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Empirical Research Paper
The Ability of Previous Quarterly Earnings, Net Interest Margin, andAverage Assets to Predict Future Earnings of Regional Pure Play Banks
Ryan Holcomb
1. Introduction
The goal of this research paper is to establish a regression model that is capable of
forecasting quarterly earnings estimates of comparable regional pure-play banks. The
regression model is constructed around several financial and economic theories that help to
explain what impacts banks future earnings, including research from several other econometric
studies that will be discussed in sections 2 and 3. Specifically, my hypothesis is that a bank’s
previous quarter earnings, net interest margin, and average assets are jointly significant in
predicting future earnings.
Earnings=B1+B2EarningsT −1+ B3 ln Net Interest Margin+B4 ln Average Assets+Ui
H0 : B2=B3=B4=0
H1 : H0 is Not True
The model is beneficial in that it establishes a connection between the X variables and Y
outcomes, but also allows the researcher to incorporate information given by the individual firm
and the economy through the ability to vary net interest margin and average assets.
The motivation for this study is based on the field of financial analysis, where analysts
are charged with following a group of companies in a specific industry or sector. Through time
and research many analysts develop an intricate knowledge of the industry and understand that
the future success of the firm can be broken down to several key variables. The aforementioned
model is a manifestation of this reality through my own research of the regional banking sector
and represents a test of the ability of regression models to predict cash flows for not only banks
but other industries as well. The interesting part of the research project lies in the ability of
regression analysis to confirm or deny the importance of certain variables on the future
earnings of a company. Many analysts have the benefit of following industries for many years
and learning the most important variables, however, for the average investor this is not the
case. Through regression analysis, less experienced investors can test the importance of
different variables and their impact on future earnings which can aid them in investing
decisions. In my own case, I have recently participated in a valuation of the regional banking
sector in which I did not utilize a regression, but rather a multiples approach, and my interest in
this project is to determine the value of regression analysis by comparing the regression
estimates to the multiples approach estimates.
The economic theory behind the regression is based on the point that profitability for
pure-play banks rests on the net-interest margins of the firm and the growth of average assets;
net interest margin is calculated by subtracting the firm’s net interest income by its net interest
expenses and dividing by its interest-earning assets—or average assets because the banks are
pure-play means that the bank’s assets are traditional loans or other interest earning assets.
(Net Interest Income−Net Interest Expense )
(Interest Earning Assets)
Due to the fact that these banks are pure-play banks, their ability to earn more income hinges
on their ability to grow assets and the net interest margin they can attain; the higher the net
interest margin the greater the profits for the bank—this means that the amount of interest the
bank receives on its loans is growing at a higher rate than what it’s paying on its deposits.
Furthermore, there have been several econometric studies that have shown a relationship
between past earnings and future earnings. Thus, theory seems to support the hypothesis that
previous quarter earnings, net interest margin, and average assets are jointly significant in
predicting future earnings.
2. Literature Review
Catherine A. Finger in her research report, “The Ability of Earnings to Predict Future
Earnings and Cash Flow”, outlines her hypothesis that there is a connection between previous
year’s earnings and previous year’s cash flow on future earnings. She maintains that current
cash flow by itself is a better predictor of earnings for shorter time horizons and that current
cash flow combined with current earnings is a better predictor of longer horizons. Since a pure-
play bank’s operating cash-flow is essentially its earnings, my model incorporates both these
hypotheses and subsequently my model should be able to predict both short and long horizons.
My regression differs from Finger’s in that my model is industry specific and incorporates other
variables besides earnings to help explain future earnings; whereas, her model is purely focused
on cash flow and earnings (Finger 210-223). Finger’s report is in response to several other
research reports including Albrecht, Lookabill, and McKeown’s 1977 report on, “The Time-Series
Properties of Annual Earnings”. In their report the authors argue that future earnings are
uncorrelated with previous year earnings and subsequently, earnings exhibit a random walk
model (Albrecht, Lookabill, and McKeown 226-244). Once again, these articles investigate the
ability of past earnings to predict future earnings which represents a component in my
regression, however my regression is unique in that I examine other variables in my model.
The importance of net interest margin on the profitability of banks is not a new
phenomenon, but rather, something that is well known in the finance discipline. This point is
evidenced by Gerald Hanweck, professor of finance at George Mason University, and Lisa Ryu,
Senior Financial Economist for the FDIC, in their report “The Sensitivity of Bank Net Interest
Margins and Profitability to Credit, Interest-Rate, and Term-Structure Shocks Across Bank
Product Specializations”, where they note:
“Despite the rising importance of fee-based income as a proportion of total
income for many banks, net interest margins (NIM) remain one of the
principal elements of bank net cash flows and after-tax earnings. As shown
in figure 1, except for very large institutions and credit card specialists,
noninterest income s till remains a relatively small and usually more stable
component of bank earnings (Hanweck, and Ryu 3).”
The important distinction between my regression and industry knowledge about key variables is
that I utilize industry knowledge to create a model that takes into account many theories in the
hope of finding a model that is jointly significant in predicting future earnings. There is a wide
variety of analysts who place importance on different variables in determining the value of a
bank, and I am trying to create a regression that finds a good combination of these theories
which will give an accurate picture of future earnings.
3. Econometric Model
As aforementioned, the econometric model of my study is that future quarterly earnings
are a function of last quarter’s earnings, net interest margin, and average assets.
Earnings=B1+B2EarningsT −1+ B3 ln Net Interest Margin+B4 ln Average Assets+Ui
The specific hypothesis that I am testing is that these variables are jointly significant in
predicting future quarterly earnings.
H0 : B2=B3=B4=0
H1 : H0 is Not True
I have included last year’s earnings in the model as a way to account for the condition of the
bank that I am analyzing; specifically, the variable provides a way to establish how well the bank
has performed the last quarter and this provides a baseline to establish the future quarter
earnings. Similarly, I included the lagged earning variable because of the past research that was
aforementioned in section 2; this research points out that past earnings are indeed correlated
with future earnings, and as such provides a variable that is capable of forecasting future
earnings. Thus, the variable was included in the model because it provides a way to establish
the general condition of the bank and to include a variable that is correlated with future
earnings.
The net interest margin variable was included in the model because of its significance in
determining the profitability of pure-play banks. Pure-banks are aptly named because most of
their profits come from traditional banking practices such as taking in deposits and offering
loans; this compared to large national banks that take on many other services such as insurance,
brokering, and mergers and acquisitions. Net interest margin, as aforementioned, is calculated
by taking the difference between net interest income and net interest expenses and dividing it
by average interest-earning assets. The net interest income is money the bank earns on loans it
handles, and the net interest expense is the amount of money the bank pays out on deposits.
The important factor in net interest margin is the fact that there is a time period difference
between the loans they issue and the deposits they carry—loans are typically longer and can
reach 30 years in length, whereas deposits such as CDs are variable in length but usually are
between 6 months to a year—and all the while the interest rates are varying so that deposits
are being updated to new interest rates while the bank’s loans are fixed at a certain interest
rate. Thus, the important variable in determining profitability is measuring the difference
between what the bank is paying out and what it is taking in, and this measure is the net
interest margin.
The asset variable was included in the model because asset growth is usually associated
with increased earnings. To determine the profits of a pure-play bank we take the average
assets and multiply this by the net interest margin; thus, the regression model incorporates
both the net interest margin and the estimated average assets the bank will have the following
quarter. The main assets of a pure-play bank are its loans and thus, as the bank increases its
loans it usually increases its earnings. An important characteristic of this variable in the model
is that it allows the analyst to vary asset growth based on industry trends and management
guidance which corresponds with a certain growth in earnings.
4. Data
The data I gathered for the regression was quarterly data based on the last 11 quarters
dating back to the second quarter of 2009. I wanted to use data sets that reflected the recovery
since the financial crisis began in 2007 and, based on some opinions, ended in the second
quarter of 2009. Based on my previous valuation of the sector, I included in my regression data
nine publicly listed regional banks which include First Midwest Bank (FMBI), Umpqua Bank
(UMPQ), MB Financial Bank (MBFI), The Privatebank and Trust Company (PVTB), National Penn
Bank (NPBC), Citizens Bank (CRBC), Banner Bank (BANR), Columbia State Bank (COLB), Sterling
Savings Bank (STSA). My original valuation was for Sterling Savings Bank which required a list of
comparable companies that were determined based on asset size, portfolio similarity, regional
growth, and capital ratings.
The earnings and asset data are from the SEC website where publicly listed companies
are required by law to submit quarterly and annual financial data (" EDGAR "). The net interest
margin data was found on the FDIC website where banks are required to provide additional
information regarding financial performance in uniform bank performance reports (“UBPR”). In
an effort to find the best regression model to predict future earnings, I also ran test regressions
using data on tier one capital levels which can be found in the uniform bank performance
reports and on GDP quarterly growth rates which can be found on the Bureau of Economic
Analysis website ("Bureau of Economic Analysis").
Summary Statistics, using the observations 1:01 - 9:11Variable Mean Median Minimum MaximumEarnings -14620.6 6391.00 -455174. 35978.0
Lagged_Earnings
-17019.5 2875.00 -455174. 35978.0
Tier_1_Capital_
9.37636 9.52000 3.82000 12.0200
GDP_Growth_Rate
3.63636 4.00000 -1.10000 5.50000
l_Net_Interes 1.33911 1.32442 0.900161 1.96991l_AVG_Assets 15.8138 15.9571 14.8006 16.2955
Variable Std. Dev. C.V. Skewness Ex. kurtosisEarnings 68503.1 4.68539 -4.33549 21.4671
Lagged_Earnings
67971.9 3.99378 -4.34071 21.6132
Tier_1_Capital_
1.48962 0.158870 -1.16958 2.63732
GDP_Growth_Rate
1.79401 0.493352 -1.55019 1.81106
l_Net_Interes 0.168220 0.125621 0.802134 2.35641l_AVG_Assets 0.405869 0.0256654 -0.969944 -0.260367
The unit of measurement for earnings, lagged earnings, and average assets are all in U.S. dollars
where the units are presented in thousands of the actual number—meaning that each number
needs to add three 0’s to get the actual number. Net Interest margin and GDP are both units of
percent, where net interest margin is percentage return on interest bearing assets and GDP is
percentage change from the previous quarter. Tier one leverage ratio is also a percent and is
calculated as the percent of equity to average assets. Due to the model utilizing logs of average
assets and net interest margin, they are interpreted as a 1 percent change in either average
assets or net interest margin results in a (b3 or b4)/100 change in earnings. Since the U.S.
Government requires strict reporting standards for all banks operating in U.S. territory I did not
have any problems finding the data for my regression.
5. Results
Model 36: Pooled OLS, using 99 observationsIncluded 9 cross-sectional units
Time-series length = 11Dependent variable: Earnings
Coefficient Std. Error t-ratio p-valueLagged_Earnings 0.452927 0.0911163 4.9709 <0.00001 ***l_Net_Interes 62446.6 32464.2 1.9236 0.05737 *l_AVG_Assets -5723.76 2796.43 -2.0468 0.04341 **
Mean dependent var -14620.58 S.D. dependent var 68503.10Sum squared resid 3.33e+11 S.E. of regression 58853.42R-squared 0.308759 Adjusted R-squared 0.294358F(3, 96) 14.29355 P-value(F) 8.98e-08Log-likelihood -1226.249 Akaike criterion 2458.499Schwarz criterion 2466.284 Hannan-Quinn 2461.649rho 0.039826 Durbin-Watson 1.863716
In analyzing the effect of the previous quarter’s earnings on the succeeding quarter’s
earnings, the regression states that, on average holding all else constant, a one dollar increase
in the previous quarter’s earnings results in a $0.45 increase in the firm’s future earnings. The
log of net interest margin states that, on average holding all else equal, a 1% increase in net
interest margin results in a $624,466 increase in the succeeding quarter’s earnings— this
number is calculated by dividing the coefficient of net interest margin by 100 and then
multiplying it by a 1000 to account for the fact that earnings are in terms of thousands. The log
of average assets states that, on average holding all else equal, a 1% increase in average assets
will result in a $-57,237.6 decrease in the succeeding quarter’s earnings—this number is
calculated once again by dividing the coefficient of average assets by 100 and then multiplying
by 1000.
62446.6100
=624.466∗1000=$ 624,466
−5723.76100
=−57.2376∗1000=$−57,237.6
In interpreting the results of the regression, I first analyzed the lagged earnings coefficient and
the results matched my expectation of a positive correlation of the previous quarter earnings
with future earnings; specifically, an increase in the previous quarter’s earnings results in an
increase in the succeeding quarter’s earnings. This follows the expected results outlined in
Finger’s analysis and confirms intuition that greater earnings last quarter results in more
earnings next quarter. Similarly, the variable is shown to be individually significant for a two
tailed test at a 95 percent confidence level.
Null Hypothesis H 0:b2=0
Alternative Hypothesis H 1:b2 ≠ 0
T−Statistic=4.971 ;T−Critical=1.980
4.971>1.980 Reject the Null Hypothesis
Due to the fact that the t-statistic is greater than the t-critical value, we reject the null
hypothesis and conclude that the variable is statistically relevant.
The log of net interest margin coefficient also confirms my expectations of a positive
relationship. As a bank’s net interest margin increases the greater the divide between net
interest income and net interest expense becomes and thus, as this ratio increases, we would
expect greater earnings. This coefficient is also found to be individually significant for a one
tailed test at a 95 percent confidence level.
Null Hypothesis H 0:b3≤ 0
Alternative Hypothesis H 1:b3>0
T−Statistic=1.924 ;T−Critical=1.658
1.924>1.658 Reject the Null Hypothesis
Due to the fact that the t-statistic is greater than the t-critical value, we reject the null
hypothesis and conclude that the net interest margin coefficient is statistically relevant.
In analyzing the log of average assets there appears to be a divergence from expectation
in terms of a negative relationship; this at first appears to be a misstep in the model, however,
after reviewing the data this appears to be the correct correlation. Specifically, during the
financial crisis many banks were carrying a lot of non-performing assets which they
subsequently wrote-off from their balance sheets, and as they wrote off the assets they became
more profitable. Thus, the model is correctly identifying that as assets decreased during this
time period the banks became more profitable. Under normal conditions we would expect to
see a positive relationship between asset growth and earnings; this is due to the notion that
companies undertake positive net present value projects and as they grow they should become
more profitable. As the model is updated in future years I fully expect it to incorporate a
positive relationship between asset growth and increased profitability. This coefficient was also
found to be individually significant for a two-tailed test at a 95 percent confidence level.
Null Hypothesis H 0:b4=0
Alternative Hypothesis H 1:b4 ≠ 0
T−Statistic=−2.047 ;T−Critical=1.980
−2.047>−1.980 Reject the Null Hypothesis
Due to the fact that the t-statistic is greater than the t-critical value, we reject the null
hypothesis and conclude that the variable is statistically relevant.
The goal of this regression was to create a model that was jointly significant in predicting
the future earnings of regional pure-play banks and based on the F-test this goal was
accomplished.
Null Hypothesis H0 : B2=B3=B4=0
Alternative Hypothesis H1 : H0 is Not True
F−Stat istic=14.29355 ; F−Critical=2.68
14.29355>2.68 Reject the null hypothesis
Due to the fact that the f-statistic is greater than the f-critical value, we reject the null
hypothesis and conclude that the model is jointly significant. This result was not a surprise to
me as I have already analyzed and studied the regional banking sector and I knew that these
variables were the most important for determining the profitability of pure-play banks. The one
thing that was disheartening was the low r-squared value; however, there are many things that
can affect the profitability of a bank and to include all of them in the model would be
unrealistic. The take away is that I believe I have a very realistic model that would be fairly
accurate at determining future earnings.
0
2e-006
4e-006
6e-006
8e-006
1e-005
1.2e-005
-500000 -400000 -300000 -200000 -100000 0 100000
Densi
ty
uhat46
uhat46N(-20.587,58853)
Test statistic for normality:
Chi-square(2) = 303.203 [0.0000]
The first test that I ran to check that my model followed the Classic Linear Regression
Model (CLRM) assumptions and is a Best Linear Unbiased Estimator (BLUE) was the test of
normality, to make sure that my error terms were normally distributed.
Null Hypothesis: H 0 : Error Terms are Normally Distributed
Alternative Hypothesis : H 0is false
Test Statistic=303.203
Chi−Squared Critical=59.1963
303.203>59.1963 Reject the Null Hypothesis
Based on the test of normality we reject the null hypothesis and conclude that the error terms
are not normally distributed. This finding violates a CLRM assumption that the error terms are
normally distributed; fortunately though this does not mean that my regression is not BLUE.
This is due to the fact that if the error terms are not normally distributed then the parameters
may not be normally distributed; thus, my hypothesis tests may be unreliable. However, the
model is still BLUE and thus, it should still provide reliable estimates.
The next test I ran was the AIC and SC tests to examine whether a lin-log model was
better than a linear form. The results were really close, where I decided to rely on the fact that
the r-squared and individual significance of the variables increased under the lin-log model,
thus I would use the lin-log form. I also analyzed the graphs of each variable against Y, however,
there were no definitive patterns to the data.
Model 48: Pooled OLS, using 99 observations
Included 9 cross-sectional unitsTime-series length = 11
Dependent variable: Earnings
Coefficient Std. Error t-ratio p-valueLagged_Earnings 0.452927 0.0911163 4.9709 <0.00001 ***l_Net_Interes 62446.6 32464.2 1.9236 0.05737 *l_AVG_Assets -5723.76 2796.43 -2.0468 0.04341 **
Mean dependent var -14620.58 S.D. dependent var 68503.10Sum squared resid 3.33e+11 S.E. of regression 58853.42R-squared 0.308759 Adjusted R-squared 0.294358F(3, 96) 14.29355 P-value(F) 8.98e-08Log-likelihood -1226.249 Akaike criterion 2458.499Schwarz criterion 2466.284 Hannan-Quinn 2461.649rho 0.039826 Durbin-Watson 1.863716
Model 49: Pooled OLS, using 99 observations
Included 9 cross-sectional unitsTime-series length = 11
Dependent variable: Earnings
Coefficient Std. Error t-ratio p-valueLagged_Earnings 0.470373 0.0898422 5.2355 <0.00001 ***Net_Interest_Ma 4778.55 3516.19 1.3590 0.17733AVG_Assets -0.00311653 0.00169702 -1.8365 0.06938 *
Mean dependent var -14620.58 S.D. dependent var 68503.10Sum squared resid 3.36e+11 S.E. of regression 59128.42R-squared 0.302284 Adjusted R-squared 0.287748F(3, 96) 13.86395 P-value(F) 1.39e-07Log-likelihood -1226.711 Akaike criterion 2459.422Schwarz criterion 2467.207 Hannan-Quinn 2462.572rho 0.040031 Durbin-Watson 1.867537
To check the functional form of the model I utilized the Ramsey reset test; based on the
observations below the squares and cubes model is statistically significant at 95 percent
confidence level, however, it is not significant at a 99 percent confidence level. I utilized the 99
percent confidence interval because I feel that the lin-log model better represents the data and
if I were going to change the functional form of my model I want the suggested change to be
absolutely positive of the effectiveness of the change. Thus, based on a 99 percent confidence
level I retained the lin-log functional form.
RESET test for specification (squares and cubes)Test statistic: F = 2.704172,with p-value = P(F(2,94) > 2.70417) = 0.0721
RESET test for specification (squares only)Test statistic: F = 0.020194,with p-value = P(F(1,95) > 0.0201941) = 0.887
RESET test for specification (cubes only)Test statistic: F = 0.580199,
with p-value = P(F(1,95) > 0.580199) = 0.448
In interpreting the validity of the regression I performed some tests to check for
multicollinearity. The first test that I performed was a pairwise test between explanatory
variables.
Correlation coefficients, using the observations 1:01 - 9:115% critical value (two-tailed) = 0.1975 for n = 99
Lagged_Earnings
l_Net_Interes
l_AVG_Assets
GDP_Growth_Rate
Tier_1_Capital_
1.0000 0.2846 -0.1657 -0.1194 0.5794 Lagged_Earnings
1.0000 -0.5925 0.2107 0.6042 l_Net_Interes
1.0000 0.0193 -0.5722 l_AVG_Assets
1.0000 0.0213 GDP_Growth_Rate
1.0000 Tier_1_Capital_
The results from the pairwise test show that average assets and net interest margin have some
correlation between them which may be some cause for concern. Also, tier one capital was
highly correlated with several of the other explanatory variables. The next test I performed was
an auxiliary test to further determine the extent of multicollinearity.
Model 38: Pooled OLS, using 99 observationsIncluded 9 cross-sectional units
Time-series length = 11Dependent variable: l_Net_Interes
Coefficient Std. Error t-ratio p-valueLagged_Earnings 7.76879e-07 2.7384e-07 2.8370 0.00555 ***l_AVG_Assets 0.0853144 0.00120719 70.6716 <0.00001 ***
Mean dependent var 1.339114 S.D. dependent var 0.168220Sum squared resid 3.286502 S.E. of regression 0.184069R-squared 0.981772 Adjusted R-squared 0.981584F(2, 97) 2612.288 P-value(F) 4.42e-85Log-likelihood 28.08725 Akaike criterion -52.17449Schwarz criterion -46.98425 Hannan-Quinn -50.07451rho 0.877714 Durbin-Watson 0.239597
Model 39: Pooled OLS, using 99 observationsIncluded 9 cross-sectional units
Time-series length = 11Dependent variable: Lagged_Earnings
Coefficient Std. Error t-ratio p-valuel_AVG_Assets -9423.66 2965.64 -3.1776 0.00199 ***l_Net_Interes 98621.4 34762.7 2.8370 0.00555 ***
Mean dependent var -17019.45 S.D. dependent var 67971.92Sum squared resid 4.17e+11 S.E. of regression 65582.81R-squared 0.133444 Adjusted R-squared 0.124510F(2, 97) 7.468680 P-value(F) 0.000962Log-likelihood -1237.480 Akaike criterion 2478.961Schwarz criterion 2484.151 Hannan-Quinn 2481.061rho 0.433457 Durbin-Watson 1.110663
Model 40: Pooled OLS, using 99 observationsIncluded 9 cross-sectional units
Time-series length = 11Dependent variable: l_AVG_Assets
Coefficient Std. Error t-ratio p-valuel_Net_Interes 11.498 0.162697 70.6716 <0.00001 ***
Lagged_Earnings -1.00047e-05 3.14849e-06 -3.1776 0.00199 ***
Mean dependent var 15.81383 S.D. dependent var 0.405869Sum squared resid 442.9307 S.E. of regression 2.136889R-squared 0.982121 Adjusted R-squared 0.981937F(2, 97) 2664.180 P-value(F) 1.73e-85Log-likelihood -214.6404 Akaike criterion 433.2809Schwarz criterion 438.4711 Hannan-Quinn 435.3809rho 0.854732 Durbin-Watson 0.256332
The auxiliary regressions shown above confirm that there is a multicollinearity problem
between average assets and net interest margin due to the extremely high r-squared values; the
r-squared values show how much of the variation in Y is explained by the model, and when we
perform the auxiliary regression we want the variation explained to be very minimal. If the
dependent variables are collinear with each other, then this violates the Classic Linear
Regression Model (CLRM) assumptions and fails to be Best Linear Unbiased Estimator (BLUE).
VIF=1
(1−.982121 )=55.93
55.93>5Conclude there is multicollinearity
To try to correct the model I tried several fixes including dropping average assets from the
model; however, this resulted in a lower r-squared value and the sign on net interest margin
was wrong.
Model 41: Pooled OLS, using 99 observationsIncluded 9 cross-sectional units
Time-series length = 11Dependent variable: Earnings
Coefficient Std. Error t-ratio p-valuel_Net_Interes -3365.44 4554.01 -0.7390 0.46169Lagged_Earnings 0.510192 0.0881288 5.7892 <0.00001 ***
Mean dependent var -14620.58 S.D. dependent var 68503.10Sum squared resid 3.47e+11 S.E. of regression 59813.17R-squared 0.278593 Adjusted R-squared 0.271156F(2, 97) 18.72976 P-value(F) 1.32e-07Log-likelihood -1228.364 Akaike criterion 2460.728Schwarz criterion 2465.918 Hannan-Quinn 2462.828rho 0.033911 Durbin-Watson 1.883325
Next I tried to replace average assets with a similar variable—GDP quarterly change— which
should mimic average assets in the sense that as GDP increases so should the assets of the
bank. However, this also decreased the r-squared value and net interest margin had the wrong
sign.
Model 42: Pooled OLS, using 99 observationsIncluded 9 cross-sectional units
Time-series length = 11Dependent variable: Earnings
Coefficient Std. Error t-ratio p-valuel_Net_Interes -14554.7 10345.7 -1.4068 0.16271Lagged_Earnings 0.531302 0.089657 5.9259 <0.00001 ***GDP_Growth_Rate
4215.23 3501.48 1.2038 0.23161
Mean dependent var -14620.58 S.D. dependent var 68503.10Sum squared resid 3.42e+11 S.E. of regression 59675.15R-squared 0.289322 Adjusted R-squared 0.274516F(3, 96) 13.02742 P-value(F) 3.30e-07Log-likelihood -1227.622 Akaike criterion 2461.244Schwarz criterion 2469.030 Hannan-Quinn 2464.394rho -0.004167 Durbin-Watson 1.967984
In the end I decided to leave both variables in the model because theory states that it should be
in the model. The consequences of leaving both variables in the model are that my regression is
no longer minimum variance and that I might have insignificant t-ratios; however, my estimators
are still unbiased and I still have a jointly significant model that is still capable of forecasting.
The next step in my regression was to test for heteroskedasticity and I utilized White’s
General Heteroskedasticity Test. I also graphed my residuals against my explanatory variables
and did not see any patterns. However, it was hard to determine definitively.
White's test for heteroskedasticityOLS, using 99 observationsDependent variable: uhat^2
coefficient std. error t-ratio p-value ----------------------------------------------------------------------- Lagged_Earnings -1.85724e+06 5.58768e+06 -0.3324 0.7404 l_Net_Interes 7.98169e+011 8.04721e+011 0.9919 0.3239 l_AVG_Assets -7.43743e+010 7.30595e+010 -1.018 0.3114 sq_Lagged_Ear -0.255329 0.269383 -0.9478 0.3458 X1_X2 315791 579132 0.5453 0.5869 X1_X3 85613.9 326219 0.2624 0.7936 sq_l_Net_Inte -3.12691e+010 5.73187e+010 -0.5455 0.5867 X2_X3 -4.57842e+010 4.32055e+010 -1.060 0.2921 sq_l_AVG_Asse 4.53392e+09 4.27631e+09 1.060 0.2919
Warning: data matrix close to singularity!
Unadjusted R-squared = 0.096162
Test statistic: TR^2 = 9.520080,with p-value = P(Chi-square(8) > 9.520080) = 0.300337
Null Hypothesis: H 0=Homoskedasticity
Alternative Hypothesis : H 1=H 0is false
Test−Statistic=9.520080 ;Chi−Squared Critical=67.3276
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67.3276>9.520080 Fail ¿ Reject the null hypothesis
Based on White’s General Heteroskedasticity Test, the chi-squared critical value is greater than
the test statistic, thus, we fail to reject the null hypothesis and conclude that there is no
heteroskedasticity based on a 95 percent confidence level.
The next step in my regression was to test for autocorrelation or that observations of my
error term are correlated with each other over time and space. In plotting the residuals against
time, I notice that there may be some correlation between my error terms possibly negative;
however, when looking at a graph with last period residuals on the x-axis and current residuals
on the y-axis, it looks like there might be positive autocorrelation.
To determine definitively if the model suffers from autocorrelation I utilized the runs test; I used
this test as opposed to the popular Durbin-Watson test because my model includes a lagged
variable which the Durbin-Watson test does not allow.
N=99 ; N 1=68 ; N 2=31 ; K=17
Mean=( 2∗68∗3199 )+1=43.58585859
2∗68∗31 (2∗68∗31−99 )
992 (99−1 )=18.07111727
Variance=¿
43.59 ± 1.96∗√18.07=(35.26,51.92)Confidence Interval=¿
H 0:The residuals are random
H 1:Otherwise
Due to the fact that the number of runs is not included in the confidence interval we reject the
null hypothesis and conclude that the residuals are not random and there is autocorrelation. To
solve this problem I used robust standard errors, which corrects the standard errors, but leaves
the coefficients the same.
Time-series length = 11Dependent variable: EarningsRobust (HAC) standard errors
Coefficient Std. Error t-ratio p-valueLagged_Earnings 0.452927 0.0725466 6.2433 <0.00001 ***l_Net_Interes 62446.6 31864.1 1.9598 0.05292 *l_AVG_Assets -5723.76 2878.92 -1.9882 0.04964 **
Mean dependent var -14620.58 S.D. dependent var 68503.10Sum squared resid 3.33e+11 S.E. of regression 58853.42R-squared 0.308759 Adjusted R-squared 0.294358F(3, 96) 14.29355 P-value(F) 8.98e-08Log-likelihood -1226.249 Akaike criterion 2458.499Schwarz criterion 2466.284 Hannan-Quinn 2461.649rho 0.039826 Durbin-Watson 1.863716
6. Conclusion
The goal of this regression analysis was to come with a model that was capable of
providing estimates of future earnings for regional pure-play banks and based on my analysis I
would conclude that I have a capable working model. Based on the findings of the model, on
average holding all else equal earnings should increase by $0.45 for every one dollar increase in
previous quarter earnings. Furthermore, on average holding all else equal, a one percent
increase in net interest margin results in a $624,466 increase in earnings. Finally, on average
holding all else equal, a one percent increase in average assets results in a decrease in earnings
of $-57,237.6.
Now that I have a working model the goal of future research is to continue updating and
testing different variables to create the best fitting regression possible. Similarly, the goal of
future research is to create regressions for different industries and sectors that can aid in
predicting future earnings for a multitude of investment opportunities. The process of building
a regression not only helps in determining future earnings but also allows the researcher to test
different theories on the most important variables. Thus, the greatest benefit of the models is
finding out which variables have the greatest impact on future earnings.
Bibliography
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Earn
ings
l_Net_Interes
Earnings versus l_Net_Interes (with least squares fit)
Y = -1.80e+005 + 1.24e+005X
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ings
Lagged_Earnings
Earnings versus Lagged_Earnings (with least squares fit)
Y = -6.07e+003 + 0.502X
Albrecht, Steve, Larry Lookabill , and James McKeown. "The Time-Series Properties of Annual Earnings." Journal of Accounting Research. 15.2 (1977): 226-244. Print. <http://www.jstor.org/stable/2490350>.
Bureau of Economic Analysis. U.S. Department of Commerce, n.d. Web. 6 Mar 2012. <http://www.bea.gov/national/>.
EDGAR . SEC, n.d. Web. 6 Mar 2012. <http://www.sec.gov/edgar/searchedgar/companysearch.html>.
Finger, Catherine. "The Ability of Earnings to Predict Future Earnings and Cash Flow." Journal of Accounting Research. 32.2 (1994): 210-223. Print. <http://www.jstor.org/stable/2491282>.
Hanweck, Gerald , and Lisa Ryu. U.S. FDIC. Sensitivity of Bank Net Interest Margins and Profitability to Credit, Interest-Rate, and Term-Structure Shocks Across Bank Product Specializations. 2005. Print. <http://www.fdic.gov/bank/analytical/working/wp2005/WP2005_2.pdf>.
"UBPR Reports." . FDIC, n.d. Web. 6 Mar 2012. <https://cdr.ffiec.gov/public/ManageFacsimiles.asp&xgt;.
Appendices
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14.8 15 15.2 15.4 15.6 15.8 16 16.2
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ings
l_AVG_Assets
Earnings versus l_AVG_Assets (with least squares fit)
Y = 4.86e+005 - 3.16e+004X