Ambiguity about Return Volatility and The Family Firm Puzzle:
Why do US Family Owners Choose Concentrated Portfolios?
Ronald Anderson, Temple University
Nan Li, Shanghai Jiao Tong University
David M. Reeb, National University of Singapore
January 23, 2017
[Abstract]
Conventional wisdom suggests that family shareholders should exit their large, concentrated
equity stakes in publicly-traded firms and seek benefits arising from diversification. To provide
insights into families’ puzzling investment decision of remaining in the firm, we consider an
investment model with ambiguity about both expected return and return volatility. We find that
ambiguity about return volatility is critical to understand the quantitative aspect of the seemingly
puzzling decision of US family owners to hold a large proportion of their wealth in a single firm.
Our model also sheds light on factors driving family exit-decisions. Our empirical analysis lends
support to the model’s predictions and indicates that family ownership bears a strong relation to
corporate ambiguity, family risk reference, family wealth. The theoretical explanation and
empirical evidence of the importance of ambiguity on family ownership decisions provides an
essential element for research on the economic impact of ambiguity on corporate decisions.
JEL Codes: G11; D81; L22
1. Introduction
Standard investment analysis builds on the notion that investors in countries with welldeveloped equity markets benefit from holding a diversified portfolio rather than concentrated
stakes in a single or small number of firms. Yet, founding families in the U.S. continue to maintain
a substantive and undiversified stake in a substantial number of publicly-traded firms (Shleifer and
Vishny, 1986; Klasa, 2007). Leland and Pyle (1977) indicate that family owners have private
information about the firm’s future prospects and hold large stakes to signal firm quality.
Extending this notion, Zingales (1995) suggests that family owners will slowly decrease their
position in the firm after the initial IPO. DeMarzo and Urusevic (2006) highlight the trade-off
between agency considerations and diversification in the family exit decision. Alternatively, family
owners could act as a commitment device to mitigate risk-shifting activities (Anderson et al.,
2003), relying on private payoffs to justify foregoing the benefits of diversification (Shleifer and
Vishny, 1986; Morck and Yeung, 2003). Burkart et al. (2003) show that family ownership may be
an optimal ownership structure to protect shareholder interests in economies offering weak
shareholder protections and/or economies with undeveloped equity markets. The shareholder
protection and private benefits perspectives provide substantial insights into the cross-country
patterns of family ownership (Faccio and Lang, 2002). However, a puzzling issue remains as to
why family ownership remains so prevalent among publicly-traded firms in countries with welldeveloped equity markets and strong legal systems.
The strong shareholder protections in the U.S. indicates that investors need not make the
trade-off between holding concentrated equity stakes or holding a diversified portfolio, suggesting
that family ownership should not persist. However, Anderson et al. (2009) show that family
owners in the U.S. maintain large, concentrated stakes in almost one-half of the Russell 3000,
frequently holding the vast majority of their investable wealth in the family firm. A simple
reference model provides a method to gauge the magnitude of private benefits that family
shareholders need to capture to justify holding a single stock versus a diversified portfolio. Using
1
a mean-variance framework for the Russell 3000 stocks, the reference model indicates that family
owners should hold about three percent of their investable wealth in the family firm and the
remainder in a broad portfolio of other assets to obtain diversification benefits. To justify the
actual stakes we observe in practice (about 70% of wealth in the family firm), the reference model
indicates that the family would need to extract an additional $700 million over the life of the firm
to be an indifferent between a concentrated stake relative to holding a diversified portfolio. 1
Anecdotally, the model suggests that the Walton family (of Wal-Mart Stores) would need to
privately capture over an additional $2 billion per year to justify their huge ownership position
relative to holding a well-diversified portfolio. Presumably, even if the Walton family were to
reduce their substantial equity holdings from 50% to 25% of the firm’s outstanding equity, they
could still achieve the same private benefits of control.
Given the foregone diversification benefits of investing large faction of the family’s wealth
in a single firm, a puzzling question arises: Why do these wealthy families continue to hold these
large, undiversified stakes in publicly-traded firms and not seek the benefits of a well-diversified
portfolio? This question is not just a qualitative but also a quantitative puzzle. We propose to
examine this puzzle by considering an portfolio choice model where investors are both risk and
ambiguity/ambiguity averse and possess information advantage on some risky assets. More
specifically, our model incorporates ambiguity about both expected return and return volatility in
a portfolio choice model where family owners are less ambiguous about their own firm equity
relative to a diversified portfolio of other equities on the market, as they have private information
about the firms they own. We find that the ambiguity about volatility plays an important role to
explain the quantitative family firm puzzle.
Classical asset pricing models (Markowitz 1952 and Merton 1971) are based on rationalexpectation assumption that economic decision makers know the unique probability law implied
These estimates are computed in a Markowitz (1952) framework using a negative exponential utility function,
with absolute risk aversion of 0.2, risk free rate of 2%, expected return of 9%, single stock standard return
deviation of 0.4924, a portfolio return standard deviation of 0.1921 (see Elton and Gruber, 1977) and family
ownership of $1.5 billion.
1
2
by the economic model. However, as early as Knight (1921), researchers in decision science and
economics have found the economic decision makers may not know and are uncertain about the
probability distribution that governs the states of the world. Based on laboratory experiments,
Ellsberg (1961), Borghans et al (2009) and others show that most people prefer a risky lottery with
known probabilities to a risky lottery with unknown proabilities, that is, they are ambiguity averse2.
The impact of ambiguity on asset prices and investment decisions has been extensively studied in
theories. Hansen (2007) show that ambiguity aversion induces extra caution in investment choices
and investor concerns about statistical ambiguity are reflected in equilibrium asset prices3. A large
body of theoretical studies show that ambiguity aversion can help explain the household portfolio
choice puzzles such as limited participation4 and under diversification5 puzzles, which are closely
related to the family firm puzzle we document above. However, most of the existing literature
assume investors are ambiguous about expected return, do not allow for ambiguity about return
volatility6 and focus on the qualitative instead of quantitative aspect of the puzzles. Epstein and Ji
(2013) recently propose a theoretical model featuring ambiguity about volatility but leaves the
empirical importance of ambiguity about volatility as an open question. On the other hand,
Bloom (2009), Bloom, Floetotto, Jaimovich, Sapora-Eksten, and Terry (2012), Ordonez (2011)
2
Dimmock et al (2016) provide non-laboratory empirical evidence on ambiguity aversion using US household
survey data.
3 Collard et al. (2011), Jahan-Parvar and Liu (2014), Ju and Miao (2012), and Miao et al. (2012) study the impact
of ambiguity on asset prices.
4 Bossaerts et al (2010), Cao, Wang, and Zhang (2005), Dow and Werlang (1992), Easley and O’Hara (2009),
Epstein and Schneider (2010), Garlappi, Uppal, and Wang (2007), and Peijnenburg (2014) show that ambiguous
aversion may cause investors not investing or reducing the faction of investment in stocks, if investors find
stock returns not only risky but also ambiguous.
5 French and Poterba (1991) document the home-bias puzzle, and the own-company stock puzzle is
documented by Benartzi (2001), Meulbrook(2005), Mitchell and Utkus (2003). Boyle et al (2012), Boyle, Uppal,
and Wang (2003), Cao et al (2011), Epstein and Miao (2003), Uppal and Wang (2003), and others show in
theoretical models that ambiguity aversion can help explain the puzzling facts that households heavily
overweight one type of equity (domestic stocks in home-bias puzzle and own-company stock in own-companystock puzzle) relative to the optimal asset allocation implied by mean-variance model without ambiguity.
6 The prevailing justification of this assumption is that volatility can be estimated rather precisely from high
frequency stock return data. However, Carr and Lee (2009) and Branger, Schlag and Thimme (2016) point out
that noises in the observed data may generates noise in the estimate and it is questionable whether a modeler
can correctly select any parametric stochastic process from a large menu consistent alternatives, which may lead
to pronounced ambiguity about volatility.
3
and Pastor and Veronesi (2012) show that the volatility appears to change dramatically over time
and volatility shocks can explain business cycles, financial crises and asset price fluctuations. A
recent study by Orlik and Veldkamp (2016) show that revisions in estimates of unobserved tail
events (black swan event) explain most of the fluctions in volatility. Kozeniauskas, Orlik and
Veldkamp (2016) suggest that time-varying disaster risk and volatility shocks are not distinct
phenomena, and they are outcomes of a quantitatively plausible belief updating process. Due to
the time-varying nature of volatility, investors may exhibit great if not more concern over
ambiguity about return volatility than expected return.
By incorporating ambiguity about both expected return and return volatility, our model
allows us to compute implied levels of family ownership with differing ambiguity about expected
returns and ambiguity about return volatility, and confront quantitative implication of the theory
with the data. Our simulation results show that the family owners should hold about six percent
of their wealth in the family if they are only ambiguous about expected returns. In contrast, with
reasonable ambiguity about expected returns and return volatility, the model indicates that the
family owners may invest about 70 percent or more of their wealth in the family firm. Prior
empirical research indicates that family owners, on average, hold about 25 percent of the firm’s
outstanding equity, equating to more than 80% of their wealth invested in the firm, suggesting
that ambiguity about volatility indeed plays an important role in the family’s investment decision.
Intuitively, the family owner’s private information about their own firm reduces ambiguity about
the expected return and return volatility of family firm, allowing them to hold a single-stock
portfolio dominated by the (unobserved) efficiency frontier in mean-variance space. As the old
wisdom in a western idiom “Better the devil you know than the devil you don't”, and a Chinese
old saying “People fear that happens once in ten thousand times not those happens ten thousand
times”, it is the ambiguity about volatility that investors concern most.
Furthermore, comparative statistics based on the explicit solution of our model allows us
to derive rich testable implications of the extra caution induced by ambiguity aversion on the
4
family equity-ownership and exiting decision. Using a large sample of U.S. family firms from 2001
through 2010, we examine the model’s predictions via two testing procedures. First, our model
indicates that the level of family investment in the firm are directly related to ambiguity
surrounding the firm’s prospects, which vary across industries. One of the challenges is to
measure ambiguity and we develop several proxies such as innovation level, competitor entry
intensity, barriers to entry and earnings shocks (volatility and kurtosis). Second, we focus on
family-exit decisions using a hazard or survival model. Family-exit decisions describe the situation
where the family consciously makes a choice to move from a single-firm portfolio to investing in
a diversified portfolio of firms. We examine several predictions of the ambiguity hypothesis by
focusing on the relation between family exits and industry and family characteristics.
In cross-sectional testing, we exploit differences in family ownership levels to test the
ambiguity hypothesis.7 Using a conservative estimate of 20% of ownership to maintain control in
U.S. firms, we contrast high and low levels of family ownership against proxies for industry-level
ambiguity. Our analysis suggests that families tend to hold larger equity stakes in industries with
less ambiguity. Our model also indicates that a family with knowledge about the nature of the
firm’s cash flow cycle – even if they are volatile – may have relatively less ambiguity about the
firm’s prospects and thus retains their ownership position.
Van Nieuwerburgh and Veldkamp (2009) investigate information advantage and home
biases and find that “information advantages are not only sustainable when information is mobile,
but that asymmetry can be amplified when investors can choose what to learn”. Consistent with
their findings, our model predicts that family owners are less likely to exit their equity stakes when
their private information and experience allows the family to learn more and know better the
Family owners may receive several potential non-monetary benefits from controlling the firm (Gomez-Mejia et
al., 2007). Yet, family control does not appear to require large and substantive stakes in the firm to achieve
these ends. For instance, Anderson and Reeb (2004) highlight how family owners with stakes ranging from 5%
to 10% maintain control of the firm through the director nomination process and thus limit outside influence or
interference. Others emphasize family use of dual-class shares as a control enhancing mechanism (Almeida and
Wolfenzon, 2006).
7
5
firm’s environment. More specifically, our model implies that families should be less likely to selloff their ownership stakes (exit the firm) with: (i) greater tenure in the firm, (ii) greater absolute
levels of wealth invested in the firm and (iii) greater (absolute) risk-aversion, all relative to the
mean family owners. These predictions seem especially notable as they run counter to the adverse
selection story in Leland and Pyle (1977), where the family incrementally sells down their stakes to
obtain a diversified portfolio. In addition, the model predicts that family exits should be positively
related to ambiguity about future earnings. Again, this prediction provides a sharp distinction with
the traditional adverse selection framework for evaluating family ownership, which implies that
earnings variance rather than ambiguity about earnings is positively related to family exits (e.g.,
Villalonga and Amit, 2010).
To confront the model implication on family’s decision to exit and the data, we examine
100 family-exits relative to a propensity score matched sample of family firms (not exiting) to
examine whether ambiguity surrounding the firm’s information environment affects the family’s
decision to sell-off their ownership stake. Strikingly, we find that families are indeed less likely to
exit their ownership stakes as family wealth increases, family experience in the firm increases, and
family risk-aversion increases. The results are statistically and economically significant. We
instrument for family risk aversion using representation by female family members on the board
of directors and/or as large shareholders.8 Our analysis suggests that families are significantly less
likely to exit the firm when more female family members remain as board members and/or large
shareholders. Further tests indicate that family owners are less likely to exit the firm when family
members serve as CEO (relative to external CEOs); suggesting family members face fewer
information constraints (less ambiguity) when actively running the firm. The analysis supports the
Croson and Gneezy (2009) and Bertrand (2011) provide comprehensive surveys on the literature on
differences in risk aversion between women and men. Levin et al. (1988) and Bruce and Johnson (1994) provide
evidence based from betting that women exhibit greater risk aversion than men. Barsky et al. (1997) document
that women actively report lower risk propensities than men. Jianakaoplos and Bernasek (1998) and Sundén and
Surette (1998) document that women are significantly more risk-averse in their allocation of wealth than men of
equal economic status. Borghans et al. (2009) provide experimental evidence of greater risk aversion in women
relative to men, while any ambiguity aversion differences appear relatively inconsequential.
8
6
predictions of the model; suggesting that family owners are more likely to retain their ownership
stakes when facing less ambiguity about the firm’s future prospects.
Our paper joins the growing literature on the continued control by founding families of
publicly-traded firms in well developed economies and the vast literature on the important impact
of ambiguity on economic decision. By incorporating ambiguity about return volatility as well as
expected return, and the private information of family owners, we generate substantial insights
about portfolio choice with ambiguity aversion. These findings not only provide new insights
regarding the continued ownership and control of large public firms by founding families, but also
extend the literature on ambiguity aversion and empirically test the importance of ambiguity about
volatility. We confront the model predictions with the data on actual investment decision of
family owners, and find empirical evidences consistent with our model implications.
In sum, we present theoretical explanations and empirical evidences based on family
ownership and exit decision for the notion that ambiguity about volatility has great impact on the
investment decision, and provide both explanation for the family owners’ decision to maintain
ownership and control in countries with well-developed financial markets and strong legal regimes.
2. The model
We focus on the quantitative aspect of the puzzle why family owners invest a large
proportion of their wealth in a single family firm, and what drives their decision to exit from the
family firm and invest in a diversified portfolio. We seek to answer these questions in a model of
investment decision with ambiguity-averse investors (family owners) who choose between
investing in two risky assets with different degree of ambiguity about expected return and return
volatility, namely, a single stock (family firm) and a diversified portfolio of other equities.
In the classic portfolio choice model proposed by Markowitz (1952) and Merton (1971), it
is assumed that investors make decisions with the knowledge about the unique probability
distribution of stock prices and firm fundamentals. However, investors do not observe the true
7
distribution or model of asset prices. They usually form multiple perceptions about the
distribution or model with the information at hand and try to make optimal decisions given the
existence of multiple scenarios. The quality and quantity of available information about the firm
differs for different classes of investors. Inside investors of a firm, such as CEOs or family
owners, have access to more accurate information about company fundamentals than outside
investors and thus can make better inferences about the true distribution of asset prices. That is,
inside investors have less ambiguity about the distribution of future stock prices than outside
investors. On the other hand, corporate insiders (CEOs and family owners) do not possess an
information advantage with outside firms or a diversified portfolio of outside firms, thus have the
same degree of ambiguity as other outside investors with respect to these investment choices.
Our model resembles the models that relate ambiguity aversion to the portfolio choice
puzzles such as nonparticipation puzzle and under diversification puzzle. However, the important
feature of our model that differentiates our model from most of the existing portfolio choice
models with ambiguity is that we allow ambiguity about both expected return and return volatility9.
In the general framework with ambiguity, investors are uncertain about the entire distribution of
the asset return. More importantly, decision makers with ambiguity aversion care about the
ambiguity regarding the potential downfall in returns, which is captured by the ambiguity about
the volatility rather than the ambiguity about the expected return. Actually, we do find that
ambiguity about expected return is not enough to rationalize the concentrated ownership of
family owners; ambiguity regarding the volatility of the return matters the most. In Table A.1, we
report the calibration of the share of wealth invested in the family firm and the diversified
portfolio with different degrees of ambiguity about expected return and return volatility. If there
is no ambiguity about volatility, then even if the ambiguity about the expected return of the
diversified portfolio is so high that the family owners think the minimum expected return of a
9
Easley and O'Hara (2009) also allow for ambiguity about both mean and standard deviation of returns when
studying nonparticipation in stock markets.
8
single stock is 150% of that of the diversified portfolio, they will only invest 6% of their wealth in
the single stock On the other hand, if the family owners care about ambiguity surrounding
volatility, then with moderate ambiguity about the volatility such that the family owners think the
maximum volatility of a single firm is same as that of the diversified portfolio, then they will
invest 50% of their wealth in the single firm. The impact on ownership level with respect to the
relative ambiguity about volatility is much larger than the relative ambiguity about the expected
return.
Gilboa and Schmeidler (1989) provide an axiomatic foundation for maxmin expected
utility (MEU) preferences that incorporate ambiguity in decision making models. Klibanoff et al.
(2005) propose “smooth ambiguity aversion” preferences that allow separation between degrees
of ambiguity and attitude for ambiguity (ambiguity aversion). In both theoretical frameworks, the
ambiguity is about the distribution not just the mean of the random variables. Our model builds
on the MEU framework of Gilboa and Schmeidler (1989), and we do not separate ambiguity and
ambiguity aversion as Klibanoff et al. (2005). Klibanoff et al. (2005) show that the maxminpreference model is a limiting case of the smooth recursive preferences when the degree of
ambiguity aversion trends to infinity. 10 This framework is useful in studying the economic
equilibrium impact of changing ambiguity aversion while holding ambiguity constant or vice versa.
However, due to data limitations, neither ambiguity aversion nor ambiguity is easily observed or
measured, and variations in ambiguity aversion and ambiguity are often observationally equivalent.
Hence, we adopt the MEU framework, which allow us to solve the model explicitly and derive
rich testable implications that relate the family ownership and family exit decision to the
observable characteristics of the family owner and the family firm. Furthermore, our model
implications are consistent with that of Klibanoff et al. (2005) based on numerical simulation.
10
Both approaches have widely varying implications for optimal portfolio allocation, Abdellaoui et al. (2010),
Bossaerts et al. (2010) Hyayshi and Wada (2010) and Dimmock et al. (2013) examine the effect of uncertainty
on portfolio choice via experiments. Peijnenburg (2014) shows that the maxmin approach better matches the
data. Ahn et al. (2014) explicitly compare the maxmin preferences and smooth preference via a portfolio choice
experiment to explore which describes actual behavior and find evidence in favor of a kinked specification.
9
To focus on the decision of family owners, we assume the choice set of family owners
contains two risky assets with different degrees of ambiguity and no risk-free asset. From a
practical perspective, investors rarely find a true risk free asset. Table A.2 shows for example, the
average real return and volatility (of real returns) for treasury bonds versus the real return on the
CRSP market index from 1995 to 2013. The volatility of the 5-year treasury bonds is 5.93%,
significantly different from zero, and the volatility of 30-year bonds is 17.61%, close to that of the
CRSP stock market index (20.19%). Furthermore, we obtain similar implications on the
relationship between the family ownership and characteristics of the family owner and the family
firm in a model with two risky assets and a government bond11.
2.1 The portfolio choice with no risk free asset and with ambiguity about return volatility and expected return
We consider a static discrete time economy with two risky assets. Asset 1 refers to the
stock of a single firm (family firm) and asset 2 is a diversified portfolio. The return on each risky
asset is
(1)
where
stems from the earnings and other learnable fundamentals of firm operations by those
with inside information, while
stems from external forces that no one can understand or learn.
We assume that the learnable fundamentals
and
and the noises
and
are independent of
each other and all follow normal distributions so that the returns on both risky assets,
and
,
also follow normal distributions and are independent of each other. 12 The true values of the
expected return and return volatility on both assets are denoted as (
), for i =1, 2.
2.1.1 The portfolio choice without ambiguity
In the classic Markowitz (1952) mean-variance analysis, investors are assumed to make
decisions with knowledge about the true value of expected return and risk, (
) for i=1,2. For
11 See
Appendix A.2 for details.
maintain the normality assumption so that means and variances are sufficient statistics of the distributions.
The assumption of independence is not essential to our results, with the main results continuing to hold if we
allow for a correlation between returns on the family firm and the diversified portfolio.
12 We
10
investors with constant absolute risk aversion (CARA) utility for wealth and risk aversion
coefficient γ > 0, they choose the share (α) invested in asset 1 (single firm) to maximize expected
utility in each period t,
(2)
where Wt is the wealth of the investor given at time t. It is straightforward to show that problem
(2) is equivalent to the following optimization problem,
(3)
and the solution to this problem is,
(4)
We are interested in the scenario where the two risky assets have identical expected returns
(
), but different return volatilities (
), the volatility of the diversified portfolio is
less than that of a single stock, then we obtain the diversification result of Markowitz (1952),
The family chooses the minimum variance portfolio and invests more in the asset with relatively
lower risk, i.e. the diversified portfolio. Thus, the family owners’ decision to retain a large portion
of their wealth in the higher risk family firm raises a puzzling question. In Appendix 1, we
calibrate our model to show the implied share of wealth that an individual should invest in a single
firm when the single firm and the diversified portfolio exhibit the same risk – about 3% without
ambiguity. Even if the expected return of single firm is 150% of that of the diversified portfolio,
the investor without ambiguity aversion still chooses to invest only 6% of her wealth in a single
stock. Thus, without concern for ambiguity, a family’s decision to invest large stakes in a single
firm becomes difficult to justify.
11
2.1.2 The portfolio choice with ambiguity
In financial markets, investors do not observe the true value of expected return and
volatility and rely on other data to make inferences about these values. In a general model with
ambiguity, investors are uncertain about the distribution of the asset returns. With the normality
assumption of the distribution, it is sufficient to assume that investors are uncertain about the
mean and standard deviation of returns. We assume investors believe that the expected return of
each asset i draws from a set of N possible values
true value of the expected return (
, which contains the
), for i =1,2. That is,
,
where
and
, for i = 1, 2. In addition, we assume
the investors believe that the return volatility on asset i come from a set of M possible values,
, which contains the true values of return volatility (
), for i = 1,2.
That is,
,
where
and
, for i = 1, 2.
We model ambiguity aversion in the maxmin expected utility (MEU) framework proposed
by Gilboa and Schmeidler (1989). That is, investors care about the ambiguity regarding the
distribution of returns, and choose the optimal portfolio to maximize their utility in the worsecase scenario. In this framework, there is no separation between ambiguity and aversion to
ambiguity, and we allow the range of potential expected return and return volatility to capture
both the ambiguity about the returns and the ambiguity aversion of the investors. Naturally,
investors who are more ambiguity averse or face more ambiguity will exhibit concerns about
wider ranges of potential expected returns and volatility.13 Consequently, this simple framework
13
In this optimal portfolio choice problem within the maxmin framework, it is the worse-case, risk-return
tradeoff that measures ambiguity and ambiguity aversion.
12
allows us to represent family investors who face more ambiguity as those that tend to consider a
wider range of possible values of expected returns.
We further assume that the family owners possess private information regarding the
fundamentals of the family firm that allows them to reduce the ambiguity about the fundamentals
of their own firm over time and through experience. However, like other outside investors, the
family owners do not possess material private information about other firms in the diversified
portfolio as they do not manage these other firms. In our setup, the reduction in the ambiguity
regarding the family firm relative to the diversified portfolio is captured by the shrinkage in the
distance between the worse-case and the true values of expected return and volatility. Hence, for
the family owners who can exploit private information to reduce the ambiguity regarding the
family firm, the ambiguity range of the expected return and volatility of family firm is tighter than
that of the diversified portfolio, i.e.
and
.
For each time period t, the portfolio choice problem of the ambiguity-averse family
owners with CARA utility can be formulated as
(5)
Let's first examine the minimization problem of (5). Since (5) is monotonically decreasing in
, the maximum possible standard deviation is always chosen, that is,
If the family is long in both the family firm and the diversified portfolio (
), then the
minimum possible mean returns are chosen for both assets. If the family shorts the diversified
portfolio (
), then the maximum possible mean return of the diversified portfolio and
minimum possible mean return of the family stock is chosen, and vice versa, that is,
13
Given the solution to the minimization problem, the optimal share invested in the family
business ( ) can be then characterized as following,
(6)
Comparing the optimal portfolio in the model with ambiguity (6) and without ambiguity (4), it is
straightforward that the ambiguity-averse investor makes decision based on the worse-case
expected return and variance; while the naï
ve investor without concern for ambiguity makes
decision based on the true value of the expected return and variance.
We focus on the scenario where the two risky assets have identical expected returns
(
), but different return volatility (
), and the true value of the volatility of the
diversified portfolio is less than that of a single stock. Hence, if ambiguity about the expected
return of the family firm is less (more) than that of the diversified portfolio, then
. In the model without ambiguity, the investor would choose to invest more in the
diversified portfolio; but in the model with ambiguity, it depends on the relative ambiguity of the
two risky assets. Note that due to “mean blur” (Luenberger, 2008), it is much more difficult to
estimate mean than volatility, and harder for family owners to use private information to reduce
the ambiguity regarding the expected return than the ambiguity regarding the volatility. Hence it is
reasonable to assume that
is close to
if
. Even if the true value of the
volatility of the diversified portfolio is smaller than that of the family firm (
), the family
owners may be able to exploit their private information to reduce the ambiguity regarding the
volatility of the family firm such that
. If the information possessed by the family
owners allow them to reduce the ambiguity about the family firm, then the family owners would
invest more in the single firm. That is, if
14
,
then the share of wealth invested in the family firm (α*) is larger than 1/2. If the relative
ambiguity of the family firm is reduced even further, such that
,
then the family owners would invest 100% of their wealth in the family firm.
We compare the choice sets of investors with and without ambiguity in Figure 1. Note
that if the family owners believe the minimum expected return of the family firm is larger than
that of a diversified portfolio, that is,
, then the family owners would always hold
a positive share of their wealth in the family firm unless the volatility or ambiguity about the
volatility of the family firm gets large enough (
exiting family”. On the other hand, if
), we refer to this case as the “non, then the family owners would consider
exiting when their risk aversion, wealth and ambiguity about the expected return or return
volatility of the family firm changes. We refer to this case as the “exiting family”. Panel A of
Figure 1 illustrates the scenario for non-exiting family owners (
). For investors
without ambiguity aversion, the choice set is represented by (F0, D0), where F0 represents the
family firm and D0 represents the diversified portfolio. Based on numerical calibration results, we
find that the family owners would hold merely 3% of their wealth in the family firm (F0). For a
family with ambiguity aversion, but only with respect to expected return, the choice set is
represented by (DB, FB). In this case, the family owners would hold just 6% of their wealth in the
family firm (FB) if
. For the family with ambiguity aversion with respect to
expected return and return volatility, the choice set is represented by (DA, FA). In this case, the
family owners would hold over 80% of their wealth in the family firm (FA) if
and
.
Panel A in Figure 1 also shows that a more risk-averse investor would hold less in the
family firm than a less risk-averse investor. A simple comparative statics analysis also implies that
for the non-exiting family owners, the share of the wealth invested in the family business is a
15
decreasing function of the risk or the relative ambiguity of the family firm, and a decreasing
function of risk aversion and family wealth. Furthermore, the more experience the family has with
the firm, the better they understand the family business, hence the less ambiguity about the
expected return and return volatility, and the more investment in the family firm. The above
analysis thus leads to the first set of hypothesis in our empirical tests as following:
Hypothesis 1.1: The family invests more in their own business in industries where it is easier to
use private information to assess the expected return and return volatility.
Hypothesis 1.2: The family invests more in their own business when the family owners are less
risk averse
Hypothesis 1.3: The family invests more in their own business when the family owners are less
wealthy.
Hypothesis 1.4: The family invests more in their own business when the family tenure is longer.
In our empirical tests, we develop proxies such as industry innovation, branding, and entry
barriers to measure the riskiness and/or the ambiguity of industries in which family firms operate.
Because the empiricist can neither directly observe nor measure ambiguity, our proxies for
industry ambiguity likely capture both a component of industry risk as well as industry ambiguity.
Our model however, predicts that the family owners invest less in industries with more risk
and/or ambiguity. In the next section, we investigate the factors that impact the exit decision of
the family owners.
2.2. The family’s exit decision
The family exit decision depends crucially on the relative ambiguity regarding the expected
return and return volatility of the family firm relative to the diversified portfolio. When private
information no longer permits the family owners to reduce the ambiguity about their firm relative
to other firms, the family owners will exit. Intuitively, this indicates the family owners will exit
when they become less certain about their firm’s expected return and volatility relative to the
diversified portfolio. If the family owners believe the worse-case expected return of the family
16
firm is small enough or the worse-case volatility of the family firm return is large enough, then
they are likely to exit. Note that solution (6) implies that the necessary conditions for family
owners to exit are,
(7.a)
or
(7.b)
indicating that either the ambiguity about the family-firm expected return increases such that the
family owners think the worse-case expected return of the family firm is lower than the worsecase expected return of the diversified portfolio; or the ambiguity about the risk of the family firm
increases dramatically.
2.2.1 The impact of industry risk or ambiguity on the family exit decision
Condition (7) is more likely to be satisfied in industries with more uncertainty where it is
harder for the family owners to exploit private information to resolve the ambiguity regarding the
expected return. Hence, the family owners are more likely to exit in industries with more risk or
ambiguity.
2.2.2. The impact of family wealth and risk aversion on the family exit decision
A simple comparative statics analysis under condition (7.a) implies that the family owners are
more likely to exit as their risk aversion and wealth decreases. This prediction may seem surprising,
as the model predicts the investor would invest more in a riskier asset (family firm) when they are
more risk averse or wealthier. However, this prediction arises when unexpected shocks enlarge the
ambiguity about the family firms such that the worse-case expected return of the family firm is
smaller than the worse-case expected return of the diversified portfolio. In this situation, the
family firm appears to be an asset with lower expected return and possibly lower risk; hence the
less risk averse family owners invest less, instead of more, in the family firm. The family owners
may consider exiting in this situation and would be more likely to exit if they are less risk averse.
This prediction sharply contradicts the implication of models based on agency costs or
overconfidence that indicate less risk averse families are less likely to exit.
17
Panel B in Figure 1 illustrates the investment decision for the exiting family (
).
For family owners with ambiguity aversion and are ambiguous about both expected return and
risk (volatility of return), their choice set is represented by (DE, FE). Risk neutral family owners
would choose to invest 100% of their wealth in the diversified portfolio (DE). The optimal
portfolio of a risk-averse investor is represented by E, which is between DE and FE. By comparing
the optimal portfolio choice of a risk neutral and a risk averse investor, we find that the
ownership of the family firm increases with risk aversion, that is, the family owners are more likely
to exit when they are less risk averse. 14
2.2.3. The role of family experience on the family exit decision
It is straightforward to show that families can reduce the ambiguity of their own firm through
Bayesian updating by using their private information about the firm’s fundamentals. The longer
the family’s experience with the firm, the less ambiguity about the firm, hence the family holds a
larger stake. The implication is that the greater (longer) the family’s experience (time) in the firm,
the less likely the family will be to exit the firm, all else equal. Note that we do not make any
assumptions about investment horizons of either family or outside investors. Our model predicts
that family owners with longer tenure in the firm will be less likely to exit the firm. In this context,
our model provides important insights on family owners’ horizons.15
Our analysis leads to a second set of hypotheses concerning family exits, these are;
Hypothesis 2.1: The family is more likely to exit in industries with more uncertainty where it is
more difficult to use private information to assess the expected return and return volatility.
Hypothesis 2.2: The family is more likely to exit when the family owners are less risk averse.
Hypothesis 2.3: The family is more likely to exit when the family owners are less wealthy.
Hypothesis 2.4: The family is more likely to exit when the family is younger.
The standard agency model implies a negative relation between (relative) risk aversion and ownership (Bitler
et al., 2005). Faccio et al. (2011) emphasize how family owners may seek diversification through firm-level
investments.
15 Empirical literature on family firm argues that family owners have longer horizons than non-family firms. For
instance, Anderson and Reeb (2003) posit that the long horizon of family owners leads them to make better
investment choices. However, the mechanism for this longer horizon is typically not addressed.
14
18
Notably, these comparative statics on the family owners’ share invested in the family firm, as
relative ambiguity increases, are unchanged for family owners exiting the firm and for family
owners remaining in the firm. That is, the comparative statics are unchanged regardless of
whether the family owners think the worse expected return of the family firm is bigger or smaller
than that of the diversified portfolio. As long as the family owners develop more ambiguity about
their own firm or the relative ambiguity of diversified portfolio decreases, the family owners tend
to invest less in the (relatively riskier) family firm, or are more likely to exit. This arises because
diversification benefits increase as the relative ambiguity of the diversified portfolio decreases.
Our results regarding risk aversion and family wealth however, are sensitive to the
relationship between the worse-case expected return of the family firm and the diversified
portfolio16. On the one hand, if the worse-case expected return of family firm is larger than that of
the diversified portfolio (
), the share invested in the family firm increases as family
risk aversion or family wealth decreases. Intuitively, this arises because an increase in the owners'
risk aversion mitigates the benefit of holding a less uncertain asset at the cost of higher risk. On
the other hand, if the ambiguity regarding the family firms increases such that the worse-case
expected return of the family firm is less than that of the diversified portfolio (
),
then the family firm appears to be an asset with less expected return and possibly lower risk as
compared with the diversified portfolio. A decrease in the risk aversion would make the family
firm less attractive to family owners. The family owners would invest less in the family firm until
they exit completely. If the worse-case expected return of the family firm is same as that of the
diversified portfolio, then the share invested in the family is constant in risk aversion and family
wealth.
16
Klibanoff et al. (2005) obtain the same results through numerical comparative statics in an example where
investors with smooth ambiguity aversion chooses between a risky asset and an ambiguous asset. They found
that increases in the ambiguity aversion (relative ambiguity in our context) leads to decrease in the share of
wealth invested in the ambiguous asset. However, the impact of risk aversion depends on “the direction of
diversification”, that is, the relationship between expected return of risky asset and ambiguous asset.
19
2.4. Contrast with extant theory on the predictions of the family’s exit decision
To explain the concentrated equity stakes of family owners, extant theories build on
market frictions, private benefits of control, and/or non-pecuniary benefits of control. Leland and
Pyle (1977) argue that family owners hold large stakes to signal firm quality. DeMarzo and
Urusevic (2006) highlight the trade-off between agency considerations and diversification in the
family exit decision. Shleifer and Vishny (1986) rely on private payoffs to justify foregoing the
benefits of diversification. Morck and Yeung (2003) and Roussanov (2010) indicate that family
owners could receive non-pecuniary benefits, thus explaining their decision to hold a large,
concentrated stake. A common theme running through extant theories indicates that risk-averse
investors receive compensation through other channels for holding a concentrated stake in a
single firm. These theories indicate that the cost of concentrated ownership increases as risk
aversion increases, as family wealth invested in the firm increases, and as the riskiness of the firm
increases; suggesting that family owners will exit as family risk aversion, wealth, and industry risk
increase. The hypotheses from our model (hypotheses 2.1 – 2.3) stand in sharp contrast to the
predictions from these existing models.
Investor overconfidence offers another explanation for the under diversification of
corporate insiders. Odean (1998) shows that overconfident investors who believe they have
precise knowledge of security value – but in actuality have less precision than believed – hold
riskier portfolios than rationale investors with the same degree of risk aversion. Overconfident
investors hold unrealistic beliefs about the precision of their estimates and about superior future
returns. Unlike the overconfident investor, the ambiguity-averse investor in our model rationally
improves the precision of their estimates using relevant information. Overconfidence models
explain investor under diversification and thus, predict that family owners are more like to exit the
firm as family risk aversion and wealth increase or when the family firm operates in a less risky
industry. These predictions from overconfidence models again, stand in sharp contrast to
Hypothesis 2.1-2.3 from our model.
20
Another generally accepted explanation on family ownership suggests that the family
owners will exit the firm as soon as possible after going public to obtain the benefits of a
diversified portfolio (Admati et al., 1994). Zingales (1995) models the family exit decision,
suggesting that the family continuously reduces their stake in the firm until they hold only a
control stake which they then sell to outside investors at a premium. Similarly, Mello and Parsons
(1998) describe family exits as sequential processes; sell small stakes to atomistic shareholders and
then sell the control stake to an active investor at a premium price. In each of these settings, the
benefits of diversification suggest that the longer the family remains in the firm, the more likely
the family decides to sell their control stake and exit the firm. Hypothesis 2.4 of our model
predicts the opposite effect.
Ambiguity, by definition, is neither directly observed nor easily differentiated from risk in
empirical analysis. The testable hypotheses obtained through our comparative statics however,
allow us to test the model’s predictions by developing proxies for ambiguity and then partitioning
family investors by the degree or level of ambiguity they face. Most of the hypotheses from our
model stand in sharp contrast to predictions from models without ambiguity, i.e., opposing signs.
In the next section, we setup our empirical analysis to test the hypotheses from our model.
3. Primary variable measurement
In this section, we test the implications of our model. The model yields several hypotheses
that indicate that family owners’ ambiguity aversion and ambiguity about returns affect their
decision to hold large, concentrated equity stakes in a single firm. To examine the predictions and
hypotheses of the model, we start with the 2,000 largest industrial firms in the U.S. with a fiscal
year-end in 2001. To collect the sample, we pull all firms from CompuStat for data-year 2001
with information available for total assets. We exclude public utilities (SIC codes 4812, 4813, and
4911 through 4991), financial firms (SIC codes 6020 through 6799), firms listed as master limited
partnerships (21-firms), foreign firms, and firms with a share price less than $0.25. These firms are
21
excluded to make our work comparable to previous literature on family ownership and because
government regulation potentially affects firm ownership structure, corporate transparency, and
performance.
We manually collect family-ownership data from corporate proxy statements and 10-k’s
from 2001 through 2010, including ownership level, dual-class share structures, voting power, and
CEO type. Corporate histories (i.e., family lineage) are garnered from RefereneforBusiness.com,
FundingUniverse.com, and individual company websites.17 To control for survivorship bias, we
allow firms to exit and re-enter the sample. Consistent with previous research, family firms are
those where the founding family continues to maintain a five percent or larger ownership stake in
the firm (Shleifer and Vishny, 1986; Villalonga and Amit, 2006). To measure family presence,
similar to McConnell and Servaes (1990), we use the fractional level of family ownership.
Specifically, we determine the total number of shares held by the family (and their relatives), and
divide by total outstanding shares – including both traded and untraded share classes (dual-class
firms). Firms without family owners are referred to as diffuse shareholder firms, i.e., nonfamily
firms with professional managers. After developing our proxies for industry ambiguity and
collecting control variables from CompuStat and IBES, our final sample of family firms consists
of 535 family firms from 2001 through 2010, yielding 4,028 firm-year observations.
3.1. Level of family ownership
In our first set of tests, we examine the relationship between the level of family ownership
and industry-level proxies of ambiguity. Studies with non-U.S. data typically use minimum
thresholds for family ownership (e.g., 10%, 20%) to delineate between these controlling
shareholders and diffuse shareholder firms (Claesssens et al., 2000; Dyck and Zingales, 2002). For
this test, we choose an arbitrary benchmark of a 20% ownership stake to maintain firm control.
In designating family firms, we do not include shares held by charitable foundations as part of the family
holdings. Foundations hold substantial equity stakes in several firms (e.g., Hershey Co, Eli Lilly & Co, Kellogg
Co, Hormel Foods Corp, and etcetera – less than 20 firms) with the express intent of promoting public welfare
rather than financially or economically benefiting family members.
17
22
Shleifer and Vishny (1997) indicate that the size of the equity stake needed for firm control
depends on the degree of legal protection afforded to shareholders; suggesting that in the U.S., a
20% ownership would provide ample influence to control firm policies and direction. The mean
ownership stake across our family firm sample (family firms only) is 23.08% of the firm’s
outstanding equity. We define high (low) levels of family ownership as an equity stake greater
(less) than 20% of the firm’s outstanding equity.18
3.2. Family owners exiting the firm
Across our sample of family firms from 2001 through 2010, we find 100 incidences of
family owners selling their equity stake and exiting the firm. Notably, in all of these cases, the firm
continues to operate after the family’s sale of their ownership. In our family-exit sample, we
observe that families hold a mean (median) ownership of 17.9% (14.1%), 5-years prior to the final
exit. The family’s mean (median) ownership stake in their last (reported) year in the firm is 7.85%
(6.34%). The year following the exit, family owners are no longer reported in the proxy statement
as shareholders, directors, or managers. Because individual and institutional shareholders are only
required to report their holdings when exceeding 5% or more of the outstanding shares, family
owners could conceivably still be in the firm with smaller (<5%) equity holdings. Our hazard
testing model compares family-exit firms to family firms (no exit). If families do not completely
exit the firm (i.e., remain a family firm), this would bias our testing results towards not finding a
family-exit effect in our empirical analysis. For our analysis, we use the 5-years preceding families’
exits as our testing period.19 Notably, we have no cases where the family exited the firm and then
reentered the firm.
Different cut-off levels for high and low ownership (15% and 25%) provide similar results.
In the sale of the family’s shares to external investors, we note that in all cases that the outside investors are
either institutional shareholders (i.e., mutual funds) or to shareholders with less than a 5 percent ownership
stake. Specifically, the shares were not sold to another concentrated, undiversified investor but rather the shares
become diffusely held across a wide shareholder base.
18
19
23
We compare the family-exit firms to a matched sample where the family continuously
maintains their ownership position (i.e., do not exit). To develop our matched samples, we use
propensity score matching methodology (Austin, 2011). Specifically, we construct a propensity
score matched sample of family-exit firms to family firms. The matching criteria are firm size
(natural log of total assets), leverage (long-term debt divided by total assets), firm performance
(ROA based on EBITDA), growth opportunities (market value of equity to book value of equity),
the level of equity issuance (equity issued dived by total assets), and the standard deviation of the
growth of income before extraordinary items for the prior 20-quarters for each firm. We do not
match on industry as many of ambiguity measures are based on industry characteristics. The
propensity score model uses one-to-one firm matching with no replacement, nearest neighbor, a
caliper of 0.20 , and a common support range of [0.1 to 0.9] (Villalonga and Amit, 2010; Caliendo
and Kopeining, 2008).20 The matching process for family-exit firms to family firms yields a total
sample of 832 firm-yeas (416 family-exit firm years (100 unique firms) and 416 family firm years
(334 unique firms)).
3.3. Measures of ambiguity
3.3.1. Ambiguity proxies for the industry level analysis
As noted earlier, we can neither directly observe nor directly measure ambiguity for
empirical analysis. To examine the comparative statistics of our model, we develop proxies based
on industry and family characteristics that potentially affect family shareholders’ ability to assess
the firm’s future prospects and thus the ambiguity surrounding their investment.
Firms in highly innovative industries face greater potential disruption and thus greater
innovation ambiguity than firms in industries with little innovation (Tushman and Anderson,
1986); suggesting that family shareholders experience greater ambiguity and thus may be less
We varied our propensity score matching procedure by allowing firm replacement, varying the caliper size,
and varying the common support range. Notably, with these various models, the inferences from the Cox
hazard model remain qualitatively identical (same sign and significance) and quantitatively highly similar (same
sign and significance but with different values on the coefficient estimates).
20
24
willing to remain in such industries. We capture innovation ambiguity as the sum of R&D for all
firms in each Fama-French industry group divided by the sum of total assets for all firms in each
industry group. Similarly, industries with many new entrants are likely more difficult for family
owners to forecast because new entrants maintain strong incentives to undertake radical actions
that undermine existing industry patterns (Henderson, 1993). We measure ambiguity arising from
industry entry as a dummy variable that equals one when the fraction of new firms entering each
industry group is greater than 1% of the total firms in the industry and zero otherwise. The
fraction of new firms entering each industry is calculated as the increase in the number of firms
from time t-1 to t divided by the number of firms at time t-1.
In contrast to industry innovation and industry new-entrants, family owners may
experience less ambiguity in relation to their investment in industries with substantive corporate
branding or barriers to entry. Dranove and Jin (2010) argue that branding is difficult to establish
and costly to maintain, suggesting that the likely investment outcomes in the industry are well
defined.
We measure ambiguity arising from industry branding as the sum of advertising
expenses for all firms in each Fama-French industry group divided by the sum of total assets for
all firms in each industry group. Research in accounting indicates that in industries with greater
barriers to entry, management appears better able to forecast future performance (Bamber and
Cheon, 1998). We capture ambiguity arising from barriers to entry as the Herfindahl Index of
intangible assets which is defined as: Herfindahlj = ∑s2ij, where sij is the intangible asset share of
each firm i in industry j (Hou and Robinson, 2006).
Anderson, Ghysels, and Juergens (2009) indicate that dispersion of analysts’ forecasts
provides a measure of ambiguity. Thus, our final measure of industry ambiguity focuses on equity
analysts’ ability to predict future earnings. Industries providing greater (less) earnings predictability
arguably present family owners with less (more) ambiguity about the firm’s future prospects. We
proxy for industry earnings ambiguity as the kurtosis of analysts’ forecast error measured as
analysts’ forecast errors for all firms in each Fama-French industry group divided by the value-
25
weighted average book –to-market ratio of firms in the industry. We use the kurtosis, rather than
standard deviation, to capture a greater number of potential outcomes and term this industry
forecast error. Industry-level measures are based on the Fama-French 48-industry groupings less
regulated utilities and financials.
3.3.2. Proxies for ambiguity and risk aversion in the family-exit analysis
We examine the relationship between family-exit decisions and industry ambiguity as well
as family characteristics. To capture industry ambiguity, we use industry innovation and industry
forecast error as noted earlier. Our model yields predictions that family owners are less likely to
exit the firm as their total wealth increases. Family absolute wealth levels are not directly
observable. However, Anderson and Reeb (2003) note that family shareholders, on average, hold
about 69% of their total wealth in their firm’s stock; suggesting that the majority of family wealth
resides in the firm’s stock. We measure family wealth as the natural log of the family’s fractional
equity stake multiplied by year-end firm’s total market value of equity. To measure market value
for firms with an untraded class of stock (dual-class shares), we use the share price of the traded
class as a proxy for the price of the untraded class.
The model further indicates that family shareholders are less likely to exit their ownership
positions as family risk aversion increases. Because family risk aversion cannot be directly
observed, we follow Borghans et al. (2009) and others who find that women are more risk averse
than men based on experiment data. We instrument for risk aversion of family owners using the
presence of women in family firms using a binary variable that equals one when a female member
of the family serves on the firm’s board of directors and/or is listed in the proxy statement as
holding a 5% or larger equity stake in the firm and zero otherwise. Due to legacy issues of families
commonly giving directorships to male family members or listing male family members as share
owners, we potentially understate the influence of female family members on decision making and
thus, understate the level of risk aversion. If so, we potentially bias our results towards zero.
Our model also predicts that family owners are less likely to exit the firm as family
26
experience in the firm increases. We proxy for family experience as the natural log of the number
of years since the firm’s inception or more generally, the number of years since firm founded by
the family.
3.4. Control variables
We include several controls variables in our analysis. Firm size is measured as the natural log
of total assets (Arora and Ceccagnoli, 2006). Leverage is long-term total debt divided by total
assets (Elkamhi, Pungaliya, and Vijh, 2014).
Performance is earnings before interest, tax,
depreciation and amortization (EBITDA) divided by total assets, measured at t-1. Risk is the
standard deviation of the growth of income before extraordinary times for the prior 20-quarters
for each firm (Faccio et al., 2011). Firm age is the natural log of the number of years since the
firm’s founding (Anderson and Reeb, 2003). Growth opportunities are measured as the market
value of equity divided by total assets (Bekaert, Harvey, Lundbald and Siegel, 2007). Equity
issuance is measured as the sum of common and preferred stock annual issuances divided by total
assets (Masulis and Korwar, 1986). All regressions, where noted, include industry-level dummies
based on the Fama-French 48 industry grouping (less those groupings for financial and regulated
public utilities). We obtain data and data definitions for the Fama-French industry groups from
Kenneth French’s website21. Table I provides a description of the variables used in our analysis.
3.5.
Descriptive statistics
3.5.1. Cross-sectional analysis of family ownership levels
Our first set of tests exploit cross-sectional differences in the level of family ownership
across our full sample of family firms to test the ambiguity hypothesis. We segregate family firms
into low- and high- control stakes based on the level of family ownership. Families with a control
stake of less than 20% of the firm’s equity are classified as low ownership (2,237 firm-year
21
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/
27
observations) and families with a 20% or large stake are classified as high ownership (1,791 firmyear observations).
We proxy for information ambiguity using industry innovation, industry branding, industry
barriers to entry, industry entrants, and industry kurtosis. As discussed in Section 3.3.1, industries
with greater innovation, more entrants, and a greater likelihood of extreme earnings shocks
(kurtosis) present family owners with greater ambiguity about the firm’s future prospects. In
contrast, industries with greater branding and higher barriers to entry can shield family owners
from industry-wide disruptions thereby reducing ambiguity on the firm’s prospects. Our analysis
indicates a robust relation between family ownership levels and industry-level measures of
ambiguity. Table II, Panel A presents summary statistics and univariate test results for family
firms with high- and low- control stakes. We note that families with high control stakes (relative
to families with low control stakes) appear be associated with industries with less innovation and
fewer entrants, suggesting less industry disruption and thus less ambiguity for family owners.
Similarly, families with high control stakes are also associated with industries with greater
branding, again indicating less industry disruption and family ambiguity about the firm’s future
prospects. Table II, Panel B provides a correlation matrix of the key variables in our analysis and
confirms the results from the univariate tests.
3.4.2. Family-exit firms versus family firms
Table II, Panels C, D, and E provide summary statistics and a correlation matrix for the
propensity-score matched samples of family-exit firms to family firms. The statistics are calculated
by aggregating each variable for the 5-years prior to the family’s exit from the firm.
Panel C examines the quality of the matching process between family-exit firms and family
firms. We use two tests to examine the match quality. The first test examines the difference of
means for the variables that we use in the propensity-score matching process. These variables are
natural log of total assets, long-term debt divided by total assets, ROA based on EBITDA divided
by total assets, the standard deviation of the growth of income before extraordinary items for the
28
prior 20-quarters for each firm, the market value of equity to the book value of equity, and equity
issuance. The p-value for the t-test is shown in the last column of Table II, Panel C as the number
in italics only. We do not reject the null hypothesis (i.e., equal means) for any of the matching
variables and infer a relatively strong match based on difference of mean tests.
In the second test, we use the Kolmogorov-Smirnov (KS) procedure to examine the
equality of the distributions for the matching variables. The p-value for the KS test is shown in
the last column of Table II, Panel C as the number in bold and italics. With the exception of firm
size and debt ratio, we do not reject the null hypothesis (i.e., equal distributions) and again infer a
relatively strong match based on this test. The matching variables are included in regression
specifications to capture any differences between the two sub-samples.
Table II, Panel D displays our ambiguity proxies for the family-exit firms (column 2)
versus family firms (column 3) and a difference of mean tests (column 4). We find that family
owners are more likely to exit when the firm operates in an innovative industry, when families
have less absolute wealth invested in the firm, and when family members do not serve in
managerial posts (all relative to non-exiting family firms). We further explore the relation between
family exits and ambiguity in a hazard model framework in Section 5.2.
4. Multivariate tests
4.1. Cross-sectional analysis of family ownership and ambiguity
Our first set of multivariate tests to examine the ambiguity hypothesis exploit crosssectional differences in the level of family ownership across a large sample of family firms. The
model indicates family investors will tend to hold larger (smaller) equity stakes in industries with
less (more) ambiguity with respect to the firm’s future prospects. We examine this proposition
using the following OLS specification:
(High-Low Family Control) = α + β1-5(Proxies of Industry Ambiguity) + Xi,tβ + εi,t
29
The variables are defined in Table I with X representing a vector of control variables. We
control for serial correlation and heteroskedasticity using the Huber-White sandwich estimator
(clustered on firm-level identifier) for the standard errors on the coefficient estimates. In the
empirical analysis, we use proxies for industry ambiguity to examine whether ambiguity affects the
level of family ownership. Arguably, as our ambiguity measures are calculated on aggregate
industry characteristics rather than firm level characteristics, we mitigate reverse causality concerns
because family ownership (dependent variable) is unlikely to determine industrial structure
(independent variable).
Our analysis indicates a robust relation between the level of family ownership and
industry-level proxies of information ambiguity. Table III presents OLS regression results. We
note that families with high control stakes (relative to families with low control stakes) appear be
associated with industries with less innovation (column 1), fewer entrants (column 2), and a lower
level of industry forecast error (column 5); suggesting less ambiguity for family shareholders with
high ownership levels. Similarly, families with high control stakes (relative to families with low
control stakes) are associated with industries with greater branding (column 3) and greater barriers
to entry (column 4); again indicating less industry ambiguity for family shareholders with high
ownership levels. Overall, our cross-sectional analysis based on family ownership levels supports
Hypotheses 1.1 and 2.1 of our ambiguity model; suggesting that families maintain larger
ownership stakes in industries where it is easier to use private information to assess the expected
return and risk of their investment.
4.2. Family-exit firms versus family firms
Our central argument suggests that families will be less likely to exit the firm in situations
where;
(1) the family’s private information provides a competitive advantage in assessing expected returns and
return volatility (H1.1 and H2.1),
(2) the family is less risk averse relative to other family owners (H1.2 and H2.2),
30
(3) the family has more wealth invested in the firm relative to other family owners (H1.3 and H2.3),
(4) the family has less tenure (time) in the firm relative to other family owners (H1.4 and H2.4).
To examine these propositions, we examine family-exit firms versus family firms using a
Cox hazard or survival rate specification:
(Family Time in Firm, Family Exit Dummy) = α + β1-2(Industry Characteristicsi,t) +
β3-7(Family or Firm Characteristicsi,t) + Xi,tβ + εi,t
The variables are defined in Table I with X representing a vector of control variables. In the Cox
survival model (Lane, Looney, and Wansley, 1986), we relate the time that passes before the
family exits to our series of covariates on industry ambiguity and family characteristics that
potentially affect the family’s exit decision. For example, we examine whether family management
influences the family’s decision to exit their equity ownership stake.
A negative (positive)
coefficient on the family-management variable indicates that a family exit is less (more) likely to
happen if family members serve as managers relative to no family members serving as managers.
We control for serial correlation and heteroskedasticity using the Huber-White sandwich
estimator (clustered on firm-level identifier) for the standard errors on the coefficient estimates.
Table IV displays the results for family-exit firms versus the propensity score matched
family firms. The results indicate that families are more likely to exit their ownership position as
the level of industry ambiguity increases. We use two proxies of industry ambiguity; industry
innovation and industry forecast dispersion. Innovation captures the level of R&D intensity in the
industry with the underlying intuition that more innovative industries present greater ambiguity to
family owners. Similarly, forecast dispersion captures the ability of investors (analysts) to predict
future industry earnings, i.e., greater dispersion relating to more ambiguity. Providing evidence
consistent with H1.1 and H2.1, we find the family owners are far more likely to exit the firm in
industries with greater innovation and greater forecast dispersion. The coefficient estimates on
industry innovation (column 1) and industry forecast dispersion (column 2) are positive and
significant, indicating a greater likelihood of family exits in industries experiencing more ambiguity.
31
Columns 3, 4 and 5 of Table IV display the Cox regression results when examining family
characteristics. The model predicts that family owners with superior private information will be
less likely to exit the firm relative to families with less private information (H1.1 and H2.1).
Family members serving as CEO of the firm arguably provides the family shareholders with
superior, private information regarding the firm’s future prospects versus an external professional
manager serving as CEO. If so, we expect firm’s with family CEOs to experience less ambiguity
to family firms with professional CEOs and thus less likely to exit their ownership positions.
Column 3 of Table IV presents the family-exit results when a family member serves as CEO. The
analysis indicates that family exits are significantly less likely to occur when a family member
serves as CEO; suggesting that families with superior private information tend to remain in the
firm relative to families with less private information. The results provide further support to H1.1
and H2.1.
Our model also predicts that family owners should be less likely to exit their ownership
stake as family risk aversion increases, i.e., families will maintain their ownership position as their
level of risk aversion increases, all else equal. We instrument for risk aversion using a dummy
variable if a female member of the family serves on the board of directors and/or holds a 5% or
larger stake in the firm (Borghans et al., 2009). The analysis strongly indicates that family exits are
far less likely to occur as family risk aversion increase (female representation increases). Column 4
of Table IV displays the results.22 Our results on family risk aversion support hypotheses 1.2 and
2.2 of the model; all else equal, families with greater risk aversion tend to stay invested in the firm.
Our model predicts that wealthier families are less likely to exit the firm than less wealthy
families, i.e., families with a larger absolute, dollar wealth stake should be less likely to exit than
families with smaller absolute wealth stakes. The results in column 5 lend support to hypotheses
An alternative explanation for our finding on family women centers on the notion that because women are
more risk averse than men, family owners may be more willing to place female family members on board in
sectors characterized by high (or low) risk. We examine this proposition by regressing firm volatility on femalefamily representation and our control variables (with and without industry controls). The analysis indicates that
female-family representation is not significantly related to firm risk (volatility).
22
32
1.3 and 2.3 of the model. In particular, we note that as invested wealth in the firm increases, the
family is significantly less likely to exit their ownership stake. Column 5 of Table IV combines our
industry-level ambiguity proxies and the family-level characteristics into a single regression with
similar results.
Finally, the model predicts that family exits should exhibit a negative relation to the
family’s experience or time-invested in the firm. Our earlier tests examining family exit decisions
use a Cox hazard model where one of the two dependent variables is the length of time that the
family has held their equity position. Consequently, we cannot use a Cox model to examine our
time-in-firm prediction as we would regress time-on-time. To examine the time-in-firm
proposition, we use a logit model where the dependent variable equals 1 for a family exit and 0 for
non-exiting family firms. The results shown in column 7 of Table V clearly indicate that families
are significantly less likely to exit the firm as their time-in-firm increases. Specifically, we find a
negative and significant coefficient estimate on the family-experience variable indicating that
family exits are less likely to occur as time-in-firm increases, thereby supporting hypotheses 1.4
and 2.4 of the model.
Overall, the family-exit analysis based on industry-level characteristics and family
characteristics supports the predictions of the model and suggests that family owners are less
likely to exit their ownership positions when faced with less ambiguity about the firm’s future
prospects, possess superior private information, exhibit greater risk aversion, and as their time-infirm increases.
5. Summary and conclusion
Classical investment theory and conventional financial advice suggests that investors
should hold well-diversified portfolios versus holding large, concentrated stakes in a single firm.
Yet, even in well-developed equity markets such as those in the U.S., we continue to observe that
founding families of many publicly traded firms invest the bulk of their wealth in just one stock.
33
With the ability to control senior management posts, board seats, and the prevalence of supervoting dual-class shares, the notion that family shareholders need to maintain such large stakes to
extract private benefits appears to be puzzling.
We propose an additional explanation for large, concentrated family stakes based on
decision theory in which investors have concern over ambiguity about both the expected return
and return volatility. For family owners, with private information about the firm to reduce the
ambiguity about their own firm relative to outside firms, this can result in a portfolio where the
majority of their investable funds are held in the family firm. In contrast, atomistic shareholders
without access to private information invest in a diversified portfolio. We find that ambiguity
about return volatility is critical to explain quantitative aspect of the puzzle that family
shareholders maintain large stakes in the family firm.
Furthermore, the model provides various testable implications, including several that
appear contrary to standard expectations in the literature on family existing decision. The model
predicts that family owners are more likely to retain their ownership stakes where private
information and experience allows the family to better understand the nature of the firm’s future
prospects. The model distinctly predicts that families will be less likely to sell-off their ownership
positions (exit the firm) as family wealth invested in the firm increases23; as family (absolute) riskaversion increases and; as family tenure in the firm increases.
We empirically investigate the model’s predictions using two testing procedures. First, we
examine family ownership, in the cross-section, for a large sample of family held U.S. industrial
firms. Second, in perhaps a more robust test environment, we examine family decisions to sell-off
their ownership stakes and exit the firm. Our first series of test, a cross-sectional analysis, suggests
that families hold larger ownership stakes in industries with less innovation, fewer new entrants
(competitors), lower likelihood of extreme industry-level earning shocks, greater branding, and
Bitler et al. (2005) argue that the standard agency model also implies a positive relationship between wealth
and ownership, as absolute risk aversion is typically thought to decreasing in wealth. However, for investors
with constant absolute risk aversion, this implied positive relationship between wealth and ownership does not
hold.
23
34
larger barriers to entry. Our second series of tests examining family exits also confirms that
families tend to remain in industries with less innovation and greater branding. Notably, the exit
analysis also indicates that families are less likely to sell-off their ownership stakes as their invested
wealth increases, their tenure in the firm increases, as their risk aversion increases, and when the
family actively manages the firm. In total, the empirical analysis support the models’ predictions,
suggesting that families rationally choose to hold an undiversified portfolio when their private
information allows them to reduce ambiguity about the firm’s future prospects relative to outside
firms.
Our analysis is motivated by the quantitative feature of the family firm puzzle, that is why
family owners defy conventional finance wisdom by maintaining large, concentrated stakes in a
single firm. We show that information advantage on the family firm allows the family owners to
reduce the ambiguity about expected return and especially about return volatility of the family
own stock relative to that of a diversified portfolio of other firms. Yet, family blockholders are
not the only type of investor with large shareholdings in the asset markets. Financial
intermediaries also often hold large equity stakes in firms. Although some financial intermediaries,
such as mutual funds and hedge funds typically hold well-diversified portfolios, others such as
private equity funds and venture capitalists hold less well-diversified portfolios relative to mutual
funds but still frequently hold 20 or more firms in their asset mix (Robinson and Sensoy, 2013).
Our model does not directly link to the holdings of financial intermediaries. However, one could
conceivably use this type of analysis to investigate the limited diversification found in venture
capital and private equity firms relative to mutual funds.
35
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39
Appendix 1: Model Implied Family Ownership
In this appendix, we present the implied share of family wealth invested in the family firm
for various levels of relative ambiguity and expected returns in the model with ambiguity. The
implied family-ownership is computed for different levels of ambiguity about the diversified
portfolio relative to the family firm, and for three cases where the worse expected return of the
family firm is the same, less, and more than that of the diversified portfolio. For comparison, we
also present the implied ownership of a single stock in the model without ambiguity.
Table A.1.
Calibration of Stock Ownership
Model implied share of wealth invested in the single stock in models with and without ambiguity24.
These estimates are computed in the benchmark model in Section 2. In the model without
ambiguity, the true values of annual expected return ( ) and variance ( ) of the diversified
portfolio are assumed to be 9% and 0.037, respectively. The true value of annual return variance
(
) of the single stock is assumed to 0.242, the correlation coefficient between diversified
portfolio and single stock assumed to be 0.123 (see Elton and Gruber, 1977). In the model with
ambiguity, the worse-case values of annual expected return (
) and variance (
) of the
diversified portfolio are assumed to be same as the true values in the model without ambiguity.
Panel A: Model with Ambiguity
Relative Ambiguity
of Return Volatility
(
Relative Ambiguity of Expected Returns
)
Infinity
100%
81%
>100%
4.00
82%
65%
98%
2.00
68%
54%
82%
1.00
50%
39%
61%
0.50
30%
22%
38%
0.25
13%
8%
17%
Panel B: Model without Ambiguity about Return Volatility
Relative Return Volatility
Relative Ambiguity of Expected Returns
(
)
0.15
3%
0%
6%
The risk aversion and wealth level are calibrated such that 30% of wealth is invested in the risky portfolio and
70% invested in the safe asset, in Markowitz (1952) framework that contains a safe asset with return of 2% and
a risky asset with expected return of 9%.
24
40
Appendix 2: Family investment decision with Treasury Bills
In this appendix, we consider the optimal portfolio choice problem faced by the family
owners who choose to invest in three assets, the family’s firm with return
portfolio with return
and Treasury Bills with return
, a diversified
. We use Treasury Bills as a proxy for the
25
risk free asset with nonzero variance.
Table A.2.
Summary Statistics of Return on Treasury Bonds and Market Index
Summary statistics of annual real returns on Treasuries and CRSP Stock Market Index. The
returns are deflated using inflation rate computed from CPI. The returns on treasuries, CPI and
market index are from CRSP dataset available on WRDS.
Annual Return (%)
1942-2013
Annual Volatility (%)
1942-2013
Annual Return (%)
1995-2013
Annual Volatility (%)
1995-2013
Treasury Bonds/Bills
10 year 5 year 2 year
Market
Index
30 year
9.15
2.11
1.86
1.80
1.31
0.15
18.50
13.51
9.71
7.10
5.20
3.55
9.56
6.10
4.38
3.64
2.16
0.41
20.19
17.61
8.95
5.93
3.59
2.11
30 day
Table A.2 shows that the average return and standard deviation of 30-day Treasury Bills is
significantly lower than that of the market portfolio, and the standard deviation of the return on
Treasury Bills is significantly different from zero. The standard deviation of longer term Treasury
Bonds is much higher.
We assume that returns on all three assets, ,
and
, are independent and normally
distributed. To focus on the investment choice between the family firm and the market portfolio,
we assume no ambiguity regarding the return on Treasury Bills. That is, we assume the true value
of the mean and variance of returns on the family firm and the market portfolio,
and
, are
unknown to investors while the true value of the mean and variance of returns on Treasury Bills
are known to all investors. The true value of the mean and variance of the return on asset i, , is
denoted as (
) for i =1, 2, 3. Investors perceive that the mean and variance of
and
30-day Treasury Bills are commonly used as a proxy for the risk free asset in asset pricing and optimal
portfolio choice literatures.
25
41
belong to a set of possible values
and
which contain the true values of mean and standard
deviation (
), for i = 1, 2. That is, the true values
and
lie between
and
respectively, for i = 1, 2. We further assume that the mean return on Treasury
Bills is smaller than the minimum mean returns on the family firm and the market portfolio, and
the variance of return on Treasury Bills is smaller than the minimum variances of returns on the
family firm and the market portfolio, that is,
(A.1)
As in our benchmark model, we assume that family owners have private information
regarding the fundamentals of the family firm, which allows them to reduce the ambiguity about
the fundamentals of their own firms over time and through experience. However, the family
owners cannot obtain material, non-public information about firms in the broad portfolio as they
do not manage these other firms. In our setup, the reduction in the ambiguity is captured by the
shrinkage in the range of all possible means and variances on the return on the family firm.
A.1.1 The family’s investment decision
For each time period t, the decision problem of the family owners with CARA utility can
be formulated as
(A.2)
where Wt is the wealth of the family at time t,
,
and
firm, market portfolio and Treasury Bills at time t+1, respectively.
are the returns on the family
and
are the shares of
wealth invested in the family firm and market portfolio, respectively. We allow for short sales in
all the assets, and do not restrict
and
to be positive and less than one.
It can be easily shown that the decision problem of the family owners can be transformed
as,
(A.3)
Let's first examine the minimization problem of (A.3). Since the objective function in (A.3) is
42
monotonically decreasing in
and
, the maximum possible value of variance is always chosen,
that is
As long as the family is long in the assets, they only care about the minimum possible expected
return of this asset. If the family shorts the asset, then the maximum possible mean return of this
asset is chosen, that is,
Assumption (A.1) implies that it is never optimal for the family owners to short both the family
firm and the market portfolio at the same time. Given the solution to the minimization problem
(A.3), the optimal share invested in the family business and the market portfolio can be
characterized as following:
Case 1: If the following condition is satisfied,
then the family owners go long on the family stock and short the diversified portfolio
This is the case when the family’s private information allows them to significantly reduce the
ambiguity of their family firm relative to the other firms, and the minimum expected return of
family firm is much larger than the maximum possible expected return of the diversified portfolio
(in excess of return on Treasury Bills), then the family chooses to invest as much as possible in
their own firm. In this case, the share invested in the family firm decreases with the risk aversion
and family wealth. However, we argue this is an extreme case and does not apply to the marginal
family owners who may exit, as the family would never exit in this case. Furthermore, we argue
this is a case rare in the reality, as it is extreme for the family to think the minimum risk adjusted
expected return of the family firm is much larger than the maximum possible expected return of
43
the diversified portfolio.
Case 2: If the following condition is satisfied,
,
then the family owners invest positive shares in both the family stock and the diversified portfolio
In this case, the family owners still have less ambiguity about the expected return on their own
firm relative to other firms. However, the private information advantage is not as large as it is in
Case 1, so the family firm chooses to invest positive share of wealth in both the family firm and
the diversified portfolio.
Case 3: If the following condition is satisfied,
then the family owners short the family stock and go long on the diversified portfolio
This is scenario where the private information does not help to reduce the ambiguity of the family
firm enough, so that the minimum possible expected return of the family business is less than the
minimum possible expected return of the diversified portfolio.
Let us again focus on Case 2 where family owners invest positive shares in both the family
firm and the diversified portfolio. In this case, we can rewrite the optimal investment share in the
family firm as
(A.4)
The optimal share depends on the Sharpe ratio of the family firm relative to the treasury bills as
44
well as the market portfolio. When the family has less ambiguity about the variance and the
expected return of the family firm, that is, the smaller are
larger are
and
and
or the
, the more likely the family will continue to
invest in the family firm. Thus, the key concern about risk adjusted return centers on the
ambiguity of the variance rather than the level of the variance. Moreover, if the family has little
information about the return volatility of the diversified portfolio (relative to their own firm), then
they would put a very high upper bound on the perceived return volatility of this asset (
is
high). This implies that they would invest little in the diversified portfolio. Suppose the family is
extremely averse to ambiguity, or the relative ambiguity about the return volatility of the
diversified portfolio gets extremely large, then the family would invest nothing in the diversified
portfolio, regardless of their risk aversion or wealth level.
To study the relationship between the share invested in the family firm and the
characteristics of the family such as risk aversion and wealth of the family, we found it is
necessary to focus on the Case 2. Taking the derivative of the optimal share in family share (
)
with respect to risk aversion (γ) and wealth (Wt), we have
(A.5)
If the family owners have less ambiguity regarding the family firm and think the return on their
family firm is so good that the minimum return is sufficiently larger than that of the market
portfolio such that the Sharpe ratio relative to the market portfolio is larger than the Sharpe ratio
relative to the Treasury Bills, that is,
then the family will always invest positive share in the family business will not consider exiting.
However, we are more interested in the case where
The family thinks the minimum expected return of the family business is smaller than that of the
market portfolio. This is the case that captures the marginal family investors who might consider
the exit decision. In this case, (A.5) is positive and the more risk averse is the family or the more
wealth the family has, the larger share of wealth is invested in the family firm, and the less likely
for the family to exit, ceteris paribus. Hence, the predictions of our benchmark model still hold
45
when the choice set of the family owners includes not only two risky assets with different levels of
ambiguity but also a government bond that proxies for the relatively low risk asset without
ambiguity.
46
Figure 1. Optimal Portfolio Choice of Family Owners
Expected
Return
Optimal Choice of Risk
Neutral Investor
D0
F0
FB
FA
Optimal Choice of
Risk Averse Investor
DB
DA
Risk (σ)
Panel A: Non-Exiting Case (
)
FA corresponds to the worse-case scenario return-volatility pair of the family firm stock (
), DA
corresponds to the worse-case-scenario return-volatility pair of the diversified portfolio (
). FB and
DB correspond to the worse-case scenario of return-volatility pair of the family firm stock and the diversified
portfolio, respectively, in the case where there is no ambiguity about return volatility.
Expected
Return
D0
F0
Optimal Choice of
Risk Neutral Investor
DE
DB
FB
FE
Optimal Choice of
Risk Averse Investor
Risk (σ)
Panel B: Exiting Case (
)
FE corresponds to the worse-case scenario return-risk of family firm stock (
), DE corresponds to
the worse-case-scenario return-risk of the diversified portfolio (
). FB and DB correspond to the
worse-case scenario return-risk of the family firm stock and the diversified portfolio, respectively, in the case
where there is no ambiguity about risk of the returns.
47
Table I – Variable Definitions
Debt Ratio – year-end long-term debt divided by total assets for each firm.
Equity issuance – the sum of common and preferred stock annual issuances divided by total assets.
Family Experience – natural log of the number of years since the firm’s inception.
Family Firm – binary variable that equals one when the family holds a five percent or larger ownership
stake and zero otherwise.
Family Management – binary variable that equals one when either the founder or a founder’s descendant
serves as CEO of the firm; equals zero when an outside professional manager serves as CEO of
the firm.
Family Ownership – the percent of common equity held by the family.
Family Risk Aversion – equals one when a female member of the family serves on the firm’s board of
directors and/or holds a 5% or larger equity stake.
Family Wealth – family fractional equity ownership stake multiplied by year-end firm total market value.
Firm Age – the number of years since the firm’s founding.
Growth Opportunities – market value of equity divided by total assets.
High-Low Family Ownership – level of family ownership less 20%.
Industry Barriers to Entry – is the Herfindahl Index of intangible assets which is defined as: Herfindahlj =
∑s2ij, where sij is the intangible asset share of each firm i in industry j. We perform the above
calculation for each Fama-French industry group for each year.
Industry Branding – average of advertising expense divided by total assets for all firms in each of the
Fama-French industry groups.
Industry Dummy - equals one for each Fama-French industry group and zero otherwise.
Industry Entry – a dummy variable that equals one when the fraction of new firms entering each FamaFrench industry is greater than 10% of the total firms in the industry and zero otherwise. The
fraction of new firms entering in each of the Fama-French industry groups is calculated as the
increase in the number of firm from time t-1 to t divided by number of firms in the industry at
time t-1.
Industry Forecast Error – industry average kurtosis of the analysts’ forecast error of all firms in each of the
Fama-French industry groups, divided by the industry value-weighted average book-to-market
ratio.
Industry Innovation – average of R&D expense divided by total assets for all firm in each of the FamaFrench industry groups.
Industry Risk – the standard deviation of the free-cash flows to assets for all firms in each of the FamaFrench industry groups.
Return on Assetst-1 – earnings before interest, tax, depreciation and amortization (EBITDA) divided by
total assets for the prior year-end for each firm.
Total Assets – year-end total assets for each firm.
Volatility – standard deviation of the growth of income before extraordinary items (ibq) for the prior 20quarters for each firm.
48
Table II – Summary Statistics
Panel A: This panel provides annual summary statistics and difference of mean tests for Low- and HighFamily Control Stakes. Low Ownership is defined as family ownership stakes less than 20%. High
Ownership is defined as family ownership stakes greater than or equal to 20%. Unique observations
reflect the number of firms in the first year (2001) of the sample. The variables are defined in Table I. tstatistics are corrected for serial correlation and heteroskedasticity by clustering on firm-level identifier.
***, **, and * indicate significance at the 1%, 5% and 10% levels, respectively.
Observations
Unique Firms
Family Ownership
Industry Risk
Industry Innovation
Industry Branding
Industry Barriers to Entry
Industry Forecast Dispersion
Industry Entrants
Ln(total assets)
Debt Ratio
Return on Assetst-1 %
Volatility
Firm Age
Mkt Value of Eqty/Assets
Equity Issuance/Assets
Summary Statistics for High-Low Family Ownership
All Family
Low Ownership High Ownership
Firms
4,028
2,237
1,791
535
283
252
23.26
11.00
38.57
16.61
17.09
15.98
2.37
2.69
1.97
1.42
1.30
1.57
9.99
9.76
10.30
2.82
2.90
2.73
0.38
0.43
0.32
7.02
7.10
6.91
18.30
18.30
18.29
11.99
11.32
12.84
23.67
18.13
30.60
42.88
42.59
43.25
1.27
1.26
1.29
1.66
1.92
1.34
t-test
30.16***
1.82*
3.42***
2.23*
0.84
1.24
1.76*
1.84*
0.01
2.39***
0.50
0.25
0.40
3.63**
Panel B: This panel provides Spearman correlation coefficients for the annual measures used in the Lowand High- Family Ownership Analysis. The variables are defined in Table I. * indicates significance at the
5% level or higher.
(1) Industry Risk
(2) Family Ownership
(3) Industry Innovation
(4) Industry Entry
(5) Industry Branding
(6) Industry Barriers to Entry
(7) Industry Forecast Dispersion
(1)
1.00
-0.04*
0.17*
0.19*
-0.31*
0.09*
-0.30*
(2)
(3)
(4)
(5)
(6)
1.00
-0.17*
-0.03
0.11*
0.06*
-0.05*
1.00
-0.09*
-0.17*
-0.17*
0.40*
1.00
-0.13*
0.07*
-0.15*
1.00
0.41*
0.14*
1.00
-0.19*
49
Table II – Summary Statistics (Continued)
Panel C: This panel examines the quality of the propensity-score matching process. The variables are
defined in Table I. Min., 25%, 50%, 75%, Max., and Mean are the corresponding values at each point of
the distribution for Family Exit Firms (n=416) to Family Firms (n=416). Test statistics are; the p-value for
the Kolmogorov-Smirnov equality of distribution tests (italics and bold) and, directly beneath, the p-value
for the difference of means tests between the two distributions (italics). Family-exit firms are matched to
family firms based on propensity score matching techniques (see pages 23 and 24). p-values are corrected
for serial correlation and heteroskedasticity by clustering on firm-level identifier. * indicates significance at
the 5% level or better.
Obs.
Min.
25%
50%
Family Exit Firm-years
Family Firm-years
416
416
3.42
3.60
5.87
5.73
6.37
6.30
Family Exit Firm-years
Family Firm-years
416
416
0.00
0.00
1.40
0.34
Family Exit Firm-years
Family Firm-years
416
416
-87.22
-38.06
Family Exit Firm-years
Family Firm-years
416
416
0.07
0.05
Family Exit Firm-years
Family Firm-years
416
416
0.02
0.01
Family Exit Firm-years
Family Firm-years
416
416
0.00
0.00
75%
KS-test
Max.
Mean
t-test
(p-values)
7.32
7.38
11.17
11.84
6.65
6.60
0.05*
16.18
14.13
31.69
30.98
81.10
94.33
19.62
19.04
0.04*
4.56
5.47
9.84
10.36
15.68
15.73
56.88
50.25
9.48
9.76
1.21
1.12
2.68
2.55
5.47
6.51
130.20
121.89
19.64
18.16
0.24
0.55
0.49
0.95
0.87
1.53
1.52
7.17
7.81
1.20
1.19
0.36
0.20
0.08
0.63
0.46
1.36
1.32
57.40
63.48
1.88
2.01
0.24
Firm Size (Ln(total Assets)
Debt Ratio
Return on Assetst-1
Volatility
Growth Opportunities
Equity Issuance x 100
0.42
0.31
0.81
0.23
0.30
0.10
0.32
50
Table II – Summary Statistics (Continued)
Panel D: This panel provides annual summary statistics and difference of mean tests for family-exit firms
versus family firms. The analysis period is the 5-year preceding the family’s exit from the firm and the
corresponding values from the matched sample. The variables are defined in Table I. Family-exit firms
are matched to family firms based on propensity score matching techniques (see pages 23 and 24). tstatistics are corrected for serial correlation and heteroskedasticity by clustering on firm-level identifier. *
indicates significance at the 5% level or better.
Summary Statistics for Family-Exit Firms and Family Firms
(1)
(2)
(3)
All Firms
Family-Exit
Family
Firms
Firms
Obs
832
409
409
Unique Firms
100
334
Industry Innovation (%)
2.79
3.17
2.41
Industry Forecast Dispersion
3.04
3.13
2.95
Family Management
0.54
0.43
0.66
Family Risk Aversion (women)
0.16
8.65
22.60
Family Wealth
4.43
4.22
4.64
Family Experience (Firm Age)
34.7
35.20
34.11
(4)
t-test
2.27 *
0.87
4.85
4.08*
2.79*
0.35
Panel E: This panel provides Spearman correlation coefficients for the annual measures of family-exit
firms and family firms. The analysis period is the 5-year preceding the family’s exit from the firm and the
corresponding values from the matched sample. The variables are defined in Table I. Family-exit firms are
matched to family firms based on propensity score matching techniques (see pages 23 and 24). .* indicates
significance at the 5% level or better.
(1) Industry Risk
(2) Industry Innovation
(3) Industry Forecast Dispersion
(4) Family Management
(5) Family Risk Aversion (women)
(6)Family Wealth
(1)
1.00
0.27*
0.32*
0.02
-0.07*
-0.02
(2)
(3)
(4)
(5)
1.00
0.33*
0.01
-0.12*
-0.05
1.00
0.06
0.01
0.01
1.00
-0.02
0.03
1.00
0.20*
51
Table III
High-Low Ownership Analysis
This table presents OLS regression results of High-Low Family Ownership on industry-level characteristics.
High-Low family ownership is the level of family ownership less 20%. The variables are defined in Table I.
These regressions include only family firms. t-values are reported in parentheses and are corrected for
serial correlation and heteroskedasticity by clustering on firm level identifiers. ***, **, and * indicate
significance at the 1%, 5% and 10% levels, respectively.
Industry Innovation
Industry Entry
(1)
-1.093***
(4.36)
-
Dependent Variable = High-Low Family Control
(2)
(3)
(4)
-
Industry Branding
-
-0.543***
(2.71)
-
Industry Barriers to Entry
-
-
1.472***
(2.86)
-
Industry Forecast Dispersion
-
-
-
0.288***
(2.47)
-
-0.021***
(3.94)
0.045
(1.01)
0.034
(0.69)
0.007
(0.80)
0.012*
(1.80)
-0.343***
(4.38)
0.152***
(3.15)
Yes
5.65
4,028
-0.014***
(3.32)
0.037
(1.12)
0.082**
(1.99)
0.014*
(1.95)
0.004
(0.69)
-0.221***
(3.64)
0.030
(0.82)
Yes
3.19
4,028
-0.019***
(3.60)
0.077*
(1.77)
0.100**
(2.02)
0.007
(0.85)
0.005
(0.74)
-0.354***
(4.47)
0.085*
(1.87)
Yes
4.44
4,028
-0.019***
(3.59)
0.066
(1.47)
0.122***
(2.43)
0.008
(0.86)
0.005
(0.74)
-0.358***
(4.55)
0.088*
(1.88)
Yes
4.26
4,028
Ln (Total Assets)
Debt Ratio
Return on Assetst-1
Ln (Firm Age)
Growth Opportunities
Equity Issuance
Constant
Year Dummies
Overall R2 (%)
Observations
(5)
-
-
-
-
-
-0.470**
(2.01)
--0.019***
(3.49)
0.057
(1.29)
0.108**
(2.23)
0.009*
(1.04)
0.007
(1.06)
-0.400***
(5.16)
0.117***
(2.41)
Yes
3.54
4,028
52
Table IV
Family Exit Analysis: Family Characteristics
Columns 1 through 6 report coefficient estimates from a Cox model of family exits and propensity score matched firms (see page 23 and 24). Column 7
reports the results of a logit regression of family exits on firm age (0=no family exit, 1=family exit). The variables are defined in Table I. z-values are
reported in parentheses and are corrected for serial correlation and heteroskedasticity by clustering on firm level identifiers. ***, **, and * indicate
significance at the 1%, 5% and 10% levels, respectively.
Industry Innovation
Industry Forecast Error
(1)
(2)
(3)
(4)
(5)
(6)
(7)
12.363***
(3.07)
-
-
-
-
-
-
-
-
-
-
-
8.394*
(1.78)
0.102**
(2.56)
-0.704***
(2.95)
-1.096***
(3.28)
-0.353***
(4.32)
0.013
(0.09)
1.016*
(1.69)
-2.719***
(3.01)
0.001
(0.25)
0.281**
(2.03)
-0.622
(0.33)
Yes
832
Family Management
-
0.092**
(2.41)
-
Family Risk Aversion (women)
-
-
-0.880***
(3.94)
-
Ln (Family Wealth)
-
-
-
-1.462***
(4.29)
-
Ln(Family Experience)
-
-
-
-
-0.446***
(6.04)
-
-0.240*
(1.92)
1.126*
(1.86)
-3.026***
(3.27)
-0.001
(0.38)
0.025
(0.20)
-0.124
(0.06)
Yes
832
-0.276**
(2.34)
1.095*
(1.78)
-3.786***
(4.21)
-0.001
(0.07)
0.132
(1.30)
0.038
(0.02)
Yes
832
-0.340**
(2.72)
1.298**
(2.06)
-3.679***
(4.18)
0.001
(0.08)
0.195*
(1.83)
0.356
(0.21)
Yes
832
-0.314**
(2.63)
1.143*
(1.86)
-3.762***
(4.35)
-0.002
(0.02)
0.138
(1.36)
-0.346
(0.19)
Yes
832
0.100
(0.77)
0.685
(1.24)
-3.062***
(3.46)
0.001
(0.06)
0.408***
(3.41)
-0.224
(0.13)
Yes
832
Ln (Total Assets)
Debt Ratio
Return on Assetst-1
Volatility
Growth Opportunities
Equity Issuance
Industry Dummies
Overall R2 (%)
Observations
-0.277***
(2.92)
0.158**
(2.23)
0.196
(0.51)
1.736***
(2.72)
0.001
(0.88)
-0.093
(1.23)
-1.143
(0.92)
Yes
8.37
832