Volatility and Market Behaviour - Essay Example

MARKET FRACTION APPROACH TO UNDERSTANDING THE RELATIONSHIP BETWEEN ASSET PRICES, VOLATILITY AND MARKET BEHAVIOUR Submission Date: Introduction There are different measures and approaches used to assess the performance of companies on the market. One of these common means is by the use of the performance of the shares of the said company on the stock market (Brammer, Brooks and Pavelin, 2009). Consequently, the rate of change in the price of an asset such as the share of a company is a very strong indicator for business performance of the company in question and the stock market at large (Cao, 2009). Meanwhile, Baldauf and Santoni (2011) noted that there are several factors that account for, or influence the behaviour of assets such as shares. The aim of this project is therefore to analyse the behaviour of the share price of a given company by finding the relationship between share price inflation and other key market determinants and variables such as market index and Treasury bill interest rate. This means that share price of the company is the dependent variable for the study, while market index and Treasury bill interest rate are the independent variables for the study. The study is conducted with the approach of performing time series that checks for stationarity by applying the formal unit root tests of Augmented Dickey-Fuller (ADF) test. To get a better understanding of the relationship between the dependent variable and independent variables, the researcher will take a step further to estimate time series dynamics through the use of the GARCH family models. Because shares are traded with their derivatives, there is a common discussion in literature of the impact of the introduction of derivatives on volatility. Through the GARCH model, the effect of derivatives on the underlying market will also be determined. In pursuant to the achievement of the aim of the study discussed above, the researcher conducted a research that was based on both theoretical background and empirical evidence. The theoretical background of the research was performed mainly by the use of a brief literature review, which forms the second component of the study’s report. Under the literature review, the findings of major studies on stock price behaviour are critiqued by comparing different schools of thoughts against each other. This makes it possible to give the rationale behind various findings from literature. The third component of the study is the econometric methodology, where the researcher presented a detailed analysis of the methodology adopted for the study. Under this section, the market fraction hypothesis and how it was used to test the stationarity of the variables of the study was given. In the fourth section of the paper, a presentation is made of the empirical results gathered from the study. The empirical testing was performed with the STATA statistical software. The presentation of empirical results comes with the analysis and discussion of findings. The last section gives a conclusion to the study, based on the outcomes from the theoretical background and empirical study. The conclusion was given by comparing the outcomes of the theoretical findings to the empirical findings. This way, the researcher was able to identify major gaps in literature and how the empirical data collected from the study helped in bridging the gap. A Brief Literature Review The literature review is dedicated to reviewing existing works of literature that are related and relevant to the current research problem. Articles were searched and selected from highly credible academic sources including JSTOR, Blackwell and Journal of Financial Economics. The review is looks at two major themes of factors causing the rise and fall in share prices, and stock price behaviour and market efficiency. Factors that cause the rise and fall in share prices Writing on the behaviour of share prices, Arnott, Hsu and Moore (2009) argued that there is no simple way to tell what the behaviour of the stock market will be. In support of this opinion, Brammer, Brooks and Pavelin (2009) mentioned that there are several factors that cause rises and falls in share prices and this may happen either as a gradual change over time or as a sharp spike. In what seems to a rebuttal, Hamilton (2009) indicated that the stock market actually presents several variables that makes it possible to under the behaviour of share prices. One of these variables was noted to be the need to study trends of individual stocks and weigh this against the broad market behaviour. What this implies is that the key factor causing the rise and fall of share prices is the broad market behaviour. As far as the broad market behaviour is concerned, there are various factors that other researchers and authors have noted as being responsible for the possible rise and fall of share prices. Oikonomou, Brooks and Pavelin (2012) mentioned corporate actions as one of these important factors that cause the rise and fall of share prices. Explaining further, it was indicated that key actions taken within corporations trigger public opinion, which in turn bring about either hope or fear. Examples of such corporate actions that can trigger public opinions have been mentioned by Oikonomou, Brooks and Pavelin (2012) to include the resignation of the CEO of a company and corporate governance practices. Once the public opinion from such actions leads to fear, share prices will begin to fall. If the public opinion from the corporate action leads to hope, then share prices will begin to rise. The earning of individual companies was also mentioned by Arnott, Hsu and Moore (2009) as one of the most influential conditions that influence the rise and fall of share prices. In this, it was indicated that investors would commonly compare the quarterly earnings of companies. Where previous earnings are better than the current quarter, share prices are likely to fall because there is lost of investor confidence in the performance of the company. When the opposite happens and there are increases in the earnings of the company over the previous quarter, the most resulting effect on share prices is a rise in share prices. The factors given so far give indication to internal factors and conditions that the companies have to control in other trigger the behaviour of share prices. On the other hand, Bollerslev (2006) also gave indications of market wide factors that affect the behaviour of share prices. Such market wide prices are noted to be external factors that the companies can hardly have any control over. One of these external factors was noted to be inflation. Explaining further, Cao (2009) indicated whenever there is rise in inflation consumer spending capacity automatically goes down. But because the consumer spending capacity affects business profits, it means that profits will go down, as well as investor confidence. To respond, companies will increase the selling of prices but the demand for these shares will be low, causing stock prices to fall. Interest rate was also mentioned as another external factor that influences the behaviour of share prices. Fernholz, Garvy and Hannon (2008) actually posited that when interest rates are high, money borrowing goes down, affecting business growth. But because investors will not invest in an ailing business, share prices will also begin to drop. Stock Price Behaviour and Market Efficiency Market efficiency has been explained to be the extent to which stock prices reflect all available and relevant information (Haugen and Baker, 2011). Based on this, the efficient market hypothesis (EMH) was developed by Eugene Fama to debate that it is not possible for an investor to beat the market because needed information are always built in stock prices (Bollerslev, 2006). From this assertion, a number of researchers have tried to investigate the relationship between stock price behaviour and market efficiency. In a study by Hull and White (2010), it was found that investor behaviour is largely influenced by the overall market performance. This is because such investors understand that it is not possible to beat the market and so the overall market performance is a perfect indication of information available on the market. With this noted, the understanding that is developed is that individual share price behaviour can hardly be independent of themselves when the market on which they are do not perform well (Mayhew and Mihov, 2004). Based on this, Haugen and Baker (2011) noted that individual companies can take advantage of the overall market efficiency by studying how quickly the market responds to information. It has been said for example that market responds to new information within 30 minutes. What this means is that the best time to take advantage of the market is at the very early stages when information is available on a market wide basis. Based on this assertion, the market index must always be selected as an important determinant of forecasting the behaviour of individual share prices (Hull and White, 2010). Econometric Methodology The econometric methodology for the study was based on the use of the market fraction approach or the market fraction hypothesis. It would be noted that for any given market, there are different types of trading strategies that are used. According to Antoniou and Holmes (2005) these different trading strategies are selected based on key market determinants of the market such as the overall market index and interest rate. The proportion of all these trading strategies come together to form the market fraction (Mayhew and Mihov, 2004). Based the market fraction, the market fraction hypothesis (MFH) is used to determine the swings on the market over time. The rationale for selecting the MFH is that it is based on the fundamental assumption that trading strategies are static and pre-determined. With the use of data of the share price of the company, market index, and Treasury bill interest rate from 2000 to 2007, it should be possible to perform time series for stationarity to rest the validity of the assumption that trading strategies are static and pre-determined. It was possible to use the test of the stationarity of the time series to determine the validity of the assumption given the fact that stationarity actually represents time series with statistical properties that are constant over time. The stationarity was measured by the use of unit roots tests of ADF from computations performed by the use of the EViews software. Key statistical properties that were tested to be constant were mean, standard deviation, autocorrelation, S.E of regression, and R-squared. To test the effect of asset pricing on volatility, the GARCH family procedure was used. This was done by the use of the daily returns for the closing prices of the stock market represented by the SPM. The daily returns was computed with the equation given as: Rt = Log (Pt / Pt-1)---------------------------------------------------(1) As part of the GARCH procedure, a dummy variable was introduced as a conditional volatility model. The essence of this dummy variable was basically to produce a value that would be use to determine whether the derivatives of the stock market, which are futures and options had led to increased volatility or decreased volatility. The error term for the conditional volatility model was given as follows: Rt = 1DM + 2DTU + 3DW + 4DTH + 5DFR +6Rt-1 + ut --------- (2) The GARCH model GARCH (1,1) was used to reflect the mean and variance of the component variables being tested. The model’s equation was given as: ---------------------------------------- (3) β represents shocks to conditional variance take longer to cancel out. This is done to ensure persistent volatility. on the other hand represents the daily return made on the SPM index whiles represents lagged returns. Finally, a GARCH (p, q) model is given by the following equation. Yt = α0 + α1Xi + εt -------------------------- (4) εt / Ψt ~ ( 0, ht ) h2t = α0 + α1 ε2t-1 + -----------(5) In line with the general topic area which is the behaviour of asset prices, the econometrics methodology aided the researcher to determine the behaviour of the share prices of the company as it was influenced by volatility. Empirical Results Stationarity of Time Series The study was undertaken with a company code named s30. The share prices of the company from January 2000 to February 2007 were therefore used as the dependent variable and presented at the appendix section of the study. The share prices were used as dependent variable so as the measure the effect of other variables on share prices as a type of asset. The other variables used were Treasury bill interest rate and market index. The raw data obtained for all these variables have been presented at the appendix section of the study. Below, the researcher tested for stationarity of the time series by performing unit roots test in EViews. Stationarity Test for Share Price (s30) Computation for testing for the stationarity for share price is based on the following equations: Given that s30t = Yt , the Dickey-Fuller (DF) Unit Root Test are based on the following regression: Without Constant and Trend From the regression form given above, the following decision rules apply: If t* > ADF crtitical value, ==> not reject null hypothesis, which means unit root exists. If t* < ADF critical value, ==> reject null hypothesis, which means unit root does not exist. The hypotheses used are given as: Details of the outcome of the test performed have been presented at the appendix. Meanwhile, a summary table that is used to determine if the s30 has unit root is given below. Table 1: Summary of ADF Test on s30 t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -0.386428  0.9058 Test critical values: 1% level -3.509281 5% level -2.895924 10% level -2.585172 From the table above, it is seen that the ADF t-statistic is -0.386428. This value is greater than all three critical values which are given at -3.86428, -2.895924 and -2.585172 at 1%, 5% and 10% significant levels respectively. From this finding, we cannot reject the null hypothesis (Ho). The implication for stationarity is that the share price, s30 has an unit root problem. The implication here is that the s30 series is a non-stationary series, meaning that the joint probability distribution of the stochastic process of share price for s30 changes with shifts in time. To draw a valid conclusion on the autocorrelation, it is important to bring to question the Durbin-Watson stat. Based on the test statistic And et is the residual associated with the time t, when d = 2, the indication is that there is no autocorrelation problem. As shown at the appendix for the ADF Test on s30, the Durban-Watson stat is 2.022438. This means that there is no autocorrelation, implying that successive error terms are generally much different in value from one another, giving rise to negative correlation between the share prices within time. The empirical outcomes produced above are further tested with a graphical production, which is given below. Figure 1: Share Price from 2000 to 2007 Stationarity Test for Treasury Bill Interest Rate (TB) In existing literature, there are two major schools of thought when it comes to the impact of impact of Treasury bill interest rate on share prices. One school of thought argues that the possible cause of the behaviour of the share price of a company which is non-stationary can be attributed to other market variables and determinants, including interest rate (Fernholz, Garvy and Hannon, 2008). The argument of this school of thought is that the performance of the Treasury bill interest rate can cause investors to divert their investment towards the Treasury bill market instead of on the direct spending, which helps in maintaining share prices. There is another school of thought that actually suggest that when other market determinants like Treasury bill interest rate experience non-stationarity, share prices are affected to perform same because investors tend to derive the trend of their investment on shares from drift of the Treasury bill interest rate (Antoniou and Holmes, 2005). Based on the differences in the assertions, the stationarity of Treasury bill interest rate was tested to see if there was any relation between the stationarity of share price and Treasury bill interest rate. To do this, the same constants and hypothesis are maintained as used for s30 above. The full outcome of ADF Test has been produced at the appendix. The summary of statistical table for analysis is however presented below. Table 2: Summary of ADF Test on TB t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -1.913915  0.3245 Test critical values: 1% level -3.511262 5% level -2.896779 10% level -2.585626 From table 2, it is seen that the ADF t-statistic is given as -1.913915, which is greater than all three test critical values at 1%, 5% and 10%. The implication is that there is unit root, which also means that the TB series is non-stationary. A further analysis is performed on the Durbin-Watson stat to find if there is an auto-correlation. From the complete table produced for the outcome of ADF for TB in the appendix section, the Durbin-Watson stat is given as 2.012195. This value is greater than 2, which gives an indication that there is no autocorrelation for the TB, implying that TB interest rates are different in value from one another, which gives rise to negative correlation between the rates within time. The graphical representation of the TB non-stationarity is given by the graph below Figure 2: Treasury bill Interest Rate from 2000 to 2007 Stationarity Test for Stock Market Index (SPM) Another area of controversy in literature has to do with the impact of the overall stock market on individual share prices of companies. Whereas some argue that the market index and share prices of individual companies are independent of one another (Baldauf and Santoni, 2011), others debate that the two are dependent (Bollerslev, 2006). A time series test for stationarity was therefore performed for SPM to find out if it behaves in the same way as individual asset, s30. Details of the statistical analysis are presented at the appendix. In the table below however, summary of key findings are presented for analysis. Table 3: Summary of ADF Test for SPM t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -0.892867  0.7861 Test critical values: 1% level -3.509281 5% level -2.895924 10% level -2.585172 Table 3 shows that there is a unit root problem for the SPM series. This is because the t-statistic value given is greater than all the test critical values, which are given at levels of 1%, 5% and 10%. By implication, there is non-stationarity between the market indexes with change in time. The test for autocorrelation by the use of Durbin-Watson stat also produced a value of 2.067288, which is greater than 2 and therefore implies that there is no autocorrelation between the values of market index given for the period under consideration. The graph below shows the pictorial representation of the non-stationary SPM. Figure 3: SPM trend from 2000 to 2007 Comparison between Share Price, T-Bill Interest Rate and Market Index In the graph below, the researcher compared all three variables to determine the relationship that exists between them over the time lag given for the study. Figure 4: Comparison between all three variables Figure 4 gives a better outlook of the three variables when it comes to their stationarity. This is because the graph shows that even though there is unit root problem with all three variables and that there is no autocorrelation among any of the variable, the share prices have better stability when compared to the other two independent variables. Effect of Market Index on Volatility Using the GARCH approach, the impact of derivatives via the futures and options of the market index where tested to know how they affect volatility of the spot market. Table 4: Impact of SPM Options and Futures on the Spot Market (GARCH 1,1) SL. Closing price Return 1 Variable Co-efficients Significance 2 Constant 4.67E-05 6.443154 3 SPM Index 0.046665 1.926546 4 ARCH 1 0.146552 11.01077 5 GARCH 1 0.749017 30.41610 6 O&F DUMMY -2.84E-05 -5.527339 The outcome of table 4 is that SPM return is regressed when it is computed against its core lag value which makes use of the dummy variables as presented in equation (2). In the closing price, it is seen that the co-efficient for the dummy variable is -2.84E-05. Meanwhile, the dummy variable is significant only at 1 percent level against the index. By implication, it can be said that within the period under study, the introduction of options and returns as the main derivatives of the market index led to a reduction in the underlying market volatility. Meanwhile in study where Aretz and Bartram (2010) related volatility to market behaviour, it was noted that where there is reduction in market volatility, it implies that there is much stability on the underlying market. Such stability boasts investor confidence and leads to more activities on the stock market. When this happens also, individual share prices begin to improve. Conclusion The findings from the econometrics give rise to key discussions, based on which conclusions can be made for the study. In the first place, it can be noted that all three variables tested in the study had unit root problems, which means that they were all non-stationary series. The main policy point here is that the independent variables which are Treasury bill interest rate and market index are positively correlated with the dependent variable which was share prices for s30. This explains that the school of thought that investors base their activities with individual share prices on the overall market index and Treasury bill interest rate can be justified. The second point of discussion is that the market index as presented by SPM index actually led to low market volatility and thus market stability. Meanwhile, within this time period, the individual share price of s30 as showed in figure 1 experiences a steady growth rate. This means that the overall market index and for that matter the stability on the market goes a long way to influence the behaviour of asset prices. The study can therefore be concluded on the statement that the behaviour of asset prices is largely dependent on market index and Treasury bill interest rate. All these variables tend to perform in a much related way. Therefore, decline in market index performance and Treasure bill interest rate will affect share prices negatively. The researcher approached the study with as much effort to overcome key limitation as possible. However, a major limitation that was encountered had to do with the number of variables that were tested. Indeed, there are several other variables based on monetary policy determinants that might have an effect on the asset price. It is therefore recommended that future researchers will expand on the number of independent variables. By so doing, it will be possible to generalise the outcome of the study for a very large research setting. References Antoniou A. and Holmes P. (2005) "Futures trading, information and spot price volatility: evidence for the FTSE-100 Stock index futures contract using GARCH"Journal of Banking & Finance, 19, 117-129. Aretz, K and Bartram, S. M. (2010). "Corporate Hedging and Shareholder Value". Journal of Financial Research 33 (4): 317–371 Arnott, R. D.; Hsu, J.; and Moore, P. (2009). "Fundamental Indexation". Financial Analysts Journal 60 (2): 83–99. JSTOR 4480658 Baldauf B. and Santoni G.J. (2011) “Stock price volatility: Some evidence form an ARCH model” The Journal of Futures Markets, 11, 2, 191-200. Bollerslev T. (2006) “Generalized autoregressive conditional heteroskedasticity” Journal of Econometrics, 31, 307-327. Brammer, S, Brooks, C. and Pavelin, S. (2009). "The stock performance of Americas 100 best corporate citizens". The Quarterly Review of Economics and Finance 49 (3): 1065–1080. Brorsen B.W. (2011) “Futures trading, transactions costs, and stock market volatility”, The Journal of Futures Markets 11, 2, 153-163. Cao, H.H., (2009). “The effect of derivative assets on information acquisition and price behavior in a rational expectations equilibrium”, Review of Financial Studies 12, 131-163. Fernholz, R.; Garvy, R. and Hannon, J. (2008). "Diversity-Weighted Indexing". Journal of Portfolio Management 24 (2): 74–82. Hamilton, J., (2009). “Causes and consequences of the oil shock of 2007-2008”, Working paper, UC San Diego. Haugen, R. A. and Baker, N. L. (2011). "The Efficient Market Inefficiency of Capitalization-Weighted Stock Portfolios". Journal of Portfolio Management 17 (3): 35–40. Hull, J. and White, A., (2010). “Valuing credit default swaps I: No counterparty default risk”, Journal of Derivatives 8, p. 29-40. Mayhew, S. and Mihov, V., (2004). “How do exchanges select stocks for option listing?”, Journal of Finance 59, 447-471 Oikonomou, I, Brooks, C. and Pavelin, S. (2012). "The impact of corporate social performance on financial risk and utility: a longitudinal analysis". Financial Management 41 (2): 483–515. Appendix Augmented Dickey-Fuller Unit Root Test on s30 Null Hypothesis: S30 has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -0.386428  0.9058 Test critical values: 1% level -3.509281 5% level -2.895924 10% level -2.585172 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(S30) Method: Least Squares Date: 07/28/14 Time: 06:03 Sample (adjusted): 2000M02 2007M02 Included observations: 85 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   S30(-1) -0.013060 0.033798 -0.386428 0.7002 C 23.22261 35.10946 0.661434 0.5102 R-squared 0.001796     Mean dependent var 9.894118 Adjusted R-squared -0.010231     S.D. dependent var 60.15655 S.E. of regression 60.46348     Akaike info criterion 11.06520 Sum squared resid 303434.1     Schwarz criterion 11.12268 Log likelihood -468.2712     Hannan-Quinn criter. 11.08832 F-statistic 0.149327     Durbin-Watson stat 2.022438 Prob(F-statistic) 0.700169 Augmented Dickey-Fuller Unit Root Test on TB Null Hypothesis: TB has a unit root Exogenous: Constant Lag Length: 2 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -1.913915  0.3245 Test critical values: 1% level -3.511262 5% level -2.896779 10% level -2.585626 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(TB) Method: Least Squares Date: 07/28/14 Time: 06:39 Sample (adjusted): 2000M04 2007M02 Included observations: 83 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   TB(-1) -0.030903 0.016146 -1.913915 0.0593 D(TB(-1)) 0.321102 0.107020 3.000403 0.0036 D(TB(-2)) 0.248702 0.107647 2.310354 0.0235 C 0.136476 0.073540 1.855798 0.0672 R-squared 0.261583     Mean dependent var -0.006867 Adjusted R-squared 0.233542     S.D. dependent var 0.116681 S.E. of regression 0.102151     Akaike info criterion -1.677729 Sum squared resid 0.824358     Schwarz criterion -1.561158 Log likelihood 73.62575     Hannan-Quinn criter. -1.630897 F-statistic 9.328560     Durbin-Watson stat 2.012195 Prob(F-statistic) 0.000024 Augmented Dickey-Fuller Unit Root Test on SPM Null Hypothesis: SPM has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=11) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -0.892867  0.7861 Test critical values: 1% level -3.509281 5% level -2.895924 10% level -2.585172 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(SPM) Method: Least Squares Date: 07/28/14 Time: 07:01 Sample (adjusted): 2000M02 2007M02 Included observations: 85 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   SPM(-1) -0.021673 0.024274 -0.892867 0.3745 C 113.8742 127.1557 0.895550 0.3731 R-squared 0.009514     Mean dependent var 1.796471 Adjusted R-squared -0.002420     S.D. dependent var 186.8748 S.E. of regression 187.1007     Akaike info criterion 13.32442 Sum squared resid 2905555.     Schwarz criterion 13.38189 Log likelihood -564.2878     Hannan-Quinn criter. 13.34754 F-statistic 0.797211     Durbin-Watson stat 2.067288 Prob(F-statistic) 0.374510 Read More