Introduction to Financial Econometrics - Assignment Example

Introduction to Financial Econometrics Submitted by…………………….. Introduction This essay examines the link between monthly share price and returns for a given stock. It again ties to find out if the data is randomly distributed other than examining whether the log series follow normal distribution or not. The paper also performs a CAPM analysis for the data and test whether the log series is stationary or not. This was done according to some questions given as: Question a After data was gathered and worthy log calculations done, we looked into the variables that affect stock share prices. The study model will be explained by the help of these variables though there were various other variables those shaped stock prices indexes. The conclusion of this paper was however entirely dependent on the above determinants. The dependent variable was log prices of monthly stock and the independent variable was log returns of the stock. In use were many statistical models to issue graphs and descriptive statistics that examine the log share prices and log returns of our company. Some of the tests under this subject were; Test for Randomness A run test was put underway to see if the observations are serially independent- that is whether they happen in a random order by counting how many runs up or below a threshold. Normality test A series of normality tests were also conducted for log return series, noting that there is a possibility of an effect on outliers analyzed in the past point. Techniques that were used descriptively are; mean median, standard deviation and percentile to describe the main indicators of each of the return series. A descriptive summary statistic results were arrived at as displayed in the tables 1 Table 1: Descriptive summary statistics Variable Obs Mean Std. Dev. Min Max Log share prices 240 2.45508 0.195333 2.021189 2.86629 Log returns 240 0.38161 0.513098 -0.6349803 0.8749281 The mean for log share prices and log returns was calculated as 2.45508 and 0.38161 respectively. On the other side, the variance, that is, the deviation from these mean, were 0.195333 and 0.513098 for log share prices and log returns respectively. For the log share prices, most observations were concentrated between the 1st quartile and the mean (2nd quartile) and also above the 3rd quartile. This information is displayed in graph 1 in Appendices. However, for log returns, much of the observations were between 0 to +0.5, which were observations above the 1st quartile (see graph 2 in Appendices). Table 2 puts together our normality test. Table 2. Normality test Variable Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2 Log prices 240 0.1305 0.0215 7.16 0.0279 Log returns 240 0.0000 0.0000 64.52 0.0000 From the table, the p-value, in connection with the log return, is 0.0000 for skewness and 0.0000 for kurtosis. Similarly, the p-value for log share prices is 0.0215 for kurtosis and 0.1305 for skewness of observations. These results revealed that the kurtosis of the two data set are majorly different from the distribution shape we can get from the kurtosis of any normally distributed observation, at least at the 5% level of significance. From the run test, the table 3&4 looks into the statistical importance of this impression. Table 3. Random test: log returns Description value N(Logreturns 0.38161008) 133 Observations 240 N(runs) 22 z -12.78 Prob>|z| 0 Table 4. Random test: log prices A total of 22 runs are available in the log return series observations and 2 runs in log prices series observations. An evaluation to the factual distribution of the runs number makes the 22 and 2 runs in these series negligible compared to what would be seen if the observations were serially independent. As such, the data were not random. Question b In considering this question, we undertook unit root test to see whether each log series are stationary or not. This dataset has 240 observations on the monthly stock prices and returns from 1995 through 2014. A summary of stationary test is displayed in Table 5. Table 5. Augmented Dickey-Fuller test for unit root Augmented Dickey-Fuller test for unit root No. of obs = 240 Test statistic 1% critical 5% critical 10% critical value value value Z(t) -5.834 -3.047 -2.345 -2.143 Mackinnon p-value for Z(t) = 0.0000 Log share prices Coef. Std. Err. t P >/t/ 95% conf. Interval 0.4585 0.75373 -5.83 0.0000 -0.578284 -0.38294 -cons 0.32338 0.6928 3.34 0.0000 0.49274 5.3848 From this we can staunchly reject argument of a unit root at all important levels this is because from the regression p-value is 0.0000. the argument that the data is stationary is always rejected when the p-value is less than or equal to a given significance level, always 0.05 (5%), or 0.01 (1%) and even 0.1 (10%). From our results, the p-value is less than all the critical value. As such, we can say our series data is non-stationary. As such, the predictions for our series cannot then be "untransformed," just by reversing whatever statistical transformations which were previously utilized so as to obtain forecasts for the true stock series. Question c In regard to this question, we come up with a regression model for an estimating how the series relate. The theoretical framework look into how changes in log share prices influences changes happening in log returns. To summarize it, our research model was formulated as; dlogyt (log share prices ) = α + βdlogtbt  + ut………………………………………………………………..….(model 1) Where; dlogyt = log share prices for our company (dependent variable); dlogtbt = log returns for the company stocks (independent variable); ut = error term; and α and β were coefficients of the variables. STATA was used to estimate the model`s coefficients and the results was summarized as given in Figure 1 (see appendices). From the findings, there is a negative relationship between log share prices and log returns. That is, if log return series changes by at least one unit log share prices series changes by 0.160174. However, going by the R2, our model only fit the data at 17.36%. That is, only 17.36% of the data was explained by the model. Question d This part uses CAPM analysis to estimate beta. As such, we able to formally ascertain whether our company can be categorized as defensive, neutral or aggressive. We explored CAPM technique by using the model: Log share Price (Ri)j = β (Rmj – Rfj) + Rfj Where Rfj = risk-free rate the firm Rmj = log return for the firm; and β = beta α = intercept which showed how worse or even better the firm performed than CAPM predicted We wanted to put to test the hypothesis: Ho: β = 0 (No significant beta) H1: β ≠ 0 (Significant beta exist) The results of the test is as shown in Table 6. Table 6. CAPM analysis Beta Intercept R2 t-statistics Critical value 0.019937 (0.006733) 0.03947 (0.0938) 0.5228 4.38 0.000 From the findings in the table, we rejected Ho for the firm because t-statistic was greater than the critical value. This meant that significant beta was there for the firm and its market risks were shown by beta. Beta is the gradient of the model line. Usually, alpha, the intercept, showed how much better or worse the firm did than CAPM predicted (negative alpha illustrated how much worse the fund performed and vice versa). Our alpha though, was positive thus this company performed well enough. The fitness of our model was shown by our R2. While an R2 of 1.0 would imply that this model fit the monthly data well (100%) and that the performance of the firm was illustrated by its risk outcome, as gauged by beta. Nonetheless, this was not the case as evidenced in different R2 of our model in the Table 6. The model explains of 52.28% of the data. Going by the value of beta, we can confidently say our firm is neutral since it accepts as much level of risk as the returns. Question e i. Bull Market This describes a market that appears to be in a long term climb. This always arises when the economy is strong, the unemployment rate is low, and inflation is on check. An emotional and psychological state of the investors also affects the market. Fort instance if investors have hope that the incline trend in stock prices will prolong, they are most likely to buy more stocks. ii. Bear Market A bear market is a market that seems to be in long term decline. These kind of markets develop when the economy plunges into recession, when unemployment is high and inflation is on the rise. Investors lose hope in the market as a whole, and this leads in a decline of demand for stocks. A standard bear market is something that is expected to take place from time to time, and that previously, the stock market has gone up more than it has declined. From the graph 3, we can see that bull market was between 2004 – 2007 while bear market was between 2000 – 2004. As such, we tested whether the beta is statistically different between bull and bear markets. The test hypothesis was: Ho: β = β1 (No significant difference) H1: β ≠ β1 (Significant difference exist) From the results in Table 7, we rejected Ho since our t-statistics was greater than our critical value. Table 7. Bull and Bear market beta Beta t-statistics Critical value Bull market 0.01983 (0.00673) 3.394 0.000 Bear market -0.00283 (0.00562) 2.483 0.386 This implies that the market risk for the two markets (as exemplified by beta) is explained differently from the market risk of the entire data. Reference Chandra, P. 2008. Investment analysis and portfolio management. S.l.: Tata Mcgraw-Hill. Chapman, R. J. 2013. Simple tools and techniques for enterprise risk management. Hoboken, N.J: Wiley. Elton, E. J. 2010. Modern portfolio theory and investment analysis. Hoboken, NJ: J. Wiley & Sons. Vollmer, M. 2014. A beta-return efficient portfolio optimisation following the CAPM: An analysis of international markets and sectors. Appendices Graph 1. Quartile plot for log prices Figure 1. Regression output for model 1 Graph 2. Quartile plot for log returns Read More