Financial Modelling and Return on Stock - Essay Example

? MN7024-Financial Modelling Executive summary This project is aimed at establishing whether there is any relationship between stock return on one hand, and beta, book-to-market ratio, size of firm, as well as different regions of the world on the other hand. The project entails plotting of dependent variable against the five independent variables and also amongst the independent variables with the aim of finding out whether any relationship exists; and if it exists, establish whether it is direct or indirect. In addition, regression analysis will be conducted to especially find out the patterns of the regression equations and the p-value. This will help support the null hypothesis that the predictors play some role in the stock return. A number of theories will be put forward to try and explain the results of the study. MN7024-Financial Modelling Introduction Return on stock is influenced by various factors, among them including the size of a firm, book-to-market ratio, and beta. In addition, different regions of the world have exhibited different patterns in regards to stock return depending on the prevailing market conditions during a particular time (Zhang, Shu and Brenner, 2010). In this project, it will be hypothesized that return on stock is subject to the size of the firm, the book-to-market ratio as well as beta; and that different regions of the world have different impacts on the stock returns, among them including America, Asia and Europe. Owing to the strong impact that 2008 financial crisis caused in the financial markets especially by exacerbating market volatility; this project will also compare the variable relationships before the crisis and after the crisis with the aim of finding out whether the crisis had caused any significant changes in the stock market dynamics. The analysis will primarily involve generation of line graphs, scatter plots, relationship tables, and use of regression analysis to compare the relationship between various variables. Analysis of regression statistics and scatter plots will be generated by SPSS while charts will be generated by Microsoft excel worksheets. The output generated from SPSS will be synthesized and presented in tables in a manner that is easy to read and understand. The dependent variable will be the return and the independent variables will include size of firm, book-to-market ratio, beta and three geographical regions including America, Asia and Europe. The three variables will be presented as dummy variables to enable multi-regression analysis. Consequently, number 1 will be assigned to the region that the sample has been obtained; and 0 will be assigned to the other regions that the sample has not been obtained. Graphical representation of data Beta and stock return Beta is used in CAPM to measure systematic risk or volatility of a particular security relative to the market as a whole (Zhang, Shu and Brenner, 2010). Therefore, the securities with higher beta have more risk than the market and many investors would not want to invest in them. However, it is widely accepted that the securities that have high return will also have a high risk. As such, from the figure 1 and 2 below, the beta is directly proportional to the stock return, meaning that as the beta increases, the return on stocks will also increase and vice versa. The essence of a higher return in the stocks with a higher beta is to compensate the investors for the higher risk they are exposed to. This relationship is not very strong where beta is very high because investors tend to accept low return from high beta considering that low beta securities require the use of leverage. From figure 2 below, the positive relationship between these two variables appears to be maintained. Figure 1: Return vs. beta before 2008 Figure 2: return vs. beta after 2008 The Book-to-market ratio versus Stock Returns Figure 3 and 4 below shows the return of stock compared with book-to-market. Studies undertaken by Fama and French (1992) revealed that book-to-market ratio is positively related with stock returns; however, other underplaying factors can lead to the opposite of this observation. As such, there are some other factors that create some negative effect when book-to-market ratio changes, hence countering its effect, among them being market leverage, which is negatively correlated with the successive stock returns. These entwined factors have made the relationship of book-to-market ration and stock returns so unpredictable, no wonder the graphs below exhibit irregularity. Figure 3: Return vs. Book-to-market ratio before 2008 Figure 1: Return vs, Book-to-market after 2008. Firm size and stock return Figure 5 below shows that the size of a firm (market capitalization) is positively correlated with stock price. These relationships show that those small firms have lower returns than big firms. This theory has been explained by the fact that size of firms is substituted by for exposure to certain risks. Chen (1988), for example, affirms that since small firms are marginally positioned, they respond more to business cycles and hence exposing them to higher risk relative to the adjusting risk premium. On average, therefore, small firms are exposed to higher risks than their larger counterparts, which results in a positive relationship between return and size of firms in the cross-section. Figure 4: Firm size vs. stock return before 2008 The Relation between Size and Beta Since the stock return is positively correlated with the firm’s size, it would be expected that firm’s size would also be positively correlated to beta, considering that beta is positively correlated with returns as it was earlier discussed. Figure 7 below confirms this relationship, though it is not very strong. Figure 5: Firm size vs. beta before 2008 Descriptive statistics Regression analysis before 2008 Below is the regression result after returns on stock (dependent variable) is run against independent variables including beta, size of the firm, market-to-book ratio; and the three regions including America Asia and Europe. Model Summary Model R R square Adjusted R square Std error of the estimate Change statistics R- square change F change Df1 Df2 Sig. f change 1 .645a .416 .385 .1627214 .416 13.391 5 94 .000 a. Predictors: (Constant), R3, beta, size, book, R1 ANOVAa Model Sum of shares Df Mean square F Sig. Regression Residual Total 1.773 2.489 4.262 5 94 99 .335 .026 13.391 .000b Coefficients Mode Unstandardized coefficient Standrdaized coefficient b Std. error beta (constant) Beta 1 Size Market-to-book ratio(MTB) America Asia -0.475 0.596 0.004312 -0.070 0.009 -0.034 .121 .008 .000 .023 .040 .041 .548 -.111 -.246 .019 -.077 a. Dependent Variable: return The Adjusted R2 measures the degree to which the model is fit for predicting the dependent variable. In this case, this value is very far from 100 % ( 38.5%), suggesting that only 38.5% of the relationship are attributable to independent variables while 61.5 is as a result of sampling error. Therefore, this model is highly erroneous and its results should not be strongly relied upon. To find out a better model that can help us determine the factors that predict returns, we shall eliminate some of the variables in a later stage and re-run the regression. Notably, the p-value is Read More