The Relationship between Stock and Market - Example

Analytical Methods in Economics and Finance Customer Inserts His/her Name Customer Inserts Grade Course Customer Inserts Tutor’s Name 16th May, 2011 Outline I Return of XOM and MKT II Risk premium III Descriptive statistics of monthly returns IV The CAPM model V Intercept parameter VI Hypothesis for beta VII Risk premium VIII The relationship between stock and market Reference List Return of XOM and MKT The graph below shows the fluctuations in the relationship of returns of the market and Mobil-Exxon. This means that the market and Mobil-Exxon returns have high volatility. The observations are scattered widely around the characteristic line, indicating a good deal of unsystematic risk. However, this variability can be reduced through diversification. Suppose you diversify by investing in all 6 stocks whose weighted average returns is the same as the slope of the characteristic line in graph. One can see that with reasonable diversification, the scatter of excess-return observations about the characteristic line is reduced considerably. It is not eliminated because it would take more stocks to do that. However, the scatter is much less than it is for the individual security, and this is the essence of diversification. The CAPM assumes that all risk other systematic risk has been diversified away. Stated differently, if capital markets are efficient and investors at the margin are well diversified, the important risk of a stock is its unavoidable or systematic risk. The risk of a well- diversified portfolio is a value-weighted average of the systematic risks of the stocks comprising that portfolio. Unsystematic, or diversifiable, risk plays no role (Graham, 2006; Nalin and Martha, 2004). b). Risk premium – The risk premium represents extra returns demanded by investors as compensation of the risk if the cash flow would not materialize; while the time value of money is based on the concept that investors prefer to have returns of their immediately but because they will have to wait for the returns over a period of time depending on how long the investment would take. The delay experienced for the investors to realize returns of their investment need to be compensated for the investment to be viable. The amount tied up in the investment if it is kept in a bank account or used in other way it would be earning interest(Myers, 1984). The investor should compare the returns being earned from the investment and the returns foregone such an interest and decide if it is profitable. It is determined by subtracting the risk free rate from market rate. If volatility shocks persist indefinitely, they may move the whole term structure of risk premium, and are therefore likely to have a significant impact on investment (Sharpe, 1970). The risk premium has been calculated using the following formulae; Risk premium = expected return – risk- free rate =E (RJ) – R f This formulae has been in calculating the figures in excel Therefore the premiums Microsoft, the market and free rate is shown in the excel file with a different colour from other figures. The average risk as shown from the excel output is -0.023547 or -2.35% for Microsoft and -0.029592 or -2.96% for market. c). descriptive statistics of monthly returns DIS GE GM IBM Mean 0.001379 0.001361 -0.00908 0.008332 Standard Error 0.007038 0.006087 0.011083 0.007876 Median 0.005859 -0.00472 -0.01302 0.006482 Standard Deviation 0.080866 0.069934 0.127328 0.090485 Sample Variance 0.006539 0.004891 0.016213 0.008187 Kurtosis 1.326697 1.052085 0.494691 2.007017 Skewness -0.07669 -0.00696 -0.22474 0.484854 Range 0.509247 0.427294 0.665932 0.580252 Minimum -0.26779 -0.2349 -0.38931 -0.22645 Maximum 0.241453 0.192392 0.276619 0.353799 Sum 0.181988 0.179644 -1.19876 1.099792 Count 132 132 132 132 The standard deviation measures the risk of deviation from the mean. It shows the variability of the average mean thus the risk of not getting average return. More dispersion or variability about security‘s expected return meant the security was riskier than one with less dispersion. In this case General Motors has a high variability in terms of returns followed by IBM incorporated while a GE has lowest variability. The reduction of risk of a portfolio by blending into it a security whose risk is greater than that of any of the securities held initially suggests that deducing the riskiness of a portfolio simply by knowing the riskiness of individual securities is not possible. It is vital that we also know the interactive risk between securities(Graham, 2006). The simple fact that securities carry differing degrees of expected risk leads most investors to the notion of holding more than one security at a time, in an attempt to spread risks by not putting all their eggs into one basket. Diversification of one’s holding is intended to reduce risk in an economy in which every asset’s returns are subject to some degree of uncertainty. Even the value of cash suffers from the inroads of inflation. Most investors hope that if they hold several assets, even if one goes bad, the others will provide some protection from an extreme loss (Knight and Satchell, 2002). d). The arguments are mostly right in their stand of having CAPM method effective as a means to judge the degree of profitability an investor will have when dealing with a certain stock. There are also weaknesses with the type of analysis done by some analysts in making use of the values computed for a single holding period only and basing their decision on that foundation. The CAPM method can be used in a variety of ways. The problem lies with how the analyst is using it. All in all, the paper has been very clear that CAPM is very useful when used properly in the proper context(McLaney, 2003). The risk is indeed properly calculated by CAPM method but it does not predict the future earnings perfectly simply because the future is too complex to be predicted. The CAPM method at least allows investors some degree of measurement on how to value their investments or potential investments and assist in decision making but it should not be treated as the absolute measure of value and allocation decisions(Nalin and Martha, 2004). The following formulae will be used to calculate the beta Beta = Where n is the number of observations, y is stock return and x is market return. From excel file the following table represents the information required to calculate the beta; Description xy ∑ ()2 Microsoft 0.00310 0.331499 1.129469 0.30875443 (0.331499)2 = 0.1099 GM 0.00294 0.331499 -1.198761 0.30875443 (0.331499)2 = 0.1099 BetaMSFT = = 0.0088 BetaGM = = 0.1981 The effectiveness of beta as a measure of risk and returns is good but it is limited in the sense that it incorporates only the changes in the stock price but not the risk that can be understood only from reading the financial statements from a fundamental viewpoint. Beta is one of the important indicators though of the risk and return relationship of stocks when you are just concerned with trading them and not holding them for an indefinite period of time(Pandey, 2009). The analysis of stocks and capital using standard deviation would be enhanced because the average deviation of stocks would be clear to the analysts and will provide a better understanding of the type of risk involved when dealing with a particular stock. The analyst could then perform better capital allocation decisions. e). Alpha = y- beta(x) Where y is the average return of the stock and x is the average return of the market. Alpha for MSFT = 0.008557- 0.0088(0.002511) Alpha for GM = -0.009082- 0.19(0.002511) Alpha for MSFT = 0.008535 Alpha for GM = -0.0096 The intercept parameters are not zero but this does not mean the results are not correct. The difference is associated with errors and estimation made during the calculation. f) Null hypothesis is supposed to be rejected whenever the computed value, which is the z-value, is less the critical value. The decision, in other words, is to reject a null hypothesis whenever z-value is less than the size of the test (Santa-Clara and Shu, 2006). An alternative hypothesis is, therefore, accepted whenever the size of a test is greater than a z-value. The value of beta of beta is estimated to be 1. The null and alternative hypothesis for the case is as below: H0: ß = 1 Ha: ß< 1 Where ß is the beta for Microsoft, H0: null hypothesis and Ha: alternative hypothesis Step 2: set the level of significance The level of significance is 1% Step 3: critical value at 0.05 or 95% level of significance Do not reject H0 if zcalc z crit = -2.33 Step 4: calculate the test statistics z=  z= = -9213.61 Step: 5: Comparing Since z calc > zcrit (33.74>-2.33), reject H0 Therefore, there is sufficient evidence from the sample, which suggest that the mean is less than 1. It means that we accept alternative hypothesis and reject null hypothesis at the 1% level of significance. g). The risk premium is the raw portfolio return less a risk-free return, that is,Rm – Rf, which we know is the basic reward for bearing risk(Fisher and Jordan, 2006). Risk premium = expected return- risk- free rate = (RJ) - Rf In this case 0.0321031 of 3.21%. At the rate of 2% and 7% and risk free rate of 3.21% At the rate of 2% =2% - 3.21% =-1.21% At the rate of 7% =7% - 3.21% = 3.79% (Fisher and Jordan, 2006). i). The data obtained within the time span of analysis predicts a negative predictive value, there is absolutely higher betas in this criteria that therefore, posses a lot of risks in the investments. Since the standard deviation is well above the historical total returns this shows a risky approach in the investments. However, such data should only be used as predictions and the actual facts upon which one can make concrete decision when planning and investing funds(Campbell and Thompson, 2008; Harrington, 1987). Reference List Campbell, J. & Thompson, S., 2008. “Predictive Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average?” Review of Financial Studies. Fisher, D, & Jordan, RJ 2006. Security analysis and portfolio management. New Delhi: Prentice hall of India private limited Graham, B., 2006. The intelligent investor. New York: Harper Business Essentials. Harrington, R., 1987. Modern portfolio theory. Englewood cliffs, N J: Prentice Hall, Knight, F, & Satchell, S 2002. Forecasting Volatility in Financial Markets. London: Butterworth-Heinemann. McLaney, E., 2003. Business finance: theory and practice. New York: Prentice Hall. Myers, SC 1984. Finance theory and financial strategy. The Institute of Management Sciences 14: pp: 126–137. Nalin, K, & Martha, A 2004. Real Options: Managing Strategic Investment in an Uncertain World, Boston: MIT Press. Pandey, I., 2009. Financial management. New Delhi: Vikas Publishing House PVT ltd Santa-Clara, P. & Shu Y. , 2006. “Crashes, Volatility, and the Equity Premium: Lessons from S&P 500 Options.” Review of Economics and Statistics. Sharpe, W. 1970. Portfolio Theory and Capital Markets. New York: McGraw-hill, 1970 Read More