To investigate a credit channel of monetary policy transmission
Table of Contents
Introduction. Research Goals
. Datasets
. Analysis of stock market
behavior
. Our two-step approach: brief
definition with major advantages over earlier methods
. Comparison of portfolios’
performances
Conclusion
Introduction. Research Goals
This research, foremost, is aimed to
give a clue to the question of how monetary policy in the United States is
transmitted to the stock market. On the one hand, the decision of the Federal
Reserve System about short-term overnight lending rate (known as the Federal
funds rate, or the target rate) is watched closely by market participants, and
is a large common single determinant of the market response on the announcement
day. On the other hand, according to the efficient-market hypothesis (EMH)
developed in (Fama, 1970), in semi-strong form of market efficiency stocks must
incorporate all known past information and current news. There are debates over
the time that stocks take to absorb the news, and a study of (Chan, 2001) showed
that stocks tend to underreact to news. Furthermore, (Bernanke & Kuttner,
2005) showed that one-month stock reaction is slightly larger than a one-day
reaction to the announcement of the target rate, which implies a market
under-reaction. Nevertheless, estimates of immediate market responses to
announcement of the target rate are large enough to believe that the current
monetary policy objectives are mostly reflected in the stock prices. We will
give estimates of market response in the first part of the work.real obstacle
that is debated over years is the channel of transmission of the target rate
announcement to the equity market. Since (Bernanke & Blinder, 1992) defined
two channels (demand and credit) of policy transmission, evidences have been
presented for existence of both of them. Furthermore, in (Bernanke &
Kuttner, 2005) it was clear that there can be more ways by which the change in
the Federal funds rate connected to equity market response.goal of the paper is
to investigate a credit channel of monetary policy transmission. We propose new
financial ratios, which, to our best knowledge, haven’t been used in this field
so far. Furthermore, and more interestingly, we propose a new method to
investigate the existence of credit channel instead of commonly used multiple
regression analysis: the tow-step approach involving clustering as a first step
and t-test for the difference of portfolio means for paired data as a second
step. This method is proposed foremost because current regression analysis relies
on the estimate of unexpected change in monetary policy, while our methodology
does not require such estimation. Scarceness of the futures data necessary for
obtaining good estimates of unexpected monetary policy change makes the
analysis applicable to a limited number of countries. Furthermore, ambiguity in
derivation continuous futures prices makes questionable the regression
estimates of credit factor effects, apart from the fact that regression
equation may suffer from omitted variable bias. The latter fact means that
standard errors are generally not applicable, hence, conclusions for the
influence of effects should be drawn consciously. Our two-step approach does
not depend on futures data, and therefore, eliminates the kind of flaws
outlined above; furthermore, it enables a researcher to investigate credit
channel of monetary policy for a wider range of countries. We describe the
procedure, and show results for the United States in section and summarize the
results in the last part of the work.
1. Data used
For the main part of our research we
use a sample of value-weighted returns, which we call “S&P 500*”. We
searched for stock prices for 500 companies listed in the S&P 500 index as
of 31 October, 2015 for the period from March 25, 1997 to December 16, 2008.
Some companies were not listed during the period; some have been private for
some time during the outlined period; some companies became bankrupt, and some
were the objects of acquisitions. Therefore, the actual sample consists of at
least of 321 and of at most 450 stock returns but represented by companies of
all 10 S&P 500 sectors, defined for this index by Standard and Poor’s.would
be better to use a list of S&P 500 companies most closely dated to 2008 to
have more stocks in the sample but such data was limited. The sample would have
been enlarged by companies, which went public after December 16, 2008, however,
this was the last day of change of the Fed funds rate, which is at the core of
our study. The only change in the target rate, which occurred since then, is
dated at December 16, 2015, however, monthly equity market values were not
available for the previous month in the main source of companies’ financial
information for our research - COMPUSTAT GLOBAL. Likewise, we could not extend
the scope of research beyond March 25, 1997 because the previous change in fed
funds rate occurred on January 31, 1996, and we the same data on monthly equity
market values for individual companies was limited to December, 1996.needed
monthly equity market values in order to go from raw stock price changes to
value-weighted returns, in order to construct a proxy for a broad market
value-weighted return and work later with value-weighted portfolio returns. So,
for example, a broad market return is just a sum across all individual
value-weighted stock returns, and is equal to:
;
where is a 1-day index (S&P 500*)
return, is a 1-day raw stock return of
individual company i on day t at month m, is an average market capitalization
of a company i in the previous month m-1, hence is a weight by market
capitalization of each individual stock. This weight is stable for individual
companies during a particular month, and changes across months. The sum of
individual companies’ returns on day t gives a value-weighted return for that
day. We use this method for every day in our time range.data on monetary policy
changes, or target rate announcements, which we use as equivalent expression in
the context of the work, during 1997-2008 there were a total of 101 FOMC
meetings, of which 49 resulted in a change in the Federal funds rate, and 52 -
in no action. The first of such changes occurred on March 25, 1997, and the
last one on December 16, 2008.the later analysis we excluded a 50-base point
interest rate cut by the FRS on September 17, 2001 from the sample because that
occurred after the terrorist attack in September 11, 2001; in doing so we
followed (Bernanke & Kuttner, 2005). Hence, the resulting sample consists
of 100 FOMC meetings, including 48 rate changes.we have noted we also used
financial information for the individual companies that constituted our S&P
500 list. The financial data included standard balance sheet and income
statement entries, extracted from the COMPUSTAT GLOBAL database. Based on this
information we calculated 4 financial ratios: debt-to-capital, interest
coverage, current ratio (current assets divided by current liabilities), and
payables turnover ratio.
2. Analysis
of stock market behavior
Before we proceed to analysis of
credit channel of monetary policy transmission we need to compare our data on
stock returns with that used in study of (Ehrmann & Fratzcher, 2004). They
used the same data as (Bernanke & Kuttner, 2005), which is provided by CRSP
institute, and which represents 500 largest public US companies. Periods of
both studies are the same. We have to indirectly compare two sources of data in
order to be reduce “measurement error” factor. It is not possible to eliminate
the measurement error entirely due to the peculiarities of our data discussed
above, however, at most we can hope that the S&P 500* broad market index of
value-weighted stock returns sufficiently reproduces the true CRSP-based market
return. To investigate the latter point, we compare regression results of the
general model in (Bernanke & Kuttner, 2005). However, we cannot directly
compare two datasets because their time frames are different.
That is why we obtained data by CRSP
institute aggregated in 10 size-sorted portfolios by K.R. French. Using cutoff
levels of market capitalization (published in the same resource) we created an
aggregate CRSP value-weighted market index, and call the sample of returns as
“CRSP 500*”.
Table 1. Descriptive statistics
Source - Period
|
Bernanke (2005) - CRSP vwr May
1989 - December 2002
|
CRSP 500* vwr
March
1997 - December 2008
|
S&P 500* vwr March 1997 -
December 2008
|
Corr. coefficient between CRSP
500* and S&P500* vwr
|
FOMC meetings (event days)
|
131
|
100
|
100
|
|
Rate changes (action d.)
|
54
(May 89 - Jan 94 / Feb 94 - Dec 02)
|
48 (Mar
97 - Dec 08)
|
48 (Mar
97 - Dec 08)
|
|
St.dev. of eq. ret. on event days
|
0.80
/ 1.26
|
1.413
|
1.565
|
95.72%
|
St.dev. of eq. ret. on nonevent
days
|
0.71
/ 1.11
|
1.356
|
1.419
|
97.57%
|
St.dev. of eq. ret. on action days
|
-
|
1.506
|
1.710
|
95.67%
|
The table reports selected
descriptive statistics for federal funds rate changes for two overlapping
periods, and the CRSP value-weighted returns as in Bernanke (2005), and
value-weighted equity returns in the S&P 500* and in the CRSP 500*. They
are mentioned in column headings. All statistics exclude the September 17, 2001
observation. Numbers are in percentage points. St.dev. means standard
deviation, eq.ret. stays for equity returns, vwr stays for value-weighted
returns, corr. means correlation.of all, we note that estimates are not the
same between the two samples: the CRSP 500* and the S&P 500*. The mentioned
difference in standard deviation comes foremost because the number of companies
in the latter index is significantly less than that in the CRSP 500* for
earlier times. We see that for the largest coinciding sample of non-event days
standard deviations are equal up to 1 decimal point (1.4%), while actual
difference is 5bp. As samples are getting smaller, they include only FOMC
meetings or even action days, and the difference in standard deviations
enlarges up to 16 and 20 bp, respectively. In all instances, our sample tends
to overestimate volatility of the whole market.analysis of returns over similar
samples reveals that on event and action days estimates of market returns
deviate further. This is probably due to smaller number of observations.main
qualitative finding is that equity markets have become more volatile through
time. Standard deviation of equity returns on all nonevent days was at least 25
and 65 bp higher for the period 1997-2008 than for two periods 1994-2002 and
1989-1994, respectively. On event days (every FOMC meeting, excluding Sep 17,
2001), standard deviation of equity returns is higher by at least 15 and 41 bp,
respectively. We also note much higher volatility of stock market on action
days during the later period.the Table 2 columns (a), (b) and (c) show
estimates of the second regression equation in (Bernanke & Kuttner, 2005):
where is a broad market return, is an expected portion, - surprise portion of the actual
change of the target rate.
2. The
Response of Broad Equity Market to Announcements of the Federal Funds Interest
Rate.
Regressor
|
Bernanke
(2005) (a)
|
CRSP 500* (b)
|
S&P 500* (c)
|
Intercept
|
0.12
(1.35)
|
0.31
(0.16)
|
0.41
(0.18)
|
Expected
change
|
1.04
(2.17)
|
-0.83 (1.44)
|
-0.37 (1.67)
|
Unexpected
change
|
-4.68
(3.03)
|
-2.84
(2.97)
|
-5.19
(3.68)
|
R2
|
0.171
|
0.085
|
0.137
|
Prob > F
|
0.0000
|
0.2045
|
0.1076
|
The table reports the results from
regressions of the 1-day value-weighted index returns on the expected and
unanticipated components of the actual Federal funds rate change (columns (a),
(b) and (c)). In a sample denoted “Bernanke (2005)” there are 131 observations;
in both of our samples there are 100 observations, of which 48 are rate changes
and 52 are meetings that resulted in no rate change. All values are written in
percentage terms. Parentheses include t-statistics, calculated using
heteroscedasticity-consistent estimates of standard errors.
R2 and explanatory power
of a basic equation has diminished comparatively to (Bernanke & Kuttner,
2005) estimate, presumably because of chaotic market reaction during two
crises, and fewer number of observations. However, an estimate of market
reaction to unexpected change in target interest rate increased (-5.19% vs.
-4.68%) but was insignificant; increase in estimate may signal a more stressful
situation in our sample. Expected change and an intercept remained highly
insignificant., we obtained more close estimates to those in (Bernanke &
Kuttner, 2005) using S&P 500* index return as a gauge for a broad equities’
market, comparatively to CRSP 500*. Thus, it can be a case that the CRSP 500*
may contain some measurement bias itself, which makes it impractical to compare
only it with our sample.back to regressions, we might want to insert slope
dummy variables to control for the two recessions (namely, impose dummies for
periods Mar 2000 - Oct 2002, and Oct 2007 - Dec 2008). The fit of the model
will generally improve:
Table 3. The Response of Broad
Equity Market to Changes of the Federal Funds Interest Rate.
Regressor
|
Full sample
|
Sample of 48 FOMC actions
|
|
(a)
|
(b)
|
(c)
|
(d)
|
(e)
|
(f)
|
Intercept
|
0.41
(0.18)
|
0.37
(0.12)
|
0.44
(0.12)
|
0.41 (0.20)
|
0.56 (0.22)
|
0.52
(0.24)
|
Expected
change
|
-0.37 (1.67)
|
-0.12
(1.48)
|
-0.10 (1.51)
|
-0.11 (1.39)
|
-0.02
(1.29)
|
-0.02
(1.31)
|
Unexpected
change
|
-5.19
(3.68)
|
-5.04 (3.39)
|
-5.89 (3.21)
|
-2.07 (4.30)
|
-7.60
(2.09)
|
-5.96 (3.19)
|
Unexp x 2 Crises
|
|
-
|
1.26 (5.66)
|
-
|
-
|
-
|
Unexp x 00-02 Crisis
|
|
-
|
-
|
-6.97 (4.85)
|
-
|
-2.82
(4.49)
|
Unexp x 07-08 Crisis
|
|
-
|
-
|
-
|
10.34
(7.62)
|
8.57
(8.46)
|
R2
|
0.137
|
0.160
|
0.162
|
0.234
|
0.286
|
0.294
|
Prob > F
|
0.1076
|
0.098
|
0.141
|
0.025
|
0.002
|
0.017
|
The table reports the results from
regressions of the 1-day S&P 500* value-weighted returns on expected and
surprise components of changes in the Federal Funds rate (column (b)). Then
(col. c) we introduce a dummy variable for both crises periods (sets 1 if the
unexpected change falls either on the 2000-02 or 2007-08 period), a separate
dummy for each crisis period (col. d and col. e) and a combination of these
dummies (col. f). The sample contains 48 observations - FOMC meetings - for the
period Mar 1997 - Dec 2008, when the target rate was changed. For the reference
the equation results on the full sample from col. c (Table 2) are inserted in
the column (a). All values are in percentage terms. Parentheses include
t-statistics, calculated using heteroscedasticity-consistent estimates of
standard errors.see that control for combined crises periods does not improve
equation, however, imposing a control for different crises works better. We
conclude that the highest and most significant coefficient estimate of unexpected
rate changes is -7.60% when 2007-2008 crisis dummy is included alone. In this
specification F-statistic has the lowest p-value among all 6 equations, and R2
is very high (28.6%). Interestingly, and, somewhat controversially, is that the
coefficient estimate of the unexpected changes is positive and unusually high
(10.34%), though insignificant. The estimate means that during economic
recession a stock market co-moves with the change in target interest rate,
which historically means that stock market declines as the target interest rate
is decreased. This may be as a result of market dissatisfaction with the
movement of the Federal Reserve System, and expectation of stronger action.
Controversially, futures decomposition (see the table in the Application) shows
that negative unexpected changes were higher in absolute value than positive
unexpected changes, and the former also were more frequent; hence, the market
tended to underestimate the reaction of the FRS. It might also be a case that
orthogonality broke during the crisis. Orthogonality means that the FRS does
not cut rates following a stock market decrease. (Bernanke & Kuttner, 2005)
said that there was no clear evidence for that. Another possible explanation is
that during long stock market and economic recession investors look for more
structural changes from government authorities, and the influence of a single
instrument - money supply - diminishes for a time.
Notwithstanding the true reason of
this stock market behavior, we need to pay a special attention to periods of
both economic downturns when analyzing factor portfolios.conclude about the
validity of the S&P 500* sample, we have to bear in mind sample that it
might be subject to some measurement error, expressed in the fact that it overestimates
a broad market return. We do not know, whether it overestimates particular
companies, which is the worst case, or it overestimates equally every company’s
return in the sample. If the last point is true, then qualitatively our
conclusions of effects of financial ratios will be likely to hold. We assume
that the latter is true and proceed to the further analysis; after all, any
sample may be subject to some degree of measurement error, which cannot be
explicitly identified.
Past analysis of stock reaction to
the changes in monetary policy with regression.of the credit channel of
monetary policy transmission is usually done with multiple regression analysis.
The equation usually incorporates unexpected portion of actual change of the
key interest rate because, as (Bernanke & Kuttner, 2005) showed, inclusion
of unexpected rate change significantly improves fit of the model. In the
framework of the New Keynesian Model the theory of rational expectations
implies policy ineffectiveness proposition (PIP), which states that anticipated
portion of monetary action does not matter for real economy, while unexpected
monetary policy has effects on real variables in short run. As stocks are
rights on cash flows generated by real assets, such as factories and equipment,
they can be thought of as representatives of real economic variables, which
must react in the short-run to unexpected monetary actions, according to the
theory.order to count for expectations of Federal funds raw change prior to its
announcement there had been proposed a variety of different models. However, (Krueger
& Kuttner, 1996), and later (Gurkaynak, 2005), showed that the usage of
Federal funds futures rates provides efficient and precise estimates of
surprise components of the raw target changes. This idea was thoroughly
discussed in (Kuttner, 2000) and applied to testing the relationship between
the Federal funds rate and bond rates. In that paper, K. Kuttner defined
advantages of his method as:, there is no issue of model selection; second, the
vintage of the data used to produce the forecast is not an issue; and third,
there are no generated regressor problems.underlying idea of this method is
that the federal funds futures price on the day prior to the FOMC’s
announcement “embodies near-term expectations of the Federal funds rate”
(because, essentially, 30-day futures rate is an average of the effective
federal funds rate over the past 30 days). Consequently, a change in the settle
price of the futures contracts at the end of the announcement day (ta)
reflects a surprise portion of the actual change in the interest rate. However,
as thoroughly explained in (Kuttner, 2000), the difference in settle futures
prices must be scaled up by a fraction that reflects the number of days in the
month, which will be affected by the change in interest rate:
,
where is a surprise component of the real
change in the Federal Funds rate, and are the current-month futures rates
on the day of announcement and on the previous day, and Tm is the
number of days in the month. The expected component (), therefore, is defined as the
difference between the actual change () and the surprise component:
.
Then this
method provides “a nearly pure measure” of the one-day surprise change in the
Federal funds rate under the assumption of no further changes within the month.
This assumption “is not entirely justified”: during 1989 - 2008 there had been
6 cases when two changes occured within a month: July 1989, December 1990, and
December 1991, January 2001, August 2007, and October 2008. Another potential
issue left is the end-month noise in the effective funds rate, which is
minimized by using unscaled change in 1-month futures rate when the target
change occurs within the last three days of the month. Similarly, the unscaled
change in 1-month futures is used when the Federal funds change occurs on the
first day of the month.the paper (Bernanke & Kuttner, 2005) analyzed broad
market reaction on the Fed funds rate change. They applied two models:
and showed
that the second equation is better because instead of using actual changes in
the target rate as one explanatory variable it embeds decomposition of the raw
change into expected and surprise components. Therefore, the second equation
accounts for unfulfilled expectations about the new target rate.on this
conclusion, (Ehrmann & Fratzcher, 2004) applied an aggregate three-factor
regression model to estimate firm-specific effects on monetary policy effect:
where st
- is an unexpected portion of a monetary policy change, xi,t - is a
specific factor characteristic of a firm, either time-varying or fixed
(industry-specific). Z index of the x-variable also indicates, whether a firm’s
characteristic falls in low, or high category, in order to compare effects.
Surprise rate changes were estimated using Reuters polls of expectations, which
were backed by similar conclusion using Kuttner’s fed funds futures method. The
authors aggregated data on S&P 500 companies across 9 years (1994-2003, 79
FOMC meetings), with some stocks not being observed at some meetings (though
authors did not provide the numbers). They estimated data using OLS with
panel-corrected standard errors, which corrects for heteroscedasticity and
assumes correlation of residuals (correlation across stocks, e.g. of the
similar industry, on a particular day).other factors that might explain
heteroschedastic reaction of stocks to unexpected changes of the target
interest rate, (Ehrmann & Fratzcher, 2004) explored credit channel of
monetary policy transmission. We summarize their finding in the following
table:
Table 4
|
Significant factor
|
Proxy
|
Conclusion
|
1.
|
Firm’s size
|
Number of employee. Market
capitalization
|
Small firms react more strongly to
monetary shocks than medium-sized or large firms.
|
2.
|
Size of cash flows
|
Cash flow/Net Income
|
Firms with low cash flows react
“significantly” more strongly to monetary shocks.
|
3.
|
Financial (credit) constraint
|
Moody’s investment rating. Moody’s
bank loan rating
|
Firms with either good rating are
more “immune” to monetary policy shocks than firms with “poor” ratings.
|
4.
|
Financial (credit) constraint
|
Debt-to-capital ratio
|
“Nonlinear effect”: firms with
either very low and very high ratios react more strongly to monetary shocks.
|
5.
|
Future earnings
|
Trailing P/E
|
Firms with higher P/E are affected
more strongly by monetary shocks.
|
found that firms with limited
ability to finance their operations are affected more severely than
unconstrained firms. That is, either small firms, firms with low cash flows,
firms with poor investment or bank loan rating, and high P/E are affected pore
significantly than their counterpats. These results were in line with initial
hypothesis of the authors. Controversially, firms with either low or high
Debt-to-Capital ratio were found to be affected more strongly by the surprise
change in the target interest rate. The authors explained this result as firms
with low Debt-to-Capital are already constrained with bank loans and may be
limited in the ability to increase financing through debt issuance.presence of
low debt firms with high cash flow and good bank rating gives rise to question
this conclusion. Therefore, we will explore this ratio in our work, among the
others, which we propose.
. Our two-step approach: brief
definition with major advantages over earlier methods
In contrast with common approach of
estimating firm-specific effects with multiple regression we propose a two-step
approach, which consist of:
. Clustering
. Test the difference in
mean portfolio returnsis aimed to find cutoff levels in factors, which are then
utilized to form portfolios of stocks, whose mean returns are tested on
statistically significant difference. The null hypothesis is that mean returns
of portfolios of different stocks are not statistically different, which
implies that a factor does not explain heterogeneous stocks’ reaction to
surprise target rate changes. If we have sufficient evidence to reject the null
hypothesis, then in context of the work we conclude that a factor contributes
to a credit channel of monetary policy transmission on equities market.believe
that our approach has advantages over the commonly used multiple regression
method:
Table 5
No estimate of a surprise ate
change
|
Presence of such a variable in
multiple regression equation requires aggregating specific data, which might
narrow researching field to countries, for which this kind of data is
available. The data can either consist of experts’ expectations drawn from
surveys, or the short-term futures on the implied target rate. A researcher
can avoid this data using indirect methods of extracting unexpected rate
change, such as identified vector autoregressive models (VAR); however,
futures “more cleanly isolates the unanticipated element of policy actions”.
As a target rate change is not involved in clustering algorithm, which
concentrates solely on firm
|
No omitted variable bias.
|
A multiple regression such that in
(Ehrmann & Fratzcher, 2004) which investigates each significant factor at
once may suffer from omitted variable bias, which may lead to inconsistent
standard errors of estimates.
|
are two main disadvantages of the
approach:
. No direct method for
testing results of k-medians clustering. Therefore, the reliability of
estimates of true cutoff level is questionable.
. Time-consuming.
Implementing the approach is somewhat more difficult than that of multiple
regression., before we can rely on the cutoff estimates a more sophisticated
research of applicable clustering algorithms can be done. We experimented only
with k-mean and k-median clustering methods, and did not change their standard
similarity measures (distances between objects)., we also cannot say that our
estimates are “bad”, meaning that they are far away from true gauge levels.
They may be very close but we just do not have a direct method of testing this.
With regard to this discussion, the last advantage is reduced. Notwithstanding
this, these estimates can be a useful starting point for differentiating
companies based on a specified financial ratio. After all, according to (Everitt,
1993), “Clustering methods are intended largely for generating rather than
testing hypotheses”.second issue, more time is somewhat compensated by fewer
data inputs.work introduces the new approach, and, hence, does not explore its
wide applicability. Apart from the disadvantages of the approach, we list the
most important limitations of our work in the table:
Table 6.
Limitations of the work
1.
|
One-factor analysis, and one
cutoff level to divide companies in only “high” and “low” portfolio
categories.
|
The method implies that several
factors may be tested at once. Clustering can be done in d-dimensionsl space,
where d-1 is a number of factors combined. Portfolios can be easily formed by
several factors, for a total number of (d-1)*(k-1), where k is a number of
clusters, k-1 is a number of cutoff levels.
|
2.
|
Test for the differnence in
portfolios’ mean returns is limited to a simple t-test for paired samples,
whose variance is unknown.
|
This limitation follows directly
from the first one. To test the difference in several mean returns at once, a
more sophisticated statistical method, such as ANOVA for paired data, can be
easily applied.
|
3.
|
Data is restricted to a US stock
market.
|
Our approach simplifies
requirements for input data, hence it may be extended to analyze a wide range
of countries.
|
4.
|
Clustering method
|
We used a k-medians clustering
algorithm, which is an exclusive, intrinsic, partitional way of
classification. This method worked better than k-means clustering only for
the input data in this work, which in no means exhausts testing possibilities:
k-means may work better for other factors, and generally there might be other
clustering algorithms, which more efficient estimates of true cutoff
portfolio levels.
|
conclude, we believe that if the
method is advanced further, it will find more applications in the literature of
estimating factor effects. For now, we start with basic steps and present
results for a small number of companies.
C. K-medians cluster analysis and
portfolios’ breakpoints.of all, we eliminate all missing information from our
initial datasets to form uniform samples on each day. The resulting samples
contain data on 4 financial ratios and value-weighted returns for a number of
companies from the S&P 500 index, which we define as samples “before
outliers”. The actual number of companies in each such sample is referred to in
the “Applications” section. It depends firstly on the availability of data in
the COMPUSTAT GLOBAL database for the companies in S&P500 list as of October,
2015. Undoubtedly, there are fewer companies in earlier periods, than in later
ones because new companies had emerged during the 2000’s and some older firms,
once in the S&P500, had gone bankrupt. They do not appear in our dataset.
Secondly, a small number of companies in the S&P 500 list did not have
stock price information for some past periods. They may have been private
before going public, or may have been merged and gone private after being
public, therefore they could have either changed the ticker, or been delisted
from the stock exchange. These are the two only sources of missing
information.we have worked through the missing data we started the first round
of k-medians cluster analysis. K-medians is just a variation of k-means
clustering, which is a simple and popular method of a partitional
classification. Essentially, in order to understand the basic principles of the
k-means clustering it is important to understand its place among the whole set
of methods to classify data.
“Clustering is a special kind of
classification”. K-means clustering is referred to exclusive, intrinsic,
partitional type of classification in the textbook “Algorithms for Clustering
Data” by (Jain & Dubes, 1988) (following a tree of classification problems
proposed by (Lance & Williams, 1967)).classification assigns an object to
one particular cluster, whereas non-exclusive or overlapping allows one object
being labeled to more than one clusters. An example of the first is the
division of students on the basis of test results, an example of the second -
classification of the winners of Grand Slam in tennis: some players have won
more than one different Grand Slam tournaments.classification does not use
category labels a priori assigned by a researcher to an object. The task is therefore
to find a similar property for some objects, which at the same time
differentiates them from other objects in initial sample of observations. On
the contrary, extrinsic classification relies on the choice of dissimilarity
matrix made by the external observer, or a “teacher”. In computer programming
literature, intrinsic classification is called an “unsupervised learning”, and
“is the essence of cluster analysis”.
“Exclusive, intrinsic
classifications are subdivided into hierarchical and partitional
classifications by the type of structure imposed on the data”. Hierarchical
techniques are popular in biological, social, and behavioral sciences because
of the need to systematize data in consequent groups, or levels. We usually
find the application of hierarchical method in the field of linguistics, when a
researcher is interested in constructing families of languages. Another
prominent example in biological sciences is the classification of an object to
consecutive levels, such as family, genus, species and class.classification
refers to a clustering, whose result is a set of clusters, or groups, of
similar objects, whereas clusters are distinct from one another. As described
in the textbook (Jain & Dubes, 1988) “given n patterns in a d-dimensional
metric space” this method divides patterns into K clusters, such that “the
patterns in a cluster are more similar to each other than to patterns in
different clusters”. Then a clustering criterion, either a global or a local,
must be defined. A global criterion utilizes cluster “prototype”, or unique
characteristic, and assigns the objects to clusters according to similar
characteristics. A local criterion divides objects into clusters following
local similarities, such that clusters can be formed by identifying
high-density regions, for example. An example of a clearly defined criterion is
a square-error, which is a squared distance between objects in a d-dimensional
vector space, which must be minimized for within-cluster objects.are hundreds
of clustering criteria, and, hence, partitional clustering algorithms, because
there is no unique definition of a cluster: clusters vary in size and form. So,
the result of partional clustering depends on the researcher’s choice of the
specific algorithm. Furthermore, there is no straightforward procedure of
testing the alternative clustering ways, like the F-test of improvement in fit
for multiple regression, for example.chose one of the simplest and commonly
known method - k-median clustering. K-median is a counterpart of k-mean
clustering, described in the work of MacQueen (1967); k-median is an exclusive,
intrinsic, and partitional type of clustering the data, as the k-mean
algorithm. The only difference between k-median and k-mean is that the former
algorithm defines cluster centers as medians, not means. Therefore, the task is
to form compact clusters around k number of centers, so as to minimize the
Manhattan-distance (absolute value) between observations. These observations in
our work are the points in two-dimensional Eucledian space (because we
investigate the influence of one factor only). Minimization of distance between
points defined as absolute value is distinct from minimization of squared error
function, which is the objective of k-mean clustering. Some say that k-median
algorithm is more reliable for discrete data sets, while (Jain & Dubes,
1988) suggest that a researcher tries several clustering algorithms.applied
both k-mean and k-median clustering method, and chose the latter because it
suited better both our objectives. The first was to form approximately equal
groups of companies. That is to divide a sample of data in two clusters
containing approximately equal data points. The second objective was to make
non-overlapping groups of factors, which means that the maximum value of a
factor within one group is less than the minimum value of this factor in
another cluster. In the raw data (not cleaned of outliers) k-median clustering
provided better results than k-mean clustering.median is also confused with k-medoids
algorithm, whose centers of clusters are the observations from the raw data,
however, the k-median clustering may produce centroids, which are not part of
initial dataset. However, we do not concentrate on the centers of clusters. We
need to find the maximum value of a factor within the “lower” cluster and the
minimum value of this factor within the “higher” cluster in order to find a
cutoff level for a portfolio. That is why we specified a crucial objective for
a clustering algorithm that clusters contain non-overlapping ranges of factor
values.procedure of k-median clustering is the following:
1. Select an initial partition
with K clusters.
Repeat steps 2 through 5 until the
cluster membership stabilizes.
2. Generate a new partition by
assigning each pattern to its closest cluster center.
3. Compute new cluster centers
as centroids of the clusters.
. Repeat steps 2 and 3 until
an optimum value of the criterion function is found.
. Adjust the number of
clusters by merging and splitting existing clusters or by removing small, or
outlier, clusters.are several problems with k-medians clustering. First of all,
the number K is ambigious and dependent on the choice of researcher. For our
research, we set K=2. Therefore, there is no guarantee that an optimal number
of clusters is selected. As a consequence, in the literature it is suggested to
try different number of clusters. We chose between 2, 3, 4, 5, and 6 and the
better results were achieved using only 2 clusters. We infer that an increased
number of clusters forced the clustering algorithm to sort out outliers in
small groups, which was a reason for generally unequal groups in any of the
factors tested. Only when K was 2, approximately equal groups of companies were
chosen in the raw data (based on debt-to-equity or current ratio dissimilarity
measures). We need approximately equal groups so that in the next step of our
research portfolios of stocks contain approximately equal number of companies.
Furthermore, (Jain & Dubes, 1988) suggested that some clustering algorithms
identify “small” clusters as outliers.problem is that a statistical package
uses heuristic algorithms to sidestep complex iterative partitions of large
number of objects. One of the consequences of this is the convergence to a
local optimum: because there is a constrained number of iterations (in Stata,
we used a default number - 10,000 iterations) and because number of clusters k,
chosen by a researcher, could be less than optimal. It is possible, that using
7 or more clusters will generate more equal groups in all 3 factors tested and
contribute to more precise estimates of cutoff levels. The consequence of the
fact of high possibility of convergence of a k-median clustering to a local
optimum, not global one, is that we may have assigned companies to “wrong”
portfolios based on “wrong” cutoff levels. However, there is no way to test
this other than to conduct several studies or, probably, to use a Monte-Carlo
simulation; this is outside the scope of the present work., as a result of simplified
computations the usage of larger sets of data leads to smaller precision of
estimated centroids, and hence, cutoff estimate may be far away from true
values., k-median clustering cannot be applied to any combined set of the raw
data; in particular, we cannot merge the data on stock returns and
company-specific factors from 48 days into one large data set and run a
k-median clustering. The issue is the consequence of two problems outlined
above. This makes it impossible to pool data from all days into one sample to
determine a cutoff level at once.solution to the problem is to determine cutoff
levels on each of the day, and then weight the sum of cutoffs to get one common
cutoff for each factor. Obviously, a process of weighted summing of cutoff
levels for each of the day in the sample is a very-time consuming process
because one needs to run clustering for each variable for each day. For 48 days
and 3 factor variables this converges to running a k-median clustering 144
times. The problem intensifies after one checks each factor variable for
outliers and then runs another set of k-median clustering for a total of 288
attempts. This makes the whole method too clumsy and makes it less efficient in
terms of time tradeoff., we proposed to combine data following two criteria.
The first is the target official rate absolute change and the direction of this
change. They were the same for merged samples. Another important factor that
may influence the clustering procedure is the distribution of factor values. We
set a restriction that medians in each of factor values on each day in new
combined sample are approximately equal to each other. Means are not applicable
because they are influenced by the outliers. Furthermore, we cannot use a
standard deviation as factor distributions have skewed tales. The presence of
several severe outliers, according to (Hoaglin, et al., 1981) gives an evidence
that samples were not drawn from normal distributions., a criterion
“approximately equal” gives rise to ambiguity. We used a 3% density of sample
observations around the median value. So, for example, if there are 101
observations in any two samples, we compare the 51st observation
(the median) in the first sample with a range of values of 3 central
observations from the second sample. If the median is inside the range, we
merge two samples (given that the first criterion is satisfied), regardless
whether the median is an observation, or the simple average of two close
observations., we constructed 8 groups of raw data based on the criteria, and
cleared samples from mild and severe outliers. We weighted the resulting cutoff
levels for each of three factors according to the formula:
Which means that we give more weight
to a cutoff, Ci of the group, which has the largest number of
observations.turn, Ci equals simple average of the minimum value of
observation in a cluster with the higher median and the maximum value of
observation in a cluster with lower median, i.e. in the second cluster because there
are only two clusters.
Table 7.
Cutoff levels for factor portfolios.
Cutoff levels
|
Group
|
DEBT-TO-CAPITAL,
%
|
TOBIN'S
Q
|
INTEREST
COVERAGE
|
-75
|
1
|
33.595
|
1.372099
|
16.63
|
-50
|
2
|
35.495
|
2.0715
|
10.7835
|
-25_1
|
3
|
24.175
|
2.22044
|
20.966
|
-25_2
|
4
|
35.41
|
2.322599
|
9.9945
|
-25_3
|
5
|
26.66
|
2.272133
|
15.628
|
25_1
|
6
|
31.505
|
2.516775
|
11.3195
|
25_2
|
7
|
29.21
|
2.274438
|
15.291
|
50
|
8
|
35.86
|
1.991328
|
10.768
|
Number
of observations
|
|
|
|
|
-75
|
1
|
500
|
483
|
458
|
-50
|
2
|
1561
|
1451
|
1382
|
-25_1
|
3
|
454
|
428
|
410
|
-25_2
|
4
|
794
|
753
|
700
|
-25_3
|
5
|
726
|
715
|
651
|
25_1
|
6
|
999
|
923
|
866
|
25_2
|
7
|
3905
|
3782
|
3433
|
50
|
8
|
197
|
185
|
173
|
total
|
total
|
9136
|
8720
|
8073
|
Resulting Cutoff
|
31.004
|
2.111
|
12.308
|
, we differentiate our portfolios
into Low and High categories based on the fact, whether companies’ financials
at the given date fall below or above these cutoff levels.
4. Comparison of
portfolios’ performances
In this section we constructed 3x2
factor portfolios based on reported cutoff levels, and calculated their mean
returns for each of the action day.null hypothesis is that there is no
significant difference between portfolio means. This implies that the factors
that we investigate do not contribute to a credit channel of monetary policy
transmission. If we have enough evidence to reject the null hypothesis, we
conclude that specified factors do explain heterogeneous stock reaction to
surprised target rate change, and that this various reaction is explained by
different attitude to financial constraint by firms.the papers of (Ehrmann
& Fratzcher, 2004) and (Owen, et al., 2001) we used a Tobin’s Q and
Debt-to-Capital measures of financial constraint faced by a firm. We also added
a third variable to the analysis - Interest Coverage ratio. This ratio is
introduced in (Leiwy & Perks, 2013) as one of the four key estimates of the
company’s financial health.calculated these ratios for each firm among 480, for
which corresponding financial data (from Balance Sheet and Income Statement)
from COMPUSTAT was available, according to formulas:
Debt-to-Capital
= ,
where
Stockholders’ Equity includes Common Equity (key elements of which are common
share, paid-in capital, retained earnings), and Preferred Share capital.
Tobin’s Q
= ,
where market
value of Total Assets were defined as the sum of balance value of Total Assets
and market value of Common Equity, minus the sum of balance value of Common
Equity and deferred Long-term Taxes.
Interest
Coverage
= .
Concerning
the first and the third ratios, they have a slightly different meaning for
financial organizations, especially banks. Unlike industrial corporations,
banks’ interest expense is the primary source of expenses, and they usually
operate with higher debt-to-capital ratio, as it is defined here. Therefore, we
will also eliminate this entire sector and go through the same two-step
procedure to obtain mean portfolio returns for each day. We also recalculated value-weighted
returns, so that the weights for industrial companies summed up to 1 in reduced
sample. We eliminated a total of 82 financial companies among 480 companies in
our S&P 500* sample.fact that in our analysis we did not need to use a
decomposition of actual changes in interest rate on expected and unexpected
portions does not mean that we simplify the analysis by ignoring the theory of
rational; expectations. In fact, correlation analysis of 3x2 factor portfolios’
returns with changes in target interest rates revealed similar patterns as
regressions in the first part of the work did: there is little correlation
between equities’ returns and actual federal funds rate changes, approximately
no correlation between portfolio stock returns and expected rate changes, and
high degree of correlation (up to 50% in absolute value) between returns and
surprise rate changes:
Table 8
F1
|
actual
|
exp
|
unexp
|
1
|
-6%
|
7%
|
-40%
|
2
|
-5%
|
11%
|
-48%
|
F2
|
actual
|
exp
|
unexp
|
1
|
3%
|
22%
|
-55%
|
2
|
-17%
|
-12%
|
-18%
|
F3
|
actual
|
exp
|
unexp
|
1
|
14%
|
-49%
|
2
|
-10%
|
2%
|
-38%
|
then we claimed that we do not need
to decompose the rate change into two portions? The answer is that during 11
years in our sample from 1997 to 2008 only 9 times out of 49 the unexpected
rate changes equaled zero. Combining K. Kuttner’s estimates with this data, and
our estimate of a surprise change on December 16, 2015 (consistent with our
previous estimates and equal to 2 bp) we see that for the last 26 years (from
1989 to 2015) there were only 11 times out of 85 action days when the market
fully expected the rate change. Therefore, we impose an assumption, which is at
least true for the United States, that the market is not able to consistently
fully anticipate a key interest rate change. However, in order to enlarge our
approach for research of the role of financial ratios in explaining
heterogeneous equities’ reaction, it is necessary to investigate how well
market participants in particular country anticipated a rate change.
9. Mean Portfolio
Returns Full Sample
Factor
|
Debt-to-Capital
|
Tobin's
Q
|
Interest
Coverage
|
High
Portfolio
|
8.789
(4.018)
|
20.773
(9.223)
|
19.659
(9.158)
|
Low
Portfolio
|
22.085
(9.501)
|
10.184
(5.800)
|
11.249
(4.337)
|
Table 10. Mean Portfolio Returns
Excl Financials
Factor
|
Debt-to-Capital
|
Interest Coverage
|
High Portfolio
|
12.192 (7.772)
|
48.018 (20.686)
|
Low Portfolio
|
33.798 (15.356)
|
6.596
(3.832)
|
We have found evidence that the
three ratios do influence stocks performance on the days of change of monetary
policy. The strongest evidence is for the Debt-to-Capital ratio. In both full
and reduced sample a group of companies with the ratio less than 31.004% and
less than 50% respectively outperformed groups of higher indebted companies.
The results are significant at 3% and 1% significance levels respectively. In
the full sample companies with Interest Coverage ratio below 12.308
outperformed their counterparts, though the result is significant only at 10%
level. However, in the reduced sample firms with Interest Coverage ratio below
2.0 outperformed another group, with the result significant at 2% level. This
interesting finding suggests that we might have obtained not optimal cutoff
level in the full sample, which could be the consequence of a large number of
outliers for this particular ratio (on average, there were much less outliers
in samples for Tobin’s Q and even fewer for Debt-to-Capital ratio). As for the
last measure of a financial constraint, Tobin’s Q, a Low-category portfolio of
companies with Q < 2.111 outperformed High-category portfolio, though this
is significant only at 10% level., we have found another supportive evidence
for the existence of the credit channel. At least, we have shown that
particular measures of financial constraint - Debt-to-Capital, Tobin’s Q, and
newly introduced Interest Coverage - influence stocks behavior on days of
change of the federal funds interest rate during 1997 - 2008. More importantly,
we have introduced a new approach to this analysis, and have shown that it
provides similar conclusions.from the one, which we found particularly
interesting. (Ehrmann & Fratzcher, 2004) came to a conclusion that low
levels of Debt-to-Capital ratio are signs of higher financial constraint faced
by firms, because their shares were more responsive to a monetary policy change
than that of the firms in the middle group. Based on our results we suggest
that low levels of debt - particularly lower than 31% for a whole range of
firms - is a sign of healthy position because these stocks outperformed the
other.
Conclusions
So, in this work we suggested a new
approach to estimating the role of financial ratios in explaining equities
reaction to surprise changes in the target interest rate. Thus far, we have
found new evidence for existence of credit channel of monetary policy
transmission on equities’ market. In particular, we’ve established supportive
evidence for these measures of financial health of the firms - Debt-to-Capital
ratio, Tobin’s Q, and Interest Coverage ratio.the limitations of the work
capabilities of our two-step approach are not entirely investigated and we have
a lot of space for future research.
credit portfolio stock market
Bibliography
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Blinder, A.S., 1992. The Federal Funds Rate and the Channels of Monetary
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Gertler, M., 1995. Inside the Black Box: The Credit Channel of Monetary Policy
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Kuttner, K.N., 2005. What Explains the Stock Market's Reaction to Federal
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Introduction to Econometrics. 4 ed. Oxford: Oxford University Press.
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M., 2004. Taking Stock: Monetary Policy Transmission to Equity Markets. Journal
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K.N., 1996. The Fed Funds Futures Rate As a Predictor of Federal Reserve
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Appendix
Table of Actual changes, Expected
and Surprise components of the Real Changes and “No-Action” events, in
comparison with K. Kuttner’s (2001) estimates for overlapping dates:
# total
|
Date of the announcement
|
∆R, bp
Actual
|
∆Re, bp
Expected
|
∆Ru, bp
Unexpected
|
∆Ru, bp
(Kuttner’s)
|
101
|
12/16/08
|
-75
|
-58.5
|
-16.5
|
n/a
|
100
|
10/29/08
|
-50
|
-27.5
|
-22.5
|
n/a
|
99
|
10/08/08
|
-50
|
-37.5
|
-12.5
|
n/a
|
98
|
09/16/08
|
0
|
-9
|
+9
|
n/a
|
97
|
08/05/08
|
0
|
+0.5
|
-0.5
|
n/a
|
96
|
06/25/08
|
0
|
+1
|
-1
|
n/a
|
95
|
04/30/08
|
-25
|
-23.5
|
-1.5
|
n/a
|
94
|
03/18/08
|
-75
|
-96
|
+21
|
n/a
|
93
|
01/30/08
|
-50
|
-30
|
-20
|
n/a
|
92
|
12/11/07
|
-25
|
-26
|
+1
|
n/a
|
91
|
10/31/07
|
-25
|
-18
|
-7
|
n/a
|
90
|
09/18/07
|
-50
|
-34
|
-16
|
n/a
|
89
|
08/17/07
|
0
|
-2.5
|
+2.5
|
n/a
|
88
|
08/07/07
|
0
|
-4
|
+4
|
n/a
|
87
|
06/28/07
|
0
|
+0.5
|
-0.5
|
n/a
|
86
|
05/09/07
|
0
|
-0.5
|
+0.5
|
n/a
|
85
|
03/21/07
|
0
|
0
|
0
|
n/a
|
84
|
01/31/07
|
0
|
-0.5
|
+0.5
|
n/a
|
83
|
12/12/06
|
0
|
0
|
0
|
n/a
|
82
|
10/25/06
|
0
|
0
|
0
|
n/a
|
81
|
09/20/06
|
0
|
0
|
0
|
n/a
|
80
|
08/08/06
|
0
|
+4
|
-4
|
n/a
|
79
|
06/29/06
|
+25
|
+14.5
|
+10.5
|
n/a
|
78
|
05/10/06
|
+25
|
+25
|
0
|
n/a
|
77
|
03/28/06
|
+25
|
+24.5
|
+0.5
|
n/a
|
76
|
01/31/06
|
+25
|
+21.5
|
+3.5
|
n/a
|
75
|
12/13/05
|
+25
|
+25
|
0
|
n/a
|
74
|
11/01/05
|
+25
|
+10
|
+15
|
n/a
|
73
|
09/20/05
|
+25
|
+21.5
|
+3.5
|
n/a
|
72
|
08/09/05
|
+25
|
+25
|
0
|
n/a
|
71
|
06/30/05
|
+25
|
+7.5
|
+17.5
|
n/a
|
70
|
05/03/05
|
+25
|
+24.5
|
+0.5
|
n/a
|
69
|
03/22/05
|
+25
|
+25
|
0
|
n/a
|
68
|
02/02/05
|
+25
|
+25
|
0
|
n/a
|
67
|
12/14/04
|
+25
|
+25
|
0
|
n/a
|
66
|
11/10/04
|
+25
|
+24.5
|
+0.5
|
n/a
|
65
|
09/21/04
|
+25
|
+25
|
0
|
n/a
|
64
|
08/10/04
|
+25
|
+23
|
+2
|
n/a
|
63
|
06/30/04
|
+25
|
+4
|
+21
|
n/a
|
62
|
05/04/04
|
0
|
+1
|
-1
|
n/a
|
61
|
03/16/04
|
0
|
0
|
0
|
n/a
|
60
|
01/28/04
|
0
|
0
|
0
|
n/a
|
59
|
12/09/03
|
0
|
0
|
0
|
n/a
|
58
|
10/20/03
|
0
|
0
|
0
|
n/a
|
57
|
09/16/03
|
0
|
0
|
0
|
n/a
|
56
|
08/12/03
|
0
|
0
|
0
|
n/a
|
55
|
06/25/03
|
-25
|
-37.5
|
+12.5
|
n/a
|
54
|
05/06/03
|
0
|
-1.5
|
+1.5
|
n/a
|
53
|
0
|
-2.5
|
+2.5
|
n/a
|
52
|
01/29/03
|
0
|
+1.5
|
-1.5
|
n/a
|
51
|
12/10/02
|
0
|
0
|
0
|
n/a
|
50
|
11/06/02
|
-50
|
-34
|
-16
|
n/a
|
49
|
09/24/02
|
0
|
-2
|
+2
|
n/a
|
48
|
08/13/02
|
0
|
-3
|
+3
|
n/a
|
47
|
06/26/02
|
0
|
+2
|
-2
|
n/a
|
46
|
05/07/02
|
0
|
0
|
0
|
n/a
|
45
|
03/19/02
|
0
|
+2
|
-2
|
n/a
|
44
|
01/30/02
|
0
|
-2
|
+2
|
n/a
|
43
|
12/11/01
|
-25
|
-26
|
+1
|
n/a
|
42
|
11/06/01
|
-50
|
-39.5
|
-10.5
|
n/a
|
41
|
10/02/01
|
-50
|
-41.5
|
-8.5
|
n/a
|
40*
|
09/17/01
|
-50
|
n/a
|
n/a
|
n/a
|
* the observation is dropped from
the analysis
|
|
39
|
08/21/01
|
-25
|
-27
|
+2
|
n/a
|
38
|
06/27/01
|
-25
|
-33.5
|
+8.5
|
n/a
|
37
|
05/15/01
|
-50
|
-42.5
|
-7.5
|
n/a
|
36
|
04/18/01
|
-50
|
-8
|
-42
|
n/a
|
35
|
03/20/01
|
-50
|
-52.5
|
+2.5
|
n/a
|
34
|
01/31/01
|
-50
|
-33.5
|
-16.5
|
n/a
|
33
|
01/03/01
|
-50
|
-21
|
-29
|
n/a
|
32
|
12/19/00
|
0
|
-5.5
|
+5.5
|
n/a
|
31
|
11/15/00
|
0
|
0
|
0
|
n/a
|
30
|
10/03/00
|
0
|
0
|
0
|
n/a
|
29
|
08/22/00
|
0
|
0
|
0
|
n/a
|
28
|
06/28/00
|
0
|
-3
|
+3
|
n/a
|
27
|
05/16/00
|
+50
|
+46
|
+4
|
n/a
|
26
|
03/21/00
|
+50
|
+27
|
-2
|
n/a
|
25
|
02/02/00
|
+25
|
+28.5
|
-3.5
|
-5
|
24
|
12/21/99
|
0
|
0
|
0
|
n/a
|
23
|
11/16/99
|
+25
|
+17
|
+8
|
+9
|
22
|
10/05/99
|
0
|
+1.5
|
-1.5
|
n/a
|
21
|
08/24/99
|
+25
|
+22
|
+3
|
+2
|
20
|
06/30/99
|
+25
|
+29
|
-4
|
-4
|
19
|
05/18/99
|
0
|
+1
|
-1
|
n/a
|
18
|
03/30/99
|
0
|
-1
|
+1
|
n/a
|
17
|
02/03/99
|
0
|
+1
|
-1
|
n/a
|
16
|
12/22/98
|
0
|
0
|
0
|
n/a
|
15
|
11/17/98
|
-25
|
-19
|
-6
|
-6
|
14
|
10/15/98
|
-25
|
-9
|
-16
|
-26
|
13
|
09/29/98
|
-25
|
-31
|
+6
|
0
|
12
|
08/18/98
|
0
|
-1
|
+1
|
n/a
|
11
|
07/01/98
|
0
|
+1
|
-1
|
n/a
|
10
|
05/19/98
|
0
|
+2
|
-2
|
n/a
|
9
|
03/31/98
|
0
|
-1
|
+1
|
n/a
|
8
|
02/04/98
|
0
|
-1
|
+1
|
n/a
|
7
|
12/16/97
|
0
|
+1
|
-1
|
n/a
|
6
|
11/12/97
|
0
|
+2
|
-2
|
n/a
|
5
|
09/30/97
|
0
|
-3
|
+3
|
n/a
|
4
|
08/19/97
|
0
|
-1
|
+1
|
n/a
|
3
|
07/02/97
|
0
|
+1
|
-1
|
n/a
|
2
|
05/20/97
|
0
|
+9
|
-9
|
n/a
|
1
|
03/25/97
|
+25
|
+21
|
+4
|
+3
|
2. Minimum and maximum values in
clusters with higher and lower medians.
min
- high median group
|
Group
|
DEBT-TO-CAPITAL,
%
|
TOBIN'S
Q
|
INTEREST
COVERAGE
|
-75
|
1
|
33.81
|
0.845466
|
17.078
|
-50
|
2
|
35.66
|
2.0719
|
11.037
|
-25_1
|
3
|
24.64
|
2.22404
|
21.725
|
-25_2
|
4
|
35.49
|
2.32048
|
10.355
|
-25_3
|
5
|
26.84
|
2.281742
|
15.807
|
25_1
|
6
|
2.51387
|
11.364
|
25_2
|
7
|
29.21
|
2.275665
|
15.317
|
50
|
8
|
36.04
|
2.000405
|
11.037
|
max
- low median group
|
Group
|
DEBT-TO-CAPITAL,
%
|
TOBIN'S
Q
|
INTEREST
COVERAGE
|
-75
|
1
|
33.38
|
1.898733
|
16.182
|
-50
|
2
|
35.33
|
2.0711
|
10.53
|
-25_1
|
3
|
23.71
|
2.21684
|
20.207
|
-25_2
|
4
|
35.33
|
2.324718
|
9.634
|
-25_3
|
5
|
26.48
|
2.262523
|
15.449
|
25_1
|
6
|
31.45
|
2.51968
|
11.275
|
25_2
|
7
|
29.21
|
2.273211
|
15.265
|
50
|
8
|
35.68
|
1.982251
|
10.499
|