue that the exercise of growth options changes a firm’s exposure to systematic risk.

3

of low growth. During periods of high growth, the model predicts that there should be little

difference in returns since firm value is then composed largely by the value of assets-in-place.

The empirical results of this study support the proposition that diversified and focused

firms have different growth options. Using a pooled sample of 57,395 firm-years comprising

of both diversified and focused firms taken from the CRSP/Compustat Merged Database

(CCM) during the period of 1980 to 2008, I show that on average, focused firms have

significantly higher returns than diversified firms during periods of low growth, with little

difference in returns during periods of high growth. These results are consistent with the

empirical predictions derived earlier. Furthermore, the return disparities between diversified

and focused firms persist even when alternative measures of diversification are applied, thus

providing strong evidence of differing growth options.

The results satisfy other related predictions of the model such as the difference in

return spreads for low-minus-high growth portfolios of focused and diversified firms. Return

differentials for low-minus-high growth portfolios that are statistically and economically

significant demonstrate the importance of growth options to firm valuation, whereas a larger

(smaller) return differential implies the presence of growth options with higher (lower)

systemic risk during periods of low growth. Similar to the findings of Kester (1984) and

Danbolt, Hirst and Jones (2002) that highlight the large contribution of growth options to

firm value, I find that that the return differential for low-minus-high growth portfolios of both

diversified and focused firms to be economically large and significant. In line with

expectations of differing growth options between diversified and focused firms, the low-

minus-high growth return differential for portfolios of focused firms is 8 times larger than

that of diversified firms. These results are also robust to alternative diversification measures.

The study contributes to existing knowledge in both the corporate finance and asset

pricing literature. First, on the corporate finance front, a significant new finding is that

diversified and focused firms have different growth options. On average, diversified firms

have growth options with lower systematic risk than focused firms, leading to lower future

returns. More importantly, the empirical results validate the warning put forth by Graham,

Lemmon and Wolf (2002) that failure to account for systematic differences between business

segments of diversified firms and benchmark single-segment industry firms may lead to

incorrect inferences about the diversification discount.

4

Separately, in related work, Stowe and Xing (2006) investigate the possibility of

differing growth options between diversified and focused firms by examining a limited

sample of 230 diversifying firms using proxies for growth options that have questionable

theoretical basis. The authors find no evidence of differing growth options between

diversified and focused firms. In contrast, this paper provides evidence of differing growth

options between diversified and focused firms that may explain the diversification discount.

Other key differentiating elements for this study include the reliance on established theory to

develop empirical predictions and the use of a much larger panel data sample of focused and

diversified firms. Use of established theoretical frameworks is important to developing

empirical predictions linking unobservable growth options to firm value to avoid misguided

interpretations. Further, firms do not change firm structure (from focused to diversified, or

vice versa) frequently. Use of a diversifying sample also sheds limited insight on the impact

of firm structure on growth options since diversifying events are relatively rare.

Second, on the asset pricing front, the study adds new empirical support to the

theoretical model of Berk, Green and Naik (1999) who show that the value of the firm is

equal to the value of assets-in-place and growth options. The findings also validates the

negative relationship between asset growth and firm returns, also known as the asset growth

effect, as detailed by Cooper, Gulen and Schill (2008). It extends their contribution with new

evidence that the asset growth effect is not only pervasive in the cross-section of stocks but

also independent of firm structure. Separately, by employing both dependent and independent

portfolio sorts of asset growth and diversification measures, I demonstrate that the low-

minus-high growth return differentials for focused firms are robust across portfolio variations

and hold potential for spread portfolios which may be of interest to industry practitioners.

In addition, the use of total asset growth as a proxy for growth options has important

implications for recent arguments which suggest that the asset growth effect is a result of

mispricing. Cooper, Gulen and Schill (2008) show that standard models of risk, such as the

three-factor model of Fama and French (1993) and four-factor model of Carhart (1997), have

difficulty in explaining the variation in returns associated with asset growth portfolios. More

recently, Gray and Johnson (2010) test the asset growth effect in Australian stock returns and

document its presence but likewise find no evidence to support a risk-based explanation. In

contrast, the results of this study present a rational alternative to these mispricing arguments

based on established theory. The link between total asset growth and growth options as

demonstrated in this study may be of interest to future investment-based asset pricing models.

5

Finally, this paper is related to other research that connects growth options to firm

value. Concurring with investment-based theoretical models, Anderson and Garcia-Feijoo

(2006) report strong support for the linkages between real investment options and changes in

both firm valuation and expected stock returns. Cao, Simin and Zhao (2008) find that growth

options explain an increasing trend of idiosyncratic risk over the past 4 decades beyond

alternative explanations. The innovation of this paper is the linkage of growth options with

varying systemic risk to the diversified form that in turn influences firm value.

The remainder of the paper is organized as follows. Section 2 discusses the linkages

between corporate diversification, growth options and firm value. Section 3 describes the

sample selection criteria, measures for diversification and total asset growth, as well as

empirical predictions. Section 4 presents the results. Section 5 concludes.

2. Related literature and hypotheses development

2.1 Risky growth options

The relative importance of growth options versus existing assets in determining firm

value is well documented in the literature. Gomes, Kogan and Lu (2003) demonstrate that

growth options are riskier than assets-in-place as these options are "leveraged" on existing

assets. In particular, they show that the association between capital spending (exercise of

growth options) and subsequent returns should be negative.5 From a real options context,

Carlson, Fisher and Giammarino (2004) extend this view by using simulations to empirically

examine related aspects of the investment problem such as operating leverage, reversible real

options, fixed adjustment costs, and finite growth options. Their model shows that asset betas

vary over time with historical investment decisions and the current product market demand,

effectively demonstrating that the ratio of growth options to assets-in-place can explain the

conditional dynamics in expected stock returns.

Similarly, Berk, Green and Naik (1999) shed light on how consumption of these risky

growth options can provide predictive inputs for firm value. Firm value in their model is

decomposed into risky growth options and existing assets-in-place. They reason that growth

options are heterogeneous and thus embody different levels of risk. As opportunities with

5 Similarly, Cooper, Gulen and Schill (2008) document a significant and persistent negative relationship between total asset growth and the cross-section of stock returns.

6

differing risk characteristics arrive and existing assets expire, firms respond optimally by

choosing growth options with lower systematic risk for new investment.6 Growth options

with low systematic risk are more attractive as systematic risk cannot be diversified away

while idiosyncratic project risk can be hedged. Consuming growth options with low

systematic risk reduces the average systematic risk of the firm’s cash flows in subsequent

periods, leading to lower realized firm returns on average. Overall, changing levels in the

firm’s asset portfolio leads to an explanatory role for market value because it alters the

relative importance of growth options versus existing assets within the firm.

2.2 The diversification advantage in the selection of growth options

The diversified form has important implications for how these risky growth options

are exploited. The extent to which a firm is able to influence its specific choice of investment

is naturally limited to the growth options uniquely available to it. In a larger context, the total

number and diversity of growth options accessible by a firm is limited by the number of

business segments and/or industries that it participates in. Since growth options intrinsically

have systemic risk that are unique to a specific product category, focused firms select from a

singular set of growth options within a narrow band of systematic risk as all cash flows are

derived from operations concentrated in one business segment. In contrast, diversified firms

have a larger set of growth options and can also optimally select growth options from a wider

range of systematic risk due to imperfectly correlated cash flows from diverse product

segments in one or more industries. Consequentially, due to inherently greater investment

flexibility, diversified firms are better positioned to “cherry-pick” attractive growth options.

Of course, this assumes that diversified firms have unique organizational advantages

that enhance the comparison and subsequent exercise of potential growth options. The

literature provides evidence of such efficiencies unique to diversified firms as well. Chandler

(1977) argues that diversified firms with multiple business divisions create a level of

management concerned with coordination of specialized divisions.7 Such specialization of

skill allows diversified firms to be more efficient and profitable than their lines of business

6 Systematic risk is the risk inherent in the aggregate market that cannot be solved by diversification. Some common sources of market risk are recessions, wars, interest rates and others that cannot be avoided through a diversified portfolio of products or industry mix. 7 Similarly, Matsusaka (1993) finds evidence of perceived benefits from managerial economies of scale in the merger and acquisition space by analysing announcement effects on firm value for diversifying acquisitions in which a firm acquires a target company in an unrelated industry. In the study, acquiring firms retaining the target’s management earned the largest positive abnormal returns, suggesting that the market favoured the diversifying acquisition because managerial synergies were exploited.

7

would be separately. Comparatively, focused firms are unlikely to have specialized layers of

management.

Weston (1970) contends that diversified firms allocate resources more efficiently due

to more efficient internal than external capital markets. Stulz (1990) extends this argument by

showing that diversified firms, by creating an internal capital market, reduce the

underinvestment problem described by Myers (1977), and allow diversified firms to make

more positive net present value investments than their segments would make as separate

entities. Collectively, consistent with the notion of a diversification advantage in the selection

of growth options proposed in this study, the literature suggests that diversified firms possess

organizational advantages over focused firms that enhance investment capabilities.

2.3 Diversification’s impact on asset growth and returns

The interaction of diversification and growth options leads to predictions for firm

value during different periods of asset turnover (asset growth). Firm value is determined

largely by the value of risky growth options during times of low asset turnover (low asset

growth firms). Since growth options are heterogeneous, firms that access growth options with

lower levels of systematic risk will have lower future returns. Following earlier arguments

that diversified firms have growth options with lower systematic risk than focused firms, the

returns of diversified firms are predicted to be lower than focused firms during periods of low

asset growth.

Conversely, during times of high asset turnover (high asset growth firms), firm value

is determined largely by the value of assets-in-place. Under constraints of investment

irreversibility, a firm has negligibly few growth options during periods of high asset growth

since all its resources are already committed to selected projects. The value of high asset

growth firms is then based predominantly on the firm’s existing assets-in-place that are

already generating cash flows. Assuming markets are efficient at valuing these cash flows, it

is predicted that high growth firms will have low future returns, regardless of firm structure.

The return differential between diversified and focused firms during periods of high asset

growth is thus predicted to be small.

The predictions for diversified and focused firms due to differing growth options

during different periods of growth are described by the following equations:

8

𝐹𝑂𝐶𝐿𝐴𝐺 > 𝐷𝐼𝑉𝐿𝐴𝐺 (1)

𝐹𝑂𝐶𝐻𝐴𝐺 ≅ 𝐷𝐼𝑉𝐻𝐴𝐺 (2)

Where,

𝐷𝐼𝑉𝐿𝐴𝐺 = return for low asset-growth portfolio of diversified firms

𝐹𝑂𝐶𝐿𝐴𝐺 = return for low asset-growth portfolio of focused firms

𝐷𝐼𝑉𝐻𝐴𝐺 = return for high asset-growth portfolio of diversified firms

𝐹𝑂𝐶𝐻𝐴𝐺 = return for high asset-growth portfolio of focused firms

The creation of low-minus-high asset growth portfolios of diversified and focused

firms is also predicted to generate contrasting return spreads. Return differentials between

low-minus-high growth segments that are statistically significant demonstrate the importance

of growth options to firm valuation, while larger (smaller) return differential implies the

presence of growth options with higher (lower) systemic risk. The following equation

describing return differentials for low-minus-high asset growth portfolios demonstrate the

return expectations for this scenario:

𝐹𝑂𝐶𝐿𝐴𝐺 − 𝐹𝑂𝐶𝐻𝐴𝐺 > 𝐷𝐼𝑉𝐿𝐴𝐺 − 𝐷𝐼𝑉𝐻𝐴𝐺 (3)

Where,

𝐹𝑂𝐶𝐿𝐴𝐺 − 𝐹𝑂𝐶𝐻𝐴𝐺= low-minus-high asset growth spread for focused firms

𝐷𝐼𝑉𝐿𝐴𝐺 − 𝐷𝐼𝑉𝐻𝐴𝐺 = low-minus-high asset growth spread for diversified firms

3. Sample selection and variable measures

3.1 Sample selection

Collated business segment and price data from the CRSP/Compustat Merged

Database (CCM) is used in this study. 8 Financial Accounting Standards Board (FASB)

regulation No. 14 and SEC Regulation S-K require firms to report audited footnote

8 CCM data draws from two separate sources: monthly price data for firms listed on the NYSE, AMEX or NASDAQ exchanges from the Centre for Research in Security Prices (CRSP) database and business segment data from the Compustat Industry Segment (CIS) database.

9

information for segments where sales, assets, or profits exceed 10% of consolidated totals for

fiscal years ending after December 15, 1977. The number of segments in a firm is also

reported. The initial data sample consists of firms from the CCM during the sample period

between 1978 and 2011.

Following Berger and Ofek (1995) and Lamont and Polk (2002), the data is refined

according to the following criteria. Firms are required to have total sales of at least $20

million. Firms with missing or negative segment information on sales, assets or capital

expenditures are excluded, as are firms with any segments in the one-digit standard industry

classification (SIC) codes of 6 or 9.9 In addition, information on outstanding shares required

to calculate market value and the measures of growth opportunities (total asset growth) and

diversification (Herfindahl Index) must be available. To keep the data sample comparable

with Cooper, Gulen and Schill (2008), firms in the sample are required to have at least three

consecutive years of firm data before and after the portfolio formation date to be included in

the sample.10 This step also corrects for survivor bias in the calculation of monthly returns,

caused by the backfilling of data by Compustat (see Fama and French (1993)). The sample is

also limited to firms with eight segments or less. This filter does not create a selection bias as

more than the 99 percent of the firm segment data is captured and also allows for better

representation of the typical firm in the cross-section. The final refined sample contains

57,395 firm year observations that lie in the year range of 1980 to 2008.

3.2 Measure of asset growth

A comprehensive measure of firm growth, total asset growth, or the year-on-year

percentage change in firm total assets, is used as a proxy for the interaction of growth options

and assets-in-place. 11 I use total asset growth as a proxy for three reasons. First, growth

options are unobservable in nature. Observable firm characteristics that are can serve as

accurate proxies for growth options as described by established theoretical models are rare. In

this study, a comprehensive measure of firm growth, total asset growth, or the year-on-year

9 SIC 6 data contains financial firms, where the market-to-book ratio and industry regulation makes asset growth difficult to interpret. SIC 9 data contain mostly non-operating divisions. 10 Cooper, Gulen and Schill (2008) require 5 consecutive years of accounting data and 3 consecutive years of price data around the portfolio formation date to calculate the 5-year change in the number of shares outstanding (ISSUANCE) and 36-month buy-and-hold return (BHRET36) variables respectively. The requirements for long consecutive data periods complement the goal of the study as corporate diversification rarely changes over time. Effectively, this allows for a better comparison of growth options available to focused and diversified firms. 11 In contrast, Berk, Green and Naik (1999) simplify the risk associated with firm assets such that size and book-to-market are sufficient statistics for the aggregate risk of assets-in-place.

10

percentage change in firm total assets, is a suitable proxy for the interaction of growth options

and assets-in-place as described by the model of Berk, Green and Naik (1999) model.

Second, Stowe and Xing (2006) suggest that proxies for growth options must be

forward-looking since only future growth options matter in firm valuation. Cooper, Gulen

and Schill (2008) demonstrate that total asset growth is an economically and statistically

significant predictor of the cross-section of stock returns that is not subsumed by the

explanatory power of prevailing measures such as book-to-market, firm capitalization, short-

and long-horizon lagged returns, but also dominates other growth measures in the literature.12

The authors also document persistence in the asset growth effect, both in the cross-section of

returns and over time. These considerations are important to the analysis since firms do not

change firm structure (from focused to diversified, or vice versa) frequently. Third, data on

any firm characteristic must be available at the segment level in order to allow for a detailed

comparison of growth options between focused and diversified firms. Data on segment assets

meets this criterion.

The base methodology for calculating the asset growth variable is adapted from

Cooper, Gulen and Schill (2008).13 The annual firm total asset growth rate (AG) is calculated

using the year-on-year percentage change in total assets. A firm must have non-zero total

assets in both year’s (t−1) and (t−2) in order to compute this measure. The firm’s asset

growth rate for year (t) is estimated as the percentage change in total assets from fiscal year

ending in calendar year (t−2) to fiscal year ending in calendar year (t−1), as depicted below:

𝐴𝐺(𝑡) = �𝐴𝐺(𝑡−1)−𝐴𝐺(𝑡−2) �𝐴𝐺(𝑡−2)

(4)

Asset growth is calculated for stocks which have at least 2 years of consecutive data

for total assets. Portfolios are formed in December of each year. Since regulations FASB No.

14 and SEC Regulation S-K were enforced for firms only after December 15, 1977, and at

least 2 years of consecutive data is required to calculate total asset growth, the first portfolio

12 In comparison with traditional growth measures such as capital investment, accruals, sales growth rates, and capital-raising, asset growth is the sum of the subcomponents of growth from both the left-hand or right-hand side of the balance sheet. As such, the authors suggest that the variable synergistically benefits from the predictability of all sub-components of growth, allowing asset growth to better predict the cross-section of returns relative to any single component of growth. 13 Cooper, Gulen and Schill (2008) employ both positive and negative asset growth values in their study. In contrast, Gray and Johnson (2010) differentiate between positive and negative asset growth values through separation into two different portfolios. While negative asset growth rates may signal speculative interpretations of firm distress or underperformance, there is no evidence linking it to firm structure in the corporate finance literature. Accordingly, both positive and negative asset growth values are included for analysis.

11

formation year is 1980. This portfolio formation procedure is repeated annually through to

December 2008.

3.3 Measures of diversification

Three diversification measures used by Comment and Jarrell (1995) are employed to

calculate firm diversification: (1) an asset based Herfindahl index (H_AT), (2) a sales based

Herfindahl index (H_SALE), and (3) the number of business segments (SEG) reported by

management. The Herfindahl index is calculated across 𝑁𝑗, segments for the j th firm in fiscal

year t as the sum of the squares of each segment i’s revenue as a proportion of total revenue,

where 𝑋𝑖𝑗𝑡 is the revenue attributable to a corporate segment:

𝐻𝑒𝑟𝑓𝑖𝑛𝑑𝑎ℎ𝑙 𝐼𝑛𝑑𝑒𝑥,𝐻 = ∑ � 𝑋𝑖𝑗𝑡∑ 𝑋𝑖𝑗𝑡𝑁𝑗𝑡𝑖=1

�2

𝑁𝑗𝑡𝑖=1 (5)

An illustration: if a firm with only one business segment will have a Herfindahl index

value of 1; if a firm has 10 business segments that each contribute 10 percent of the sales, its

Herfindahl sales index value is 0.1. In other words, the Herfindahl index value decreases as

firm diversification increases. A high Herfindahl index value describes a more focused firm

with a concentration of activities in fewer segments. A low Herfindahl index value describes

a more diversified firm with activities spanning multiple business segments and/or industries.

An asset-based index is calculated using the book value of identifiable assets per

segment. A sale-based Herfindahl index reflects the degree to which revenues are diversified

across a company’s business segments. The third measure of diversification, the number of

business segments (SEG), is a direct count of the number of segments declared by the

managers of the firm. Focused firms have only 1 business segment while diversified firms

have more than one business segment, ranging from 2 to a maximum of 8 segments.

Accordingly, firms become more diversified as the number of firm segments increases.

3.4 Summary statistics

Table 1 presents summary statistics for all firms (Panel A) in the pooled sample

during the sample period of 1980 to 2008 for a total of 57,395 firm-years. The median value

of unity for all 3 measures of diversification points to a higher proportion of focused firms in

the sample population. Total asset growth rates have a median of 8.17%, less than half of the

average growth rate of 21.59% for all firms. Statistics on SIZE reveal that the median firm

12

market capitalization is one-tenth of the average for the sample. While focused firms

naturally have a single segment per firm, the typical diversified firm has 2 business segments

per firm with a standard deviation of around 2 segments.

Table 1 Summary statistics

This table reports the pooled cross-sectional averages for each variable over the period of 1980 to 2008. Herfindahl index values for a firm’s total assets (total sales), H_AT (H_SALE), is calculated across n business segments as the sum of the squares of each segment i’s assets (sales), Si, as a proportion of total assets (sales). Segments are the number of lines of business (SEG) for which separate accounting disclosures are made by management in accordance with FASB No. 14 and SEC Regulation S-K. Total asset growth (AG) is defined as the percentage change in total assets from the fiscal year ending in calendar year t−2 to fiscal year ending in calendar year (t−1), in millions of dollars. Size (SIZE) is the market value of a firm calculated using the price and the number of shares outstanding at the end of year (t), in millions of dollars. RET12 is the buy-and-hold return for 1 year, from July (t) to June (t+1), where t is the portfolio formation year. All variables are calculated using data from the CRSP-Compustat merged database. All numbers, with the exception of SEG and SIZE, are in decimal form, that is 0.01 is 1%. Panel A reports results for the full sample while Panel B provides correlation data and coefficients among variables over the sample period. All variables are calculated using data from the CRSP-Compustat merged database. ***, ** and * indicate significance at 1%, 5% and 10% levels, respectively.

Panel A: Full Sample Variable N Mean Median Standard Deviation H_AT 57395 0.7810 1 0.2771 H_SALE 57395 0.7857 1 0.2701 SEG 57395 2 1 2 AG 57395 0.2159 0.0817 3.4768 SIZE 57395 2029 211 9426 RET12 57395 0.1392 0.0006 1.2459

Panel B: Correlation Data Variables H_AT H_SALE SEG AG SIZE RET12 H_AT 1 H_SALE 0.946*** 1 SEG -0.774*** -0.773*** 1 AG -0.013*** -0.014*** 0.012*** 1 SIZE -0.089*** -0.079*** 0.136*** 0.017*** 1 RET12 0.015*** 0.014*** -0.016*** -0.007* -0.023*** 1

Panel B of Table 1 reports the Spearman’s correlation results between the main

variables of interest. Not surprisingly, the measures of diversification have some measure of

correlation. The correlation coefficient is negative and significant between asset growth and 2

Herfindahl index measures of segment assets and segment sales. In contrast, there is positive

and significant correlation between asset growth and the number of firm segments. This is

expected due to an inverse relationship between the Herfindahl diversification measures of

segment assets or sales, and the number of firm segments. More importantly, there is no

13

correlation (significant at the 1% level) between all measures of diversification and asset

growth, firm size or stock returns, as well as between asset growth and firm returns.

4. Results

4.1 Fama and MacBeth regressions

Following Cooper, Gulen and Schill (2008), Fama and French (2008) and Gray and

Johnson (2010), I employ Fama and MacBeth (1973) (Fama-MacBeth) cross-sectional

regressions of annual firm stock returns on a base set of variables that include the three

diversification measures, namely the Herfindahl index values for segment assets (H_AT),

segment sales (H_SALE) and number of firm segments (SEG) as well as asset growth (AG).

The additional diversification measures of segment sales and firm segments are included as

robustness checks. I seek to determine if there is persistence in the predictive ability of the

base variables or if they are merely a manifestation of other determinants of the cross-section

of returns. The results of the regressions are shown in Table 2.

In models 1 and 2 of Table 2, Herfindahl index measures for segment assets (H_AT)

and segment sales (H_SALE) have t-stats that are both positive at 4.09 and 3.82 respectively

and significant at the 1% level. Meanwhile the diversification measure of number of firm

segments (SEG) in model 3 is also significant, but negative (-3.70). I interpret these findings

as supportive of the notion that diversification contains significant information for stock

returns. Model 4 of Table 3 estimates the Fama-MacBeth slopes for asset growth. Consistent

with Cooper, Gulen and Schill (2008) who likewise perform Fama-MacBeth regressions for

asset growth, the t-statistic for asset growth (AG) is negative and significant at -2.80.

Of particular interest are models 5 to 7 which competes the persistence of each

diversification measure against asset growth in the same Fama-MacBeth regression. Model 5

combines the Herfindahl measure of segment assets (H_AT) and asset growth (AG) together,

H_AT is not subsumed by asset growth but instead becomes stronger with a larger t-stat value

of -4.49, significant at the 1% level. In contrast, the t-stat for AG is slightly reduced from an

earlier value of -2.80 to -2.77. This trend for the change in slopes is consistent when the 2

other measures of diversification, H_SALE and SEG, are competed with asset growth in

models 6 and 7. However, the results suggest that H_AT is the strongest determinant among

the diversification factors.

14

Table 2 Fama–MacBeth regressions of annual stock returns on key characteristics

Annual stock returns from July 1980 to June 2008 are regressed on lagged accounting variables. Herfindahl index values for a firm’s total assets (total sales), H_AT (H_SALE), is calculated across n business segments as the sum of the squares of each segment’s assets (sales), as a proportion of total assets (sales). Segments are the number of lines of business (SEG) for which separate accounting disclosures are made by management in accordance with FASB No. 14 and SEC Regulation S-K. Asset growth (AG) is defined as the percentage change in total assets from the fiscal year ending in calendar year t−2 to fiscal year ending in calendar year (t−1), in millions of dollars. ***, ** and * indicate significance at 1%, 5% and 10% levels, respectively.

Model Constant H_AT H_SALE SEG AG BM SIZE 1 Beta 0.0711* 0.0794*** t-statistic (1.75) (4.09)

2 Beta 0.0706* 0.0799*** t-statistic (1.80) (3.82)

3 Beta 0.1664*** -0.0155*** t-statistic (3.62) (-3.70)

4 Beta 0.1472*** -0.0933*** t-statistic (3.48) (-2.80)

5 Beta 0.0814* 0.0817*** -0.0935*** t-statistic (1.98) (4.05) (-2.77)

6 Beta 0.0818** 0.0811*** -0.0934*** t-statistic (2.05) (3.78) (-2.77)

7 Beta 0.1786*** -0.0153*** -0.0924*** t-statistic (3.80) (-3.77) (-2.77)

8 Beta 0.0712* 0.0782*** -0.0833** 0.0142 -4.31E-06**

t-statistic (1.78) (3.82) (-2.52) (1.11) (-2.09) 9 Beta 0.0708* 0.0787*** -0.0831** 0.0140 -4.33E-06**

t-statistic (1.82) (3.62) (-2.52) (1.10) (-2.12) 10 Beta 0.1633*** -0.0142*** -0.0824** 0.0140 -4.09E-06**

t-statistic (3.62) (-3.55) (-2.53) (1.09) (-2.09)

In models 8 to 10, the base set of variables is now augmented by the control variables

of book-to-market (BM) and size (SIZE). Interestingly, BM is rendered completely

insignificant in all 3 models while SIZE maintains significance but at the lower 5% level. The

coefficients and t-statistics on diversification measures and asset growth remain strongly

statistically significant albeit marginally reduced, confirming the strong and economically

significant relation between the base variables and returns.

To summarize the results of the Fama-MacBeth regressions, H_AT is not subsumed

by the other important determinants of the cross-section, and in fact appears to be the

strongest determinant, in terms of t-statistics, of the cross-section of annual returns relative to

segment sales (H_ SALE), number of firm segments (SEG) and more importantly, asset

15

growth (AG). Overall, these findings suggest a significant economic relation between

diversification and firm returns.

4.2 Univariate portfolio sort on asset growth

Prior studies such as Cooper, Gulen and Schill (2008), Gray and Johnson (2010) and

Yao, Yu, Zhang and Chen (2011) document a negative relationship between total asset

growth and firm returns that is strongly robust across the cross-section of stocks and in

international markets. High asset growth firms earn lower future returns than low asset

growth firms. To verify the presence of an asset growth effect in the data sample, I construct

univariate portfolios based on asset growth deciles for each of the 29 years in the sample

period and then report the time-series average of yearly returns. At the end of June of each

year t over the sample period of July 1980 to June of 2008, stocks are allocated into decile

portfolios based on annual key characteristics. The portfolios are held for 1 year, from July of

year (t) to June of year (t+1), and then rebalanced. Portfolio returns are calculated for each

decile every year around the portfolio formation year (t) over the period. Firm return statistics

of the time-series average of yearly returns for each decile are reported in Panel A of Table 3.

The univariate portfolio sorts provide similar evidence to past studies. Conditioning

on growth rates creates a large and economically significant dispersion in average returns

across the 10 portfolios in the year after portfolio formation. Over this period, firms with the

lowest growth rates in decile 1 generate the largest significant returns of 35.89% per annum

on average, with a corresponding t-statistic of 4.03. Conversely, firms with the highest

growth in decile 10 report the lowest return at 5.09% per annum on average.

As in Cooper, Gulen and Schill (2008), the negative relation between growth and

returns is perfectly monotonic across all 10 deciles, with decile 2 growth firms earning 20.75%

per month, which smoothly decreases to 5.09% per month for decile 9 firms. Especially

notable is the significant large return spread (low-minus-high growth) of 30.80% with a t-

statistic of 4.21 between low and high asset growth portfolios (decile 1 minus decile 10). This

finding confirms that the negative relationship between firm asset growth and returns is

robust and pervasive in the data sample period.

16

Table 3 Univariate portfolio returns sorted on key characteristics in event time

At the end of June of each year (t) over 1980 to 2008, stocks are allocated into portfolios based on key characteristics. The portfolios are held for 1 year, from July of year t to June of year t+1, and then rebalanced. Portfolio return statistics are reported every year around the portfolio formation year (t) over the period of July 1980 to June of 2008. Panel F reports returns from stock portfolios sorted into deciles according to their asset growth rates. Asset growth (AG) is defined as the percentage change in total assets from the fiscal year ending in calendar year t−2 to fiscal year ending in calendar year t−1. Panel B reports returns from stock portfolios sorted into deciles according to their segment assets (sales) Herfindahl index value. Herfindahl index values for a firm’s total assets (total sales), H_AT (H_SALE), is calculated across n business segments as the sum of the squares of each segment’s assets (sales), as a proportion of total assets (sales). Stocks with Herfindahl index values less than 1 are sorted into 9 portfolios. Focused firms that have a Herfindahl index value of 1 are allocated to the portfolio 1. Panel C reports returns from stock portfolios sorted by the number of firm segments. Segments are the number of lines of business (SEG) for which separate accounting disclosures are made by management in accordance with FASB No. 14 and SEC Regulation S-K. Focused firms are those reporting exactly one segment whereas diversified firms are those reporting two or more segments.

Panel A: Univariate portfolio returns sorted by asset growth (AG)

Portfolio 1 2 3 4 5 6 7 8 9 10 Spread

(Low asset growth) (High asset growth) (1-10) AG RET12 0.3589 0.2075 0.1791 0.1265 0.1180 0.0868 0.0775 0.0709 0.0694 0.0509 0.3080

t-stat (4.03) (4.17) (3.51) (3.11) (3.33) (2.66) (2.29) (1.89) (1.72) (1.23) (4.21)

Panel B: Univariate portfolio returns sorted by Herfindahl index values for segment assets (H_AT) and segment sales (H_Sales)

Portfolio 1 2 3 4 5 6 7 8 9 10 Spread

(Focused) (Diversified) (1-10)

H_AT RET12 0.1502 0.1287 0.0979 0.1422 0.1153 0.1373 0.1297 0.0891 0.0855 0.0836 0.0666 t-stat (3.50) (3.19) (2.41) (2.77) (2.33) (3.12) (2.54) (2.02) (2.44) (2.16) (2.91)

H_SALE RET12 0.1504 0.1268 0.1184 0.1180 0.1169 0.0909 0.1394 0.0953 0.0999 0.0899 0.0605 t-stat (3.51) (2.87) (2.41) (2.59) (2.76) (2.23) (2.46) (2.22) (2.53) (2.36) (2.63)

Panel C: Univariate portfolio returns sorted by number of segments (SEG)

SEG 1 2 3 4 5 6 7 8 Spread

(Focused) (Diversified) (1-8) RET12 0.1529 0.1297 0.1044 0.1101 0.1004 0.0740 0.2851 0.0859 0.0428 t-stat (3.54) (2.82) (2.61) (2.88) (2.67) (2.05) (1.85) (1.79) (1.59)

17

4.3 Univariate portfolio sorts on diversification measures

Similarly, univariate portfolios based on the three diversification measures are

likewise constructed in Panels B and C of Table 3 for comparison and to discern for any

patterns in returns. Table 3, Panel B, reports returns from stock portfolios sorted into deciles

according to their Herfindahl index values for segment asset (sales). A Herfindahl index

value for a firm’s total assets (total sales), H_AT (H_SALE), is calculated across its business

segments as the sum of the squares of each segment’s assets (sales), as a proportion of total

assets (sales) for the firm. Stocks with Herfindahl index values less than 1 are diversified and

are sorted into decile 2 to 10, with decile 10 containing the most highly diversified stocks

according to segment assets (sales). Decile 1 stocks Herfindahl index values of unity and

contain focused firms.

Unlike portfolios sorted on asset growth, there is no clear pattern of monotonic returns

across the deciles for either diversification measure. Both diversification measures report the

largest returns of about 15% per annum for focused portfolios (decile 1) and the smallest

returns of about 8% per annum for highly diversified portfolios (decile 10). However, the

behaviour of returns in intermediate range is more random. For the Herfindahl index measure

of segment assets, decile 3 with more focused firms reports a significant 9.8% return, much

smaller than deciles 4 to 7 which have more diversified firms. Similarly, for the Herfindahl

measure of segment sales, deciles 3 to 5 report significant annual returns of about 11.8%,

smaller than decile 7 which returns a significant 14%.

For completeness, Panel C of Table 3 reports returns from portfolios sorted by the

third diversification measure – the number of firm segments. Firm segments are the number

of lines of business (SEG) for which separate accounting disclosures are made by

management in accordance with FASB No. 14 and SEC Regulation S-K. Focused firms are

those reporting exactly one segment whereas diversified firms are those reporting two or

more segments. Like earlier univariate portfolios based on Herfindahl index values, there is

no clear pattern in the returns of stocks sorted by the number of segments although the

extremes of the returns are more pronounced than either Herfindahl univariate sorts. In a

break from prior trends, single-segment focused firms no longer yield the largest returns

(15.29% per annum versus 28.51% for firms with 7 segments) while the most diversified

firms in decile 8 (highest number of segments) yield 4.28% per annum, which is no longer

18

the lowest return. The lowest return for the one-way sorts is reported by firms with 6

segments for a return of 7.40%.

Overall, univariate portfolio sorts on diversification measures are unable to reproduce

the monotonicity in returns across deciles evidenced by asset growth. I interpret these

findings as evidence that the diversification factor alone does not generate any clear pattern

of returns in the cross-section although results from the regression analysis earlier clearly

imply that diversification has information content relevant to firm value.

4.4 Returns to independent portfolio sorts on asset growth and diversification measures

In this section, I focus on the interaction of the diversification measure and asset

growth through independent portfolio sorts. This is first investigated through the construction

of portfolios based on independent sorts of the key variables, namely asset growth (AG)

against the measure of diversification individually. At the end of June of each year (t) over

1980 to 2008, stocks are allocated by a four-by-four sorting process into 16 independently

sorted portfolios based on the respective diversification measures and asset growth

characteristic. The portfolios are held for 1 year, from July of year (t) to June of year (t+1),

and then rebalanced. The time-series of portfolio returns around the portfolio formation year

(t) over the period of July 1980 to June of 2008 are then averaged.

Allocation of firms into portfolios sorted by the diversification measure of Herfindahl

index values differ slightly from the diversification measure of number of firm segments

(SEG) because Herfindahl index values range from 1 (focused) to values less than 1 but

greater than 0 (diversified), while firm segments are separated by integer values ranging from

1 (focused) to 8 (diversified). As such, portfolios sorted by Herfindahl index values have

focused firms (Herfindahl index values = 1) allocated to portfolios 1 while diversified firms

(0<Herfindahl index values < 1) are allocated to portfolios 2 to 4, with portfolio 4 being the

most diversified. To allow for comparison, firms sorted by number of segments are likewise

allocated into 4 portfolios. Focused firms are consolidated into portfolio 1 while diversified

firms (2 to 8 firm segments) are assigned to portfolios 2 to 4. Portfolios 2, 3 and 4 have

diversified firms of 2 to 3, 4 to 5 and 6 to 8 segments respectively.

Table 4 reports 3 panels (A,B and C) that tabulate independent sorts of asset growth

against each of the three diversification measures respectively, namely Herfindahl index

values for firm segment assets (H_AT) and firm segment sales (H_SALE) as well as the

19

number of firm segments (SEG). Several general characteristics stand out for all three panel

results. First, for all panels, low growth stocks (row 1) generally have larger returns than high

growth stocks (row 4). This trend is also robust across all columns or more specifically, for

both focused and diversified firms. This finding is no surprise as a strong and robust negative

relationship between asset growth and firm returns is reported in the literature and also

documented in the univariate portfolio sorts of this study.

Table 4 Independent portfolio returns sorted on key characteristics in event time

At the end of June of each year (t) over 1980 to 2008, stocks are allocated by a four-by-four independent sorting process into 16 independently sorted portfolios based on asset growth (AG) and the corresponding diversification measure. The portfolios are held for 1 year, from July of year (t) to June of year (t+1), and then rebalanced. Portfolio returns around the portfolio formation year (t) over the period of July 1980 to June of 2008 are then averaged. Portfolios sorted by Herfindahl index values have focused firms (Herfindahl index values = 1) allocated to portfolios 1 while diversified firms (0<Herfindahl index values < 1) are allocated to portfolios 2 to 4, with portfolio 4 being the most diversified. Panel A and B report independent portfolio sorts of AG by Herfindahl index values for segment assets (H_AT) and segment sales (H_SALE) respectively. Firms sorted by number of segments (SEG) are likewise allocated to 4 portfolios. Focused firms are consolidated into portfolio 1 while diversified firms (2 to 8 firm segments) are assigned to portfolios 2 to 4. Panel C reports independent portfolio sorts by AG and SEG.

Panel A: Independent portfolio sort of asset growth (AG) by segment assets (H_AT)

Assets Herfindahl Index (H_AT) Portfolio

1 2 3 4 Spread Focused-minus-

diversified Focused Diversified

Asset Growth (AG)

1 (Low growth)

RET12 0.3290 0.1830 0.2293 0.1126 Low growth

t-statistic (4.47) (3.36) (3.27) (2.54) 0.2164

Sample 261 81 78 74 (4.43)

2

RET13 0.1382 0.1540 0.1192 0.0990 t-statistic (3.40) (3.35) (2.66) (2.56) Sample 277 76 70 73

3


4 (High

growth)

RET14 0.0513 0.0485 0.0676 0.0775 High growth

t-statistic (1.24) (1.18) (1.54) (1.96) -0.0262

Sample 275 63 81 76 (-1.26)

Spread Focused Diversified Low-minus-high growth 0.2777 0.0351 t-statistic (5.26) (1.58)

20

Panel B: Independent portfolio sort of asset growth (AG) by segment sales (H_SALE)

Sales Herfindahl Index (H_SALE) Portfolio

1 2 3 4 Spread Focused-minus-

diversified Focused Diversified

Asset Growth (AG)

1 (Low growth)

RET12 0.3282 0.2116 0.2119 0.1193 Low growth

t-statistic (4.46) (3.50) (3.66) (2.54) 0.2089

Sample 258 82 77 77 (4.25)

2


3


4 (High

growth)

RET14 0.0505 0.0498 0.0531 0.0902 High growth

t-statistic (1.22) (1.19) (1.30) (2.18) -0.0397

Sample 274 60 83 77 (-1.58)


Panel C: Independent portfolio sort of asset growth (AG) by number of segments (SEG)

Number of segments (SEG)

Portfolio 1 2-3 4-5 6-8 Spread

Focused-minus-diversified Focused Diversified

Asset Growth (AG)

1 (Low growth)

RET12 0.3103 0.1494 0.1432 0.1629 Low growth

t-statistic (4.48) (3.06) (2.92) (2.50) 0.2141

Sample 330 112 40 13 (3.65)

2


3


4 (High

growth)

RET14 0.0605 0.0796 0.0587 0.0522 High growth

t-statistic (1.44) (1.94) (1.53) (0.82) 0.0124

Sample 345 95 41 18 (0.45)

Spread Focused Diversified

Low-minus-high growth 0.2669 0.0652

t-statistic (5.28) (1.81)

21

Panel A of Table 4 reports independent portfolio sorts on AG and H_AT. Low-growth

diversified firms post a return of 11.26% versus 7.75% per annum for high-growth,

diversified firms. The corresponding low-minus-high growth return spread for diversified

firms is 3.51%. In contrast, low-growth focused firms in the same panel report a 32.90%

return (almost 3 times that of low-growth diversified firms) while high-growth focused firms

have a significant and smaller return of 5.13%. Correspondingly, the low-minus-high growth

return differential for focused firms is a much larger at 27.77% or a multiple of almost 8

times that of the low-minus-high growth return differential for diversified firms.

Panel B, Table 4, tabulates returns for independent portfolio sorts on AG and H_SALE.

Returns for the low-growth and high-growth portfolios are qualitatively identical for both

diversified and focused portfolio partitions to earlier findings for H_AT in Panel A. In this

case, the low-minus-high growth return spread for diversified firms is 2.91%, while focused

firms earn a low-minus-high growth return of 23.80% for a similar multiple of about 8 times

that of diversified firms.

I repeat the analysis for independent portfolio sorts on AG and SEG in Panel C, Table

4, and find a similar pattern in returns for diversified and focused firms in phases of high and

low asset growth. Specifically, low-growth diversified firms (6 to 8 segments per firm) post a

significant return of 16.29% versus 5.22% for high-growth diversified firms, with a low-

minus-high growth return differential of 6.52%. Returns for low-growth focused firms came

to 31.03% while high-growth focused firms yielded 6.05%. A large and significant low-

minus-high growth return differential of 26.69% per annum with t-statistic of 5.28 is repeated

for this portfolio. In this instance, the low-minus-high growth return differential for focused

firms is a smaller albeit economically significant multiple of 4 times that of diversified firms.

4.5 Returns to dependent portfolio sorts on asset growth and diversification measures

Rather than base ensuing conclusions on the independent portfolio sort in Table 5, it

is instructive to examine dependent sorts of the base variables to see if the return patterns

documenting the interaction of diversification and asset growth are robust across portfolio

variations. This step allows for an assessment of the extent to which the valuation effect of

differing growth options between diversified and focused firms is pervasive in the cross-

section of returns, and for industry application, also provides an indication of the attainability

of reported returns to spread portfolios.

22

As before, at the end of June of each year (t) over 1980 to 2008, stocks are allocated

by a four-by-four sorting process into 16 sorted portfolios. However, the four-by-four sorting

process is now based on first ranking the pool of stocks for every year by the dependent

measure into 4 portfolios, and then subsequently ranking each of these portfolios into another

4 portfolios by ranking on the alternate variable measure of interest.

Table 5 Dependent portfolio returns sorted on key characteristics in event time

At the end of June of each year (t) over 1980 to 2008, stocks are allocated by a four-by-four dependent sorting process into 16 dependently sorted portfolios by alternating asset growth (AG) and the corresponding diversification measure as dependent and independent variables. The portfolios are held for 1 year, from July of year (t) to June of year (t+1), and then rebalanced. Portfolio returns around the portfolio formation year (t) over the period of July 1980 to June of 2008 are then averaged. Portfolios sorted by Herfindahl index values have focused firms (Herfindahl index values = 1) allocated to portfolios 1 while diversified firms (0<Herfindahl index values < 1) are allocated to portfolios 2 to 4, with portfolio 4 being the most diversified. Firms sorted by number of segments (SEG) are likewise allocated to 4 portfolios. Focused firms are consolidated into portfolio 1 while diversified firms (2 to 8 firm segments) are assigned to portfolios 2 to 4. Panels A and C report dependent portfolio sorts first by AG followed by the Herfindahl index values for segment assets (H_AT) and segment sales (H_SALE), respectively. Panels B, C and D report dependent portfolio sorts first by each diversification measure H_AT, H_SALE and SEG followed by AG, respectively.

Panel A: Dependent portfolio sort of asset growth (AG) by Herfindahl index value of segment assets (H_AT)

Assets Herfindahl Index (H_AT)

Portfolio 1 2 3 4 Spread


Asset Growth (AG)

1 (Low growth)

RET12 0.3290 0.1774 0.2479 0.1100 Low growth

t-statistic (4.47) (3.37) (3.25) (2.49) 0.2190 Sample 261 78 78 77 (4.51)

2

RET13 0.1382 0.1545 0.1203 0.1008 t-statistic (3.40) (3.30) (2.67) (2.67)

Sample 277 72 73 72

3

RET13 0.0859 0.0840 0.0540 0.0532

t-statistic (2.58) (2.38) (1.42) (1.52)

Sample 291 69 68 68

4 (High

growth)

RET14 0.0513 0.0527 0.0632 0.0753 High growth

t-statistic (1.24) (1.22) (1.49) (1.91) -0.0240 Sample 275 79 68 73 (-1.02)


23

Panel B: Dependent portfolio sort of Herfindahl index value of segment assets (H_AT) by asset growth (AG)

Portfolio

Asset Growth (AG) 1 2 3 4 Spread

Low-minus-high growth Low growth High

growth

Assets Herfindahl

Index (H_AT)

1 Focused

RET12 0.3252 0.1256 0.0938 0.0564 Focused


2

RET13 0.1864 0.1655 0.0764 0.0441

t-statistic (3.43) (3.22) (2.25) (1.12)

Sample 72 72 72 72

3

RET13 0.2497 0.1330 0.0793 0.0589 t-statistic (3.18) (2.72) (1.98) (1.36)

Sample 73 74 74 74

4 Diversified

RET14 0.1087 0.0903 0.0836 0.0616 Diversified


Spread Low growth High growth Focused-minus-diversified 0.2165 -0.0053 (t-statistic) (4.59) (-0.37)

Panel C: Dependent portfolio sort of asset growth (AG) by Herfindahl index value of segment sales (H_ SALE)

Sales Herfindahl Index (H_ SALE)

Portfolio 1 2 3 4 Spread


Asset Growth (AG)

1 (Low growth)

RET12 0.3282 0.2083 0.1884 0.1478 Low growth


2

RET13 0.1397 0.1523 0.1201 0.0976 t-statistic (3.45) (2.99) (2.82) (2.60)

Sample 275 73 74 73

3

RET13 0.0870 0.0718 0.0560 0.0591

t-statistic (2.61) (2.02) (1.53) (1.61)

Sample 289 69 68 68

4 (High

growth)

RET14 0.0505 0.0555 0.0364 0.0947 High growth

t-statistic (1.22) (1.25) (0.96) (2.22) -0.0262 Sample 274 78 70 73 (-1.26)

Spread Focused Diversified Low-minus-high growth 0.2777 0.0531 (t-statistic) (5.23) (1.90)

24

Panel D: Dependent portfolio sort of Herfindahl index value of segment sales (H_ SALE) by asset growth (AG)

Portfolio



growth

Sales Herfindahl

Index (H_SALE)

1 Focused

RET12 0.3256 0.1254 0.0943 0.0566 Focused


2

RET13 0.2180 0.1545 0.0702 0.0449

t-statistic (3.46) (2.95) (2.00) (1.08)

Sample 72 72 72 72

3


4 Diversified

RET14 0.1188 0.0955 0.0924 0.0734 Diversified


Spread Low growth High growth Focused-minus-diversified 0.2068 -0.0167 (t-statistic) (4.33) (-1.14)

Panel E: Dependent portfolio sort of number of segments (SEG) by asset growth (AG)

Portfolio



growth

Number of

segments (SEG)

1 Focused

RET12 0.3070 0.1355 0.0916 0.0570 0.2628 t-statistic (4.47) (3.34) (2.64) (1.38) (5.27) Sample 338 338 339 338

2-3

RET13 0.1524 0.1323 0.0651 0.0759

t-statistic (3.15) (3.04) (1.83) (1.91)

Sample 106 107 107 106

4-5

RET13 0.1428 0.0679 0.0844 0.0606

t-statistic (2.99) (1.81) (2.04) (1.70)

Sample 38 39 39 38

6-8 Diversified

RET14 0.1272 0.1606 0.5486 0.0537 0.1238 t-statistic (1.90) (1.97) (1.24) (1.03) (1.06) Sample 14 12 12 13

Spread Low growth High growth

Focused-minus-diversified 0.1203 -0.0187

(t-statistic) (1.42) (-0.70)

25

For example, for a dependent sort with AG as the dependent variable and H_AT as

the independent variable, stocks are ranked first into 4 portfolios from low to high asset

growth. Each portfolio is further subdivided into another 4 portfolios by ranking stocks based

on H_AT values into another 4 portfolios. A total of 16 portfolios are constructed through

this process.

The process is repeated by alternating H_AT as the dependent variable and AG as the

independent variable, resulting in 2 panels of dependent portfolio sorted returns. This process

is repeated for AG and all three diversification measures with the exception of the dependent

portfolio sort of AG by SEG, where only 1 table of results is produced due to the static

allocation of firms to portfolios by number of firm segments.

4.5.1 Returns to dependent portfolio sorts on asset growth and the Herfindahl index values

of segment assets

Table 5, Panel A, reports the dependent portfolio sort first by AG followed by H_AT.

Low-growth diversified firms post a return of 11% versus 7.53% for high-growth, diversified

firms. In contrast, low-growth focused firms report a significant 32.90% return while high-

growth focused firms have a substantially smaller return of 5.13%. The corresponding low-

minus-high growth return spread for focused firms is a significant 27.77% (t-statistic of 5.26)

which is 8 times that of the 3.47% return spread (weakly significant t-statistic of 1.50) for

diversified firms.

Table 5, Panel B, reports returns for a dependent sort first by H_AT followed by AG.

Low-growth highly diversified firms post a significant return of 10.87% (t-statistic of 2.48)

versus 6.16% for high-growth highly diversified firms, with a significant low-minus-high

growth return spread of 4.71% (t-statistic of 2.42). Returns for low-growth focused firms

came to 32.52% (t-statistic of 4.55) while high-growth lowly diversified firms yielded 5.64%

(t-statistic of 1.38). The large low-minus-high growth return spread for focused firms vis-à-

vis diversified firms persists, with the spread for focused firms (26.89%) being almost 6 times

larger than that of diversified firms (4.71%).

Earlier regressions and portfolio sorts demonstrate that total asset growth rates are a

strong predictor of future returns for all types of firm structure, specifically, both focused and

diversified firms. This finding is again demonstrated in the dependent sorts consistent with

earlier papers showing that firm growth should be fundamentally linked to lower expected

26

returns (Cooper, Gulen and Schill (2008), Berk, Green and Naik (1999), Gomes, Kogan and

Lu (2003), Carlson, Fisher and Giammarino (2004), Anderson and Garcia-Feijoo (2006), and

others).

A significant new finding is that portfolios conditioned on diversification measures

hold important predictions for future returns during period of low and high asset growth.

During periods of low asset growth, diversified firms have lower future returns than focused

firms while there is little difference in returns during periods of high asset growth. These

results are consistent with the interpretation that diversified firms have different growth

options with lower systematic risk compared to focused firms. This observation also fall in

line with a general theme in corporate finance literature which argues that the diversified

form is important to firm value (Lamont and Polk (2001), Campa and Kedia (2002),

Villalonga (2004), Gao, Ng and Wang (2008), Anjos (2010), and others) but presents unique

evidence that diversification has a real economic impact on the exercise of growth options

available to a firm.

4.5.2 Robustness checks: Returns to dependent portfolio sorts on asset growth and the

Herfindahl index values of segment sales and the number of firm segments

A valid consideration is whether the pattern of returns from dependent portfolio sorts

of AG followed by H_AT will hold if other measures of corporate diversification are

employed. In order to further test that these findings are not spurious results of measurement

or classification error specific to accounting information of segment assets, 2 other

established and popular measures of diversification in the literature, namely the Herfindahl

index measure of segment sales and the number of firm segments (see Berger and Ofek

(1995), Comment and Jarrell (1995), Graham, Lemmon and Wolf (2002), Mansi and Reeb

(2002),Stowe and Xing (2006), among others), are used for robustness checks.

Panel C of Table 5 reports returns for the dependent portfolio sort of first by AG

followed by H_SALE. Portfolios for low-growth focused firms yield a 33.82% return versus

5.05% for high-growth focused firms. Low-growth diversified firms yield 14.78% in returns

(2 times smaller than low-growth focused firms) and high-growth diversified portfolios report

a significant and smaller 9.47% return. The low-minus-high growth return spread is

comparatively larger than the comparable independent portfolio sort of AG by H_SALE. In

this case, the low-minus-high growth return differential for diversified firms is 5.31% (versus

2.91% for the independent sort of AG by H_SALE), while the low-minus-high growth return

27

differential for focused firms is larger 27.77% (versus 23.80% for the independent sort of AG

by H_SALE).

As for the dependent sort of first by H_SALE followed by AG reported in Panel D of

Table 5, low-growth diversified firms post 11.88% returns versus 7.34% for high-growth

firms in the same row. Consistent with earlier findings, returns for low-growth focused firms

came to 32.56% (t-statistic of 4.55), or about 5 times the 5.66% yield of high-growth lowly

diversified firms. The low-minus-high growth return spread continues to be robust at a

multiple of 6 times for focused versus diversified firms.

Lastly, the robustness check is repeated for the dependent sort of SEG followed by

AG. Low-growth diversified firms (6 to 8 segments per firm) post a return of 12.72% versus

5.37% for high-growth diversified firms, with an accompanying low-minus-high growth

insignificant return spread of 12.38%. Returns for low-growth focused firms yielded 30.70%.

High-growth focused firms yielded 5.70%. In this case, the low-minus-high growth return

differential for focused firms came in at 26.28% per annum with strongly significant t-

statistic of 5.27.

5. Conclusion

In this article, I provide new evidence that diversified and focused firms have

different growth options. This is done this by comparing future returns of diversified and

focused firms during different periods of low and high asset growth. I show that on average,

focused firms have significantly higher returns than diversified firms during periods of low

growth, with little difference in returns during periods of high growth.

The difference in return spreads for low-minus-high growth periods for portfolios of

focused and diversified firms are also economically large and significant, with the return

differential for portfolios of focused firms being larger than that of diversified firms. By

employing both dependent and independent portfolio sorts of the key variables, I show that

the diversification effect on growth options is robust to portfolio variations and holds

potential for spread portfolios.

The results of this study bring important insights to both corporate finance and asset-

pricing literature. A unique contribution is that diversified and focused firms have different

growth options. The implications of this new finding are large. While the literature

28

documents linkages between growth options and firm value, this study offers a novel

connection of growth options with varying systemic risk to the diversified form. In addition,

this connection of differing growth options to firm structure not only contest agency

explanations that firm diversification is value destroying but also offers a rational explanation

for the diversification discount.

In documenting that diversified firms have growth options with lower systemic risk

than focused firms, the results support the findings of Mansi and Reeb (2002) who argue that

the documented discount stems from risk-reducing effects of corporate diversification. 14

Separately, a rational alternative to mispricing arguments for the negative relationship

between total asset growth and stock returns, also known as the asset growth effect, is offered.

This study also has its share of weaknesses. While the results demonstrate

convincingly the relative importance of growth options to firm value during times of low and

high asset growth, there is limited insight into how assets-in-place serve as a driver of returns

during periods of high asset growth. While the model employed in this study does not

consider alternative considerations related to diversification such as internal capital markets

or the productivity of firms, this gap holds potentially interesting questions for future work.

Lastly, the process of developing this paper has also provided learning points for

future research on the diversification discount. As suggested by Graham, Lemmon and Wolf

(2002), this paper agrees that future papers connecting growth options to firm value must take

heed to account for systematic differences between business segments of diversified firms

and benchmark single-segment industry firms in order to avoid incorrect inferences. On a

more general note, this author suggests that it is imperative for empirical researchers to take

into account established theoretical models when making predictions about the influence of

unobservable factors, such as growth options, on firm value.

14 The authors observe that (a) the diversification discount is most pronounced in those firms with greater than average debt levels, (b) all equity firms do not exhibit a diversification discount, and (c) using book values of debt to compute excess value creates a downward bias for diversified firms. Together, consistent with a risk-reduction hypothesis, these results indicate that diversification is insignificantly related to excess firm value.

29

6. References

Anderson, C. W., and L. Garcia-Feijoo, 2006, Empirical evidence on capital investment, growth options, and security returns, The Journal of Finance 61, 171-194.

Anjos, Fernando, 2010, Costly refocusing, the diversification discount, and the pervasiveness of diversified firms, Journal of Corporate Finance 16, 276-287.

Berger, Philip G., and Eli Ofek, 1995, Diversification's effect on firm value, Journal of Financial Economics 37, 39-65.

Berk, Jonathan B., Richard C. Green, and Vasant Naik, 1999, Optimal investment, growth options, and security returns, The Journal of Finance 54, 1553-1607.

Campa, Jose Manuel, and Simi Kedia, 2002, Explaining the diversification discount, The Journal of Finance 57, 1731-1762.

Cao, Charles, Timothy Simin, and Jing Zhao, 2008, Can growth options explain the trend in idiosyncratic risk?, The Review of Financial Studies 21, 2599-2633.

Carhart, Mark M., 1997, On persistence in mutual fund performance, The Journal of Finance 52, 57-82.

Carlson, M., A. Fisher, and R. Giammarino, 2004, Corporate investment and asset price dynamics: Implications for the cross-section of returns, The Journal of Finance 59, 2577-2603.

Chandler, A.D., 1977, The Visible Hand Belknap Press, Cambridge, MA.

Comment, Robert, and Gregg A. Jarrell, 1995, Corporate focus and stock returns, Journal of Financial Economics 37, 67-87.

Cooper, M. J., H. Gulen, and M. J. Schill, 2008, Asset growth and the cross-section of stock returns, The Journal of Finance 63, 1609-1651.

Danbolt, J., I. Hirst, and E. Jones, 2002, Measuring growth opportunities, Applied Financial Economics 12, 203-212.

Fama, E. F., and K. R. French, 2008, Dissecting anomalies, The Journal of Finance 63, 1653-1678.

Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, 3-56.

Fama, Eugene F., and James D. MacBeth, 1973, Risk, return, and equilibrium: Empirical tests, Journal of Political Economy 81, 607.

Gao, Wenlian, Lilian Ng, and Qinghai Wang, 2008, Does geographic dispersion affect firm valuation?, Journal of Corporate Finance 14, 674-687.

Gomes, Joao, Leonid Kogan, and Zhang Lu, 2003, Equilibrium cross section of returns, Journal of Political Economy 111, 693-732.

30

Graham, John R., Michael L. Lemmon, and Jack G. Wolf, 2002, Does corporate diversification destroy value?, The Journal of Finance 57, 695-720.

Gray, Philip, and Jessica Johnson, 2010, The relationship between asset growth and the cross-section of stock returns, Journal of Banking & Finance In Press, Corrected Proof.

Jacquier, Eric, Sheridan Titman, and Atakan YalçIn, 2010, Predicting systematic risk: Implications from growth options, Journal of Empirical Finance 17, 991-1005.

Kester, W., 1984, Today’s options for tomorrow’s growth., Harvard Business Review 153– 160.

Lamont, Owen A., and Christopher Polk, 2001, The diversification discount: Cash flows versus returns, The Journal of Finance 56, 1693-1721.

Lamont, Owen A., and Christopher Polk, 2002, Does diversification destroy value? Evidence from the industry shocks, Journal of Financial Economics 63, 51-77.

Mansi, Sattar A., and David M. Reeb, 2002, Corporate diversification: What gets discounted?, The Journal of Finance 57, 2167-2183.

Matsusaka, John G., 1993, Takeover motives during the conglomerate merger wave, The RAND Journal of Economics 24, 357-379.

Myers, Stewart C., 1977, Determinants of corporate borrowing, Journal of Financial Economics 5, 147-175.

Stowe, John D., and Xuejing Xing, 2006, Can growth opportunities explain the diversification discount?, Journal of Corporate Finance 12, 783-796.

Stulz, RenéM, 1990, Managerial discretion and optimal financing policies, Journal of Financial Economics 26, 3-27.

Villalonga, Belen, 2004, Diversification discount or premium? New evidence from the business information tracking series, The Journal of Finance 59, 479-506.

Weston, J.F. , 1970, The nature and significance of conglomerate firms, St. Johns Law Review 44, 66 - 80.

Yao, Tong, Tong Yu, Ting Zhang, and Shaw Chen, 2011, Asset growth and stock returns: Evidence from asian financial markets, Pacific-Basin Finance Journal 19, 115-139.

Do diversified and focused firms have different growth ... · Evidence suggesting a bias in firm valuations between diversified and focused firms due to differing growth options also

Documents