Answer

Quantitative Research Methods

This framework emphasizes objective measurement and statistical analysis of data o9r manipulation of preexisting datasets in order to understand the nature of the variables or ascertain certain inferences. Increasingly, this quantitative research methods have become important for managerial strategizing in the midst of turbulent times for business. Regression analysis framework is one statistical technique that has enhanced business dynamics by enabling prediction of the future by understanding the present. ‘Weak form efficiency’ is a random walk theory degree of the efficient market hypothesis claiming that past price movements, volumes and earnings data do not affect stock prices and should not be used in prediction of future stock prices, basing on the fact that stock prices are highly unpredictable. This paper heavily delves on these two analysis frameworks, dividing the paper into two parts, while testing hypotheses and formulating models that aid in understanding the case studies presented.

Part 1: Regression Analysis

In this section, estimation of Ordinary Least Squares (OLS) regression model is done based on the dataset CEO.xlsx which contains information on chief executive officers for UK corporations in 2016. The Statistical Package for the Social Sciences (SPSS) is used to estimate the model and determine the hypothesis of variable relationship. The dependent variable is ‘Log Salary’ while the independent variables include ‘Return on Assets’, ‘firm Size’, ‘CEO Tenure’, ‘Gender of the CEO’, and ‘Origin of the CEO’. The model to be estimated is the have the form below:

𝑌𝑖=𝛼+𝛽1𝑅𝑂𝐴𝑖+𝛽2𝑆𝑖𝑧𝑒𝑖+𝛽3𝜎𝑖+𝛽4𝑐𝑒𝑜𝑡𝑒𝑛𝑖+𝛽5𝐹𝑒𝑚𝑎𝑙𝑒𝑖+𝛽6𝐹𝑜𝑟𝑒𝑖𝑔𝑛𝑖+𝜀𝑖

where: 𝑌𝑖 is the log salary for CEO i;

𝑅𝑂𝐴𝑖 is the return on assets % for firm i;

𝑆𝑖𝑧𝑒𝑖 is measured by the log of firm i’s total assets;

𝜎𝑖 is the volatility measured by the daily return standard deviation (%);

𝑐𝑒𝑜𝑡𝑒𝑛𝑖 is the years as CEO with company i;

𝐹𝑒𝑚𝑎𝑙𝑒𝑖 is a dummy variable, = 1 if CEO is female, = 0 otherwise.

𝐹𝑜𝑟𝑒𝑖𝑔𝑛𝑖 is a dummy variable, = 1 if CEO is foreign, 0 otherwise

The descriptive statistics of the variables in the model are as in the table below:

Table 1: Descriptive Statistics table.

The dataset is of a sample size of 65, meaning 65 corporations were sampled and their CEOs formed the participants in the study.  The variable for CEO’s annual compensation was slightly positively skewed, with the mean being higher than the median, this means that a large number of the CEOs making up the sample earned less than the mean of £4.96 Million per annum. Moreover, the range between the least paid and highest paid CEOs indicate possibility of outliers in the dataset. Other variables that are significantly skewed are ROA, ‘Female COE’ and ‘CEO Tenure’, which were all positively skewed. It is, therefore, notable that most of the CEOs were Male, and also that the return on assets for most companies was below 4.57%, and that most corporations in the sample had their CEOs tenures being less than 5.3 years.

Moreover, to determine the nature of the relationship between the dependent and the independent variables by use of OLS estimation, it is important to affirm linearity as a precondition. The scatter plots of each predictor variable against the dependent variable indicates linear relationship, as shown in the table of correlations below. The hypothesis tested is:

H₀: There is no linear correlation between the dependent and each independent variable (ρ=0)

H₁: There is linear correlation between the dependent and each independent variable (ρ≠0)

Table 2: Table of Correlations with ‘CEO Pay’ variable.

From the coefficients, there was significant linear relationship between the CEO Pay variable and the independent variables of the model to be estimated. Three variables, ROA, Female CEO and CEO Tenure depicted a p-value>0.05, dictating failure to reject the null hypothesis of no linear relationship. While Volatility, Foreign CE), and Firm Size are significant linear correlates of CEO Pay, with correlations of -0.378, 0.351 and 0.581 respectively. Therefore, it is also expected that the three variables will form significant predictor variables in the model for estimating CEO Pay as per the dataset with a 95% confidence level.

Table 3: Model summary table here shows certain important characteristics of the model. Collectively, the predictor variables show a strong or high degree correlation with the dependent variable. The R² value of 0.534 indicates that up to 53.4% of the variation in the estimated dependent variable (CEO Pay) is explained in the model.

Table 4: ANOVA Table. This table indicates that the regression model predicts the dependent variable significantly well. The p-value<0.05 indicates that, overall, the regression model statistically significantly predicts the outcome variable (i.e., it is a good fit for the data). Therefore, in testing the hypothesis of collective influence of the independent variables on the dependent, the null hypothesis of no influence is rejected based on the F=11.076>Fstat, p-value<0.05. Thus, it is conclusive that the predictor variables are significant collective influencers of the dependent variable (CEO Pay).

Table 5: Regression Table

The main regression model is:

CEO Pay = -3675.833 – 9.600 ROA + 1311.723 Firm Size – 118.228 Volatility + 720.019 Foreign CEO – 2893.184 Female CEO + 53.345 CEO Tenure + 2543.0457

While the independent variables are significant collective influencers of the predicted variable in the model, not all are significant. The t statistics and respective p-values indicate that ROA, Foreign CEO and CEO tenure are not significant predictors of CEO Pay in the inclusive model while Firm Size, Volatility and Female CEO are significant predictors. Moreover, Firm Size is the most important independent variable in the model, followed by Volatility, Female CEO, Foreign CEO, CEO Tenure, and ROA in respective order.

Discussion

Since it is inarguable that CEO compensation integrally influences firm performance, it is important to determine factors that should influence a company’s compensation plan for the man at the top (Sigler, 2011). Chalmers, Koh and Stapledon (2006) surmised that CEO compensation is topical and controversial and rightly receiving considerable attention from stake holders, with variance being especially on determinants of the compensation framework. This has set an argument that the compensations plans should be ad hoc rather than universal, with various companies determining their respective models of CEO compensation. In his study, Nulla (2013) concluded that CEO compensation has no relationship with the company’s ROA, a fact that is also evident in the current study. Previous research expeditions have also concluded, similar to the current finding in the study, that gender is a determinant in CEO compensation levels (Adams, et al., 2007). Various reasons have been suggested, including but not limited to traditional perceptions of the female gender. However, the current surge of feminism could be biased in explaining the real cause of the gender variable in CEO compensation determination. Past studies have also conformed the expected hypothesis that large firms pay executives more, this is largely influenced by the level of turnover, market presence, and competitive advantage among other possible factors (Frydman, & Saks, 2010).

Therefore, the current model for predicting CEO Pay is consistent with past studies and is verily replicable, as the determining variables are empirically outlined.

Weak Form Efficiency for Seagate Technology and Skywork Solution

Weak form efficiency, also known as the “random walk theory”, states that future securities’ prices are random and not influenced by past event. It is anchored on the advocacy that all current information is reflected in stock prices and past information has no relationship with current market prices. In stock market estimation, weak form efficiency is used to assert that an investor cannot use past returns to make estimations of future returns. The stock market prices of the two companies for the period beginning June 21, 2016 to June 21, 2018 is the benchmark dataset.

Table 6: Descriptive Statistics for stock markets returns for Technology and Skywork Solution.

The data for both corporations is highly skewed with significant positive skewness in both cases (mean significantly higher than the median). This case raises questions of biasness in the dataset which subjects analyses to questions of the returns for each of the companies.

 The scatter plots for the two corporations is shown below.

Fig 1: Scatter Plot for Seagate Technology’s stock market returns.

Fig 2: Scatter Plot for Skywork Solution stock market returns.

The time series of the stock market returns for the two companies compares favorably as follows:

Fig 3: Time Series of the Stock Market returns.

Fig 4: Histogram for Seagate Technology’s stock market returns

Fig 5: Histogram for Skywork Solution’s stock market returns.

Further, the autoregressive model is to be conducted on the data for each company to test the hypothesis of autocorrelation between the stock market returns and the lag variables.

H₀: There is no autocorrelation between stock return and lag-return

H₁: There is autocorrelation between return and lag-return

Table 7: Autoregression model output.

From the autoregression model analysis, the autocorrelation coefficients of 0.0017 and 0.0546 between stock returns and lag stock returns for Seagate Technology and Skywork Solution are too weak, pointing to a no-autocorrelation scenario. Consequently, the models fit are not significant (F value < F-Statistic, p-value > alpha – 0.05) for both corporations. Therefore, the null hypothesis of no autocorrelation is rejected at 95% confidence level.  Moreover, the autoregressive models are not significant in each case.

The model for Seagate is:

𝑅_𝑡 = 0.2335 + 0.0017𝑅_𝑡−1 + 2.5659

While the intercept coefficient is significant, the variable coefficient is not (p-value = 0.9693 > 0.05).

Skywork’s model is 𝑅_𝑡 = 0.1120 – 0.0546𝑅_𝑡−1 + 1.9615.

Both of the coefficients for this model are not significant, with the p-value > 0.05 for both.

Further, the fact that the R² values being insignificantly small in both cases (none of the models explains even 1% of the variation in the estimated stock market returns variable for a certain time), the prediction models are certainly weak.

Day of the Week Effect

The regressed moving average model for determining the day of the week effect is as follows:

R_t = β₁D₁ + β₂D₂ + β₃D₃ + β₄D₄ + β₅D₅

Where D_i are the dummy variables for the respective days of the week (1 in case of respective day of the week, 0 otherwise). D₁ is for Monday and D₅ for Friday.

H₀: β₁ = β₂ = β₃ = β_{4 =} β₅

H_0: At least one coefficient is different.

Table 7: Regression table for the dummy variables.

Based on the F statistics and the p-value>0.05, we fail to reject the null hypothesis. Therefore, there is no significant different in the respective coefficients of the days of the week. It is thus conclusive at 95% confidence level that there is no significant presence of day of the week effect in determining the stock returns for these two companies, based on the two-year dataset.

Discussion

The current study of each of the two companies deviates with past researches on stock market returns that have concluded that have reinforced that there is volatility in patterns across days of the week (Berument, & Kiymaz, 2001). This study concludes that there was no statistical difference in the effects of stock returns in the various days of the week. In spite of the insignificance of the effects of days of the week, the patterns indicate that stock returns were higher during the early days of the week, compared to the ending days. This fact is consistent with past researches that have asserted the insinuation from some past stock market studies. Steeley (2001) explained that the surface systematic day-of-the-week effects only visible when returns are partitioned by the direction of the market, a paradigm that resonates verily with the current study.