Financial Modelling - Relationship between Market Risk and Stock Return - Example

Financial Modelling Customer Inserts His/Her Name Customer Inserts Grade Course Customer Inserts Tutor’s Name 25th August 2012 Outline I. Executive summary II. Introduction III. Methodologies (a) Graphical representation of the data and a discussion of any issues or patterns which arise from this exercise. (b) Univariate and bivariate analysis and discussion which considers the effects of the given variables on firm’s returns. (c) Multivariate analysis and associated discussion which makes use of the data shown in the Appendix. IV. Findings and conclusions V. Conclusion Executive Summary People make business decisions based on financial or business models. Businesses also rely on market decisions based in the financial or market models. Financial modelling is used in almost all forms of businesses ranging from banks and other corporations. This is because these firms prepare statements of accounts such as the profit and loss (income statement), cash flow, balance sheet and cash flow statements. The financial models are also used by businesses that trade on the stock exchange. For example, the 200 firms used in this report are listed in the stock exchange. The financial models are useful in representing a firm, project or an investment. According to CAPM model there is a linear relationship between the stock return and beta (market risk). Researches also reveal that there is a direct relationship between stock return and market capitalization (MC). Additionally, a book by Litzenberger and Ramaswamy published in 1979 reveals that there is a direct relationship between dividend yield and stock return. This discovery was made from a research done between 1936 and 1977 on various stock firms that traded in the US stock exchange markets. There is also a relationship between stock return and price-to-earnings ratio. Some experts have attributed these relationships to market inefficiency. However, other researchers say that this inefficiency can be attributed to misspecification of the pricing model. This report aims at revealing the effect that the above mentioned variables have on stock return. Graphical representation and tabular analysis have been used in the variable analysis. Additionally, the univariate, bivariate and the multivariate analysis have been used to explain the relationships between one variable and another as well as the relationship with the dependent variable (stock return). Introduction A firm’s variables can be used to explain the behaviour of a firm’s stock returns. Investwell (a large investment management firm) has been identifying how historical factors can be used to explain the future performance of firms on the stock exchange. The company provides advice and administrative services to both individuals and companies in relation to portfolio selection and specific asset purchase (stocks, bonds, etc.). However, in order for Investwell to attain its objectives it has been relying on the value investment strategies which are based on the firms’ characteristics. The disadvantage of this is that several structural changes have occurred and variables used in value investment strategies are no longer useful. This is because Investwell’s studies and several other research methods that look at stock returns predictability do not use post-crisis data. Previously, various factors have been identified as possible determinants or variables of stock returns. Such are beta (CAPM), market capitalization, dividend yield and price-to-earnings ratio. Therefore, the aim is to collect, organize, analyse, tabulate and reveal to Investwell the effects that various variables have on stock returns. For the purpose of this research variables from 200 stock firms have been collected randomly. The variables and their definitions are as follows: Return: Monthly stock return for a chosen period. Stock return can be measured by the difference between the value of a firm’s stocks and the costs of running and operating the portfolios. Beta: The asset's beta used for the analysis in this assignment is an observable variable. The term observable can mean that they have effect that they have on stock return is significant. Usually, beta is between 1 and 10. Beta can be defined as “the ratio of a given stock yield and market yield covariance to market yield variance” (Rahmani, Sheri & Tajvidi 2006, p.7). MC: Market capitalization: 1 small cap shares; 2 medium cap shares; 3 large cap shares. Market capitalization is a product of the current stock price and the outstanding shares. It can also be referred to as the value of a firm’s outstanding shares (Investinganswers: market capitalization 2012). Small, medium and large cap refers to stocks of small, medium and large companies respectively. Small cap refers to companies with less than $2 billion market capitalization, medium cap refers to companies with $2 billion to $10 billion market capitalization while large cap is identified with companies with $10 billion market capitalization or more (Investopedia: Definition of ‘Market Capitalization’ 2012). Dividend Yield: Annual dividend payments divided by market capitalization. The ability of dividend yields to forecast stock returns increases with the return limit. If the relationship between dividend yield and expected returns the variation of the stock returns to grow fast. Price-to-earnings ratio (P/E): It is obtained by dividing market value by annual earnings. The market value is obtained at the stock exchange market while the annual earnings are obtained either monthly or yearly and are published as the audited financial reports. Methodologies For the purpose of this report graphs, charts and tables have been used for representation. The graphs used are as follows: beta versus return, market capitalization versus return, dividend yield versus return and price-to-earnings ratio versus return. The tables used are for purposes of portraying the univariate, bivariate and the multiivariate analysis of data. The data used in the representation is obtained from 200 firms that participate in the stock exchange. This data is already available for use. Some of the assumptions to make upon the 200 firms used in this report are: The firms are randomly selected among the stock trading firms The firms should have been traded during the period of study Hypothesis This refers to the findings, facts or the dimensions that have been used to come up with the conclusions or the already established theories about stock return and variables. The hypothesis used in this report is as follows: Hypothesis 1: There is a direct relationship between beta (market risk) and stock return. Hypothesis 2: There is an indirect relationship between beta and market capitalization Hypothesis 3: There is an indirect relationship between market capitalization and stock return Hypothesis 4: There is a direct relationship between dividend yield and stock return Hypothesis 5: There is an indirect relationship between Price-to-earnings ratio (P/E) and stock return Findings and conclusions (a) Graphical representation of the data and a discussion of any issues or patterns which arise from this exercise. The beta of a stock measures the volatility or elasticity of an asset or a firm in relation to the overall financial market volatility. The results of the first hypothesis reveal that there is a direct relationship between stock return and beta. This means that as the level of market risk (beta) rises, the level of stock return rises and vice versa. This is also evident from the graph’s positive gradient. This gradient is refers to E (R m) - R f while the y intercept is the nominal risk-free rate in the market. However, according to an influential paper published in 1992 the positive relationship between beta and stock return is as result of negative correlation between firm size (market capitalization) and beta (Davis 2001). Some researchers also state that firms that have a beta of zero have returns that change independent of changes in the market returns. Therefore, the returns of such a firm do not change as beta changes and vice versa. A positive beta means that the firm’s returns follow the market’s returns. Therefore, the firm’s return and the market return tend to be above or below average at the same time. On the other hand a negative beta means that the firm’s returns move in the opposite direction of the market returns. The market has a beta of 1.0 and different stocks are ordered according to how much they deviate from the market beta. Therefore, the stock returns that are higher than the market returns can have a beta whose value is higher than 1.0. On the other hand a stock return that is less than the market return can have a beta whose value is less than 1.0. A beta of 2.0 means that the firm’s returns change twice as much as the overall market returns. It is also worth noting that stocks with higher betas are more volatile which means that they are more risky but they have higher returns. According to a research done on the US markets in 2005 by Spiegel and Wang firms or companies with high volatility tend to have small capitalization as compared to those with small volatility. Therefore, the small firms have higher risk (beta) than the large forms. The result of the second hypothesis between MC and beta reveal that the two variables have a negative gradient; there is a negative correlation between market capitalization and beta. Market capitalization is directly proportional to firm size. Therefore, as long as firm size and beta are negatively correlated beta and stock return remain positively correlated. The returns of the small stock firms outperform the large stock firms because the small stock firms have high volatility. Therefore, stocks of the small firms or companies perform well when the market is declining which makes them to have high returns and negative betas. Such a scenario occurs among the resource stocks. On the contrary, the stocks of the large firms can pull the market down which makes them to have negative returns and high betas. Some of the firms that tend to have this behaviour are the banks. The relationship between beta and market capitalization can also be as a result of the causality effect. Advocates of this theory state that small stocks trade more frequently making them more volatile. On the contrary, the large stocks trade less frequently making them less volatile. The results of the third hypothesis reveal that there is a negative correlation between market capitalization (MC) and stock return. This is also shown by the negative gradient. This means that firms with high market capitalization (big firms) have less stock returns than the firms with low market capitalization (small firms). The proponents of CAPM argue that since small firms have higher betas than the large firms then the small firms are likely to have higher stock returns (Davis 2001). Consideration of a firm’s market capitalization for evaluation and valuation purposes has become a standard practice. Although there might be no linear relationship between market capitalization and return the effect is still pronounced in the small firms. However, the size effect is not rampant in the US stocks but it is very rampant in the Australian stock firms. Dividend yield is obtained from a firm’s annual dividend payments and Market Capitalization. The results of the fourth hypothesis reveal that dividend yield and stock return are positively correlated. This means that the firms with high dividend yield (big firms) have higher stock returns than the firms with low dividend yield (small firms). This is also evident from the positive gradient of the graph. The big firms tend to pay more dividends than the small firms because they more earnings. Although the big firms have more shareholders than the small firms their earnings are also high making the dividend payments to rise as opposed to the small firms. From the graph above the trend line is almost horizontal meaning that the change in dividend yield is less proportional to change in stock return. Therefore, small to big changes in dividend yield have little effect on dividend yield. However, the stock returns are low in the firms with low dividend yield (small firms) and high in the big firms. Price-to-earnings ratio is very dependable in predicting stock market performance. In the chart every dot represents supposed purchase at for every firm for a given period of time. The dots on the horizontal axis represent the normalized P/E ratio for every firm at the stock market for a given period of time. The dots on the vertical axis represent the total returns for individual firms used in this report. The dots move from the points of low P/E, high return to points of high P/E, low return. The diagonal line is the trend line or line of best fit. The results of the fifth hypothesis of P/E against stock return reveal that the two variables are negatively correlated. This is also evident from the negative gradient. Big firms are likely to have a lower P/E ratio than the small firms. This is because they have higher annual returns (denominator) than the smaller firms. Therefore, the smaller the price-to-earnings ratio the higher the stock returns and vice versa. Additionally, according to studies by Basu (1977) it showed that stocks with low P/E ratios had much higher returns as compared to stocks with low P/E ratios (Davis 2001). (b) Univariate and bivariate analysis and discussion which considers the effects of the given variables on firm’s returns. Univariate data analysis is a simple form of analysing statistical or quantitative data by describing a single variable. It also involves the analysis of each variable at a time. On the other hand bivariate data analysis involves explanation, comparison and discussion of two sets of variables and how they relate to one another. Some of the means used in the univariate analysis are mean and standard deviation (Univariate analysis 2012). These measurements are used to look at the distribution, dispersion and central tendency. Distribution summarises the frequency of values for a given variable. This can be represented in graph form. On the other hand central tendency estimates the “centre” of various values. This is usually estimated by mode, mean and median. Mean is the average that is obtained by dividing the total values by the number of values; median is the exact middle figure of the values and mode is the most frequent value among ascending values. Dispersion is the spread of values. This can be measured using standard deviation and range. Range is the difference between the highest and the lowest values. Standard deviation is more accurate than range as it minimizes the existences of outliers. The table below shows the measures of dispersion and central tendencies of the 200 observations among the five variables as follows: Mean Mode Median Range Standard Deviation Return 0.05 0.0002 0.02295 0.8427 0.19 Beta 1.15 1.1368 1.16035 1.134 0.20 Market Capitalization 2.10 2 2 2 0.70 Dividend Yield 2.84 3.2885 2.9663 3.7128 0.60 Price-to-earnings ratio 1.27 N/A 1.17025 3.9896 0.67 Mean is a measure of the average data occurrences or standard deviation. On the other hand, standard deviation is a measure of spread or dispersion from the average mean. Therefore, if the standard deviation is high it means that the data points are spread out from the mean while if the standard deviation is low then the data points are close to the mean (Standard Deviation Calculator 2012). The above data can also be represented in a chart form as shown below. From the chart, the mean of the four dependent variables is represented in percentage form. Beta forms 16% of the total mean; price-to-earnings ratio forms 17%, dividend yield forms 39% while market capitalization forms 29%. Bivariate analysis is a simple form of analysis involving two variables and how they change together. This form of analysis can assist in testing association and causality or correlation. Bivariate is different from univariate analysis in that univariate analysis involves analysis of one variable. Additionally, unlike univariate analysis which is descriptive, bivariate analysis reveals the relationship between two variables by giving more details in to their relationships. From the bivariate analysis of the data as represented in the pie chart it is evident that: The beta and price- to- earnings ratio are less close to standard deviation as compared to the other variables. That means that the beta and P/E ratios of the two hundred firms are much dispersed. Therefore, they vary widely from each other. In addition it means that the there is a wide gap between the market risk and performance of the large firms. Unlike the small firms.as observed from the graphs there is a direct relationship between market risk (beta) and stock return. This means that the small firms have low returns as compared to the big firms. The table below is an example of bivariate analysis of stock return among the small, medium and the large size firms. Market Capitalization Stock return Small cap shares 35% Medium cap shares 33% Large cap shares 32% Total number of cases: 200 Missing cases: 0 The total number of firms used in the analysis is 200. Of these the number of small size firms (small cap shares) is 40, the medium size firms (medium cap shares) are 100 and the large size firms (large cap shares) are 60. The total stock return is 27.7661. The total stock return for the small size, medium size and large size firms is 9.6562, 9.1327 and 8.9772 consecutively. Additionally, the percentages of the total stock returns for small, medium and large firms to the total stock return are 35%, 33% and 32% consecutively. For the purposes of this report there are zero (0) missing cases meaning that all the firms presented have been used in the bivariate analysis. Various variables have different types of analysis that best suits them. These analyses vary according to the level of measurement of the variables of interest. (c) Multivariate analysis and associated discussion which makes use of the data shown in the Appendix. Multivariate data analysis is a statistical method that analyses data that comes from various variables. This occurs in situations where a decision involves several variables. When data is available in form of tables consisting of rows and columns it makes multivariate analysis more meaningful in information processing. Multivariate analysis techniques are useful in various fields (Multivariate Data Analysis 2012). Some of these are: Consumer research as well as market research. Various companies and businesses use market and consumer research in order to obtain data relating to consumer satisfaction. Some of the variables used to measure this satisfaction are consumption sizes and spending habits. Therefore, through consumer or market research a company or firm is able to determine the product costs, size and quantity that lead to changes in consumers’ spending habits. Various industries as a measure of quality. For example, it is used in food and beverage, pharmaceuticals and telecommunications industries among others. These industries use multivariate analysis in order to determine that effect that changes in product components has on health, cost, quality, size or even weight of a product. Process control as well as optimization: here it is used to analyse the effect that quantity of ingredients has on a products quality and quantity. The aim of this is to find out the components that result to the marginal change in the optimum weight, size or cost measurements. Therefore, multivariate analysis can compare the behaviour of one variable against another in order to determine the effect that certain changes in variables have on the production process. Some of the industries that use multivariate analysis are the production, manufacturing and telecommunications industries. In research and development: multivariate analysis can be used to compare the cost, quality, quantity, health effects of changes in product measurements. Therefore, when analysis of one component against another is done it becomes possible to determine the optimum product size, quality and other measurements. Some of the industries that use multivariate analysis are the health, food and nutrition, hotel and pharmaceutical industries among others. In this report multivariate analysis is used to determine the effect that variables like market capitalization, beta, dividend yield and price-to-earnings ratio have on stock returns. The big firms (firms with high annual returns and market share) are found to have high stock returns. On the other hand, the small firms (firms with low annual returns and market share) have low stock returns. Market capitalization also affects a firm’s stock returns. For example, firms that have high market capitalization have lower returns. This could be attributed to their smaller betas as compared to the small firms. Predictions of a firm’s returns over a long period using the current characteristics of a firm’s variables reveal that the stock turnovers are more stable. The relationship between firm characteristics and industries reveal that the stock turnovers are more stable. Financial firms are omitted in the multivariate analysis because they have high debt ratios which can distort the relationship between valuation ratios and stock. Conclusion The evidence presented from the graphs suggests that small firms have much higher risk in the stock returns than the larger firms. The effect in size is not linear in the stock market but it is much evident in the small firms. This effect also changes with time. However, these observations are not based on theories. Therefore, firm size may not necessarily be a factor that affects stock returns. For example, it has been observed that P/E ratio is a proxy factor of size and not the other way round. This is not as a result of market inefficiency but it could be due to use of inappropriate pricing models. Therefore, the market efficiency tests rely on data from firms with different sizes and these tests end up being unreliable. Klein and Bawa’s model explains the size of the firm effect on stock returns. From the findings it was found that if there is lack of sufficient information about a firm’s securities some investors tend to sell thefirm’s securities due to estimated risk. This is because the investors are uncertain about the expected returns. Consequently, the customers that differ in the level of information available tend to distribute their investments in different securities available in the market. Since the amount of information available is related to firm size, many investors desire to possess the stocks of the large firms. On the contrary very few investors desire to hold stocks of the small firms. Securities that are sought by few investors have higher risk-adjusted returns unlike those that are sought by all the investors. The findings also reveal that there is high negative correlation between a firm’s market capitalization and beta (market risk). It is also evident that the stock portfolios of small firms outdo the market while the highly volatile stocks outperform the stocks with lower volatility. Dividend yields relate to less than 5% of the variations in the monthly stock returns. However, dividend yields relate to more than 25% of the variances of two or more years of returns. From the analysis it has also been confirmed that there is a negative relationship between price-to-earnings ratio and stock returns. Therefore, big firms are likely to have a lower P/E ratio than the small firms. This is because they have higher annual returns than the smaller firms. This means that the smaller the price-to-earnings ratio the higher the stock returns and vice versa. A firm’s beta (market risk) is negatively related to the market size. Therefore, small firms have higher risk (beta) than the large forms. Stocks of small companies perform well when the market is declining which makes them to have high returns and negative betas. On the contrary, the stocks of the large firms can pull the market down which makes them to have negative returns and high betas. It is recommendable that Investwell adopts the variables and discussions availed in this paper in order to analyse stock returns. However, the company should also be on the lookout for more effective and reliable variables especially for post-crisis analysis. Reference Davis, J 2001, Explaining Stock Returns: A Literature Survey, viewed 20 August 2012, . Investinganswers: market capitalization 2012, viewed 20 August 2012, . Investopedia: Definition of ‘Market Capitalization’ 2012, viewed 20 August 2012, . Multivariate Data Analysis 2012, viewed 20 August 2012, . Rahmani, A, Sheri, S & Tajvidi, E 2006, ‘Accounting Variables, Market Variables and Stock Return in Emerging Markets: Case of Iran’, Faculty of Management & Accounting, vol. 1 no. 1, pp. 1-14. Standard Deviation Calculator 2012, viewed 20 August 2012, . Univariate analysis 2012, viewed 20 August 2012, . Read More