9 DATA ANALYSIS - COMPOSITION, STRUCTURE & RISK-TAKING

The purpose of the following section is to test the hypotheses on the chosen risk measure.

First, the four test models are presented. Then, the results of the backward elimination model (the statistical analysis chosen for this thesis) are summarized to provide an overview for the reader. Then, each variable’s impact on the model (and thus on risk-taking) is thoroughly analyzed, before a correlation analysis is conducted. Finally, all significant variables in the four respective models are presented.

9.1 Regression analysis

A linear multiple regression analysis is performed on the independent variables as described at length above (see section 6 and 8) to test the hypotheses outlined in section 5. Selecting a multiple regression approach allows for a calculation of a significance level for the degree to which one numerical value predicts the values of a separate numerical value ((Canavos, Miller 1999) and thus fits the purpose of this data analysis well. More specifically, the significance of the independent variables in relation to the dependent variable are tested via a partial F-statistic: the reason for not applying a full-fitted model (a regular multiple linear regression) is because the null hypothesis tested in such a model states that that none of the variables, combined, affect Y. These are not the null hypotheses in this paper. Instead, the null hypothesis for each variable is that one independent variable (each at a time) does not contribute to the variance of Y and thus, they are tested as individual contributors but in a combined model. The model best suited to fulfill this purpose is seen as a backward elimination (Kemp, Kemp 2004), which can be expressed in the following full model type to be tested:

1 2

0 1 2 n n ε

β β β β

Υ = +

Χ

+^…

Χ

9.2 Models for analysis

Considering the division of variables on group (board) level and the variables relating to the individual director (see section 5.1), as well as the two scenarios including/excluding employee-elected representatives (see section 6.3), four models emerge for analysis (for full regression output, see Appendix 14)

Model 1a

1 2 3 4 5 6

t INDP BRDEX GENDER MULT TENURE FINED

t INDP BRDEX GENDER MULT TENURE FINED

L/D: Is the Loan/Deposit rate

t: Year 2007

INDP: Independence “1” if independent, otherwise “0”

BRDEX: Board experience “1” if experience, otherwise “0”

GENDER: Female “1” male “0”

MULT: Number of seats “1” if ≤ three, otherwise “0”

TENURE: Number of years served on the board

FINED: Financially educated “1” if educated, otherwise “0”

BRDSIZE: Average number of seats in the board from 2003-2007 SHARES: Stock (option) incentive program “1” if given, otherwise “0”

BONUS: Bonus incentive program “1” if given, otherwise “0”

CEOvBRD CEO tenure divided average board tenure ultimo 2007

9.3 Statistical results

Through backwards elimination, the following significant models are returned³⁵:

Table 9.1 Model statistics

* = significant at the 90 % confidence level ** = significant at the 95 % level *** = significant at the 99 % level

To each variable, the prediction is stated with the F-statistic in parenthesis underneath. The higher the F-statistic, the more significant the variable. This is reflected at Prob > F, the probability that the null hypothesis holds.

Other statistical models generate R-square statistics, but these are not calculated in this particular type of test model for the variables that remain in the model. When using a stepwise regression model like the backwards elimination model, the F-statistic is the explanatory variable as F-statistics are used when including more than two variables in a model (if there are just two variables, the t-statistic is used). The excluded variables do not return a parameter estimate, but do return (low) F-statistics.

9.3 Reference categories

The reference categories describe the situation in which the significant predicting independent variables are assigned the value = 0. This situation is used as a ‘base case’ from which to

35 The model output is that commonly used for stepwise, backward elimination regressions. The standard error is not included, but is considered if important to the result. The full output is found in Appendix 14.

PARAMETER MODEL 1A MODEL 1B MODEL 2A MODEL 2B PROB A > F PROB B > F

117,96 104,09 -

-(1771,57) (392,24)

- 14,1 -

-(1,04) (10,52)

-5,11 -5,03 -

-(6,21) (4,14)

- - -

-(0,74) (0,83)

-3,59 -4 -

-(2,80) (3,21)

0,31 0,33 -

-(4,18) (3,50)

5,39 8,15 -

-(5,32) (8,20)

- - 113,68 102,59

(878,47) (258,39)

- - -

-(0,53) 0,09

- - 16,77 18,35

(5,81) (7,63)

- - 15,87 14,82

(4,48) (4,15)

- - - 4,78

0,74 (2,89)

***<.0001

*0,7685

***0,0076

**0,046

*0,0944 BONUS

***<.0001

**0,47

**0,0189

**0,0384 0,3925

**0,0412

**0,0213

***<.0001

***0,0013

**0,0423 0,3635

*0,0737

*0,0619

***0,0044

BRDSIZE SHARES

CEOvBRD FINED

***<.0001 0,306

**0,0129 0,3903

*0,0944

Intercept

Intercept INDP

BRDEX GENDER MULTDIR TENURE

describe the impact of an assigned value of the independent variable studied. Relating to the models, the reference category is not when the null hypotheses are confirmed, β = 0 rather it is when the measure of the independent variables is zero:

L/D

= α ε +

The reference variables are described from the variable’s view, thus including both model 1a and 1b on the individual level regarding the board composition and both model 2a and 2b regarding the board structure.

9.4.1 Individual level, including employee-elected representatives

The reference category for model 1a includes the following significant independent variables:

financial education, board experience, number of multiple simultaneous directorships, and number of years served on the board. When the variables are held at zero, the intercept yields a loan/deposit rate of 117.96. This translates, in model 1a, to a director without financial education, without board experience, with more than three simultaneous directorships and with zero years served on the board.

9.4.2 Individual level, excluding employee-elected representatives

The reference category for model 1b includes the following significant independent variables:

Independence, financial education, board experience, number of multiple simultaneous directorships, and number of years served on the board. When the variables are held at zero, the intercept yields a loan/deposit rate of 104.09. This translates, in model 1b, to a director who is dependent, without financial education, without board experience, with more than three simultaneous directorships and with zero years served on the board.

9.4.3 Board level, including employee-elected representatives

The reference category for model 2a includes the following significant independent variables:

bonus and shares. When the variables are held at zero, the intercept yields a loan/deposit rate of 113.68. This translates, in model 2a, to a board which has not granted the top management either of those incentives payment programs.

9.4.4 Board level, excluding employee-elected representatives

The reference category for model 2b includes the following significant independent variables:

bonus, shares and CEO/board. When the variables are held at zero, the intercept yields a

loan/deposit rate of 102.59. This translates, in model 2b, to a board which has not granted the top management either of those incentives payment programs and which has a board with (much) longer tenure than the CEO³⁶.

9.5 Results

Having established the reference categories, the analysis moves on to investigate the impact of each independent variable, assuming the rest are held constant (as in the reference category scenario) to evaluate their individual impact when assigned a value. As described in section 5, the variables have been assigned each their null hypothesis which will be either confirmed or rejected and in the latter case, if the null hypothesis can be rejected, the variable’s significance will be examined.

9.5.1 Individual independent variables

The results of the individual independent variables will be summarized one-by-one in the following:

9.5.2. Independence

In model 1a, the independence variable is excluded in the backward elimination and the null hypothesis cannot be rejected (see section 5.2.1). Thus, independence in model 1a is not a significant predictor of risk taken as measured by the loan/deposit rate.

In model 1b, the independence variable is included in the backward elimination and the null hypothesis is in this case rejected (see section 5.2.1). Hence, independence becomes a significant predictor of risk at the 95 % confidence level. More specifically, an independent board member will add 14.10 to the loan/deposit rate, all other things equal. This means that hypothesis H1 is confirmed; there is a positive relation (in model 1b) between independence and risk-taking.

9.5.3 Board experience

In model 1a, the board experience variable is included in the backward elimination and the null hypothesis is rejected (see section 5.2.2) while the alternative hypothesis H2 is also rejected, and is reversed. Thus, board experience in model 1a is a significant predictor of

36 To avoid any confusion regarding the value ”0” in a fraction: the fraction is CEO/Board, which means that either could, in theory, be zero and yield a ”0” result. However, if the board is “0”, the fraction does not compute and this value is thus not double-directional. Rather, holding the fraction at “0” is at best an approximation going towards zero, because there is always a CEO and there is always a board and both have some tenure. However, with a board of e.g. ten years mean experience and a CEO on his first day, the fraction will be infinitesimally small, approximately “0”.

taking at the 95 % confidence level, the relation is however negative. A board director with previous board experience will decrease the loan/deposit rate by -5.11, all other things equal.

In model 1b, the board experience variable is also included in the backward elimination and the null hypothesis is rejected (see section 5.2.2) while the alternative hypothesis H2 is also rejected, and is again reversed. Thus, board experience in model 1b is a significant predictor of risk-taking, too, and the exclusion of employee-elected representatives does not alter the direction of the causal relation between board experience and risk-taking. This variable is also significant at the 95 % confidence level. The degree alters slightly though, as a board director with previous board experience in model 1b will decrease the loan/deposit rate by -5.03.

9.5.4 Gender

In model 1a as well as in model 1b, gender is excluded from the backward elimination model.

The null hypothesis (see section 5.2.3) can therefore not be rejected and as a consequence, gender is not a significant predictor variable in this study.

9.5.5 Multiple directorships held by the board member

In model 1a, the multiple directorships variable is included in the backward elimination and the null hypothesis is rejected (see section 5.2.4), while the alternative hypothesis H4 is rejected and reversed. Hence, holding three or less directorships is a significant predictor of risk, though at the 90 % confidence level³⁷. The relation is negative. A board director with three or less directorships will, ceteris paribus, decrease the loan/deposit rate by -3.59 units.

In model 1b, the multiple directorships variable is included in the backward elimination and the null hypothesis is again rejected, while the alternative hypothesis H4 is rejected and reversed. As in model 1a, holding three or less directorships is a significant predictor of risk, again at the 90 % confidence level, and the relation is negative and steeper than in model 1a.

A board director with three or less directorships will decrease the loan/deposit rate by -4.00 units.

9.5.6 Tenure (time spent on the board)

In contrast to the previously examined variables, tenure is not a binomial variable, but a scaled variable.

37 The 90 % confidence level is acknowledged to be less strong than the 95 % confidence level usually used as a cut-off in studies like this. However, since the sample size is very large compared to the population (see appendix 1), the variables at 90-94,99 % are included as well, though a certain level of caution should be exercised when extrapolating to (another) general population in these variables.

In model 1a, the tenure variable is included in the backward elimination and the null hypothesis is rejected (see section 5.2.5), while the alternative hypothesis H5 is confirmed.

Hence, the years spent by a director on a board are a significant predictor of risk at the 95 % confidence level, and the relation is positive. An incremental year served on the board will increase the loan/deposit rate by 0.31 units, all other things equal.

In model 1b, the tenure variable is also included in the backward elimination and consequently, the null hypothesis is rejected and subsequently the hypothesis H5 is confirmed. At the 90 % (93.8 to be exact) level tenure is a significant predictor of risk taking behavior, the relation being positive.

9.5.7 Financial education

In model 1a, the financial education variable is left in the backward elimination model and the null hypothesis is rejected (see section 5.2.6). The alternative hypothesis H6 is confirmed and financial education emerges as a significant predictor of risk at the 95 % confidence level with a positive causal relation. A board director with financial education will increase the loan/deposit rate by 5.39.

In model 1b, the variable is again left in the backward elimination model. The null hypothesis is rejected and the alternative hypothesis H6 is confirmed, which is even at the 99 % confidence level. The relation is positive. A board director with financial education will in model 1b – without employee-elected representatives – increase the loan/deposit rate by 8.15 all other things being equal.

9.6 Board level independent variables

The following variables have been tested on the whole board, thus reducing the sample size in absolute numbers, while keeping the percentage of the total population sampled.

9.6.1 Board size

In model 2a, the board size variable is excluded in the backward elimination and the null hypothesis cannot be rejected (see section 5.3.1). Thus, board size in model 2a cannot be said to be conclusive in relation to the board’s risk-taking as measured by the loan/deposit rate.

In model 2b, the same image emerges: board size is excluded from the backward elimination model and thus, the null hypothesis still stands.

9.6.2 Stock payment / stock options

In model 2a, the stocks variable is included in the backward elimination. This rejects the null hypothesis and confirms the alternative hypothesis H8 (see section 5.3.2); the presence of

stock payment plans is a significant predictor of risk-taking in Danish banks. Stock payment plans increase the loan/deposit ratio by 16.76 and is significant at the 95 % confidence level.

In model 2b, the stocks variable is also included in the backward elimination. Again, the null hypothesis is rejected and the alternative hypothesis H8 is confirmed. In model 2b, this causal relationship is significant at the 99 % level. The presence of stock payment plans increases the loan/deposit ratio by 18.35.

9.6.3 Bonus schemes

In model 2a, the bonus variable is left in the backward elimination model. The null hypothesis is rejected; the alternative hypothesis H9 is confirmed (see section 5.3.2). Like stock options, bonus schemes are a significant predictor of risk-taking behavior, significant at the 95 % confidence level. A bonus scheme – in model 2a – increases the loan/deposit ratio by 15.87.

In model 2b, the bonus variable is also left in the backward elimination model. The null hypothesis is rejected while the alternative hypothesis H9 is confirmed. Bonus schemes in model 2b emerge as a significant predictor of risk at the 95 % confidence level and increase the loan/deposit ratio – ceteris paribus - by 14.81.

9.6.4 CEO vs. the board

In model 2a, the ratio CEO tenure vs. board tenure does not yield a significant result and is therefore excluded from the backwards elimination model. The null hypothesis (see section 5.3.3) can thus not be rejected in model 2a.

In model 2b, the CEO/board variable is left in the backward elimination model. The null hypothesis is rejected and the alternative hypothesis H10 is rejected as well, but is reversed with 90 % statistical confidence. Hence, when the CEO/board ratio increases, risk increases as well – each unit increases the loan/deposit rate by 4.78.

9.7 Correlations³⁸

In using a multiple regression method, the correlation between the independent variables can compromise the strength of the results just outlined above as predictor variables that are highly correlated will offer redundant information. In order to ensure that the results exhibit internal validity, Pearson’s correlation coefficient was tested on the significant predictor variables in all four models. See appendix for a full correlation test output.

Below is an outline of the correlation test results, which will include those variables that are significant predictor variables in the four models and which display significant correlations

38 For complete correlation output on all four models please see appendix 16

above 0.3 or below -0.3 (on a scale from -1 to +1). The value 0.3 was chosen based on graphical displays of correlations; as such no standard cut-off rule exists to determine when a predictor variable is too closely correlated to the next³⁹.

Although the general model discussion is saved for section 10, this specific part will include possible explanations for correlation and should be regarded as a brief – but consciously chosen - detour from the thesis’ outline.

9.7.1 Model 1a and 1b.

In model 1a and in model 1b as well, only the variables “board experience” and “multiple directorships” emerge as correlated with the negative coefficient of 0.58 in model 1a and -0.52 in model 1b. This negative correlation is to be expected, as the value “1” in board experience represents more experience, whereas the value “1” in “multiple directorships”

represents a director who holds three board seats or less. The correlation seems logical; those directors who are deemed “experienced” are experienced from sitting on a board (or several boards) which, ceteris paribus, increases the likelihood of being considered for other directorships. This argument is further supported by the reputation hypothesis outlined in section 5.2.4.

Moreover, model 1a includes employee-elected representatives, who in most cases hold only the directorship in the bank they are employed in and are primarily elected in their role of being employees as opposed to the outside directors. Therefore, they can gain experience through their directorship but, as the data collection shows, have much less propensity to be sitting on multiple other boards (see section 8.3.4).

It is then acknowledged that these two variables may offer some form of redundant information, as the one explains a part of what the other does as well. However, both variables are left in the models as it is the conviction that they do explain two different, clearly distinguishable characteristics of a prospective board member.

9.7.2 Model 2a and 2b

The connection between the variables “bonus” and “stocks” displays itself identically in both models as those variables are not dependent on the presence of employee-elected representatives. The correlation coefficient is 0.39 and this correlation seems logical as well:

both variables are a representation of the board’s decision to implement incentive programs for the management, only the execution and design of the incentive program differ. As

39 The appendix 15 offers scatterplots to illustrate different correlation coefficients.

described in section 8.4.2, a number of banks have both programs in order, which runs up the correlation score. Even so, the variables are kept separately in the regression models as they are not at all perfectly correlated and each on their own still hold independent, explanatory value for the 61 % that is not accounted for in the Pearson correlation analysis⁴⁰.

9.8 Full models Model 1a

1 2 3 4

t BRDEX MULT TENURE FINED

The most risk-seeking board in model 2a is that which grants share and bonus programs. In model 2b the board would additionally be one which has relatively shorter tenure compared to the CEO.

40 For complete correlation output on all four models please see appendix 16

9.10 Partial conclusion

In this section, it is found most suitable to use a graphical illustration of the results of the statistical analysis as the conclusion:

H NUMBER HYPOTHESIS H0 MODEL A H1 MODEL A H0 MODEL B H1 MODEL B

1 A positive relation between independence and risk Confirmed Rejected Rejected Confirmed 2 A positive relation between board experience and risk Rejected Reversed Rejected Reversed 3 A positive relation between women on the board and risk Confirmed Rejected Confirmed Rejected 4 A negative relation between multiple directorships and risk Rejected Reversed Rejected Reversed 5 A positive relation between tenure and risk Rejected Confirmed Rejected Confirmed 6 A positive relation between financial education and risk Rejected Confirmed Rejected Confirmed 7 A negative relation between board size and risk Confirmed Rejected Confirmed Rejected 8 A positive relation between stock option payment and risk Rejected Confirmed Rejected Confirmed 9 A positive relation between bonus payment schemes and risk Rejected Confirmed Rejected Confirmed 10 A negative relation between relatively tenured CEO's and risk Confirmed Rejected Rejected Reversed

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