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Hypothesis Testing on Representation of Females in the Board of Directors

Intermediate Quantitative Methods for Accounting ACCT5008

There is a global trend by policy makers and regulators to increase women on corporate boards. Some European countries have sought to implement gender quotas, others use networking and mentoring programs to quicken women’s rise to the top. For example, there is currently mandatory gender quota of 40% in Norway and Spain, 50% in France and penalties will be imposed for non-compliance. There is no equivalent legislative requirement in Australia but it shows a rapid voluntary increase in female directors on Australian corporate boards. According to a recent survey by the Australian Institute of Company Directors (AICD), the percentage of female directorship on the boards of Top 200 firms listed on the Australian Securities Exchange (ASX) has increased from 8.3% in 2009 to 28.2% in 2017. The AICD, therefore, wants to investigate the benefits of having gender-diversity boards so that it can make recommendations to Australian regulatory bodies.

You, as an analyst of market research division of the AICD, need to report to the AICD board of directors to see whether female participation in company boards is perceived to be valuable. You choose two measures of company profitability to investigate. The first one is return on asset (ROA). The ROA figure gives investors an idea of how effectively the company is converting the money it has to invest into net income. The higher the ROA number, the better the firm performance, because the company is earning more money on less investment. The second measure of profitability is the annual company stock market return which indicates how well the company stock performs in a given year

You start with the top 500 companies listed on the ASX as at the end of financial year 2018 (June 2018). Companies in the ASX are grouped according to their industry sectors. There are 10 industry sectors within the Australian market. They are Consumer Discretionary, Consumer Staples, Energy, Financials, Health Care, Industrials, Information Technology, Materials, Telecommunication Services, and Utilities. You choose to concentrate on three following industry groups, namely Consumer Staples, Energy and Health Care. You collected the required data for 100 companies in each of these 3 industry sectors. The board of directors with women representation is referred as a gender-diversity board. Oppositely, the board of directors with

no women representation is referred as a non-gender diversity board. Data are stored in the Excel file (ACCT5008_BR_2018_s2_datafile.xlxs) in the following ways:

Column A: Firm ID • To describe the ID of each firm in the sample, ranging from Firm 1 to Firm 300.

Column B: ROA • Return on assets (ROA) for each firm in the year 2018. • ROA is calculated as net income divided by total assets. 

Net Income for 2018/2018 Total Assets x 100

Column C: Stock market return • Annual return on company stock price in the year 2018. • The stock market return is calculated as the percentage change in company share price between 2018 and 2017

Year end share price 2018 − Year end share price 2017 /Year end share price 2017 x 100

The stock market return figure indicates the movement in company share price over the financial year 2017-2018.

Column B: Industry group • There are 3 industry groups in the sample. They are Consumer Staples, Energy and Health Care

o 1 = if a company belongs to the Consumer Staples industry sector 

o 2= if a company belongs to the Energy industry sector 

o 3 = if a company belongs to the Health Care industry sector

Column D: Gender-diversity board

o Indicate if the company board of directors has any female director. 

o Y = there is at least one female director on the board 

o N = there is no female representation on the board (non-gender diversity board)

You need to address the following four questions as part of your report to the AICD board of directors. 1. Is the representation of female directors on the board dependent on the type of industry sectors? 2. Is there any difference in stock market returns among the 3 industry sectors, that is, Consumer Staples, Energy and Health Care? 3. Do companies with non-gender diversity boards underperform (i.e. have lower stock returns), compared to companies with gender diversity boards in stock market returns? 4. Do companies with gender diversity boards outperform (i.e. have higher ROA), compared to companies with non-gender diversity boards in ROA?



Answer

Introduction

The following assignment discusses hypothesis testing in a provided dataset. The dataset provided discusses representation of females in the board of directors of organizations. A total of 300 firms have been considered that are spread across three industry sectors, namely, Consumer Staples industry, Energy Industry and Healthcare industry. Besides representation of females, the dataset also provides the firm’s return on assets as well as stock market returns. The report will look to analyse impact on these returns vis-à-vis presence of females. This will be done through hypothesis testing method.

The first step is to analyse whether data is normally distributed or not. For this, the provided returns data was plotted on a histogram as follows:


RoA

Stock market return


The returns of individual firms are highly concentrated around 20% and do not represent a bell shaped curve. Whereas, the stock market returns can be said to represent a bell shaped curve. However, for the purpose of analysis, we will assume that both the datasets follow normal distribution.

1: Representation of females on Board of Directors

The data provided for 300 firms is divided into following three industries: Consumer Staples, Energy and HealthCare industries. The provided data was used to construct a pivot table to understand the female representation in the three industries (in absolute terms as well as percentage of total):

 Gender Diversity boardGender Diversity Board in Percentage

It can be seen that there is not much difference in the number of females in various industries. In absolute terms, number of females is around 30 in every industry group. In terms of percentage of grand total, the figure is around 10%. 

The data is such that we can use point estimator to analyse data. We can say that mean representation of females in boards is around 30% irrespective of industry group.

The limitation of this technique is that it does not account for probability distribution. 

We can also use interval estimator that provides a range rather than a point. Hence, we can say that mean representation of females in boards ranges from 30% to 33% of the total number of firms.

The limitation of this technique is that it is affected by the sample size. 

2. Stock Market Returns

In order to analyse whether stock market returns vary significantly with change in industry, ANOVA test will be conducted by grouping data for each industry and understanding if the groups vary significantly. This will be done at alpha of 0.05, 0.10 and 0.01. The hypothesis created for the purpose is:

H0: μ1 = μ= μ3

H1: μ1 ≠ μ≠ μ3

Using Anova in excel, the result is as follows:

Stock Market Returns significance level 0.05

Stock Market Returns significance level 0.01Stock Market Returns significance level 0.10

It is seen that in each case of significance levels (0.05, 0.01 and 0.10), the F-value is less than F-critical value. Hence, we are unable to reject the null hypothesis. In other words, we can conclude that there is no significant difference between the mean stock market return of various industry groups above and this is true for all three significance levels. 

3. Firm Returns with diversity vs non-diversity

Again, in order to analyse whether the stock market returns vary significantly with the board being diversified or non-diversified, we will conduct a t-test to compare the two means. For this purpose, the data will be separated out for the firms with female representation versus those with no female representation.

This will be done at alpha of 0.05, 0.10 and 0.01. The hypothesis created for the purpose is:

H0: μnds < μds

H1: μnds < μds 

The data has been separated in excel spread sheet and some basic figures are as follows:

Hypothesis for Firm Returns with diversity vs non-diversity

From above, it can be seen that the mean stock returns for the two groups varies highly (32.67 versus 4.93). However, we need to ascertain whether the difference in population means is significant at various alpha levels. The assumptions for this test include:

  1. Variances of population are unequal.
  2. Normal distribution: assumed for the two populations. 
  3. The observations are independent, that is, each subject firm has single number as stock returns in the dataset.

Now, we calculate the t-statistic as follows: statistic-hypothesized value/estimated standard error

  1. Statistic = μds - μnds= 32.67-4.93 = 27.75
  2. Hypothesized value = since we are assuming means to be same for the two groups, this value is 0
  3. Standard error = √((σ12/n1)+ (σ22/n2))

Hence, t-statistic is 7.3290

Degrees of freedom = [(σ12/n1)+ (σ22/n2)] 2 /[{(σ12/n1)2/(n1-1)}+ {(σ22/n2)2/(n2-1)}] = 179.02

Since, we have a null hypothesis that says that non-diversified firm mean is less than diversified firms; we use a one-tail test.

The corresponding p-value is 3.84 which is much larger than significance level of 0.05. Hence, we fail to reject null hypothesis. Hence, we can conclude that the non-diversified firm’s mean return is less than that of diversified firms. In other words, non-diversified firms underperform as compared to diversified firms.

The same conclusion holds true at other significance levels of 0.01 and 0.10 as p-value is very large and we will fail to reject the null hypothesis.

4. RoA with diversity vs non-diversity

Again, in order to analyse whether the RoA varies significantly with the board being diversified or non-diversified, we will conduct a t-test to compare the two means. For this purpose, the data will be separated out for the firms with female representation versus those with no female representation.

This will be done at alpha of 0.05, 0.10 and 0.01. The hypothesis created for the purpose is:

H0: μds > μnds

H1: μds > μnds 

The data has been separated in excel spread sheet and some basic figures are as follows:

mean stock returns for the two groups

From above, it can be seen that the mean stock returns for the two groups varies highly (17.45 versus 4.88). However, we need to ascertain whether the difference in population means is significant at various alpha levels. The assumptions for this test include:

  1. Variances of population are unequal.
  2. Normal distribution: assumed for the two populations. 
  3. The observations are independent, that is, each subject firm has single number as stock returns in the dataset.

Now, we calculate the t-statistic as follows: statistic-hypothesized value/estimated standard error

  1. Statistic = μds - μnds= 17.45-4.88 = 12.57
  2. Hypothesized value = since we are assuming means to be same for the two groups, this value is 0
  3. Standard error = √((σ12/n1)+ (σ22/n2))

Hence, t-statistic is 7.2375

Degrees of freedom = [(σ12/n1)+ (σ22/n2)] 2 /[{(σ12/n1)2/(n1-1)}+ {(σ22/n2)2/(n2-1)}] = 95.2

Since, we have a null hypothesis that says that diversified firm mean is greater than non-diversified firms; we use a one-tail test.

The corresponding p-value is 5.87 which is much larger than significance level of 0.05. Hence, we fail to reject null hypothesis. Hence, we can conclude that the diversified firm’s mean RoA is higher than that of non-diversified firms. In other words, diversified firms over perform as compared to non-diversified firms.

The same conclusion holds true at other significance levels of 0.01 and 0.10 as p-value is very large and we will fail to reject the null hypothesis.

Conclusion

Hence, we saw that both RoA and Stock Market Returns are positively impacted when the Board is diversified through representation of females. Further, we also saw various techniques of hypothesis testing that were used for the purpose. We also observed that each testing method is based on certain assumptions and the output may be impacted if any of the assumptions get violated.

In this case, the data set for RoA was not normally distributed; however, we still did the hypothesis testing. Hence, the results and output may be subject to difference on this account.

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