Sources of bank risks: impacts and explanations.
Bracker, Kevin ; Imhof, Michael ; Lallemand, Justin 等
INTRODUCTION
The sensitivity of commercial bank stock returns to interest rate
risk has generated a substantial amount of attention, both within the
academic arena and in the business world. Although this paper studies a
multitude of risks to commercial banks, interest rate risk came to the
forefront in the 1980's, in particular, with the massive number of
Savings and Loan failures spurred on in large part by maturity
mismatches between longer-term assets (loans) and shorter-term
liabilities (deposits). In addition to the S&L failures, between
1985 and 1992, there were 1316 commercial bank failures in the U.S.
involving over $170 billion in bank assets (FDIC). The magnitude of
these failures and the instability they lent to the U.S. banking sector
compounded many of the problems generated by the S&L failures.
In addition, through much of the 1980's and 1990's, bank
regulatory bodies continued to chip away at many of the Glass-Steagal
provisions by allowing banks to indirectly participate in other nonbank
financial activities. Finally, in 1999, the Gramm-Leach-Bliley Act
removed many of the remaining barriers between financial companies
(Carow and Heron, 2002). As many larger banks began to expand their
business lines, they may have also expanded the set of risks to which
they are exposed.
Ultimately, as a result of the changes in legislation, banks began
to diversify into areas such as investments and insurance, leading to
industry consolidation and competitive restructuring (Purnanandam,
2005). These substantial changes renewed interest in the impact of
interest rate risk on bank stock returns.
While the majority of studies examining the relationship between
interest rate changes and bank stock returns indicate a predominantly
negative relationship, there have been some exceptions. Booth and
Officer (1985), Kwan (1991), Fraser, Madura and Weigand (2002), and
others find that the relation between interest rates changes and bank
stock returns is negative. Alternatively, earlier studies by Chance and
Lane (1980) and Lloyd and Schick (1977) find no significant
relationship. Fissel, Goldberg and Hanweck (2005) examine 10 large banks
and find a positive and significant relationship in 6 of the 10 banks
and a significant negative relationship in only 1 of the 10 banks (the
other 3 exhibiting negative, but not significant relationships).
Saporoschenko (2002) examines Japanese bank stock returns and finds that
the relationship varies from bank to bank. Madura and Zarruk (1995)
investigate the issue on a global basis. They examine the sensitivity of
bank stock returns to changes in interest rates for 29 money center
banks across the U.S., Canada, the U.K., Japan and Germany. Their
findings indicate a negative relationship in all countries but the U.S.
Chen and Chan (1989) find that the sensitivity between interest rates
changes and bank stock returns fluctuates depending on other
characteristics of the interest rate environment.
In addition to bank stock returns being impacted by changes in
overall interest rate levels, they can also be impacted by changes in
the structure of the yield curve, or more specifically, the difference
between long-term and short-term interest rates (yield spread). Interest
rate spreads between high-risk and low-risk securities (default risk
premium) may also impact bank stock returns. Since many banks
(especially larger banks) make loans and receive deposits in currencies
other than the U.S. Dollar, it is reasonable that fluctuations in the
value of the U.S. Dollar (exchange rate risk) could also have an impact
on the returns. Grammatikos, Saunders, and Swary (1986), Choi,
Elyasiani, and Kopecky (1992), Chamberlain, Howe, and Popper (1996),
Chow, Lee and Solt (1997), Tai (2000), and Reichert and Shyu (2003), all
examine the impact of foreign exchange rates on bank stock returns with
mixed results.
As mentioned above, the yield spread (also referred to as the slope
of the yield curve), may impact bank stock returns positively or
negatively. Because banks tend to borrow a significant portion of their
capital through deposits on a short-term basis and lend on a longer-term
basis, a maturity mismatch may arise between bank assets and
liabilities. When the slope of the yield curve declines, these banks may
experience a drop in their profit margins which can impact their equity.
Lopez (2004) argues that the yield curve is a key factor in explaining
interest rate risk exposure for banks. Demsetz and Strahan (1997)
include the yield curve in a return generating model exploring bank
diversification while Fissel, Goldberg, and Hanweck (2005) find that the
yield curve is not important in explaining returns. Based on these
studies, the influence of the yield curve risk in returns for bank
holding companies is not clear.
Also as previously indicated, banks that engage in riskier loans
may be impacted by the default risk premium. During periods when the
risk premium is high, banks have the potential to generate higher
profits from these loans. Alternatively, risk premiums increase when
investors anticipate greater chance for defaults, so the risk exposure
to banks increases when the premium increases. While the directional
impact of changes to the default risk premium is unclear, it is apparent
that such changes have the potential to significantly impact bank
returns. Demsetz and Strahan (1997) include default risk in their
diversification analysis but provide no evidence of its directional
impact.
Based on the above discussion, we have extended the traditional
two-factor (interest rates and market returns) model of bank returns to
include the impact of foreign exchange rates, yield spreads and default
risk premiums. Our paper is unique in that it is the only one (to our
knowledge) that considers the wide range of risk factors discussed.
Although other papers may have considered certain subsets of our risk
factors, a more complete picture results through the combination of all
of the proposed risk factors and the analytical framework utilized.
The literature examining the risk factors for banks and other
financial institutions typically takes two approaches. One approach
examines the impact of a particular risk factor (predominately interest
rates) on returns for the industry. The second examines the risk factor
on the firm level, allowing each financial institution to respond
differently to the risk factor. Our analysis combines these approaches.
First, we examine the impact of the risk factors on our sample of bank
holding company stocks as a whole. Second, we estimate the sensitivity
of each bank holding company to the risk factors in our model. Third, we
attempt to explain differences in the sensitivity to each risk factor
across firms based on characteristics of each firm.
DATA
Monthly returns for bank holding company stocks are generated from
CRSP from 1987 to 2004. To analyze the issue of whether or not the
coefficients of the risk factors change over time, we not only examine
the sample in full, but we also split the 18-year period into three
6-year subperiods (1987-1992, 1993-1998, and 1999-2004). This approach
gives us 404 bank holding companies in subperiod 1, 605 bank holding
companies in subperiod 2, and 564 bank holding companies in subperiod 3.
In estimating the coefficients for each risk factor, only bank holding
companies with returns over the entire subperiod are examined. This
reduces the number of bank holding companies in each subperiod to 245,
222, and 298 respectively. There are 97 bank holding companies whose
returns span the full sample period. Although this selection criterion
can result in survivorship bias, this issue is not nearly as pronounced
in banking during the full sample period. During the full sample period,
the actual number of liquidated bank holding companies was extremely
small, with most distressed banks acquired by larger, healthier firms.
In addition to the returns on bank holding company stocks, we use proxy
variables for each of the risk factors that we estimate. The data for
these variables are generated from CRSP and the Federal Reserve Economic
Data (FRED[R]) database. See Table 1 for a description of each variable.
Once the individual bank holding company betas are estimated, we
attempt to explain differences in the risk coefficients through a series
of models--one model for each risk factor being analyzed. To do this, we
obtain information on each bank holding company from their quarterly
Y-9C reports, available through the FDIC. Table 2 lists these data
points. The data points in Table 2 are then combined to create specific
variables (See Table 3) that are anticipated to influence a bank holding
company's level of exposure to the risk factors introduced in Table
1.
METHODOLOGY AND RESULTS
Estimating Risk Sensitivities for Bank Holding Companies as a Whole
Stage one of our analysis is to estimate the sensitivity of bank
holding company stock returnss as a whole to various risk factors.
Specifically, we hypothesize that bank holding company returns are a
function of market returns, changes in long-term interest rates, changes
in short-term interest rates, changes in foreign exchange rates, changes
in the yield spread and changes in the default risk premium (see Table 1
for variable descriptions). We estimate the sensitivity of bank holding
company stock returns to these factors using the following OLS
regression model
RET = [alpha] + [[beta].sub.1]VWRET + [[beta].sub.2]PCTNOTE +
[[beta].sub.3]PCFF + [[beta].sub.4]PCFX + [[beta].sub.5]DRP +
[[beta].sub.6]YSP + [epsilon] (1)
This model is estimated four times (once for each subperiod and
once for the entire sample period) with the risk betas being held
constant across each bank holding company (a measure of the risk betas
for bank holding companies as a whole).
The rationale for examining subperiods along with the entire sample
period is to examine how the impact of these risk factors changes over
time. According to Chen and Chan (1989), the sensitivity of interest
rate risk is partially dependent on the interest rate cycle. In
addition, the banking crisis of the late-80s to early-90's likely
saw banks change the way they managed risk which could lead to changes
in the estimated coefficients. Finally, the economic/regulatory
conditions during each of the subperiods varied significantly, possibly
indicating varying "regimes" from one subperiod to the next.
Our first subperiod (1987-92) is in the heart of the banking crisis and
saw the October 1987 stock market crash. The second subperiod (1993-98)
was characterized by a period of declining interest rates (the 10-year
Treasury note fell from a yield of 6.60% at the start of this period to
4.72% at the end) and saw the financial markets affected by both the
Asian Crisis of 1997 and the Long-Term Capital Management situation in
1998. The third subperiod (1999-04) is associated with an extremely
volatile equity market and the 9/11 attacks on the World Trade Center.
All periods experienced significant deregulation which not only
increased the scope of bank activities, but also motivated significant
consolidation in the banking sector (Mamun, Hassan, and Lai, 2004).
Chow Tests on the subperiods (Table 4) show that the regression
models are statistically different to a high degree over each of the
subperiods. While we feel that the analysis done by subperiods is
important due to the issues mentioned above, we have also estimated the
model over the entire time period for comparison and completeness.
Variance Inflation Factor (VIF) analysis was performed to check for
multicollinearity problems among the dependent variables. All VIF
estimates were well under 2.0 indicating that multicollinearity is not a
concern. The results of these four regressions are presented in Table 5.
In looking at the results, the first item that stands out is the
positive and statistically significant coefficient for the 10-year
Treasury Note variable capturing changes in long-term interest rates
during the first subperiod. This is a surprising result for two reasons.
First, most prior research shows that bank stock returns are inversely
related to changes in interest rates. Second, the coefficient on this
variable is negative and significant in each of the other subperiods as
well as over the entire sample period. It is interesting to note that
this period is associated with an exceptionally high period of bank
failures. According to the FDIC, there were 2100 financial institution
failures with over $700 billion in assets from 1987-1992. Included in
these numbers were 1054 commercial banks with assets of approximately
$160 billion. By comparison, the rest of the sample period (1993-2004)
saw only 120 failures (99 banks) impacting approximately $21 ($11)
billion in assets.
Not only does the coefficient on the 10-year Treasury note variable
change signs during subperiods, but we also see this pattern with
virtually every other risk factor. The foreign exchange risk factor is
positive and significant during the first two subperiods while being
negative and significant over the last subperiod. The default risk
premium is significant and negative during the first two subperiods and
positive (although insignificant) during the third subperiod. Finally,
the yield spread is significant and negative during the first two
subperiods before switching to significant and positive during the third
subperiod.
There are three possible explanations of the tendency for these
variables to exhibit different signs in different subperiods. One, bank
holding companies do not operate in a static environment. Changing
conditions in the economy, regulatory environment, and financial markets
along with implementation of new strategies and risk-management tools by
management result in changes to the influence risk factors have on
equity returns. O'Brien and Berkowitz (2005) examine trading
revenue for six large banks and find that bank dealers tend to vary
their risk exposure in both size and direction and the variation is
heterogeneous across banks. While this looks only at trading revenue for
a small sample of large banks, it supports the notion that bank risks
may vary over time. Two, we are looking at stock returns and not
measures of bank profitability. To the extent that investors anticipate
changes in the variables, there might be a differing response. For
instance, if interest rates rise but that rise was fully anticipated by
investors, we would expect no meaningful impact on stock returns even if
the change in interest rates did impact the value of the bank holding
company's assets or its profitability. Three, the combination of
bank failures and bank mergers between 1987 and 2004 meant that the
firms in our sample varied significantly from subperiod to subperiod.
For example, while there were 245 firms in subperiod 1 and 222 firms in
subperiod 2, there were only 145 firms that were in both subperiods (and
only 97 that were in all three). This indicates that the specific
characteristics of firms in each subperiod likely exhibited substantial
differences.
While we have seen that the risk coefficients do change over time,
when looking at regressions over the entire time period, some clearer
tendencies emerge. First, we see that the relationship between interest
rates changes and bank holding company returns is negative and
significant, consistent with most previous research. This is true for
both long-term interest rates (as measured by the 10-year Treasury note)
and, to a lesser extent, short-term interest rates (as measured by the
Federal Funds rate.) A second relationship that we see is a positive
relationship with the value of the US Dollar. This tells us that a
stronger US Dollar tends to benefit bank holding company stocks. The
third important relationship is the default risk premium. The
significant negative coefficient tells us that as investors become more
sensitive to default risk (demanding relatively higher returns for risky
bonds), there is a negative impact on bank holding company stock
returns. Finally, we see a significant negative coefficient for the
yield spread variable. This indicates that a wider yield spread is
associated with lower returns for bank holding company stocks. While
this may be counterintuitive at first glance (as it should lead to
higher profits on long-term loans), it makes more sense when we look at
it from the perspective of the bank holding company's assets and
liabilities. Assuming the bank holding company has not entirely hedged
its interest rate risk, an increase in the yield spread is likely to
result in the market value of the firm's assets (loans and other
long-term securities) declining at a faster rate then its liabilities
(short-term deposits). Note that the exception (when the yield spread
variable had a positive relationship with bank holding company stock
returns) was during period three. During this period, the decline in the
yield spread was predominantly caused by a decline in short-term rates.
This would likely have a bigger (positive) impact on profitability
without causing a drop in the bank holding company's asset values.
The negative coefficient associated with the default risk premium could
also be explained by the relative impact on assets vs. liabilities as an
increase in the default risk premium is likely to have a greater
(negative) impact on the assets of the bank holding company than it will
on its liabilities.
Explaining Differences in Risk Sensitivities Across Individual Bank
Holding Companies
The second stage of our analysis is focused on explaining the
differences across bank holding companies in their sensitivity to the
above risk factors. While the results discussed above focused on bank
holding company stocks as a group, there is significant variation in the
risk betas from firm to firm. See Table 6 for an overview. The
coefficients from Model (1) represent the sensitivity of bank stock
returns to each type of risk. We develop five separate models to explain
the firm-level variation in these sensitivities. Model (2) attempts to
explain the variation across firms in [[beta].sub.2], which is the
sensitivity of bank stock returns to percent changes in long-term
interest rates. Model (3) attempts to explain the variation across firms
in [[beta].sub.3], which is the sensitivity of bank stock returns to
percent changes in short-term interest rates. Model (4) attempts to
explain the variation across firms in [[beta].sub.4], which is the
sensitivity of bank stock returns to percent changes in exchange rates.
Model (5) attempts to explain the variation across firms in
[[beta].sub.5], which is the sensitivity of bank stock returns to
changes in the default risk premium, and Model (6) does the same with
[[beta].sub.6] and changes in the yield spread.
TNOTE = [alpha] + [[lambda].sub.1]GAP + [[lambda].sub.2]ASSETS +
[[lambda].sub.3]EQUITY + [[lambda].sub.4]INTDER + [member of] (2)
FFUNDS = [alpha] + [[lambda].sub.1]GAP + [[lambda].sub.2]ASSETS +
[[lambda].sub.3]EQUITY + [[lambda].sub.4]INTDER + [member of] (3)
FOREXC = [alpha] + [[lambda].sub.1]ASSETS + [[lambda].sub.2]EQUITY
+ [[lambda].sub.3]FXDER + [[lambda].sub.4]FORACT + [member of] (4)
DEFRISK = [alpha] + [[lambda].sub.1]ASSETS + [[lambda].sub.2]EQUITY
+ [[lambda].sub.3]RSKAST + [member of] (5)
YLDSPR = a + [[lambda].sub.1]GAP + [[lambda].sub.2]ASSETS +
[[lambda].sub.3]EQUITY + [member of] (6)
Where:
TNOTE = [[beta].sub.2] from Equation 1 for that particular Bank
Holding Company
FFUNDS = [[beta].sub.3] from Equation 1 for that particular Bank
Holding Company
FOREXC = [[beta].sub.4] from Equation 1 for that particular Bank
Holding Company
DEFRISK = [[beta].sub.5] from Equation 1 for that particular Bank
Holding Company
YLDSPR = [[beta].sub.6] from Equation 1 for that particular Bank
Holding Company
Table 3 provides a detailed description of each of the independent
variables used in equations 2-6. Each of the equations includes ASSETS
and EQUITY as independent variables to control for size and bank holding
company capital. All else equal, we would expect large bank holding
companies to be able to better manage their risk exposure. Also, we
would expect bank holding companies with high degrees of equity capital
to be less sensitive to risk factors. The GAP variable is designed to
measure the maturity gap between the bank holding company's assets
and liabilities. The larger this gap in maturity, the more sensitive the
bank should be to interest rate changes. Therefore, we use the GAP
variable in equations 2, 3, and 6 which are all measuring risk factors
related to interest rates. In addition, we introduce the interest rate
related derivative dummy variable in equations 2 and 3 to see if the use
of interest rate derivatives has a measurable impact on the sensitivity
of the bank holding company's stock returns to interest rate
changes. Equation 4 introduces a dummy variable for firms that use
foreign exchange related derivatives and a variable to measure the
extent of their activity with respect to foreign assets. We would bank
holding companies that have more foreign activity would be more
sensitive to foreign exchange risk. It is less clear for bank holding
companies using foreign exchange derivatives as they could using these
derivatives to hedge their risk or for speculative trading. Finally, we
introduce a variable to measure the amount of risky assets (such as
credit card loans) to our model explaining the sensitivity of the bank
holding company's stock returns to the default risk premium.
The Seemingly Unrelated Regression (SUR) method (1) developed by
Zellner (1962) is used to estimate the models over the entire 1987-2004
time period in order to capture additional efficiency in estimates
resulting from correlated error terms across equations. Each of the
dependent variables represents the corresponding risk coefficients
estimated for each firm using Model (1). The independent variables are
taken from the Y-9C Call Reports and explained in Tables 2 and 3. These
data were not available for our entire sample of firms. After
eliminating those firms that did not have sufficient data, there were
189 firms in subperiod 1, 174 firms in subperiod 2, and 220 firms in
subperiod 3. This provided a total of 583 firms available for this stage
of analysis. Table 6 provides the results.
One difficulty with this stage of analysis is in interpreting the
results. For instance, assume that we find that [[lambda].sub.1] in
equation 2 is negative. The meaning of this depends on whether or not
the risk beta for Treasury Notes ([beta].sub.2] in equation one) is
positive or negative. If the risk beta is positive, then the implication
of a negative [[lambda].sub.1] in equation 2 is that bank holding
companies with higher maturity gaps are less sensitive to changes in the
interest rate. On the other hand, if the risk beta is negative then the
implication changes. Now, a negative [[lambda].sub.1] in equation 2
implies that bank holding companies with higher maturity gaps are more
sensitive to changes in the interest rate as they will see a larger
negative response. In order to deal with this issue, we split the data
into two segments based on the sign of the risk beta. All bank holding
companies with positive risk betas were assigned to one group while all
bank holding companies with negative risk betas were assigned to the
other group. This was done for each of the risk betas (except for market
risk) in equation one. After segmenting the bank holding companies, we
estimated the set of equations (equations two-six) a total of ten times.
The results are presented in Panel A and Panel B of Table 7.
In looking at how individual bank holding companies respond to
changes in long-term interest rates, we see that there are three primary
factors impacting this response--the maturity gap, size of the bank
holding company and equity/asset ratio of the bank. First, the greater
the maturity gap, the more sensitive bank holding company stock returns
are to changes in the 10-year Treasury Note. For bank holding companies
that are inversely related to long-term interest rates, we see that the
Gap coefficient is negative indicating a stronger negative relationship.
For bank holding companies that are positively related to long-term
interest rates, we see a positive coefficient, indicating a stronger
positive relationship. Regardless of whether or not the relationship is
positive or negative, a larger gap tends to strengthen the relationship
between long-term interest rates and stock prices for bank holding
companies. Second, large bank holding companies tend be less sensitive
to interest rate changes. However, this relationship is more one-sided.
For bank holding companies with an inverse relationship to long-term
interest rates, the role of bank holding company size is not relevant.
However, for firms that are positively related to interest rates, we see
that larger bank holding companies are less sensitive to interest rate
changes. Third, the equity level of the bank holding company also
appears to act as a buffer against interest rate risk. Regardless of
whether the bank holding company has a positive or negative relationship
to the change in the 10- year Treasury note, higher levels of equity
reduce the impact.
When looking at short-term interest rate risk, we see a similar
story. While the Gap variable is no longer significant for bank holding
companies exhibiting a negative relationship to interest rates, there is
still a negative coefficient (indicating a stronger relationship). For
bank holding companies with a positive relationship, we again see a
positive and significant coefficient. Thus, it appears that regardless
of whether long-term or short-term interest rates are being analyzed,
bank holding companies with larger maturity gaps are more sensitive to
changes in interest rates. In addition, relationships between bank
holding company size and equity level are very similar to the
relationships we saw with long-term interest rates. Regardless of
whether we are looking at long- term or short-term interest rates, both
bank holding company size and equity levels appear to have a dampening
effect on the impact of interest rate changes.
The third model attempts to explain the level of foreign exchange
risk across bank holding companies. Here we see a noticeable impact in
how bank-related factors impact foreign exchange risk depending on
whether or not there is a direct or inverse relationship between
exchange rates and stock prices. For firms that are inversely related to
exchange rates, there are no significant explanatory factors. However,
when bank holding companies show a positive relationship to exchange
rates, we see several factors as being important. Both firm size and
equity again act as a dampening agent to the risk level, reducing the
role of foreign exchange fluctuations on bank stock returns. Meanwhile,
the greater the bank holding companies involvement in foreign activity
(through international loans and trading of international assets) the
greater the sensitivity of stock returns to foreign exchange rates.
Our fourth model examines the sensitivity to changes in the default
risk premium. Here we see that our models fail to do a good job of
explaining differences in the level of sensitivity to default risk
across the bank holding companies in our sample. Neither model is
statistically significant. However, there is one significant variable.
The equity level appears to reduce the impact of changes in default risk
for bank holding companies with a negative relationship.
The fifth and final model examines the sensitivity to changes in
the yield spread. While we see a significant model when looking at bank
holding companies that have a negative relationship with the yield
curve, the model does not appear to be reliable in analyzing firms with
a positive relationship. For bank holding companies that exhibit an
inverse relationship to the yield curve, our results are consistent with
what we saw in the long-term and short-term interest rate models. Both
the bank holding company size and equity level of the bank holding
company act to reduce the impact of changes in the yield curve while the
maturity gap acts to magnify the impact.
A brief review of the results of our investigation into
determinants of the sensitivity illustrates a couple of consistent
patterns. First, bank holding company size and equity levels appear to
act as forces reducing the level of interest rate and foreign exchange
risk faced by banks. This makes sense as larger bank holding companies
have the ability to employ more sophisticated risk management techniques
and have a broader base of assets which they can use to diversify their
risk. Higher levels of equity also create a cushion for the banks to
absorb these risks easier. A second pattern is the role of the maturity
gap. As expected, higher gaps make bank holding companies more sensitive
to interest rate risk. Third, derivative exposure does not appear to be
a major factor in impacting risk. This does not mean that derivatives
are not an effective risk management tool. Instead it is likely that
data limitations leading to our inability to precisely capture to
derivative strategies employed prevent us from more accurately seeing
the full implications of derivative use within bank holding companies.
SUMMARY AND CONCLUSIONS
The investigation into interest rate risk and bank holding
companies is an area that has seen significant research. We are
attempting to expand on this research by looking at more levels of risk
exposure beyond just changes in the interest rate and to examine why
individual bank holding companies may be more or less sensitive to these
risk factors. What we find is that for the industry as a whole, the
sensitivity of stock returns to most risk factors evolves over time.
This is likely due to a host of factors including economic conditions,
regulatory environments, management tools and strategies, and financial
crises. In looking at explanations for how risk sensitivities vary
across firms, we find that the maturity gap, bank size and equity levels
are often primary factors in explaining why some banks are more
sensitive to specific risk factors than others.
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American Statistical Association, 57(298), 348-368.
Kevin Bracker, Pittsburg State University
Michael Imhof, University of Missouri-Columbia
Justin Lallemand, University of Arkansas
ENDNOTE
(1) The seemingly unrelated regression (SUR) model developed by
Zellner (1962) allows us to adjust for
correlation across our model errors. These correlations may arise
because the independent variables in Model (1) are constant across the
sample of firms. Only the dependent variables, bank stock returns, vary.
Correlation among model errors is a violation of the Guass Markov
assumption that the errors are independently and identically distributed
with mean zero and constant variance. The SUR technique uses generalized
least squares (GLS) to adjust for this correlation. This improves the
efficiency of our estimated risk coefficients.
Table 1: Description of Variables used to Estimate Risk Sensitivities
Variable Description Source
RET Monthly Return (including dividends) for Bank CRSP
Stock
VWRET Monthly Return (including dividends) for the CRSP
Value Weighted Index
PCTNOTE Percentage Change in the 10-year Treasury Note FRED[R]
PCFF Percentage Change in the Federal Funds Rate FRED[R]
PCFX Percentage Change in the Foreign Exchange Rate FRED[R]
(Trade Weighted Exchange Index for Major
Currencies)
DRP Change in the Default Risk Premium (Baa FRED[R]
Corporate Bond Yield--Aaa Corporate Bond
Yield)
YSP Change in the Yield Spread (10-year Treasury FRED[R]
Note Yield minus 3-month Treasury Bill Yield)
Table 2: Data Fields from Y-9C Call Reports
The variables below are taken from the Y-9C Call Reports provided by
our bank holding companies. The Y-9C variables are then used to
prepare additional variables (see Table 3) for our analysis.
Y-9C Variable Code Variable Description
BHCK2170 Total assets
BHCK3210 Total equity
BHCK3197 Earning assets that reprice/mature within one year
BHCK3296 Interest bearing deposit liabilities that reprice/
mature within one year
BHCK3298 Long-term debt that reprices within one year
BHCK3408 Variable rate preferred stock
BHCK3409 Long-term debt that matures within one year
BHCK1296 Loans to foreign banks
BHCK1764 Commercial loans to non-US addressees
BHCK2081 Loans to foreign governments
BHCK3542 Trading assets in foreign offices
BHCKB837 Real estate loans to non-US addressees
BHCK1742 Foreign debt securities
BHCK1590 Agricultural loans
BHCK1763 Commercial loans to US addressees
BHCKB538 Credit card loans
BHCKB539 Other revolving credit
BHCK2011 Other consumer loans
BHCK8693 Futures contracts (interest rates)
BHCK8697 Forward contracts (interest rates)
BHCK8701 Exchange traded option contracts--written
(interest rates)
BHCK8705 Exchange traded options contracts--purchased
(interest rates)
BHCK8709 Over-the-counter option contracts--written
(interest rates)
BHCK8713 Over-the-counter options contracts--purchased
(interest rates)
BHCK3450 Swaps (interest rates)
BHCKA126 Total interest rate derivatives held for trading
BHCK8725 Total interest rate derivatives held for purposes
other than trading
BHCK8694 Futures contracts (foreign exchange)
BHCK8698 Forward contracts (foreign exchange)
BHCK8702 Exchange traded option contracts--written
(foreign exchange)
BHCK8706 Exchange traded options contracts--purchased
(foreign exchange)
BHCK8710 Over-the-counter option contracts--written
(foreign exchange)
BHCK8714 Over-the-counter options contracts--purchased
(foreign exchange)
BHCK3826 Swaps (foreign exchange)
BHCKA127 Total foreign exchange derivatives held for
trading
BHCK8726 Total foreign exchange derivatives held for
purposes other than trading
Table 3: Description of Variables Explaining Differences in Risk
Sensitivity Across Bank Holding Companies
Variable Description
GAP The average of the assets expected to reprice/mature within
a year less liabilities expected to reprice/mature within a
year divided by total assets [(BHCK3197--BHCK3296--BHCK3298
--BHCK3408--BHCK3409)/BHCK2170] over the 24 quarters in
each subperiod
ASSETS The natural log of the average value for total assets
(BHCK2170) over the 24 quarters in each subperiod
EQUITY The average equity divided by total assets
(BHCK3210/BHCK2170) over the 24 quarters in each subperiod
INTDER A dummy variable equal to 1 if the firm used any interest
rate derivatives (BHCK8693, BHCK8797, BHCK8701, BHCK8705,
BHCK8709, BHCK8713, BHCK3450, BHCKA126, BHCK8725) during
the subperiod and 0 otherwise
FXDER A dummy variable equal to 1 if the firm used any foreign
exchange derivatives (BHCK8694, BHCK8698, BHCK8702,
BHCK8706, BHCK8710, BHCK8714, BHCK3826, BHCKA127, BHCK8726)
during the subperiod and 0 otherwise
RSKAST The average risky assets divided by total assets [(BHCK1590
+ BHCK1763 + BHCKB538 + BHCKB539 + BHCK2011)/BHCK2170] over
the 24 quarters in each subperiod
FORACT The average level of foreign activity divided by total
assets [(BHCK1296 + BHCK1764 + BHCK2081 + BHCK3542 +
BHCKB837 + BHCK1742)/BHCK2170] over the 24 quarters in
each subperiod
Table 4: Chow Test for Subperiods
Our sample period covers 18 years (1987-2004) and is subdivided into
three 6-year periods. The primary model estimates risk factors for
bank holding company stocks using monthly data. We find that the
model experiences significant changes over the 3 subperiods.
RET = [alpha] + [[beta].sub.1]VWRET + [[beta].sub.2]PCTNOTE +
[[beta].sub.3]PCFF + [[beta].sub.4]PCFX + [[beta].sub.5]DRP +
[[beta].sub.6]YSP + [epsilon]
Subperiods 1-2 Subperiods 2-3
Sum of Squared Errors (Full Model) 117.31633 118.19212
Sum of Squared Errors (Period 1) 69.12416 50.37357
Sum of Squared Errors (Period 2) 47.4953 64.91128
K 7 7
n1 10438 10655
n2 10439 10656
F-Value 17.80981715 76.72440319
Probability 0.00000% 0.00000%
Table 5: Estimation of Bank Holding Company Risk Factors
The following regression equation is estimated for our sample of bank
holding company stocks over the 1987-2004 time period. The model uses
monthly data and examines three 6-year subperiods separately as well
as the full 18-year period. Only firms that were publicly traded over
the sample subperiod reported are included in the analysis. The 97
firms that were publicly traded during the entire sample period were
also analyzed separately over each of the three subperiods. The
results were consistent with the results presented here.
RET = [alpha] + [[beta].sub.1]VWRET + [[beta].sub.2]PCTNOTE +
[[beta].sub.3]PCFF + [[beta].sub.4]PCFX + [[beta].sub.5]DRP +
[[beta].sub.6]YSP + [epsilon]
1987-1992 1993-1998
Intercept 0.00323 0.00918
(4.29) *** (13.88) ***
Market Return 0.63766 0.72166
(38.71) *** (45.12) ***
10-Year TNote 0.13219 -0.03469
(5.09) *** (-2.01) **
Fed Funds Rate -0.13138 -0.05614
(-6.08) *** (-2.95) ***
Foreign Exchange Rate 0.58032 0.34155
(14.46) *** (8.07) ***
Default Risk Premium -0.12793 -0.18856
(-11.26) *** (-13.24) ***
Yield Spread -0.01954 -0.00723
(-5.85) *** (-2.17) **
F-Value 542.71 *** 428.45 ***
Number of Firms 245 222
1999-2004 1987-2004
Intercept 0.01119 0.00842
(20.34) *** (15.82) ***
Market Return 0.21770 0.59482
(18.69) *** (51.04) ***
10-Year TNote -0.05919 -0.10127
(-5.30) *** (-7.81) ***
Fed Funds Rate -0.01390 -0.01886
(-1.67) * (-1.81) *
Foreign Exchange Rate -0.39011 0.26657
(-11.15) *** (8.35) ***
Default Risk Premium 0.00419 -0.01950
(0.79) (-2.42) **
Yield Spread 0.01326 -0.01126
(6.22) *** (-4.91) ***
F-Value 108.95 *** 500.85 ***
Number of Firms 298 97
*** Indicates statistical significance at the 0.01 level
** Indicates statistical significance at the 0.05 level
* Indicates statistical significance at the 0.10 level
Table 6: Summary of Risk Factor Estimation for Each Bank Holding
Company
Below are the summary results from estimating the risk factors
for each bank holding company separately. The number of positive
outcomes provides another way to examine the significance of the
risk factors by evaluating whether the number of positive
coefficients for that variable are significantly more (less)
than half the firms in that period. The individual coefficients
for each bank holding company are then used to examine what
unique characteristics impact the banks sensitivity to each
risk factor (see Table 7).
RET = [alpha] + [[beta].sub.1]VWRET + [[beta].sub.2]PCTNOTE +
[[beta].sub.3]PCFF + [[beta].sub.4]PCFX + [[beta].sub.5]DRP +
[[beta].sub.6]YSP + [epsilon]
Subperiod 1 (1987-1992) - 245 Firms
VWRET PCTNOTE PCFF
Average 0.637 0.132 -0.131
Standard Deviation 0.383 0.45 0.343
Minimum -0.188 -1.326 -1.126
Maximum 1.854 2.605 1.527
Number of Positive Coefficients 238 *** 154 *** 72 ***
Subperiod 2 (1993-1998) - 222 Firms
VWRET PCTNOTE PCFF
Average 0.722 -0.035 -0.056
Standard Deviation 0.391 0.256 0.264
Minimum -0.204 -1.043 -1.26
Maximum 2.003 0.997 0.846
Number of Positive Coefficients 218 *** 95 ** 95 **
Subperiod 3 (1999-2004) - 298 Firms
VWRET PCTNOTE PCFF
Average 0.22 -0.058 -0.012
Standard Deviation 0.333 0.169 0.107
Minimum -0.493 -0.563 -0.327
Maximum 2.961 0.547 0.432
Number of Positive Coefficients 239 *** 109 *** 125 ***
Full Period (1987-2004) - 97 Firms
VWRET PCTNOTE PCFF
Average 0.595 -0.101 -0.019
Standard Deviation 0.274 0.139 0.082
Minimum 0.124 -0.466 -0.285
Maximum 1.444 0.277 0.274
Number of Positive Coefficients 97 *** 24 *** 34 ***
Subperiod 1 (1987-1992) - 245 Firms
PCFX DRP YSP
Average 0.581 -0.128 -0.02
Standard Deviation 0.704 0.175 0.045
Minimum -1.093 -0.969 -0.188
Maximum 4.381 0.286 0.153
Number of Positive Coefficients 197 *** 51 *** 83 ***
Subperiod 2 (1993-1998) - 222 Firms
PCFX DRP YSP
Average 0.341 -0.189 -0.007
Standard Deviation 0.496 0.261 0.044
Minimum -1.521 -2.015 -0.156
Maximum 1.564 0.904 0.341
Number of Positive Coefficients 171 *** 44 *** 88 ***
Subperiod 3 (1999-2004) - 298 Firms
PCFX DRP YSP
Average -0.388 0.011 0.013
Standard Deviation 0.54 0.097 0.036
Minimum -1.825 -0.257 -0.166
Maximum 2.311 0.401 0.184
Number of Positive Coefficients 62 *** 165 * 192 ***
Full Period (1987-2004) - 97 Firms
PCFX DRP YSP
Average 0.267 -0.02 -0.011
Standard Deviation 0.328 0.083 0.02
Minimum -0.558 -0.215 -0.093
Maximum 1.15 0.228 0.051
Number of Positive Coefficients 78 *** 41 24 ***
*** Indicates statistical significance at the 0.01 level
** Indicates statistical significance at the 0.05 level
* Indicates statistical significance at the 0.10 level
Table 7: Determinants of Risk Betas Across Bank Holding Companies
The following regression equations were estimated using Seemingly
Unrelated Regression to examine the characteristics that impact
differences in risk sensitivity across bank holding company stocks.
Companies were split into two segments based on whether their risk
beta was positive or negative in order to increase the ability to
interpret the results. The sample covers the entire 1987-2004
period and is not split into subperiods.
TNOTE = [alpha] + [[lambda].sub.1]GAP + [[lambda].sub.2]ASSETS +
[[lambda].sub.3]EQUITY + [[lambda].sub.4]INTDER + [epsilon]
FFUNDS = [alpha] + [[lambda].sub.1]GAP + [[lambda].sub.2]ASSETS +
[[lambda].sub.3]EQUITY + [[lambda].sub.4]INTDER + [epsilon]
FOREXC = [alpha] + [[lambda].sub.1]ASSETS + [[lambda].sub.2]EQUITY +
[[lambda].sub.3]FXDER + [[lambda].sub.4]FORACT + [epsilon]
DEFRISK = [alpha] + [[lambda].sub.1]ASSETS + [[lambda].sub.2]EQUITY +
[[lambda].sub.3]RSKAST + [epsilon]
YLDSPR = [alpha] + [[lambda].sub.1]GAP + [[lambda].sub.2]ASSETS +
[[lambda].sub.3]EQUITY + [epsilon]
Panel A: Results for Bank Holding Companies with Negative Risk Betas
TNOTE FFUNDS FOREXC
Intercept -0.34756 -0.44475 -0.90056
(-3.16) *** (-3.58) *** (-2.41) **
Gap -0.30785 -0.0989
(-4.70) *** (-1.49)
Assets 0.002359 0.001347 0.032888
(0.34) (0.18) (1.33)
Equity 1.983514 2.804294 -0.70903
(3.57) *** (5.18) *** (-0.49)
Interest Rate Derivatives 0.007742 0.036386
(0.32) (1.97) **
Foreign Exchange Derivatives -0.04148
(-0.51)
Foreign Assets 0.110775
(0.79)
Risk Assets
F-Value 9.49 *** 12.63 *** 1.80
Number of Firms 315 364 249
DEFRISK YLDSPR
Intercept -0.42112 -0.09324
(-2.81) *** (-5.22) ***
Gap -0.03061
(-3.08) ***
Assets 0.001592 0.002948
(0.28) (2.98) ***
Equity 1.029426 0.277403
(2.28) ** (3.34) ***
Interest Rate Derivatives
Foreign Exchange Derivatives
Foreign Assets
Risk Assets 0.165921
(0.96)
F-Value 1.85 8.56 ***
Number of Firms 383 311
Panel B: Results for Bank Holding Companies with Positive Risk Betas
TNOTE FFUNDS FOREXC
Intercept 1.268776 0.590155 2.251636
(4.98) *** (4.51) *** (5.35) ***
Gap 0.212076 0.395275
(1.80) * (5.26) ***
Assets -0.04522 -0.02350 -0.07605
(-2.97) *** (-2.77) *** (-2.80) ***
Equity -4.70231 -1.74114 -7.97302
(-5.04) *** (-2.75) *** (-5.01) ***
Interest Rate Derivatives -0.03858 -0.01613
(-1.12) (-0.52)
Foreign Exchange Derivatives 0.090935
(1.10)
Foreign Assets 0.474744
(3.43)***
Risk Assets
F-Value 9.58*** 11.78*** 11.03***
Number of Firms 268 219 334
DEFRISK YLDSPR
Intercept -0.09662 0.043572
(-0.68) (2.86) ***
Gap 0.000221
(0.02)
Assets -0.00044 -0.00107
(-0.11) (-1.23)
Equity 0.232586 0.009576
(0.71) (0.12)
Interest Rate Derivatives
Foreign Exchange Derivatives
Foreign Assets
Risk Assets 0.187973
(1.08)
F-Value 0.27 0.58
Number of Firms 200 272
*** Indicates statistical significance at the 0.01 level
** Indicates statistical significance at the 0.05 level
* Indicates statistical significance at the 0.10 level
