the ability of previous quarterly earnings, net interest margin, and average assets to predict...

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



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


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

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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


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



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 *


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.


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


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


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.



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 ***


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.



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



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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ings

l_AVG_Assets

Earnings versus l_AVG_Assets (with least squares fit)

Y = 4.86e+005 - 3.16e+004X

the ability of previous quarterly earnings, net interest margin, and average assets to predict...

Economy & Finance

banks assets

impacts banks future

growth of average assets

regression estimates

ability of regression

assetsor average assets

banks rests

ability of regression