Empirical Evidence of Risk Shifting Behavior in Large and Small Distressed
Firms
Chuang-Chang Chang
Department of Finance, National Central University, Taiwan
[email protected]
Yu-Jen Hsiao
Department of Finance, National Central University, Taiwan
[email protected]
Yu-Chih Lin
Department and Graduate Institute of Accounting, National Yunlin University of
Science &Technology
[email protected]
Wei-Cheng Chen
Department of Finance, National Central University, Taiwan
[email protected]
This Draft: July 29, 2008
Empirical Evidence of Risk Shifting Behavior in Large and Small
Distressed Firms
Abstract
This study uses a uniform measure across a large sample of firms to analyze the actual
existence of risk-shifting problem in large and small distressed firms. We find that
risk-shifting behavior in distressed firm that was found by Eisdorfer (2008)
completely disappears when only consider on large distressed firms. In other words,
our results provide the evidence of risk-shifting behavior only significant in small
distressed firms. Further, we use the maximum likelihood estimation method
proposed by Duan (1994; 2000) to estimate the costs of risk-shifting. According to
our estimation, the value of debt in small distressed firms is reduced by approximately
0.97%, as the result of overinvestment in high uncertainty firm-specific investments.
Moreover, we also find that the factors including shorter maturity debt, and less
growth options have significant effects on mitigating the risk-shifting behavior in
small distressed firms.
Keywords: Risk-shifting; Financial distress; Maximum likelihood estimation
1
1. Introduction
Risk-shifting (asset substitution), a conflict of interest between equity holders and
debt holders, is the most discussed agency problem in finance. Jensen and Meckling
(1976) first introduced this concept. They argue that once a debt is in place, the value
of firm’s equity is like an option due to the limited liabilities of the equity holders.
Consequently, they conclude that equity holders will have incentives to increase the
risk of the firm so as to increase the equity value at the expense of debt holders. After
Jensen and Meckling (1976) introduced risk-shifting problem, many studies have
sought to identify factors that can mitigate this problem. However, there is very little
empirical evidence of whether the problem actually exists. Until Eisdorfer (2008)
provides empirical evidence indicating substantial risk-shifting behavior in financially
distressed firms.
Eisdorfer (2008) empirically examine risk-shifting behavior in financially
distressed firms by studying the relation between investment and volatility. Before
Eisdorfer (2008), this relation is analyzed by using real option approach. Under the
real option logic, a firm’s investment decision involves a tradeoff between realizing
early cash flows by immediately investing in a project, and gaining more information
about the value of the project by delaying investment. Since the value of delaying
investment increases with the degree of uncertainty about the project’s cash flows,
they expect that current investment will decline when the volatility rises. Pindyck and
Solimano (1993), Episcopos (1995), Ghosal and Loungani (1996), Leahy and Whited
(1996), and Bulan (2003) provide the empirical evidences of the negative relation
between investment and volatility.
However, Eisdorfer (2008) argue that when a firm is in financial distress, in
addition to real option considerations, risk-shifting incentives also play a role in the
investment-volatility relation. Hence, volatility has two opposite effects on current
investment-a negative effect of the option to delay investment and a positive effect of
risk-shifting. According to the model implication of Eisdorfer (2008), the latter effect
can dominate the former.
In related Articles, Barnea et al. (1981) have argued that agency costs would be
higher in smaller firms as a small business’s owner/manager is likely to put his own
and his venture’s interest first. Michaelas, Chittenden, and Poutziouris (1999) they
also argued that solutions to agency problems are relatively more expensive to small
business, thus raising the cost of transactions between small business with their
creditors, shareholders, and other stockholders. Hence, monitoring could be more
difficult and expensive for small firms because they may not be required to disclose
2
much. Therefore, they argued that moral hazard and adverse selection problems may
be greater for small firms because of their costly held nature.
Hence, although Eisdorfer (2008) provides the empirical evidences of risk-shifting
behavior in financially distressed firms, a more interesting issue is to examine
whether the risk-shifting behavior in large distressed firms and in small distressed
firms are the same or not. Therefore, in this study, we will examine the risk-shifting
behavior in both large and small distressed firms.
Review the empirical related literatures of risk-shifting problem; Andrade and
Kaplan (1998) examine the large investments in unusually risky projects within 31
financially distressed firms and find no evidence of risk-shifting behavior. De Jong
and Van Dijk (2001) use questionnaires sent to CFOs of 102 firms listed on the
Amsterdam Stock Exchange to examine the problem and find no evidence of
risk-shifting behavior. Graham and Harvey (2001) survey CFOs of 302 U.S. and
Canadian firms and find little evidence that executives are concerned about
risk-shifting. Even though a large number of studies analyze the implication of this
problem, no study has used a uniform measure across a large sample of firms to
directly analyze the actual existence of the problem until Eisdorfer (2008).
Comparing the empirical tests of risk-shifting behavior in Eisdorfer (2008), we use
different methodology to investigate the risk-shifting behavior in financially
distressed firms. In estimating the firm’s asset value and firm’s asset volatility for
testing hypotheses and estimating the cost of risk-shifting, we do not apply Ronn and
Verma (1986) method which has a serious statistical problem,1 but we apply
maximum likelihood estimation method proposed by Duan (1994; 2000) to estimate
the firm’s asset value and firm’s asset volatility to ensure having steady statistical
inferences.
Based on our empirical results, we find that only the small distressed firms have
risk-shifting behavior. Furthermore, we also find that the changes in firm-specific
investment intensity of small distressed firms in a given year significantly increase
firm-specific realized asset volatility in the following year. The finding provides a
further evidence of risk-shifting behavior in small distressed firms. In measuring a
wealth transfer from debt holders to equity holders, we use the expected market
volatility to identify high uncertainty firm-specific investments and estimate the
investment distortion in these high uncertainty firm-specific investments in small
distressed firms (relative to small healthy firms). The results show that the value of
debt in small distressed firms is reduced by approximately 0.97%, as the results of
overinvestment in high uncertainty firm-specific investments by using maximum
likelihood estimation method proposed by Duan (1994; 2000).
Finally, review the related literatures about identifying factors that can mitigate
3
risk-shifting problem, Smith and Warner (1979) examine how debt contracts are
written to control the bondholder-stockholder conflict, and argue that restrictions on
investment, restrictions on disposition of assets, and secured debt can limit the ability
of equity holders to shift risk. Green (1984) analyzes the use of conversion features
and warrants controlling distortion incentives, and shows that convertible debt
mitigates shareholders’ incentives to take risk since it reverses the convex shape of
levered equity over the upper range of a firm’s earnings. Barnea, Haugen, and Senbet
(1980) argue that issuing short-term debt can mitigate risk incentive problem since the
value of shorter term debt is less sensitive to a shift into the lower value-higher
variance project. Smith (1986) argues that managers in regulated firms have less
ability of discretion over investment decisions than managers in unregulated firms.
Hence, we expect that deviations from optimal investment policy, including asset
substitution, are less likely to occur in regulated firms. Based on the literatures above,
we examine the effects of those factors on mitigating risk-shifting problem in this
study. Finally, the factors including shorter maturity debt, and less growth options
have significant effects on mitigating the relation between expected volatility and
investment for small distressed firms, when we use the expected market volatility to
measure uncertainty.
The remainder of this paper is organized as follows. Section 2 introduces the
estimation methods in this paper. Section 3 empirically tests the hypothesis associated
with the risk-shifting behavior, estimates the costs of the investment distortion and
examines how various factors help mitigate the problem and Section 4 concludes the
paper.
2. Estimation Method
2.1 Measuring Expected volatility
To measure conditional expected market volatility and conditional expected
industry volatilities, we follow Eisdorfer (2008) to use generalized autoregressive
conditional heteroskedasticity (GARCH) models, introduced by Engle (1982) and
developed by Bollerslev (1986). At first, we apply GARCH (1, 1) model to monthly
returns of NYSE market index and the value weighted average monthly returns of
each industry (based on two-digit SIC codes) from 1963 to 2006. Then, for each
calendar year, the expected volatility is measured by 12-month-ahead forecasted
volatility conditional on the information available in the last month of the year before.
Equation (1) and (2) are mean equation and conditional variance equation of
4
GARCH (1, 1) model, where Rt is the return in month t, and ε t ~ N (0, σ t2 ) .
Rt = γ + ε t
(1)
σ t2 = α 0 + α 1ε t2−1 + βσ t2−1
(2)
Equation (3) is derived by equation (1) and (2), and it represents the forecasted
variance for the period, conditional on the information available in month t.
[ ]
Et σ t2+ k = (α 1 + β1 )
k −1
[σ
2
t +1
]
− α 0 (1 − α 1 − β1 ) + α 0 (1 − α 1 − β1 )
(3)
Furthermore, under the assumption of the residual of mean equation are serially
independent, the expected variance in month t for the following year is given by
adding the 12-month-ahead variance forecasts, that is,
[ ] ∑ E [σ ] = ∑ (α
Et σ t2,k =
12
12
t
k =1
2
t +k
+ β1 )
k −1
1
[σ
2
t +1
]
− α 0 (1 − α 1 − β1 ) + α 0 (1 − α 1 − β1 ) (4)
k =1
Equation (4) implies that the expected annual variance is a linear function of expected
variance for the next month, σ t2+1 , and thus of the expected variance for any month
during the period. Therefore, conditional on the information available at the beginning
of the year, when we want to examine the effect of expected annual volatility on the
firm’s investment intensity in a given year, it is sufficient to regress annual investment
intensity on expected annual volatility for the first month of the year.
Figure I shows the monthly expected market volatility and the average of the
monthly expected industry volatilities over 1988 to 2006 (the test period), where the
pattern of expected volatility is consistent with previous studies ( e.g., Schwart(2002)
and Eisdorfer (2008)).
【Insert Figure I】
2.2 Measuring Investment intensity
Most studies measure firm-specific investment intensity by capital expenditures
scaled by either property, plant, and equipment (PP&E) (see Fazzari, Hubbard, and
Petersen (1988)；Hoshi, Kashyap, and Scharfstein (1991) and Eisdorfer (2008)), or
total assets (see Kaplan and Zingales (1997), Mayers (1998), and Koreamaki and
Moore (2004)). For comparison purpose, in this study, we use gross capital
expenditure divided by PP&E at the beginning of the year as the measure of
firm-specific investment intensity.
5
2.3 Estimating asset value and asset volatility
According to Merton (1974), the value of firm’s equity can be seen as a call option
on the firm’s total assets, from Black-Scholes (1973) option pricing model, we have
that:
Et = Vt N (d t ) − DN (d t − σ T − t )
(5)
Where Et is the market value of the firm’s equity, Vt is the market value of the
firm’s total assets, N (.) is the cumulative function of a standard normal distribution,
[
(
)
][
]
d t = ln(Vt D ) + σ 2 2 /(T − t ) σ T − t , σ is the asset volatility, D is the face value
of the interest-bearing debt , and T-t is time to maturity of debt. In addition, according
to Ito’s lemma from the first derivative of equation (5), we can obtain the relationship
between the equity volatility and asset volatility, shown as equation (6).
σE =
Vt N (d t )σ
Et
(6)
Equation (5) and (6) are two simultaneously equations that Ronn and Verma (1986)
used to solve the unobserved asset value and asset volatilitya, where σ E is the equity
volatility. However, Duan (1994; 2000) pointed out that this method has a serious
statistical problem. That is, under the model specification of Ronn and Verma (1986),
firm’s asset value follows a lognormal process and firm’s equity is viewed as a call
option on firm’s total assets. It implies that the equity volatility must be stochastic.
But Ronn and Verma (1986) set equity volatility a s a constant (see equation (6)), it s
not consistent with their model specification. In addition, the asset value and asset
volatility solved by their method are unable to satisfy the usual statistical properties,
such as consistency and efficiency.
Due to statistical problem mentioned in above Ronn and Verma (1986) method, we
use maximum likelihood estimation method developed by Duan (1994; 2000) to
estimate unobserved asset value and asset volatility in this paper. The advantage of
Duan (1994; 2000) method is that these estimators are asymptotically efficient and
consistent, so we can have steady statistical inferences.
The maximum likelihood estimation method of Duan (1994; 2000) is briefly
described as follows. The firm’s asset value, Vt , is assumed to follow a lognormal
process, that is:
d ln Vt = µ v dt + σ v dwt
(7)
a
Eisdorfer (2008) also follow Ronn and Verma (1986) to apply these two equations for estimating
asset value and asset volatility.
6
where wt is a Wiener process. By the process in equation (7), the one-period transition
density can be characterized by the equation (8).
ln
(
Vt +1
~ N µ v , σ v2
Vt
)
(8)
where N (µ v , σ v2 ) denotes a normal distribution with mean µ v and variance σ v2 .
Under the assumption of normality, Duan (2000) derived the log-likelihood function
for a sample of unobserved asset value as follows:
n −1
n −1
Lv (Vt , t = 1, … , n; µ v ; σ v ) = −
ln (2π ) −
ln σ v2 −
2
2
n
∑ ln V
t =2
t
−

  Vt 
 − µ v 
ln

t =2 
  Vt −1 
n
1
2σ v2
∑
2
(9)
The equity value formula in equation (5) defines an element-by-element
transformation from an unobserved sample of equity values. Hence, we can apply the
transformed data method to obtain the log-likelihood function for the observed sample
of equity values. According to Duan (2000), the log-likelihood function for the equity
values can be written as follows:
Lv (E v , t = 1, … , n; µ v ; σ v ) = −
−
n −1
n −1
ln σ v2 −
ln(2π ) −
2
2
  Vˆt (σ v ) 

 − µv 
ln

ˆ

t =2 
  Vt −1 (σ v ) 
∑ ln(N (dˆ )) − 2σ ∑
N
t
t =2
n
1
2
v
n
∑ ln Vˆ (σ )
t
v
t =2
2
(10)
Where that asset value estimate, Vˆt (σ v ) , is the unique solution to equation (5) for a
given σ v ; and d̂ t is computed by using the estimated asset value Vˆt (σ v ) .
Hence, in the following section, we will use the Duan (1994; 2000) method to
obtain the maximum likelihood estimates of asset value and asset volatility to test the
hypotheses and estimate the costs of risk-shifting.
2.4 Measuring extent of financial distress
To measure s firm’s level of financial distress and its probability of going bankrupt
in the short run, we use Altman’s Z-score, a widely used model of bankruptcy
predictionb (Eisdorfer (2008)).
3. Empirical Test
3.1 Hypotheses
b
Altman’s Z-score model for predicting bankruptcies is: Z-score=1.2(Working capital/Total
assets)+1.4( Retained earnings/ total assets)+3.3(Earnings before interest and taxes/Total
assets)+0.6(Market value of equity/Book value of total liabilities)+0.999(Sales/Total assets).
7
According to Michaelas, Chittenden, and Poutziouris (1999)’s and Eisdorfer
(2008) model’s implications, we argue that risk-shift behavior is only consistent for
small distressed firms with the following two hypotheses:
H1: The level of uncertainty has a weaker negative effect or even a positive effect
on the investment of financially distressed firms.
H2: The effect of investment on asset value in financially distressed firms
diminishes as the level of uncertainty increase.
3.2Data
Our data are obtained from CRSP and COMPUSTAT. In addition, a firm must
have sufficient data to compute asset value, asset volatility, investment intensity,
expected total firm volatility and Z-score, or it will not be included in our sample.
After including all firms traded on the NYSE, AMEX, and Nasdaq that satisfy these
conditions, the final sample contains 33,393 firm-year observations over the period
1988 to 2006, representing 1,803 different firms.
Table I presents descriptive statistics on asset value, asset volatility, investment
intensity, Z-score, market-to-book ratio, leverage, and cash flow c separately for
financially healthy and distressed firms. The asset volatility estimated by Duan (1994;
2000) method is larger than Ronn and Verma (1986) method. Furthermore, the results
in Table I show that distressed firms are small size, large volatility, high leverage and
low cash flow.
3.3Primary Results
3.3.1
The results for testing Hypothesis 1
Table II examines the effect of expected volatility on investment for financially
distressed firms. We use the expected market volatility and the expected industry
volatility as described in the previous section, respectively. One of the advantage of
focusing on expected market volatility, rather than firm-level volatility, is that the
latter may capture expected positive risk changes in distressed situations that are not
related to risk-shifting behavior(e.g., due to higher risk of losing employee, clients,
partners, new deals, or suppliers). Hence, the volatility of firms in financial distress is
c
The market-to-book ratio is the market value of equity divided by the book value of equity. Leverage
is the book value of total debt as a fraction of the book value of total asset. Cash flow is the firm’s
operating cash flow divided by PP&E at the beginning of the year.
8
expected to rise, regardless of whether managers actively shift the firm’s risk
(Eisdorfer (2008)).
Following Altman (1968), firms with Z-scores below 1.81 at the beginning of the
year are classified as financially distressed. Furthermore, Barnea et al. (1981) have
pointed out that agency problems are more severe when the level of asymmetric
information is greater, Michaelas, Chittenden, and Poutziouris (1999) argued that
moral hazard and adverse selection problems may be greater for small firms because
of their costly held nature. Thus, each panel presents results for all distressed firms,
large distressed firms, and small distressed firms, respectivelyd.
In order to exclude the effects which are unrelated to risk-shifting behavior on
firm’s investment policy, firm size, market-to-book, leverage (all as of the beginning
of the year), and lagged operating cash flow are included as control variables. In
addition, to eliminate possible market wide effects on investment, we include three
variables that represent the state of the economy, namely, the NBER recession
indicator, the default risk spread, which is the yield spread between long-term Baa
and Aaa- rated securities, and the interest rate, as measured by the nominal return on
one-month Treasury bills.
【Insert Table I】
In Table II, when we use the expected market volatility to examine the Hypothesis1,
the results of Panel A show that the expected market volatility has a significant
positive effect on current investment in all distressed firms (t-statistics of 2.37) which
consistent with Eisdorfer (2008). However, if we further examine the Hypothesis1 for
large and small distressed firms, we find that the expected market volatility also has a
significant positive effect on current investment in small distressed firms (t-statistics
of 2.34), but this significant positive effect do not exist in large distressed firms
(t-statistics of 0.80). In addition, when we use the industry-level uncertainty to
examine the Hypothesis1, the results of Panel B show that the expected industry
volatility has a weaker effect on current investments in all distressed firms (t-statistics
of -0.52). Nevertheless, if we further examine the Hypothesis1 for large and small
distressed firms, we find that the expected industry volatility also has a weaker
negative effect on current investment in small distressed firms (t-statistics of -0.46),
but a significant negative effect exists in large distressed firms (t-statistics of -4.97)
which is inconsistent with Eisdorfer (2008). In other words, although results support
d
Following Loughran and Ritter (1995), large firms are those whose market cap is greater than the
market cap of the median NYSE and Amex companies in our sample in a given year and small firms
are those whose market cap is smaller than the market cap of the median NYSE and Amex companies
in our sample in a given year.
9
the Hypothesis1 in all distressed firms when we use the expected market volatility and
the expected industry volatility to be the measure of uncertainty with this study.
However, comparing the results of Eisdorfer (2008), we find that the Hypothesis1
only holds in small distressed firms, but does not hold in large distressed firms.
【Insert Table II】
3.3.2 The results for testing Hypothesis 2
Table III examines whether investments of distressed firms generate less value than
investments of healthy firms in the presence of high-expected volatility. We regress a
given year’s asset return (estimated by using Duan(1994; 2000) method) on
investment in that year and on an interactive variable between investment and Z-score,
of the year in the presence of high-expected volatilitye. The subsamples are divided by
the median expected volatility at both market and industry levels and the results of
each panel are presented for all firms, large firms, and small firms, respectively.
The results of Table III show that the relation between investments and asset value
of all distressed firms no difference with all healthy firms (t-statistics of interactive
variable between investment and financial distress dummy is 0.34 and 0.46), when the
expected volatility is high. If we further examine the effect for large and small
distressed firms during the expected industry volatility is high, we find that the
investments of large distressed firms are more valuable during times of high
uncertainty(t-statistics of interactive variable between investment and financial
distress dummy is -2.26). These results do not support Hypothesis 2 for large
distressed firms, indicating risk-shifting considerations in investment decisions not of
large distressed firms.
【Insert Table III】
3.4 The Effect of Investment on Firm-Specific Volatility
In order to examine this effect, we regress the changes in firm-specific realized
asset volatility in a given year (measured by Duan (1994; 2000) method) on the
changes in investment intensity in the previous year. Table Ⅳ presents the results of
regression for all distressed firms, large distressed firms, and small distressed firms,
e
To ensure that changes in asset value are not driven by new issues of equity or debt, we exclude
firm-years with significant equity/debt issues.
10
respectively. For all distressed firms, positive changes in investment intensity in the
previous year significantly increase firm-specific realized asset volatility in a given
year (although not significantly; t-statistics of 1.35). In addition, when we further
examine this effect for large distressed firms, we find that positive changes in
investment intensity in the previous year significantly decrease firm-specific realized
asset volatility in a given year (t-statistics of -5.28). Hence, this finding, which is
consistent with the results reported in Table II and Table III, provides further
evidences of risk-shifting behavior not in large distressed firms.
【Insert Table Ⅳ】
3.5 Estimating the Costs of Risk Shifting
Based on the summary of Hypothesis 1 and Hypothesis 2, we argue that there exists
risk-shifting behavior only in small distressed firms. Therefore, a more important
issue is to measure the wealth transfer from debt holders to equity holders. To
estimate the risk-shifting costs imposed on debt holders, we use Eisdorfer (2008)
two-step procedure to do the estimation. In the first step, we estimate the sensitivity of
debt value to investment of distressed firms for the subsample of high expected
volatility by the slope coefficient of the following regression:
%∆V D = γ 0 + γ 1 Investment + ε
(11)
where VD is the firm’s debt value, measured by the difference between asset value
(estimated by Duan(1994; 2000) method) and the market value of equityf. Since the
risk-shifting behavior implies that investing in risky projects reduces the value of debt
in distressed firms, γ 1 is expected to be negative.
In the second step we estimate the investment distortion in distressed firms for the
subsample of high expected volatility. As reported in table II, there is a positive
relation between expected volatility and investment of small distressed firms. Hence,
the average of high uncertainty firm-specific investment intensity in small distressed
firms (relative to small healthy firms) is expected to be higher than the average of
entire firm-specific investment intensity in small distressed firms (relative to small
healthy firms). This difference is referred as the overinvestment in the high
uncertainty firm-specific investments in small distressed firms (relative to small
f
As the tests in Hypothesis 2, to ensure that changes in the market value of debt are not driven by new
issues of equity or debt, we exclude firm-years with significant equity/debt issues.
11
healthy firms).
The risk-shifting costs imposed on debt holders are therefore measured by
multiplying the estimate of the overinvestment by the sensitivity of debt value to high
uncertainty firm-specific investments:
[
Costs = γ 1 (inv d − inv h )high
volatility years
− (inv d − inv h )entire sample
period
]
(12)
where inv d and inv h are the medians of investment intensity in distressed firms and
healthy firms, respectively.
【Insert Table Ⅴ】
Panel A of Table V shows the results of first step. As expected, when volatility
high, investments of small distressed firms have a negative effect on the value of debt,
with a coefficient γ 1 of -1.16609 and a t-statistic of -0.55. On the contrary,
investments of large distressed firms have a positive effect on the value of debt, with a
coefficient γ 1 of 0.03157 and a t-statistic of 0.11. This result is consistent with
weaker effect of investment on asset value in distressed firms during periods of high
uncertainty, as reported in Table III.
3.6 Factors Affecting Risk-Shifting Behaviors
In the final part of this study, we examine the effects of several factors in reducing
the incentive or limiting the ability of shareholders to increase the firm’s risk.
Secured debt. Smith and Warner (1979) argue that secured debt gives debt holders
title to pledged assets until the debt is paid in full, and thus limits the ability of
equity holders to substitute assets and shift risk.
Convertible debt. Green (1984) shows that since convertible debt reverses the
convex shape of levered equity over the upper range of the firm’s value, it eliminates
the incentive of equity holders to increase the firm’s risk.
Debt maturity. Barnea, Haugen, and Senbet (1980) argue that because the value of
short-term debt is less sensitive than long-term debt to changes in a firm’s asset
volatility, hence, shorter-maturity debt reduces the incentive of equity holders to shift
risk.
Regulation. Smith (1986) argues that managers of regulated firms have less
discretion over investment decisions than managers in unregulated firms. This implies
that deviations from optimal investment policy, including risk-shifting behavior, are
12
less likely to occur in regulated firms.
Growth options. The risk-shifting problem represents a conflict of interest between
debt holders and equity holders as to the firm’s investment decisions. Thus,
risk-shifting behavior, as any other investment-related agency conflict, is more likely
to occur when firms have more investment opportunities. Consistent with this
argument, the empirical literature finds that firms with more growth opportunities
choose capital structures that mitigate potential agency conflicts (see Smith and Watts
(1992), Barclay and Smith (1995a, 1995b), and Rajan and Zingales (1995)).
To test the effects of these factors on risk-shifting behavior, we add dummy
variables that represent each of the above factors and regress investment intensity on
interactive variables between expected volatility (including expected market volatility
and expected industry volatility, respectively) and these dummy variables for
financially distressed firms. The regression equation can be shown as follows:
5
5
5




Investmenti = α 0 + ∑ α j D j ,i +  β 0 + ∑ β j D j ,i Vi +  δ 0 + ∑ δ j D j ,i  Z i
j =1
j =1
j =1




5


 ρ 0 + ∑ ρ j D j ,i Vi Z i + ε i


j =1


(12)
where i is the observation index, D j is a dummy variable of factor j , V is the
expected volatility (including expected market volatility and expected industry
volatility, and expected firm-specific volatility, respectively). The dummy variables
are defined as follows: D1 equals one if the fraction of the firm’s secured debt is
higher than the sample median, and zero otherwise; D2 equals one if the firm has
convertible debt in its capital structure, and zero otherwise; D3 equals one if the
maturity of the firm’s debt is shorter than the sample median, and zero otherwise; D4
equals one if the firm is in regulated industry, and zero otherwise, where, following
Hermalin and Weisbach (1988), we consider public utilities (SIC code 49), airlines
and railroads (SIC code 40-47), and financial institutions (SIC code 60-69) as
regulated industries; D5 equals one if the firm’s R&D intensity (estimated by the ratio
of R&D expenditure to sales) is lower than the sample median, and zero otherwiseg.
【Insert Table VI】
g
Following Denis, Denis and Sarin (1997), we use the ratio of R&D expenditures to sales to measure
the firm’s growth opportunities.
13
The regression results are reported in Table VI, where the table reports the main
interaction terms only. In addition, a positive coefficient of interactive variable
between expected volatility and firm characteristics dummy variable j indicates that
factor j mitigates the relation between expected volatility and investment. The results
of Table VI show that the factors including, shorter maturity debt, and less growth
options only have significant effects on mitigating the relation between expected
volatility and investment for all distressed firms, when we use the expected market
volatility to measure uncertainty. If we further examine the effects of those factors on
mitigating the relation between expected volatility and investment for small distressed
firms, the results are similar. The factors including shorter maturity debt, and less
growth options have significant effects on mitigating the relation between expected
volatility and investment for small distressed firms.
4. Conclusion
Based on the model’s implications of Eisdorfer (2008), this study uses a uniform
measure across a large sample of firms to analyze the actual existence of risk-shifting
problem. Comparing the empirical tests of risk-shifting behavior in Eisdorfer (2008),
we use different methodology (Duan (1994; 2000)) to estimating the firm’s asset
value and firm’s asset volatility for testing hypotheses and estimating the cost of
risk-shifting. Furthermore, this study also divide the sample into two subsamples
which represent large firms and small firms to investigate the risk-shifting behavior in
large and small distressed firms.
Based on our empirical results of testing two hypotheses above, if we examine
risk-shifting behavior for large and small distressed firms, we find that only the small
distressed firms consistent with these two hypotheses. This finding provides the
evidence of risk-shifting behavior in small distressed firms, but risk-shifting behavior
does not exist in large distressed firms. Furthermore, we also find that the changes in
firm-specific investment intensity of small distressed firms in a given year
significantly increase firm-specific realized asset volatility in the following year. The
finding provides a further evidence of risk-shifting behavior in small distressed firms.
In measuring a wealth transfer from debt holders to equity holders, we use the
expected market volatility to identify high uncertainty firm-specific investments and
estimate the investment distortion in these high uncertainty firm-specific investments
in small distressed firms (relative to small healthy firms). The results show that the
value of debt in small distressed firms is reduced by approximately 0.97%, as the
results of overinvestment in high uncertainty firm-specific investments by using
maximum likelihood estimation method proposed by Duan (1994; 2000).
14
Finally, we examine the effects of several factors in reducing the incentive or
limiting the ability of equity holders to increase the firm’s risk. The factors including
shorter maturity debt, and less growth options have significant effects on mitigating
the relation between expected volatility and investment for small distressed firms,
when we use the expected market volatility to measure uncertainty.
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17
18%
16%
Expected monthly Volatility
14%
12%
10%
8%
6%
4%
2%
0%
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
Figure I. Estimation of expected volatility using GARCH models. At he market level, expected
volatilities are estimated by applying GARCH(1,1) model of monthly return of the NYSE market index from 1985
to 2006. At the industry level, expected volatilities are estimated by applying the same model separately to the
average monthly return of each industry (based on two-digit SIC codes). The sample period used to generate the
industry-specific GARCH parameters is based on the availability of firm-specific return within an industry. The
solid (lower) and the dashed (upper) lines represent the monthly expected market volatility and the average of the
monthly expected industry volatilities, respectively, over the period 1988 to 2006.
18
Table I
Descriptive Statistics
This table presents descriptive statistics on the sample firms. Besides variable Z-score, other variables of observations outside the top and bottom percentiles are excluded.
P25, P50, and P75 indicate the 25th, 50th, and 75th percentiles, respectively, of each variable. Results are presented separately for financial healthy and distressed firms,
where following Altman’s (1968) model, firms with Z-score below 1.81 at the beginning of the year are classified as distressed. Asset value (in millions of dollars) and asset
volatility are estimated by Ronn and Verma (1986) method and Duan (1994; 2000) method. Investment intensity is estimated by the ratio of capital expenditures to PP&E at
the beginning of the year. The market-to-book ratio is the market value of equity divided by the book value of equity. Leverage is the book value of total debt divided by the
book value of total asset. Cash flow is the firm’s operating cash flow divided by PP&E at the beginning of the year. The results are based on 33,393 firm-year observations
over the period 1988 to 2006.
Variable
Healthy Firms
Distressed Firms
Mean
Std
P25
P50
P75
Mean
Std
P25
P50
P75
3254.764
9031.852
62.225
321.857
1849.67
2907.466
9894
11.583
69.199
1045.300
Asset volatility -Ronn and Verma(1986) 0.136
0.092
0.085
0.119
0.164
0.222
0.183
0.116
0.175
0.266
Asset value –Duan (1994,2000)
3331.549
9127.074
63.83
334.203
1925.420
2868.175
9664
11.187
67.783
1022.120
Asset volatility-Duan (1994,2000)
0.348
0.257
0.189
0.285
0.647
0.433
0.411
0.144
0.299
0.630
Investment intensity
0.265
0.325
0.135
0.211
0.329
0.316
3.871
0.071
0.150
0.279
Z-score
7.644
38.841
2.829
3.969
6.105
-6.569
64.388
-1.536
0.811
1.398
Market-to-book
2.968
68.496
1.335
2.163
3.642
3.294
104.408
0.349
1.300
2.746
Leverage
0.1795
0.1519
0.0362
0.1616
0.2867
0.5568
2.1150
0.2043
0.3893
0.5712
Cash flow
-0.08514
20.035
0.132
0.314
0.663
-3.809
55.003
-0.585
0.0664
0.217
Asset value -Ronn and Verma(1986)
＃Observations
25,341
8,052
19
Table II
Regressions of Investment Intensity on Expected Volatility for Financially
Distressed Firms
In Panel A and Panel B, the dependent variable is firm-specific actual investment intensity, estimated by the
ratio of capital expenditures in a given year to PP&E at the beginning of the year. In addition, the
independent variables of Panel A and Panel B are the expected market volatility and expected industry
volatility at the beginning of the year (estimated by using a GARCH (1, 1) model, as described in Section 2)
respectively and a set of control variables. Results are presented for financially distressed firms, where,
based on Altman’s model, firms with Z-scores below 1.81 at the beginning of the year are classified as
distress. The control variables are: firm size, estimated by the natural log of the market value of the firm’s
total assets (as measured by Duan (1994; 2000) method) ; market-to-book, estimated by the market value of
equity divided by the book value of equity; leverage, estimated by the ratio of the book value of total debt to
book value of total assets; cash flow, estimated by the ratio of operating cash flow to PP&E at the beginning
of the year; the NBER recession dummy variable; the default spread, estimated by the yield spread between
long-term Baa- and Aaa-rated securities; and the interest rate, measured by the nominal return on
one-month Treasury bills. Furthermore, each panel presents results for all distressed firms, large distressed
firms, and small distressed firms, respectively, where large firms are those whose market cap is greater than
the market cap of the median NYSE and Amex companies in our sample in a given year and small firms are
those whose market cap is smaller than the market cap of the median NYSE and Amex companies in our
sample in a given year. The table presents regression coefficients and t-statistics, based on White standard
errors, computed over the period of 1988 to 2006. ** denotes the 5% significance level, and *** denotes the
1% significance level.
Panel A: Expected Market Volatility
Intercept
Exp. volatility
Log size
Mark-to-book
Leverage
Lagged cash flow
Recession dummy
Default spread
Interest rate
＃Observations
R-square
Panel B: Expected Industry Volatility
All
Large
Small
All
Large
Small
0.4555
(1.79)
12.1764
(2.37)***
-0.0422
(-2.81)***
-0.0001
(-0.21)
0.0086
(0.42)
0.0085
(10.88)***
-0.1033
(-0.57)
-0.4669
(-1.94)
0.0012
(0.05)
8,052
0.0163
0.1014
(2.97)***
0.1833
(0.45)
0.0033
(1.15)
0.0001
(0.51)
0.0264
(1.61)
0.0007
(0.40)
0.0210
(1.37)
-0.0056
(-0.30)
0.0088
(4.33)***
1,624
0.0205
0.4731
(1.48)
14.8633
(2.34)***
-0.0489
(-1.93)
-0.0001
(-0.18)
0.0085
(0.37)
0.0085
(9.72)***
-0.1348
(-0.61)
-0.5781
(-1.92)
-0.0004
(-0.01)
6,428
0.0162
0.6972
(2.64)***
-0.4437
(-0.51)
-0.0432
(-2.86)***
-0.0001
(-0.16)
0.0087
(0.43)
0.0085
(10.91)***
-0.0961
(-0.53)
-0.1535
(-0.77)
0.0117
(0.47)
8,052
0.0156
0.1345
(3.99)***
-0.3107
(-4.93)***
0.0043
(1.53)
0.0001
(0.52)
0.0283
(1.74)*
0.0003
(0.16)
0.0252
(1.66)
-0.0051
(-0.34)
0.0098
(4.90)***
1,624
0.0349
0.7664
(2.29)***
-0.5026
(-0.46)
-0.0509
(-2.01)**
-0.0001
(-0.14)
0.0085
(0.38)
0.0085
(9.76)***
-0.1217
(-0.55)
-0.1962
(-0.78)
0.0123
(0.40)
6,428
0.0154
20
Table III
Regressions of Asset Return on an Interactive Variable between Investment and
Financially Distress in Periods of High-Expected Volatility
The dependent variable is the firm’s asset return in a given year, as derived from Duan (1994; 2000)
method. The independent variables are the firm’s investment intensity in the same year. The Firm’s
Z-score, an interactive variable between investment and Z-score; and a set of control variables, as
described in Table II. Results are presented for samples of high –expected volatilities at the beginning
of the year (at both the market and industry levels, estimated using GARCH (1, 1) models, as described
in Table II), divided by the median of the expected volatilities. Furthermore, the results of Panel A and
Panel B are presented separately for all distressed firms, large distressed firms, and small distressed
firms, where large firms are those whose market cap is greater than the market cap of the median
NYSE and Amex companies in our sample in a given year and small firms are those whose market cap
is smaller than the market cap of the median NYSE and Amex companies in our sample in a given year.
The table presents regression coefficients and t-statistics, based on White standard errors, computed
over the period of 1988 to 2006. ** denotes the 5% significance level, and *** denotes the 1%
significance level.
Expected Market Volatility
Intercept
Investment
Z-score
Investment*Z-score
Log size
Mark-to-book
Leverage
Lagged cash flow
Recession dummy
Default spread
Interest rate
＃Observations
R-square
Expected Industry Volatility
All
Large
Small
All
Large
Small
1.3466
(0.13)
0.4346
(0.25)
-0.0673
(-1.67)
0.4480
(0.34)
-0.4140
(-0.68)
-0.0003
(-0.01)
0.2330
(0.22)
0.0081
(0.19)
-3.6214
(-0.78)
0.6400
(0.09)
0.7637
(0.78)
13,393
0.0004
0.11314
(1.11)
0.0352
(0.43)
0.146
(6.67)***
0.0105
(1.55)
0.0112
(1.44)
0.0043
(3.86)***
0.0029
(0.47)
0.0004
(0.05)
-0.0888
(-2.98)***
-0.2053
(-4.62)***
0.0141
(2.18)**
4,012
0.1016
-1.6047
(-0.10)
0.3664
(0.17)
-0.0689
(-1.43)
0.0390
(0.24)
-0.0082
(-0.01)
-0.0002
(-0.01)
0.2295
(0.18)
0.0077
(0.15)
-4.7208
(-0.73)
0.9786
(0.09)
1.1005
(0.81)
9,381
0.0004
-0.0824
(-0.14)
0.0443
(0.41)
0.0001
(0.03)
0.0039
(0.46)
-0.0112
(-0.28)
-0.0006
(-0.16)
-0.0095
(-0.10)
-0.0000
(-0.00)
-0.2571
(-0.71)
0.8895
(1.96)**
-0.0461
(-0.71)
15,847
0.0004
0.54939
(2.85)***
0.1673
(1.05)
0.0220
(5.39)
-0.0152
(-2.26)**
-0.0397
(-2.34)***
0.0040
(1.46)
0.3248
(2.40)**
0.0093
(0.48)
-0.1019
(-1.34)
-0.2649
(-2.86)***
0.0022
(0.17)
4,899
0.0150
-1.0483
(-1.17)
0.0394
(0.29)
-0.0008
(-0.15)
0.0033
(0.32)
0.1257
(1.55)
-0.0008
(-0.17)
-0.0160
(-0.14)
-0.0001
(-0.03)
-0.2658
(-0.52)
1.4748
(2.24)**
-0.0540
(-0.58)
10,948
0.0010
21
Table Ⅳ
Regressions of Changes in Firm-Specific Asset Volatility on Changes in
Investment Intensity for Financially Distressed Firms
The dependent variable is the changes in firm-specific realized asset volatility in a given year, as
derived from Duan (1994; 2000) method. The independent variables are the changes in firms-specific
investment intensity in the previous year, and a set of control variables, as described in Table II.
Results are presented separately for all distressed firms, large distressed firms, and small distressed
firms, where large firms are those whose market cap is greater than the market cap of the median
NYSE and Amex companies in our sample in a given year and small firms are those whose market cap
is smaller than the market cap of the median NYSE and Amex companies in our sample in a given year.
The table presents regression coefficients and t-statistics, based on White standard errors, computed
over the period of 1988 to 2006. ** denotes the 5% significance level, and *** denotes the 1%
significance level.
D(Volatility)
Intercept
D(Investment)
Log Size
Market-to-book
Leverage
Lagged cash flow
Recession dummy
Default spread
Interest rate
＃Observations
R-square
All
Large
Small
0.01481
(0.51)
0.00128
(1.35)
-0.00484
(-2.84)***
0.00003
(0.55)
0.00226
(1.00)
-0.00005
(-0.52)
-0.0058
(-0.28)
-0.03065
(-1.28)
0.01157
(3.82)***
7,605
0.0051
-0.03454
(-0.60)
-0.32471
(-5.28)***
0.00158
(0.32)
-0.00034
(-0.87)
-0.00569
(-0.20)
0.00676
(2.11)**
0.01401
(0.53)
-0.02330
(-0.87)
0.01004
(2.72)***
1,541
0.0284
0.02823
(0.79)
0.00131
(1.26)
-0.00831
(-2.96)***
0.00003
(0.56)
0.00225
(0.92)
-0.00005
(-0.49)
-0.00970
(-0.39)
-0.03533
(-1.21)
0.01181
(3.24)***
6,064
0.0053
22
Table V
Estimation of Costs of Risk-Shifting
This table shows results of regressions of the percentage change in debt value in a given year on
investment intensity in the year and a set of control variables (as described in Table II) , divided by the
median of the expected volatilities in a subsample of financially distressed firms for those high
uncertainty firm-specific investments. Debt value is measured by the difference between asset value
(estimate by Duan(1994; 2000) method) and the market value of equity. Firm-years with significant
equity and debt issues are excluded. Furthermore, the results of Panel A and Panel B are presented
separately for all distressed firms, large distressed firms, and small distressed firms, where large firms
are those whose market cap is greater than the market cap of the median NYSE and Amex companies
in our sample in a given year and small firms are those whose market cap is smaller than the market
cap of the median NYSE and Amex companies in our sample in a given year. The table presents
regression coefficients and t-statistics, based on White standard errors, computed over the period of
1988 to 2006. ** denotes the 5% significance level, and *** denotes the 1% significance level.
Panel A: Effect of Investment on Debt Values
Expected Market Volatility
All
Intercept
Investment
Log size
Mark-to-book
Leverage
Lagged cash flow
＃Observations
R-square
Large
11.9717
-0.63157
(0.74)
(-1.88)
-1.1716
0.03157
(-0.61)
(0.11)
-0.92019
0.07851
(-0.31)
(2.20)**
-0.01147
0.00057
(-0.19)
(0.28)
1.02583
-0.06443
(0.36)
(-0.29)
0.35185
-0.00324
(1.26)
(-0.13)
3,455
677
0.0005
0.0074
Panel B: Costs of Risk-Shifting
Small
9.18493
(0.44)
-1.16609
(-0.55)
0.11129
(0.02)
-0.01182
(-0.17)
1.0425
0.33
0.35081
(1.12)
2,778
0.0005
Average Investment of large distressed firms-entire sample
Average Investment of large distressed firms-high uncertainty sample
Overinvestment of large distressed firms in high-volatility periods
Sensitivity of debt value to investment for large distressed firms in high-volatility periods
Costs of overinvestment for large distressed firms in high-volatility periods
Market-adjusted
0.1842%
0.3606%
0.1764%
0.03157
0.0056%
Average Investment of small distressed firms-entire sample
Average Investment of small distressed firms-high uncertainty sample
Overinvestment of small distressed firms in high-volatility periods
Sensitivity of debt value to investment for small distressed firms in high-volatility periods
Costs of overinvestment for small distressed firms in high-volatility periods
14.21%
15.03%
0.8321%
-1.16609
-0.97%
23
Table VI
Regressions of Investment on Interactive Variables between Expected
Volatility and a Set of Firm Characteristics
In Panel A and Panel B the dependent variable is firm-specific investment intensity in a given year. In
addition, the independent variables of Panel A and Panel B are expected market volatility and expected
industry volatility at the beginning of the year respectively, firm characteristics dummy variables,
interactive variables between expected volatility and firm characteristics dummy variables, and a set of
control variables, as described in Table II. The firm characteristics dummy variables are defined as
follows. D1 equals one if the fraction of the firm’s secured debt is higher than the sample median, and
zero otherwise. D2 equals one if the firm has convertible debt in its capital structures, and zero
otherwise. D3 equals one if the maturity of the firm’s debt is shorter than the sample median, and zero
otherwise. D4 equals one if the firm is in regulated industry, and zero otherwise, where public utilities
(SIC code 49), airlines and railroads (SIC code 40-47), and financial institutions (SIC code 60-69) are
considered as regulated industries. D5 equals one if the firm’s R&D intensity is lower than the sample
median, and zero otherwise. The regression equation is specified in equation (12), where the table
reports the results for the main interaction terms only. Furthermore, each panel presents results for all
distressed firms, large distress firms, and small distressed firms, respectively, where large firms are
those whose market cap is greater than the market cap of the median NYSE and Amex companies in
our sample in a given year and small firms are those whose market cap is smaller than the market cap
of the median NYSE and Amex companies in our sample in a given year. The table presents regression
coefficients and t-statistics, based on White standard errors, computed over the period of 1988 to 2006.
** denotes the 5% significance level, and *** denotes the 1% significance level.
Expected Market Volatility
Intercept
Exp. Volatility
Z-score
Exp. Volatility *Z-score
D1* Exp. Volatility *Z-score
D2* Exp. Volatility *Z-score
D3* Exp. Volatility *Z-score
D4* Exp. Volatility *Z-score
D5* Exp. Volatility *Z-score
Log size
Mark-to-book
Leverage
Lagged cash flow
Recession dummy
Default spread
Interest rate
＃Observations
R-square
Expected Industry Volatility
All
Large
Small
All
Large
Small
0.45272
(4.72)***
0.60250
(0.28)
0.01475
(1.75)*
-0.31773
(-1.52)
-0.57499
(-2.98)***
-3.35894
(-10.07)***
0.47950
(2.25)**
-10.83296
(-23.61)***
0.44822
(2.86)***
-0.01799
(-4.56)***
0.00007
(0.47)
-0.0282
(-1.21)
0.03171
(49.83)***
-0.00879
(-0.21)
-0.19601
(-3.49)***
0.00758
(1.24)
29,715
0.1054
0.19310
(9.01)***
0.62090
(1.39)
0.01196
(3.30)***
-0.03031
(-0.36)
0.01817
(0.26)
-0.29273
(-2.26)**
-0.17088
(-2.31)**
0.41850
(1.87)*
0.01713
(0.23)
-0.00565
(-5.27)***
0.00017
(2.59)***
-0.04196
(-4.62)***
0.01428
(19.61)***
0.00621
(0.99)
-0.04347
(-5.49)***
0.00621
(7.17)***
10,141
0.1480
0.52864
(3.58)***
0.91979
(0.28)
0.01755
(1.63)
-0.44116
(-1.65)*
-0.52602
(-2.12)**
-3.83845
(-8.70)***
0.62080
(2.26)**
-11.75857
(-19.87)***
0.43032
(2.15)**
-0.01893
(-2.10)**
0.00007
(0.35)
-0.05278
(-1.74)*
0.03186
(40.58)***
-0.01571
(-0.26)
-0.26806
(-3.13)***
0.00824
(0.88)
19,574
0.1093
0.41546
(4.90)***
-0.06111
(-0.13)
0.00749
(1.08)
-0.05177
(-0.91)
0.06602
(1.79)*
0.12406
(1.99)**
0.03997
(0.77)
-0.65493
(-8.40)***
-0.04065
(-1.03)
-.02354
(-5.90)***
0.00007
(0.47)
0.04127
(1.70)*
0.03270
(50.68)***
-0.00658
(-0.16)
-0.10728
(-2.27)**
0.00732
(1.23)
29,715
0.0834
0.18866
(11.61)***
0.05299
(0.61)
0.01379
(6.37)***
-0.03180
(-1.93)*
-0.01326
(-1.56)
0.00925
(0.54)
0.01235
(1.20)
0.21724
(5.23)***
-0.00203
(-0.13)
-0.00518
(-4.83)***
0.00017
(2.66)***
-0.03512
(-3.86)***
0.01434
(19.64)***
0.00994
(1.59)
-0.02539
(-3.87)***
0.00731
(8.65)***
10,141
0.1551
0.51207
(3.85)***
-0.07375
(-0.11)
0.01042
(1.12)
-0.09081
(-1.17)
0.09342
(1.63)
0.08971
(1.06)
0.09585
(1.28)
-0.72395
(-7.20)***
-0.05381
(-1.06)
-0.03230
(-3.54)***
0.00008
(0.38)
0.02707
(0.86)
0.03293
(41.31)***
-0.01290
(-0.21)
-0.15129
(-2.10)**
0.00600
(0.66)
19,574
0.0844
24