Analytical Methods in Economics and Finance - 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 From the graph shown below, it can be noted that the data for the two variables are scattered with some outliers. The fluctuations are many it goes up and down and they have a specific trend. The fluctuation has no a notable characteristic that is changing with time. There are bigger fluctuations; all tends to centralize in most of the time in question, which is similar to smaller ones in other periods of time. This phenomena that is quite strong in holding that a financial variable varies when the market undulates, is quite common in financial time-series (Graham, 2006; Nalin and Martha, 2004). b). Risk premium – this is the difference between the returns on a security and a risk-free rate. In our case we assume the returns provided as expected thus we can calculate the expected risk premium as the difference between the expected return on a security and return on a risk-free rate (Campbell and Thompson, 2008). The risk premium is calculated using the formulae Risk premium = expected return – risk- free rate =E (RJ) – Rf In this case, the risk premium would then be the difference between this expected return of the market and Microsoft minus the risk-free rate. This has been done in excel column J for Microsoft and K for the market. 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 Standard deviation of the returns on a stock around the expected return thus measures variability of return. Disney has a mean of 0.0014 with standard deviation 0.0809, while General Electric has the mean 0.0014 with a standard deviation 0.0699. The two stocks have a similar mean but different standard deviation. The standard deviation of Disney is higher than that of General Electric meaning that it is Disney stock is risky when comparing the two. Looking at the descriptive statistics for General Motors and IBM, the mean for General Motors -0.0091 with a standard deviation of 0.1273 and IBM has the mean of 0.0083 with standard deviation 0.0905. When comparing all the four stocks with that General Motors is the most risk assets followed by IBM then Disney and lastly General Electric when using standard deviation. At the same time General motors has lowest average returns which is negative thus it is not a good investment as compared to other stocks. IBM is a good investment as it has a good return with higher standard deviation; it said that a risky stock has a high return. In reality the variation in return below what is expected is the best measure of risk but we saw that because the distributions of returns on stock is nearly normal in a statistical sense the semi-deviation below is expected value need not be calculated(Knight and Satchell, 2002). d). The CAPM model will predict risk premium meaning that returns of a security will lie on the upward-sloping security market line. The beta for the stocks is calculated Description Average returns variances standard deviations Microsoft 0.008557=0.86% 0.01187 0.108946= 10.89% GM -0.009082=-0.91% 0.01609 0.126845= 12.68% Market 0.002511= 0.25% 0.002333 0.04830= 4.83% Covariance = cov (R I MSFT R MKT) = 0.003082 Covariance = cov (R I GM R MKT)= 0.002962 Correlation = corr (R I MSFT R MKT)= 0.003082/(0.108946 x 0.04830) = 0.5857 Correlation = corr (R I GM R MKT) = 0.002962/(0.126845 x 0.04830) = 0.4835 Beta MSFT = 0.5857 x(0.108946 / 0.04830)= 1.32 Beta GM = 0.4835 x (0.126845 / 0.04830) = 1.27 The estimated betas for the companies are more than1 meaning that the shares are risky as compared to the market. When beta is above 1 it means that the unsystematic risky is positive. If unsystematic risky is negative then the beta will be less than 1(Santa-Clara and Shu, 2006). We know that Beta is calculated when looking at the relationship between market returns and the preferred financial asset returns, in the case of Microsoft and the Beta calculated in this report there is negligible difference because the range of values over which this figure was calculated appear to have been similar thus we can see that there is a small difference in the case of GM and no difference whatsoever between the Betas calculated in this report and that calculated yahoo. Investors will find beta helpful in assessing systematic risk and understanding the impact market movements can have on the return expected from a share of stock. For example, if the market is expected to provide a 10 percent rate of return over the next year, a stock having a beta of 1.80 would be expected to experience an increase in return of approximately 18 percent over the same period. This particular stock is much more volatile than the market as a whole (Pandey, 2009). Decreases in market returns are translated into decreasing security returns and this is where the risk lies. In the preceding example, if the market is expected to experience a negative return 10 percent, then the stock with a beta of 1.8 should experience 18 percent decrease in its return stocks having betas of less than 1 will, of course, be less responsive to changing returns in the market, and therefore are considered less risky(Myers, 1984). 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- 1.32(0.002511) Alpha for GM = -0.009082- 1.27(0.002511) Alpha for MSFT = 0.0052 Alpha for GM = -0.0123 The intercept is not 0 because for general motors is intercept is –0.0123 and for Microsoft is 0.0052. The result is correct because of the volatility of the shares. f) 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= =33.74 Step: 5: Comparing Since z calc > zcrit (33.74>-2.33), we reject H0 From the test above it is clear the consultants believes that the beta is 1 is not correct as there is no sufficient evidence to support the claim. Therefore it can be conclude that the beta of Microsoft is not less than 1. g). Using our projected returns, we can calculate the projected or expected risk premium as the difference between the expected return on a risky investment and the certain return on a risk-free investment. Risk premium = expected return- risk- free rate = E (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% The expected return on a security or security or other asset is simply equal to the sum of the possible returns multiplied by their probabilities. The sum would be the expected return. The risk premium would then be the difference between this expected return and the risk-free rate(Fisher and Jordan, 2006). i). The findings of the Microsoft stock indicate that it has a low risk premium has compared to market. The standard deviation of the stock is high compared to the market as their gains with respect to market returns would not differ too much(McLaney, 2003). In the case of Microsoft gain in expected returns between June 1998 and December 2008 of nearly 0.8332%. In the case of market on the other hand we can see that the same period coincided with a rise as compared to the fall demonstrated in the case in that of Microsoft. In isolation greatly we can see that Microsoft appears to be a more riskier stock given its present standard deviation, and expected value because let’s assume a movement of a maximum of 1 standard deviation upwards or downwards the range of expected returns then moves from -0.001037 to 0.00808 or in percentages this would be a negative 0.1037% and an a positive 0.808% conversely when we apply this same model to market the situation changes by only a very small amount and assuming upward and downward movements of 1 standard deviation again we would have and expected change of either negative or a positive 8.05% thus clearly here we would hold Microsoft to be the more riskier stock of the two in a standalone investment. 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. 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. Read More