Testing the Relationship between a Company’s ESG Risk Rating and its Total Operating Expenses Using Hypothesis Testing

ESG stands for environmental, social, and governance, it is a quantifiable variable that measures how sustainable a business is. Environmental factors consider a company's impact on the planet, such as its carbon footprint or resource usage. Social factors assess a company's relationships with its employees, customers, and the communities in which it operates. Governance refers to the company's leadership, structure, and how well it follows ethical business practices. In the past years, the overarching goal for businesses has often been to maximize financial returns, oftentimes ignoring negative externalities created by their activities. However, with the introduction of new ratings, societal well-being, and environmental sustainability, more funds are being transferred to companies that focus on creating a more equitable, sustainable, and responsible world where financial gains are being used for positive social impact.

I first learned about this concept in my club, the Young Investors Society (YIS) when doing a stock pitch report on a company to make us more aware of sustainable investing. This rating acknowledges that companies are not just profit-making entities but have broader responsibilities to society and the environment. In recent years, major institutional investors have put more emphasis on ESGs. This puts pressure on firms to focus on non-financial aspects of their work like social responsibility and proper working conditions for their workers.

However, focusing on non-financial aspects of the business can lead to an increase in costs, as sustainable resources are more expensive and companies are forced to find more responsible ways of consuming resources which can be quite pricey. Therefore, I am interested in investigating if ESG rating can be one of the determinants of a company's costs of operation. It raises questions about the economic feasibility of adopting environmentally and socially responsible measures and how these choices impact the overall operational costs. Examining these determinants can provide insights into the complexities and trade-offs involved in balancing financial objectives with broader societal and environmental responsibilities.

With this investigation, I aim to determine if there is a significant difference between the mean costs of operation of companies with different ESG risk ratings.

To collect the company's ESG risk rating, I will use the website 'Sustainalytics' from MorningStar. Morningstar Sustainalytics' ESG risk ratings are highly reliable due to their decades of experience and widespread recognition by institutional investors. The higher the company's ESG score, the lower its risk rating. The lower the company's ESG score, the higher its risk rating. If a company has a high ESG score, it means it's performing well in terms of environmental responsibility, social relationships, and governance practices. This good performance is seen as reducing the risk for the company. Investors and analysts believe that companies with strong ESG practices are more likely to manage challenges effectively and sustain long-term success. Conversely, if a company has a low ESG score, it suggests that it may not be performing well in environmental, social, and governance aspects. This poor performance is seen as increasing the risk for the company. There may be concerns about its ability to adapt to changes, handle controversies, or maintain ethical practices, which could lead to negative impacts on its financial health. A higher ESG score is associated with a lower risk rating because investors believe that well-managed companies in these areas are better positioned for long-term success and are less likely to face significant risks.

Because Morningstar ratings are calculated yearly, I'll use the company's 2022 annual financial numbers, specifically the operating income and total revenue. Total revenue represents the total amount of money generated by a company from its primary business activities. It includes all the income the company receives from selling goods or services. This figure is calculated before deducting any expenses. Operating income is a measure of a company's profitability that focuses specifically on its core business operations. It is calculated by subtracting the operating expenses (costs directly associated with producing goods or services) from the total revenue. Operating income excludes non-operating items such as interest and taxes, providing a clearer view of how well the company is performing in its main activities. By subtracting the operating income from total revenue, we get the operating expenses. The costs associated with running the day-to-day operations of the business. This includes items such as salaries, rent, utilities, raw materials, and other expenses directly related to the company's core operations. Everything will be in US dollars and it will all be in millions.

For my sampling method, I'll be using random stratified sampling. This method involves dividing the population into distinct strata based on certain characteristics. I'll be using a random number generator (Calculator Soup) to collect 30 companies from different industries for each category, these categories will be 'low risk', 'medium risk', 'high risk', and 'severe risk'. There are \(1000+\) companies for each category and these companies are from a mix of different industries like Aerospace, Consumer Durables, Electricity, and Food Products. I didn't stick to one specific industry because each industry didn't have enough data for me to use. However, we have to keep in mind that each industry operates under unique conditions, regulations, and market dynamics. Therefore, it is challenging to isolate the impact of ESG factors on their costs of operation. Furthermore, the random stratified sampling won't be able to make sure we have an equal distribution of companies from different industries in each ESG risk category because some industries have a low ESG rating while others only have high ESG ratings.

There were a few criteria each company had to satisfy. Firstly, it had to be listed on the stock market in the USA. Publicly traded companies in the USA are required to disclose a wide range of information, including their financial statements, annual reports, and sustainability reports. This information is typically readily available to the public, making it easier to gather data and assess a company's ESG performance. Secondly, companies with high brand recognition were removed from consideration. Because of their brand name, their profitability wouldn't be affected by it. These companies have a loyal customer base and strong market presence which could make them less susceptible to profitability fluctuations due to ESG concerns. This means people will continue to buy from them, even if there are concerns about how environmentally friendly, socially responsible, or well-governed they are as businesses. So, the cost to operate these well-known companies is less likely to be affected by issues related to ESG. Some of the companies that I had to remove were Halliburton and Harley-Davidson. Additionally, companies with a total revenue above 10000 million dollars were also removed. Larger companies might have diverse operations and revenue streams. By setting a revenue threshold, the analysis can concentrate on companies of a particular size for more meaningful comparisons. If the company I got from the random number generator doesn't fit the criteria above, I'll use the random number generator again to find a different company.

After collecting the company's ESG risk rating, I used SeekingAlpha to collect the company's total revenue and operating income, I subtracted the operating income from the total revenue to get their operating expenses before taxes and interests. For example with Acadia Realty Trust, their total revenue was 294.4 and their operating income was 12.5, so their total cost of operations was 281.9. Most of the time, the income statements from seeking alpha won't give you the total operating expenses straight away, so sometimes you might have to find it manually.

My variables will be defined as follows: \(x\) is the ESG risk rating, the lower the risk, the higher their actual ESG score is. \(y\) or \(f(x)\) is the company's operating expenses.

This is an example of how the data will be collected, the full table will be in the appendix.

Before any calculations, I'll be graphing the points into a box plot using DataTab to visualise the operating expenses of a company across different ESG risk rating categories. (DataTab)

With reference to Figure 1, the boxplot for operating expenses for medium-risk and low-risk ESG is comparatively taller than the boxplot for operating expenses for severe and high-risk ESG. A taller boxplot suggests a wider range of values within the medium and low-risk ESG categories while the shorter boxplot may suggest a more consistent or narrow distribution of values within the severe and high-risk ESG categories. However, there are some outliers present in the severe and high-risk categories. We can see that the operating expenses for the low-risk category are skewed downwards or right as the 'whisker' is shorter on the lower end of the box. This can also be said about the medium-rish and the high-risk. The operating expenses for the severe risk look like it is normally distributed, the whiskers are about the same on both sides of the box and it looks symmetrical. The medians of each box plot lie inside of the boxes which indicates that there is likely to not be a difference between the four groups. Using the box plots, we can calculate the IQR (interquartile range) and the upper & lower quartile of each group. For the low-risk companies, Q1 is 1004.5 and Q3 is 3436.43 making their IQR 2431.9. For the medium-risk companies, Q1 is 713.9 and Q3 is 4728.58 making their IQR 4014.68. For the high-risk companies, Q1 is 589.1 and Q3 is 2064.07 making their IQR 1474.98. For the severe-risk companies, Q1 is 419.38 and Q3 is 1901.03 making their IQR 1481.65. Medium-risk companies exhibit the widest spread of operating expenses among the four categories. Low-risk companies have a moderate spread, while high-risk and severe-risk companies have relatively narrower spreads.

For the low-risk category, the mean is 2413.89, the median is 2204.85, and the standard deviation is 1750.8. The range is 6642.6, with a minimum of 240.4 and a maximum of 6883. For the medium-risk category, the mean is 2752.45, the median is 2152.2, and the standard deviation is 2119.46. The range is 7021.9, with a minimum of 270.1 and a maximum of 7292. For the high-risk category, the mean is 1492.72, the median is 1200.4, and the standard deviation is 1167.1. The range is 4832.5, with a minimum of 94.5 and a maximum of 4927. For the severe-risk category, the mean is 1315.73, the median is 992.35, and the standard deviation is 1275.09. The range is 5400.7, with a minimum of 36.8 and a maximum of 5437.5. From here, the mean operating expenses decrease as the ESG risk category increases, suggesting a potential negative correlation between ESG risk and the company's operating expenses. Similar to the mean, the median operating expenses also follow a decreasing trend as the ESG risk category increases. However, the standard deviation tends to decrease as ESG risk increases, suggesting more consistent operating expenses for higher-risk categories. The range also shows a decreasing trend, indicating that the spread of operating expenses narrows as the ESG risk category increases. Overall, these trends suggest a potential inverse relationship between ESG risk categories and total operating expenses. Companies with lower ESG risk categories tend to have higher mean and median operating expenses, as well as greater variability. Conversely, higher ESG risk categories are associated with lower mean and median operating expenses, along with more consistent and narrower ranges.

I decided to conduct a one-way ANOVA test because I am comparing the mean operating expenses of four different groups (low-risk, medium-risk, high-risk, and severe-risk). Analysis of Variance (ANOVA) is a statistical method used to compare the means of three or more groups to determine if there are statistically significant differences among them. ANOVA assesses whether the variability in the data is due to differences between group means rather than random variation within each group. The test works by comparing the variance between groups to the variance within groups. If the variation between groups is significantly greater than the variation within groups, it suggests that at least one group's mean is different from the others (Singh). ANOVA allows you to assess group differences more efficiently and determine if there is a statistically significant difference in operating expenses across the various risk categories. This approach can help me avoid the pitfalls of conducting multiple \(t\)-tests for all possible pairs as it would increase the chance of making Type I errors (false positives). Additionally, ANOVA allows for post-hoc testing to identify specific pairs of risk categories that exhibit significant differences.

To conduct an ANOVA test, a few assumptions have to be met. These include making sure the data has an equal or similar level of variance between each group, that the data is normally distributed, and that the data is independent. There are multiple ways to test whether the data has equal variance, one of them is Levene's test. The test begins by calculating the absolute deviations of individual data points from their respective group means. The average of these absolute deviations within each group is then compared to an overall measure of variability across all groups (DataTab). However, to keep this simple, we will just assume that there is a similar level of variance in each group. Next, the data has to be normally distributed. The Central Limit Theorem states that the distribution of the sum (or average) of a large number of independent, identically distributed random variables will be approximately normally distributed, regardless of the original distribution of the variables. The key conditions for the CLT include having a sufficiently large sample size and the random variables being independent. When sample sizes are around 30 or larger, the distribution of the sample mean tends to approach a normal distribution, even if the underlying data are not normally distributed. We can also use other methods such as Q-Q plots and the Shapiro-Wilk test (DataTab) but we will just assume that the data is normally distributed for this ANOVA test because of the CLT. Thirdly, the data must be randomly sampled from a population and they must be independent. The rating assigned to one company is not influenced by the ratings or profits of another company, therefore my data is independent. I also have used a random number generator, they are designed to exhibit statistical properties of randomness, making them suitable for data collection. Finally, our sample size is not more than \(5 \%\) of the population as there are millions of companies. (Kenton)

The data meets all the requirements and conditions to do an ANOVA test. For my one-way ANOVA test, I will be using a 0.05 significance level to check if there is a significant difference between the operating expenses of the companies from different ESG risk groups. It's called 'one-way' because it analyses the effect of a single independent variable, in this case, ESG, on a dependent variable, in this case operating expense. My null and alternative hypotheses will be as follows: \(H_{0}: \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}\) In other words, there is no difference between the mean operating expenses of the 4 ESG risk categories.
\(\mu_{1}\) is the mean operating expenses of companies in the low-risk category
\(\mu_{2}\) is the mean operating expenses of companies in the medium-risk category
\(\mu_{3}\) is the mean operating expenses of companies in the high-risk category
\(\mu_{4}\) is the mean operating expenses of companies in the severe-risk category
\(H_{1}\) : There is a significant difference between the mean operating expenses of the 4 ESG risk categories

Here are the equations I'll be using for the ANOVA test.

Where
\(F=\) Anova Coefficient
\(MSB=\) Mean sum of squares between the groups
\(MSW=\) Mean sum of squares within the groups
SST \(=\) total Sum of squares
\(n=\) The total number of samples in a population
SSW \(=\) Sum of squares within the groups
SSB \(=\) Sum of squares between the groups

To find the F statistic, we need to find the mean sum of squares within the groups and divide that by the mean sum of squares between the groups. As a result, we need to look at the variance between and within the groups. To calculate \(MSW\), sum all the values in the group \((g)\) for each number of groups \((G)\), we need to square the difference between each value and the mean of each group and divide that by \(k-1\). \(k\) is the total number of groups. This will give us 116. MSW is 14628983.98. To calculate \(MSB\), we need to take the sum of all individual values in each group \((g)\) for all groups \((G)\) and multiply the number of each group by the mean of each group minus the overall grand mean squared. Then we divide that by \(k-n\), where \(k\) is the number of groups and \(n\) is the total number of variables. This will give us 116. MSB is 2636352.27. As a result, \(F=\frac{MSW}{MSB} \approx 5.55\)

The p-value of .001 is smaller than the significance level of 0.05. This indicates that there is a statistically significant difference between the different groups Low, Med, High and Sev. In other words, the variability between the groups of ESG is significantly greater than the variability within the companies, based on the data provided. Therefore, the null hypothesis is rejected. There is a difference between the mean operating expenses of the 4 ESG risk categories

I would like to conduct a chi-squared test to determine if ESG risk ratings and the company's operating expenses are independent of each other. It examines whether ESG risk ratings have a statistically significant influence on operating expenses which is different from ANOVA as they don't capture the potential associations between ESG risk ratings and their operating expenses.

There are certain criteria for the chi-squared test for independence that the data has to meet. First of all, it has to be categorical, so I converted my data into counts and split them into 12 categories. Using the histogram, I categorized the operating expenses data into three categories for each ESG risk rating: "less than 1000," "1000 to 2999," and "3000 and above.". I used a histogram to be able to visualise the spread of data. The histogram analysis of operating expense values reveals a left-skewed distribution, indicating a concentration of companies with lower operating expenses. Because it is left-skewed, it might affect the distribution of expected frequencies, especially if the skewness is pronounced. If the observed frequencies deviate significantly from the expected frequencies, it may be challenging to discern whether the deviation is due to the association between operating expense and ESG risk ratings or if it's influenced by the left-skewed nature of the data. Notably, there is a distinct cluster below 1000, suggesting a significant portion of companies fall within this range. The next cluster falls from 1000 to 3000 and the rest of the operating expenses are spread out after 3000. The categorization of operating expenses into three groups, "Less than 1000," "1000 to 2999," and "3000 and above," aligns well with the observed clusters. This categorization is crucial as it allows me to transform continuous data into discrete data. This satisfies only having two categorical variables, ESG risk rating and operating expenses and it also satisfies the criteria for having two or more categories for each variable. In addition to that, they have to be mutually exclusive, so one company shouldn't be able to fit into two categories. There should also be no relationship between the subjects in each group. To ensure this, the companies I picked were independent of each other. The companies I used for this test aren't related in any way, there are no 'parent' or 'subsidy' companies. They represent a form of business ownership and control in which one company (the parent) owns a significant stake in, or complete control over, another company (the subsidiary). Furthermore, the categorical variables are not 'paired' in any way. Finally, the expected frequency for each cell has to be at least 5. This is because the sample for a chi-square test needs to be large enough for chi-square distribution (Chi-Square Distribution).

With this in mind, I constructed both an observed values table and an expected values table to make sure they fit the criteria. Using the same data as the ANOVA test, I counted the companies from each ESG risk rating that fit into each profit level and put them in my observed values table as you can see below.

To get the expected value of this table, I multiplied the row total by the column total and divided by the sample size (120). For example, the expected value of companies with a low ESG risk rating and an operating expense of less than 1000 is 11.25.
\(E(X)=\frac{30 \cdot 45}{120}=11.25\)