VaR Models in Predicting Equity Market Risk

VaR Models in Predicting Equity Market Risk Chapter 3 Research Design This chapter represents how to apply proposed VaR models in predicting equity market risk. Basically, the thesis first outlines the collected empirical data. We next focus on verifying assumptions usually engaged in the VaR models and then identifying whether the data characteristics are in line with these assumptions through examining the observed data. Various VaR models are subsequently discussed, beginning with the non-parametric approach (the historical simulation model) and followed by the parametric approaches under different distributional assumptions of returns and intentionally with the combination of the Cornish-Fisher Expansion technique. Finally, backtesting techniques are employed to value the performance of the suggested VaR models. 3.1. Data The data used in the study are financial time series that reflect the daily historical price changes for two single equity index assets, including the FTSE 100 index of the UK market and the SP 500 of the US market. Mathematically, instead of using the arithmetic return, the paper employs the daily log-returns. The full period, which the calculations are based on, stretches from 05/06/2002 to 22/06/2009 for each single index. More precisely, to implement the empirical test, the period will be divided separately into two sub-periods: the first series of empirical data, which are used to make the parameter estimation, spans from 05/06/2002 to 31/07/2007. The rest of the data, which is between 01/08/2007 and 22/06/2009, is used for predicting VaR figures and backtesting. Do note here is that the latter stage is exactly the current global financial crisis period which began from the August of 2007, dramatically peaked in the ending months of 2008 and signally reduced significantly in the middle of 2009. Consequently, the study will purposely examine the accuracy of the VaR models within the volatile time. 3.1.1. FTSE 100 index The FTSE 100 Index is a share index of the 100 most highly capitalised UK companies listed on the London Stock Exchange, began on 3rd January 1984. FTSE 100 companies represent about 81% of the market capitalisation of the whole London Stock Exchange and become the most widely used UK stock market indicator. In the dissertation, the full data used for the empirical analysis consists of 1782 observations (1782 working days) of the UK FTSE 100 index covering the period from 05/06/2002 to 22/06/2009. 3.1.2. SP 500 index The SP 500 is a value weighted index published since 1957 of the prices of 500 large-cap common stocks actively traded in the United States. The stocks listed on the SP 500 are those of large publicly held companies that trade on either of the two largest American stock market companies, the NYSE Euronext and NASDAQ OMX. After the Dow Jones Industrial Average, the SP 500 is the most widely followed index of large-cap American stocks. The SP 500 refers not only to the index, but also to the 500 companies that have their common stock included in the index and consequently considered as a bellwether for the US economy. Similar to the FTSE 100, the data for the SP 500 is also observed during the same period with 1775 observations (1775 working days). 3.2. Data Analysis For the VaR models, one of the most important aspects is assumptions relating to measuring VaR. This section first discusses several VaR assumptions and then examines the collected empirical data characteristics. 3.2.1. Assumptions 3.2.1.1. Normality assumption Normal distribution As mentioned in the chapter 2, most VaR models assume that return distribution is normally distributed with mean of 0 and standard deviation of 1 (see figure 3.1). Nonetheless, the chapter 2 also shows that the actual return in most of previous empirical investigations does not completely follow the standard distribution. Figure 3.1: Standard Normal Distribution Skewness The skewness is a measure of asymmetry of the distribution of the financial time series around its mean. Normally data is assumed to be symmetrically distributed with skewness of 0. A dataset with either a positive or negative skew deviates from the normal distribution assumptions (see figure 3.2). This can cause parametric approaches, such as the Riskmetrics and the symmetric normal-GARCH(1,1) model under the assumption of standard distributed returns, to be less effective if asset returns are heavily skewed. The result can be an overestimation or underestimation of the VaR value depending on the skew of the underlying asset returns. Figure 3.2: Plot of a positive or negative skew Kurtosis The kurtosis measures the peakedness or flatness of the distribution of a data sample and describes how concentrated the returns are around their mean. A high value of kurtosis means that more of data’s variance comes from extreme deviations. In other words, a high kurtosis means that the assets returns consist of more extreme values than modeled by the normal distribution. This positive excess kurtosis is, according to Lee and Lee (2000) called leptokurtic and a negative excess kurtosis is called platykurtic. The data which is normally distributed has kurtosis of 3. Figure 3.3: General forms of Kurtosis Jarque-Bera Statistic In statistics, Jarque-Bera (JB) is a test statistic for testing whether the series is normally distributed. In other words, the Jarque-Bera test is a goodness-of-fit measure of departure from normality, based on the sample kurtosis and skewness. The test statistic JB is defined as: where n is the number of observations, S is the sample skewness, K is the sample kurtosis. For large sample sizes, the test statistic has a Chi-square distribution with two degrees of freedom. Augmented Dickey–Fuller Statistic Augmented Dickey–Fuller test (ADF) is a test for a unit root in a time series sample. It is an augmented version of the Dickey–Fuller test for a larger and more complicated set of time series models. The ADF statistic used in the test is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence. ADF critical values: (1%) –3.4334, (5%) –2.8627, (10%) –2.5674. 3.2.1.2. Homoscedasticity assumption Homoscedasticity refers to the assumption that the dependent variable exhibits similar amounts of variance across the range of values for an independent variable. Figure 3.4: Plot of Homoscedasticity Unfortunately, the chapter 2, based on the previous empirical studies confirmed that the financial markets usually experience unexpected events, uncertainties in prices (and returns) and exhibit non-constant variance (Heteroskedasticity). Indeed, the volatility of financial asset returns changes over time, with periods when volatility is exceptionally high interspersed with periods when volatility is unusually low, namely volatility clustering. It is one of the widely stylised facts (stylised statistical properties of asset returns) which are common to a common set of financial assets. The volatility clustering reflects that high-volatility events tend to cluster in time. 3.2.1.3. Stationarity assumption According to Cont (2001), the most essential prerequisite of any statistical analysis of market data is the existence of some statistical properties of the data under study which remain constant over time, if not it is meaningless to try to recognize them. One of the hypotheses relating to the invariance of statistical properties of the return process in time is the stationarity. This hypothesis assumes that for any set of time instants ,†¦, and any time interval the joint distribution of the returns ,†¦, is the same as the joint distribution of returns ,†¦,. The Augmented Dickey-Fuller test, in turn, will also be used to test whether time-series models are accurately to examine the stationary of statistical properties of the return. 3.2.1.4. Serial independence assumption There are a large number of tests of randomness of the sample data. Autocorrelation plots are one common method test for randomness. Autocorrelation is the correlation between the returns at the different points in time. It is the same as calculating the correlation between two different time series, except that the same time series is used twice once in its original form and once lagged one or more time periods. The results can range from  +1 to -1. An autocorrelation of  +1 represents perfect positive correlation (i.e. an increase seen in one time series will lead to a proportionate increase in the other time series), while a value of -1 represents perfect negative correlation (i.e. an increase seen in one time series results in a proportionate decrease in the other time series). In terms of econometrics, the autocorrelation plot will be examined based on the Ljung-Box Q statistic test. However, instead of testing randomness at each distinct lag, it tests the overall randomness based on a number of lags. The Ljung-Box test can be defined as: where n is the sample size,is the sample autocorrelation at lag j, and h is the number of lags being tested. The hypothesis of randomness is rejected if whereis the percent point function of the Chi-square distribution and the ÃŽ ± is the quantile of the Chi-square distribution with h degrees of freedom. 3.2.2. Data Characteristics Table 3.1 gives the descriptive statistics for the FTSE 100 and the SP 500 daily stock market prices and returns. Daily returns are computed as logarithmic price relatives: Rt = ln(Pt/pt-1), where Pt is the closing daily price at time t. Figures 3.5a and 3.5b, 3.6a and 3.6b present the plots of returns and price index over time. Besides, Figures 3.7a and 3.7b, 3.8a and 3.8b illustrate the combination between the frequency distribution of the FTSE 100 and the SP 500 daily return data and a normal distribution curve imposed, spanning from 05/06/2002 through 22/06/2009. Table 3.1: Diagnostics table of statistical characteristics on the returns of the FTSE 100 Index and SP 500 index between 05/06/2002 and 22/6/2009. DIAGNOSTICS SP 500 FTSE 100 Number of observations 1774 1781 Largest return 10.96% 9.38% Smallest return -9.47% -9.26% Mean return -0.0001 -0.0001 Variance 0.0002 0.0002 Standard Deviation 0.0144 0.0141 Skewness -0.1267 -0.0978 Excess Kurtosis 9.2431 7.0322 Jarque-Bera 694.485*** 2298.153*** Augmented Dickey-Fuller (ADF) 2 -37.6418 -45.5849 Q(12) 20.0983* Autocorre: 0.04 93.3161*** Autocorre: 0.03 Q2 (12) 1348.2*** Autocorre: 0.28 1536.6*** Autocorre: 0.25 The ratio of SD/mean 144 141 Note: 1. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. 2. 95% critical value for the augmented Dickey-Fuller statistic = -3.4158 Figure 3.5a: The FTSE 100 daily returns from 05/06/2002 to 22/06/2009 Figure 3.5b: The SP 500 daily returns from 05/06/2002 to 22/06/2009 Figure 3.6a: The FTSE 100 daily closing prices from 05/06/2002 to 22/06/2009 Figure 3.6b: The SP 500 daily closing prices from 05/06/2002 to 22/06/2009 Figure 3.7a: Histogram showing the FTSE 100 daily returns combined with a normal distribution curve, spanning from 05/06/2002 through 22/06/2009 Figure 3.7b: Histogram showing the SP 500 daily returns combined with a normal distribution curve, spanning from 05/06/2002 through 22/06/2009 Figure 3.8a: Diagram showing the FTSE 100’ frequency distribution combined with a normal distribution curve, spanning from 05/06/2002 through 22/06/2009 Figure 3.8b: Diagram showing the SP 500’ frequency distribution combined with a normal distribution curve, spanning from 05/06/2002 through 22/06/2009 The Table 3.1 shows that the FTSE 100 and the SP 500 average daily return are approximately 0 percent, or at least very small compared to the sample standard deviation (the standard deviation is 141 and 144 times more than the size of the average return for the FTSE 100 and SP 500, respectively). This is why the mean is often set at zero when modelling daily portfolio returns, which reduces the uncertainty and imprecision of the estimates. In addition, large standard deviation compared to the mean supports the evidence that daily changes are dominated by randomness and small mean can be disregarded in risk measure estimates. Moreover, the paper also employes five statistics which often used in analysing data, including Skewness, Kurtosis, Jarque-Bera, Augmented Dickey-Fuller (ADF) and Ljung-Box test to examining the empirical full period, crossing from 05/06/2002 through 22/06/2009. Figure 3.7a and 3.7b demonstrate the histogram of the FTSE 100 and the SP 500 daily return data with the normal distribution imposed. The distribution of both the indexes has longer, fatter tails and higher probabilities for extreme events than for the normal distribution, in particular on the negative side (negative skewness implying that the distribution has a long left tail). Fatter negative tails mean a higher probability of large losses than the normal distribution would suggest. It is more peaked around its mean than the normal distribution, Indeed, the value for kurtosis is very high (10 and 12 for the FTSE 100 and the SP 500, respectively compared to 3 of the normal distribution) (also see Figures 3.8a and 3.8b for more details). In other words, the most prominent deviation from the normal distributional assumption is the kurtosis, which can be seen from the middle bars of the histogram rising above the normal distribution. Moreover, it is obvious that outliers still exist, which indicates that excess kurtosis is still present. The Jarque-Bera test rejects normality of returns at the 1% level of significance for both the indexes. So, the samples have all financial characteristics: volatility clustering and leptokurtosis. Besides that, the daily returns for both the indexes (presented in Figure 3.5a and 3.5b) reveal that volatility occurs in bursts; particularly the returns were very volatile at the beginning of examined period from June 2002 to the middle of June 2003. After remaining stable for about 4 years, the returns of the two well-known stock indexes in the world were highly volatile from July 2007 (when the credit crunch was about to begin) and even dramatically peaked since July 2008 to the end of June 2009. Generally, there are two recognised characteristics of the collected daily data. First, extreme outcomes occur more often and are larger than that predicted by the normal distribution (fat tails). Second, the size of market movements is not constant over time (conditional volatility). In terms of stationary, the Augmented Dickey-Fuller is adopted for the unit root test. The null hypothesis of this test is that there is a unit root (the time series is non-stationary). The alternative hypothesis is that the time series is stationary. If the null hypothesis is rejected, it means that the series is a stationary time series. In this thesis, the paper employs the ADF unit root test including an intercept and a trend term on return. The results from the ADF tests indicate that the test statistis for the FTSE 100 and the SP 500 is -45.5849 and -37.6418, respectively. Such values are significantly less than the 95% critical value for the augmented Dickey-Fuller statistic (-3.4158). Therefore, we can reject the unit root null hypothesis and sum up that the daily return series is robustly stationary. Finally, Table 3.1 shows the Ljung-Box test statistics for serial correlation of the return and squared return series for k = 12 lags, denoted by Q(k) and Q2(k), respectively. The Q(12) statistic is statistically significant implying the present of serial correlation in the FTSE 100 and the SP 500 daily return series (first moment dependencies). In other words, the return series exhibit linear dependence. Figure 3.9a: Autocorrelations of the FTSE 100 daily returns for Lags 1 through 100, covering 05/06/2002 to 22/06/2009. Figure 3.9b: Autocorrelations of the SP 500 daily returns for Lags 1 through 100, covering 05/06/2002 to 22/06/2009. Figures 3.9a and 3.9b and the autocorrelation coefficient (presented in Table 3.1) tell that the FTSE 100 and the SP 500 daily return did not display any systematic pattern and the returns have very little autocorrelations. According to Christoffersen (2003), in this situation we can write: Corr(Rt+1,Rt+1-ÃŽ ») ≈ 0, for ÃŽ » = 1,2,3†¦, 100 Therefore, returns are almost impossible to predict from their own past. One note is that since the mean of daily returns for both the indexes (-0.0001) is not significantly different from zero, and therefore, the variances of the return series are measured by squared returns. The Ljung-Box Q2 test statistic for the squared returns is much higher, indicating the presence of serial correlation in the squared return series. Figures 3.10a and 3.10b) and the autocorrelation coefficient (presented in Table 3.1) also confirm the autocorrelations in squared returns (variances) for the FTSE 100 and the SP 500 data, and more importantly, variance displays positive correlation with its own past, especially with short lags. Corr(R2t+1,R2t+1-ÃŽ ») > 0, for ÃŽ » = 1,2,3†¦, 100 Figure 3.10a: Autocorrelations of the FTSE 100 squared daily returns Figure 3.10b: Autocorrelations of the SP 500 squared daily returns 3.3. Calculation of Value At Risk The section puts much emphasis on how to calculate VaR figures for both single return indexes from proposed models, including the Historical Simulation, the Riskmetrics, the Normal-GARCH(1,1) (or N-GARCH(1,1)) and the Student-t GARCH(1,1) (or t-GARCH(1,1)) model. Except the historical simulation model which does not make any assumptions about the shape of the distribution of the assets returns, the other ones commonly have been studied under the assumption that the returns are normally distributed. Based on the previous section relating to the examining data, this assumption is rejected because observed extreme outcomes of the both single index returns occur more often and are larger than predicted by the normal distribution. Also, the volatility tends to change through time and periods of high and low volatility tend to cluster together. Consequently, the four proposed VaR models under the normal distribution either have particular limitations or unrealistic. Specifically, the historical simulation significantly assumes that the historically simulated returns are independently and identically distributed through time. Unfortunately, this assumption is impractical due to the volatility clustering of the empirical data. Similarly, although the Riskmetrics tries to avoid relying on sample observations and make use of additional information contained in the assumed distribution function, its normally distributional assumption is also unrealistic from the results of examining the collected data. The normal-GARCH(1,1) model and the student-t GARCH(1,1) model, on the other hand, can capture the fat tails and volatility clustering which occur in the observed financial time series data, but their returns standard distributional assumption is also impossible comparing to the empirical data. Despite all these, the thesis still uses the four models under the standard distributional assumption of returns to comparing and evaluating their estimated results with the predicted results based on the student distributional assumption of returns. Besides, since the empirical data experiences fatter tails more than that of the normal distribution, the essay intentionally employs the Cornish-Fisher Expansion technique to correct the z-value from the normal distribution to account for fatter tails, and then compare these results with the two results above. Therefore, in this chapter, we purposely calculate VaR by separating these three procedures into three different sections and final results will be discussed in length in chapter 4. 3.3.1. Components of VaR measures Throughout the analysis, a holding period of one-trading day will be used. For the significance level, various values for the left tail probability level will be considered, ranging from the very conservative level of 1 percent to the mid of 2.5 percent and to the less cautious 5 percent. The various VaR models will be estimated using the historical data of the two single return index samples, stretches from 05/06/2002 through 31/07/2007 (consisting of 1305 and 1298 prices observations for the FTSE 100 and the SP 500, respectively) for making the parameter estimation, and from 01/08/2007 to 22/06/2009 for predicting VaRs and backtesting. One interesting point here is that since there are few previous empirical studies examining the performance of VaR models during periods of financial crisis, the paper deliberately backtest the validity of VaR models within the current global financial crisis from the beginning in August 2007. 3.3.2. Calculation of VaR 3.3.2.1. Non-parametric approach Historical Simulation As mentioned above, the historical simulation model pretends that the change in market factors from today to tomorrow will be the same as it was some time ago, and therefore, it is computed based on the historical returns distribution. Consequently, we separate this non-parametric approach into a section. The chapter 2 has proved that calculating VaR using the historical simulation model is not mathematically complex since the measure only requires a rational period of historical data. Thus, the first task is to obtain an adequate historical time series for simulating. There are many previous studies presenting that predicted results of the model are relatively reliable once the window length of data used for simulating daily VaRs is not shorter than 1000 observed days. In this sense, the study will be based on a sliding window of the previous 1305 and 1298 prices observations (1304 and 1297 returns observations) for the FTSE 100 and the SP 500, respectively, spanning from 05/06/2002 through 31/07/2007. We have selected this rather than larger windows is since adding more historical data means adding older historical data which could be irrelevant to the future development of the returns indexes. After sorting in ascending order the past returns attributed to equally spaced classes, the predicted VaRs are determined as that log-return lies on the target percentile, say, in the thesis is on three widely percentiles of 1%, 2.5% and 5% lower tail of the return distribution. The result is a frequency distribution of returns, which is displayed as a histogram, and shown in Figure 3.11a and 3.11b below. The vertical axis shows the number of days on which returns are attributed to the various classes. The red vertical lines in the histogram separate the lowest 1%, 2.5% and 5% returns from the remaining (99%, 97.5% and 95%) returns. For FTSE 100, since the histogram is drawn from 1304 daily returns, the 99%, 97.5% and 95% daily VaRs are approximately the 13th, 33rd and 65th lowest return in this dataset which are -3.2%, -2.28% and -1.67%, respectively and are roughly marked in the histogram by the red vertical lines. The interpretation is that the VaR gives a number such that there is, say, a 1% chance of losing more than 3.2% of the single asset value tomorrow (on 01st August 2007). The SP 500 VaR figures, on the other hand, are little bit smaller than that of the UK stock index with -2.74%, -2.03% and -1.53% corresponding to 99%, 97.5% and 95% confidence levels, respectively. Figure 3.11a: Histogram of daily returns of FTSE 100 between 05/06/2002 and 31/07/2007 Figure 3.11b: Histogram of daily returns of SP 500 between 05/06/2002 and 31/07/2007 Following predicted VaRs on the first day of the predicted period, we continuously calculate VaRs for the estimated period, covering from 01/08/2007 to 22/06/2009. The question is whether the proposed non-parametric model is accurately performed in the turbulent period will be discussed in length in the chapter 4. 3.3.2.2. Parametric approaches under the normal distributional assumption of returns This section presents how to calculate the daily VaRs using the parametric approaches, including the RiskMetrics, the normal-GARCH(1,1) and the student-t GARCH(1,1) under the standard distributional assumption of returns. The results and the validity of each model during the turbulent period will deeply be considered in the chapter 4. 3.3.2.2.1. The RiskMetrics Comparing to the historical simulation model, the RiskMetrics as discussed in the chapter 2 does not solely rely on sample observations; instead, they make use of additional information contained in the normal distribution function. All that needs is the current estimate of volatility. In this sense, we first calculate daily RiskMetrics variance for both the indexes, crossing the parameter estimated period from 05/06/2002 to 31/07/2007 based on the well-known RiskMetrics variance formula (2.9). Specifically, we had the fixed decay factor ÃŽ »=0.94 (the RiskMetrics system suggested using ÃŽ »=0.94 to forecast one-day volatility). Besides, the other parameters are easily calculated, for instance, and are the squared log-return and variance of the previous day, correspondingly. After calculating the daily variance, we continuously measure VaRs for the forecasting period from 01/08/2007 to 22/06/2009 under different confidence levels of 99%, 97.5% and 95% based on the normal VaR formula (2.6), where the critical z-value of the normal distribution at each significance level is simply computed using the Excel function NORMSINV. 3.3.2.2.2. The Normal-GARCH(1,1) model For GARCH models, the chapter 2 confirms that the most important point is to estimate the model parameters ,,. These parameters has to be calculated for numerically, using the method of maximum likelihood estimation (MLE). In fact, in order to do the MLE function, many previous studies efficiently use professional econometric softwares rather than handling the mathematical calculations. In the light of evidence, the normal-GARCH(1,1) is executed by using a well-known econometric tool, STATA, to estimate the model parameters (see Table 3.2 below). Table 3.2. The parameters statistics of the Normal-GARCH(1,1) model for the FTSE 100 and the SP 500 Normal-GARCH(1,1)* Parameters FTSE 100 SP 500 0.0955952 0.0555244 0.8907231 0.9289999 0.0000012 0.0000011 + 0.9863183 0.9845243 Number of Observations 1304 1297 Log likelihood 4401.63 4386.964 * Note: In this section, we report the results from the Normal-GARCH(1,1) model using the method of maximum likelihood, under the assumption that the errors conditionally follow the normal distribution with significance level of 5%. According to Table 3.2, the coefficients of the lagged squared returns () for both the indexes are positive, concluding that strong ARCH effects are apparent for both the financial markets. Also, the coefficients of lagged conditional variance () are significantly positive and less than one, indicating that the impact of ‘old’ news on volatility is significant. The magnitude of the coefficient, is especially high (around 0.89 – 0.93), indicating a long memory in the variance. The estimate of was 1.2E-06 for the FTSE 100 and 1.1E-06 for the SP 500 implying a long run standard deviation of daily market return of about 0.94% and 0.84%, respectively. The log-likehood for this model for both the indexes was 4401.63 and 4386.964 for the FTSE 100 and the SP 500, correspondingly. The Log likehood ratios rejected the hypothesis of normality very strongly. After calculating the model parameters, we begin measuring conditional variance (volatility) for the parameter estimated period, covering from 05/06/2002 to 31/07/2007 based on the conditional variance formula (2.11), where and are the squared log-return and conditional variance of the previous day, respectively. We then measure predicted daily VaRs for the forecasting period from 01/08/2007 to 22/06/2009 under confidence levels of 99%, 97.5% and 95% using the normal VaR formula (2.6). Again, the critical z-value of the normal distribution under significance levels of 1%, 2.5% and 5% is purely computed using the Excel function NORMSINV. 3.3.2.2.3. The Student-t GARCH(1,1) model Different from the Normal-GARCH(1,1) approach, the model assumes that the volatility (or the errors of the returns) follows the Student-t distribution. In fact, many previous studies suggested that using the symmetric GARCH(1,1) model with the volatility following the Student-t distribution is more accurate than with that of the Normal distribution when examining financial time series. Accordingly, the paper additionally employs the Student-t GARCH(1,1) approach to measure VaRs. In this section, we use this model under the normal distributional assumption of returns. First is to estimate the model parameters using the method of maximum likelihood estimation and obtained by the STATA (see Table 3.3). Table 3.3. The parameters statistics of the Student-t GARCH(1,1) model for the FTSE 100 and the SP 500 Student-t GARCH(1,1)* Parameters FTSE 100 SP 500 0.0926120 0.0569293 0.8946485 0.9354794 0.0000011 0.0000006 + 0.9872605 0.9924087 Number of Observations 1304 1297 Log likelihood 4406.50 4399.24 * Note: In this section, we report the results from the Student-t GARCH(1,1) model using the method of maximum likelihood, under the assumption that the errors conditionally follow the student distribution with significance level of 5%. The Table 3.3 also identifies the same characteristics of the student-t GARCH(1,1) model parameters comparing to the normal-GARCH(1,1) approach. Specifically, the results of , expose that there were evidently strong ARCH effects occurred on the UK and US financial markets during the parameter estimated period, crossing from 05/06/2002 to 31/07/2007. Moreover, as Floros (2008) mentioned, there was also the considerable impact of ‘old’ news on volatility as well as a long memory in the variance. We at that time follow the similar steps as calculating VaRs using the normal-GARCH(1,1) model. 3.3.2.3. Parametric approaches under the normal distributional assumption of returns modified by the Cornish-Fisher Expansion technique The section 3.3.2.2 measured the VaRs using the parametric approaches under the assumption that the returns are normally distributed. Regardless of their results and performance, it is clearly that this assumption is impractical since the fact that the collected empirical data experiences fatter tails more than that of the normal distribution. Consequently, in this section the study intentionally employs the Cornish-Fisher Expansion (CFE) technique to correct the z-value from the assumption of the normal distribution to significantly account for fatter tails. Again, the question of whether the proposed models achieved powerfully within the recent damage time will be assessed in length in the chapter 4. 3.3.2.3.1. The CFE-modified RiskMetrics Similar VaR Models in Predicting Equity Market Risk VaR Models in Predicting Equity Market Risk Chapter 3 Research Design This chapter represents how to apply proposed VaR models in predicting equity market risk. Basically, the thesis first outlines the collected empirical data. We next focus on verifying assumptions usually engaged in the VaR models and then identifying whether the data characteristics are in line with these assumptions through examining the observed data. Various VaR models are subsequently discussed, beginning with the non-parametric approach (the historical simulation model) and followed by the parametric approaches under different distributional assumptions of returns and intentionally with the combination of the Cornish-Fisher Expansion technique. Finally, backtesting techniques are employed to value the performance of the suggested VaR models. 3.1. Data The data used in the study are financial time series that reflect the daily historical price changes for two single equity index assets, including the FTSE 100 index of the UK market and the SP 500 of the US market. Mathematically, instead of using the arithmetic return, the paper employs the daily log-returns. The full period, which the calculations are based on, stretches from 05/06/2002 to 22/06/2009 for each single index. More precisely, to implement the empirical test, the period will be divided separately into two sub-periods: the first series of empirical data, which are used to make the parameter estimation, spans from 05/06/2002 to 31/07/2007. The rest of the data, which is between 01/08/2007 and 22/06/2009, is used for predicting VaR figures and backtesting. Do note here is that the latter stage is exactly the current global financial crisis period which began from the August of 2007, dramatically peaked in the ending months of 2008 and signally reduced significantly in the middle of 2009. Consequently, the study will purposely examine the accuracy of the VaR models within the volatile time. 3.1.1. FTSE 100 index The FTSE 100 Index is a share index of the 100 most highly capitalised UK companies listed on the London Stock Exchange, began on 3rd January 1984. FTSE 100 companies represent about 81% of the market capitalisation of the whole London Stock Exchange and become the most widely used UK stock market indicator. In the dissertation, the full data used for the empirical analysis consists of 1782 observations (1782 working days) of the UK FTSE 100 index covering the period from 05/06/2002 to 22/06/2009. 3.1.2. SP 500 index The SP 500 is a value weighted index published since 1957 of the prices of 500 large-cap common stocks actively traded in the United States. The stocks listed on the SP 500 are those of large publicly held companies that trade on either of the two largest American stock market companies, the NYSE Euronext and NASDAQ OMX. After the Dow Jones Industrial Average, the SP 500 is the most widely followed index of large-cap American stocks. The SP 500 refers not only to the index, but also to the 500 companies that have their common stock included in the index and consequently considered as a bellwether for the US economy. Similar to the FTSE 100, the data for the SP 500 is also observed during the same period with 1775 observations (1775 working days). 3.2. Data Analysis For the VaR models, one of the most important aspects is assumptions relating to measuring VaR. This section first discusses several VaR assumptions and then examines the collected empirical data characteristics. 3.2.1. Assumptions 3.2.1.1. Normality assumption Normal distribution As mentioned in the chapter 2, most VaR models assume that return distribution is normally distributed with mean of 0 and standard deviation of 1 (see figure 3.1). Nonetheless, the chapter 2 also shows that the actual return in most of previous empirical investigations does not completely follow the standard distribution. Figure 3.1: Standard Normal Distribution Skewness The skewness is a measure of asymmetry of the distribution of the financial time series around its mean. Normally data is assumed to be symmetrically distributed with skewness of 0. A dataset with either a positive or negative skew deviates from the normal distribution assumptions (see figure 3.2). This can cause parametric approaches, such as the Riskmetrics and the symmetric normal-GARCH(1,1) model under the assumption of standard distributed returns, to be less effective if asset returns are heavily skewed. The result can be an overestimation or underestimation of the VaR value depending on the skew of the underlying asset returns. Figure 3.2: Plot of a positive or negative skew Kurtosis The kurtosis measures the peakedness or flatness of the distribution of a data sample and describes how concentrated the returns are around their mean. A high value of kurtosis means that more of data’s variance comes from extreme deviations. In other words, a high kurtosis means that the assets returns consist of more extreme values than modeled by the normal distribution. This positive excess kurtosis is, according to Lee and Lee (2000) called leptokurtic and a negative excess kurtosis is called platykurtic. The data which is normally distributed has kurtosis of 3. Figure 3.3: General forms of Kurtosis Jarque-Bera Statistic In statistics, Jarque-Bera (JB) is a test statistic for testing whether the series is normally distributed. In other words, the Jarque-Bera test is a goodness-of-fit measure of departure from normality, based on the sample kurtosis and skewness. The test statistic JB is defined as: where n is the number of observations, S is the sample skewness, K is the sample kurtosis. For large sample sizes, the test statistic has a Chi-square distribution with two degrees of freedom. Augmented Dickey–Fuller Statistic Augmented Dickey–Fuller test (ADF) is a test for a unit root in a time series sample. It is an augmented version of the Dickey–Fuller test for a larger and more complicated set of time series models. The ADF statistic used in the test is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence. ADF critical values: (1%) –3.4334, (5%) –2.8627, (10%) –2.5674. 3.2.1.2. Homoscedasticity assumption Homoscedasticity refers to the assumption that the dependent variable exhibits similar amounts of variance across the range of values for an independent variable. Figure 3.4: Plot of Homoscedasticity Unfortunately, the chapter 2, based on the previous empirical studies confirmed that the financial markets usually experience unexpected events, uncertainties in prices (and returns) and exhibit non-constant variance (Heteroskedasticity). Indeed, the volatility of financial asset returns changes over time, with periods when volatility is exceptionally high interspersed with periods when volatility is unusually low, namely volatility clustering. It is one of the widely stylised facts (stylised statistical properties of asset returns) which are common to a common set of financial assets. The volatility clustering reflects that high-volatility events tend to cluster in time. 3.2.1.3. Stationarity assumption According to Cont (2001), the most essential prerequisite of any statistical analysis of market data is the existence of some statistical properties of the data under study which remain constant over time, if not it is meaningless to try to recognize them. One of the hypotheses relating to the invariance of statistical properties of the return process in time is the stationarity. This hypothesis assumes that for any set of time instants ,†¦, and any time interval the joint distribution of the returns ,†¦, is the same as the joint distribution of returns ,†¦,. The Augmented Dickey-Fuller test, in turn, will also be used to test whether time-series models are accurately to examine the stationary of statistical properties of the return. 3.2.1.4. Serial independence assumption There are a large number of tests of randomness of the sample data. Autocorrelation plots are one common method test for randomness. Autocorrelation is the correlation between the returns at the different points in time. It is the same as calculating the correlation between two different time series, except that the same time series is used twice once in its original form and once lagged one or more time periods. The results can range from  +1 to -1. An autocorrelation of  +1 represents perfect positive correlation (i.e. an increase seen in one time series will lead to a proportionate increase in the other time series), while a value of -1 represents perfect negative correlation (i.e. an increase seen in one time series results in a proportionate decrease in the other time series). In terms of econometrics, the autocorrelation plot will be examined based on the Ljung-Box Q statistic test. However, instead of testing randomness at each distinct lag, it tests the overall randomness based on a number of lags. The Ljung-Box test can be defined as: where n is the sample size,is the sample autocorrelation at lag j, and h is the number of lags being tested. The hypothesis of randomness is rejected if whereis the percent point function of the Chi-square distribution and the ÃŽ ± is the quantile of the Chi-square distribution with h degrees of freedom. 3.2.2. Data Characteristics Table 3.1 gives the descriptive statistics for the FTSE 100 and the SP 500 daily stock market prices and returns. Daily returns are computed as logarithmic price relatives: Rt = ln(Pt/pt-1), where Pt is the closing daily price at time t. Figures 3.5a and 3.5b, 3.6a and 3.6b present the plots of returns and price index over time. Besides, Figures 3.7a and 3.7b, 3.8a and 3.8b illustrate the combination between the frequency distribution of the FTSE 100 and the SP 500 daily return data and a normal distribution curve imposed, spanning from 05/06/2002 through 22/06/2009. Table 3.1: Diagnostics table of statistical characteristics on the returns of the FTSE 100 Index and SP 500 index between 05/06/2002 and 22/6/2009. DIAGNOSTICS SP 500 FTSE 100 Number of observations 1774 1781 Largest return 10.96% 9.38% Smallest return -9.47% -9.26% Mean return -0.0001 -0.0001 Variance 0.0002 0.0002 Standard Deviation 0.0144 0.0141 Skewness -0.1267 -0.0978 Excess Kurtosis 9.2431 7.0322 Jarque-Bera 694.485*** 2298.153*** Augmented Dickey-Fuller (ADF) 2 -37.6418 -45.5849 Q(12) 20.0983* Autocorre: 0.04 93.3161*** Autocorre: 0.03 Q2 (12) 1348.2*** Autocorre: 0.28 1536.6*** Autocorre: 0.25 The ratio of SD/mean 144 141 Note: 1. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. 2. 95% critical value for the augmented Dickey-Fuller statistic = -3.4158 Figure 3.5a: The FTSE 100 daily returns from 05/06/2002 to 22/06/2009 Figure 3.5b: The SP 500 daily returns from 05/06/2002 to 22/06/2009 Figure 3.6a: The FTSE 100 daily closing prices from 05/06/2002 to 22/06/2009 Figure 3.6b: The SP 500 daily closing prices from 05/06/2002 to 22/06/2009 Figure 3.7a: Histogram showing the FTSE 100 daily returns combined with a normal distribution curve, spanning from 05/06/2002 through 22/06/2009 Figure 3.7b: Histogram showing the SP 500 daily returns combined with a normal distribution curve, spanning from 05/06/2002 through 22/06/2009 Figure 3.8a: Diagram showing the FTSE 100’ frequency distribution combined with a normal distribution curve, spanning from 05/06/2002 through 22/06/2009 Figure 3.8b: Diagram showing the SP 500’ frequency distribution combined with a normal distribution curve, spanning from 05/06/2002 through 22/06/2009 The Table 3.1 shows that the FTSE 100 and the SP 500 average daily return are approximately 0 percent, or at least very small compared to the sample standard deviation (the standard deviation is 141 and 144 times more than the size of the average return for the FTSE 100 and SP 500, respectively). This is why the mean is often set at zero when modelling daily portfolio returns, which reduces the uncertainty and imprecision of the estimates. In addition, large standard deviation compared to the mean supports the evidence that daily changes are dominated by randomness and small mean can be disregarded in risk measure estimates. Moreover, the paper also employes five statistics which often used in analysing data, including Skewness, Kurtosis, Jarque-Bera, Augmented Dickey-Fuller (ADF) and Ljung-Box test to examining the empirical full period, crossing from 05/06/2002 through 22/06/2009. Figure 3.7a and 3.7b demonstrate the histogram of the FTSE 100 and the SP 500 daily return data with the normal distribution imposed. The distribution of both the indexes has longer, fatter tails and higher probabilities for extreme events than for the normal distribution, in particular on the negative side (negative skewness implying that the distribution has a long left tail). Fatter negative tails mean a higher probability of large losses than the normal distribution would suggest. It is more peaked around its mean than the normal distribution, Indeed, the value for kurtosis is very high (10 and 12 for the FTSE 100 and the SP 500, respectively compared to 3 of the normal distribution) (also see Figures 3.8a and 3.8b for more details). In other words, the most prominent deviation from the normal distributional assumption is the kurtosis, which can be seen from the middle bars of the histogram rising above the normal distribution. Moreover, it is obvious that outliers still exist, which indicates that excess kurtosis is still present. The Jarque-Bera test rejects normality of returns at the 1% level of significance for both the indexes. So, the samples have all financial characteristics: volatility clustering and leptokurtosis. Besides that, the daily returns for both the indexes (presented in Figure 3.5a and 3.5b) reveal that volatility occurs in bursts; particularly the returns were very volatile at the beginning of examined period from June 2002 to the middle of June 2003. After remaining stable for about 4 years, the returns of the two well-known stock indexes in the world were highly volatile from July 2007 (when the credit crunch was about to begin) and even dramatically peaked since July 2008 to the end of June 2009. Generally, there are two recognised characteristics of the collected daily data. First, extreme outcomes occur more often and are larger than that predicted by the normal distribution (fat tails). Second, the size of market movements is not constant over time (conditional volatility). In terms of stationary, the Augmented Dickey-Fuller is adopted for the unit root test. The null hypothesis of this test is that there is a unit root (the time series is non-stationary). The alternative hypothesis is that the time series is stationary. If the null hypothesis is rejected, it means that the series is a stationary time series. In this thesis, the paper employs the ADF unit root test including an intercept and a trend term on return. The results from the ADF tests indicate that the test statistis for the FTSE 100 and the SP 500 is -45.5849 and -37.6418, respectively. Such values are significantly less than the 95% critical value for the augmented Dickey-Fuller statistic (-3.4158). Therefore, we can reject the unit root null hypothesis and sum up that the daily return series is robustly stationary. Finally, Table 3.1 shows the Ljung-Box test statistics for serial correlation of the return and squared return series for k = 12 lags, denoted by Q(k) and Q2(k), respectively. The Q(12) statistic is statistically significant implying the present of serial correlation in the FTSE 100 and the SP 500 daily return series (first moment dependencies). In other words, the return series exhibit linear dependence. Figure 3.9a: Autocorrelations of the FTSE 100 daily returns for Lags 1 through 100, covering 05/06/2002 to 22/06/2009. Figure 3.9b: Autocorrelations of the SP 500 daily returns for Lags 1 through 100, covering 05/06/2002 to 22/06/2009. Figures 3.9a and 3.9b and the autocorrelation coefficient (presented in Table 3.1) tell that the FTSE 100 and the SP 500 daily return did not display any systematic pattern and the returns have very little autocorrelations. According to Christoffersen (2003), in this situation we can write: Corr(Rt+1,Rt+1-ÃŽ ») ≈ 0, for ÃŽ » = 1,2,3†¦, 100 Therefore, returns are almost impossible to predict from their own past. One note is that since the mean of daily returns for both the indexes (-0.0001) is not significantly different from zero, and therefore, the variances of the return series are measured by squared returns. The Ljung-Box Q2 test statistic for the squared returns is much higher, indicating the presence of serial correlation in the squared return series. Figures 3.10a and 3.10b) and the autocorrelation coefficient (presented in Table 3.1) also confirm the autocorrelations in squared returns (variances) for the FTSE 100 and the SP 500 data, and more importantly, variance displays positive correlation with its own past, especially with short lags. Corr(R2t+1,R2t+1-ÃŽ ») > 0, for ÃŽ » = 1,2,3†¦, 100 Figure 3.10a: Autocorrelations of the FTSE 100 squared daily returns Figure 3.10b: Autocorrelations of the SP 500 squared daily returns 3.3. Calculation of Value At Risk The section puts much emphasis on how to calculate VaR figures for both single return indexes from proposed models, including the Historical Simulation, the Riskmetrics, the Normal-GARCH(1,1) (or N-GARCH(1,1)) and the Student-t GARCH(1,1) (or t-GARCH(1,1)) model. Except the historical simulation model which does not make any assumptions about the shape of the distribution of the assets returns, the other ones commonly have been studied under the assumption that the returns are normally distributed. Based on the previous section relating to the examining data, this assumption is rejected because observed extreme outcomes of the both single index returns occur more often and are larger than predicted by the normal distribution. Also, the volatility tends to change through time and periods of high and low volatility tend to cluster together. Consequently, the four proposed VaR models under the normal distribution either have particular limitations or unrealistic. Specifically, the historical simulation significantly assumes that the historically simulated returns are independently and identically distributed through time. Unfortunately, this assumption is impractical due to the volatility clustering of the empirical data. Similarly, although the Riskmetrics tries to avoid relying on sample observations and make use of additional information contained in the assumed distribution function, its normally distributional assumption is also unrealistic from the results of examining the collected data. The normal-GARCH(1,1) model and the student-t GARCH(1,1) model, on the other hand, can capture the fat tails and volatility clustering which occur in the observed financial time series data, but their returns standard distributional assumption is also impossible comparing to the empirical data. Despite all these, the thesis still uses the four models under the standard distributional assumption of returns to comparing and evaluating their estimated results with the predicted results based on the student distributional assumption of returns. Besides, since the empirical data experiences fatter tails more than that of the normal distribution, the essay intentionally employs the Cornish-Fisher Expansion technique to correct the z-value from the normal distribution to account for fatter tails, and then compare these results with the two results above. Therefore, in this chapter, we purposely calculate VaR by separating these three procedures into three different sections and final results will be discussed in length in chapter 4. 3.3.1. Components of VaR measures Throughout the analysis, a holding period of one-trading day will be used. For the significance level, various values for the left tail probability level will be considered, ranging from the very conservative level of 1 percent to the mid of 2.5 percent and to the less cautious 5 percent. The various VaR models will be estimated using the historical data of the two single return index samples, stretches from 05/06/2002 through 31/07/2007 (consisting of 1305 and 1298 prices observations for the FTSE 100 and the SP 500, respectively) for making the parameter estimation, and from 01/08/2007 to 22/06/2009 for predicting VaRs and backtesting. One interesting point here is that since there are few previous empirical studies examining the performance of VaR models during periods of financial crisis, the paper deliberately backtest the validity of VaR models within the current global financial crisis from the beginning in August 2007. 3.3.2. Calculation of VaR 3.3.2.1. Non-parametric approach Historical Simulation As mentioned above, the historical simulation model pretends that the change in market factors from today to tomorrow will be the same as it was some time ago, and therefore, it is computed based on the historical returns distribution. Consequently, we separate this non-parametric approach into a section. The chapter 2 has proved that calculating VaR using the historical simulation model is not mathematically complex since the measure only requires a rational period of historical data. Thus, the first task is to obtain an adequate historical time series for simulating. There are many previous studies presenting that predicted results of the model are relatively reliable once the window length of data used for simulating daily VaRs is not shorter than 1000 observed days. In this sense, the study will be based on a sliding window of the previous 1305 and 1298 prices observations (1304 and 1297 returns observations) for the FTSE 100 and the SP 500, respectively, spanning from 05/06/2002 through 31/07/2007. We have selected this rather than larger windows is since adding more historical data means adding older historical data which could be irrelevant to the future development of the returns indexes. After sorting in ascending order the past returns attributed to equally spaced classes, the predicted VaRs are determined as that log-return lies on the target percentile, say, in the thesis is on three widely percentiles of 1%, 2.5% and 5% lower tail of the return distribution. The result is a frequency distribution of returns, which is displayed as a histogram, and shown in Figure 3.11a and 3.11b below. The vertical axis shows the number of days on which returns are attributed to the various classes. The red vertical lines in the histogram separate the lowest 1%, 2.5% and 5% returns from the remaining (99%, 97.5% and 95%) returns. For FTSE 100, since the histogram is drawn from 1304 daily returns, the 99%, 97.5% and 95% daily VaRs are approximately the 13th, 33rd and 65th lowest return in this dataset which are -3.2%, -2.28% and -1.67%, respectively and are roughly marked in the histogram by the red vertical lines. The interpretation is that the VaR gives a number such that there is, say, a 1% chance of losing more than 3.2% of the single asset value tomorrow (on 01st August 2007). The SP 500 VaR figures, on the other hand, are little bit smaller than that of the UK stock index with -2.74%, -2.03% and -1.53% corresponding to 99%, 97.5% and 95% confidence levels, respectively. Figure 3.11a: Histogram of daily returns of FTSE 100 between 05/06/2002 and 31/07/2007 Figure 3.11b: Histogram of daily returns of SP 500 between 05/06/2002 and 31/07/2007 Following predicted VaRs on the first day of the predicted period, we continuously calculate VaRs for the estimated period, covering from 01/08/2007 to 22/06/2009. The question is whether the proposed non-parametric model is accurately performed in the turbulent period will be discussed in length in the chapter 4. 3.3.2.2. Parametric approaches under the normal distributional assumption of returns This section presents how to calculate the daily VaRs using the parametric approaches, including the RiskMetrics, the normal-GARCH(1,1) and the student-t GARCH(1,1) under the standard distributional assumption of returns. The results and the validity of each model during the turbulent period will deeply be considered in the chapter 4. 3.3.2.2.1. The RiskMetrics Comparing to the historical simulation model, the RiskMetrics as discussed in the chapter 2 does not solely rely on sample observations; instead, they make use of additional information contained in the normal distribution function. All that needs is the current estimate of volatility. In this sense, we first calculate daily RiskMetrics variance for both the indexes, crossing the parameter estimated period from 05/06/2002 to 31/07/2007 based on the well-known RiskMetrics variance formula (2.9). Specifically, we had the fixed decay factor ÃŽ »=0.94 (the RiskMetrics system suggested using ÃŽ »=0.94 to forecast one-day volatility). Besides, the other parameters are easily calculated, for instance, and are the squared log-return and variance of the previous day, correspondingly. After calculating the daily variance, we continuously measure VaRs for the forecasting period from 01/08/2007 to 22/06/2009 under different confidence levels of 99%, 97.5% and 95% based on the normal VaR formula (2.6), where the critical z-value of the normal distribution at each significance level is simply computed using the Excel function NORMSINV. 3.3.2.2.2. The Normal-GARCH(1,1) model For GARCH models, the chapter 2 confirms that the most important point is to estimate the model parameters ,,. These parameters has to be calculated for numerically, using the method of maximum likelihood estimation (MLE). In fact, in order to do the MLE function, many previous studies efficiently use professional econometric softwares rather than handling the mathematical calculations. In the light of evidence, the normal-GARCH(1,1) is executed by using a well-known econometric tool, STATA, to estimate the model parameters (see Table 3.2 below). Table 3.2. The parameters statistics of the Normal-GARCH(1,1) model for the FTSE 100 and the SP 500 Normal-GARCH(1,1)* Parameters FTSE 100 SP 500 0.0955952 0.0555244 0.8907231 0.9289999 0.0000012 0.0000011 + 0.9863183 0.9845243 Number of Observations 1304 1297 Log likelihood 4401.63 4386.964 * Note: In this section, we report the results from the Normal-GARCH(1,1) model using the method of maximum likelihood, under the assumption that the errors conditionally follow the normal distribution with significance level of 5%. According to Table 3.2, the coefficients of the lagged squared returns () for both the indexes are positive, concluding that strong ARCH effects are apparent for both the financial markets. Also, the coefficients of lagged conditional variance () are significantly positive and less than one, indicating that the impact of ‘old’ news on volatility is significant. The magnitude of the coefficient, is especially high (around 0.89 – 0.93), indicating a long memory in the variance. The estimate of was 1.2E-06 for the FTSE 100 and 1.1E-06 for the SP 500 implying a long run standard deviation of daily market return of about 0.94% and 0.84%, respectively. The log-likehood for this model for both the indexes was 4401.63 and 4386.964 for the FTSE 100 and the SP 500, correspondingly. The Log likehood ratios rejected the hypothesis of normality very strongly. After calculating the model parameters, we begin measuring conditional variance (volatility) for the parameter estimated period, covering from 05/06/2002 to 31/07/2007 based on the conditional variance formula (2.11), where and are the squared log-return and conditional variance of the previous day, respectively. We then measure predicted daily VaRs for the forecasting period from 01/08/2007 to 22/06/2009 under confidence levels of 99%, 97.5% and 95% using the normal VaR formula (2.6). Again, the critical z-value of the normal distribution under significance levels of 1%, 2.5% and 5% is purely computed using the Excel function NORMSINV. 3.3.2.2.3. The Student-t GARCH(1,1) model Different from the Normal-GARCH(1,1) approach, the model assumes that the volatility (or the errors of the returns) follows the Student-t distribution. In fact, many previous studies suggested that using the symmetric GARCH(1,1) model with the volatility following the Student-t distribution is more accurate than with that of the Normal distribution when examining financial time series. Accordingly, the paper additionally employs the Student-t GARCH(1,1) approach to measure VaRs. In this section, we use this model under the normal distributional assumption of returns. First is to estimate the model parameters using the method of maximum likelihood estimation and obtained by the STATA (see Table 3.3). Table 3.3. The parameters statistics of the Student-t GARCH(1,1) model for the FTSE 100 and the SP 500 Student-t GARCH(1,1)* Parameters FTSE 100 SP 500 0.0926120 0.0569293 0.8946485 0.9354794 0.0000011 0.0000006 + 0.9872605 0.9924087 Number of Observations 1304 1297 Log likelihood 4406.50 4399.24 * Note: In this section, we report the results from the Student-t GARCH(1,1) model using the method of maximum likelihood, under the assumption that the errors conditionally follow the student distribution with significance level of 5%. The Table 3.3 also identifies the same characteristics of the student-t GARCH(1,1) model parameters comparing to the normal-GARCH(1,1) approach. Specifically, the results of , expose that there were evidently strong ARCH effects occurred on the UK and US financial markets during the parameter estimated period, crossing from 05/06/2002 to 31/07/2007. Moreover, as Floros (2008) mentioned, there was also the considerable impact of ‘old’ news on volatility as well as a long memory in the variance. We at that time follow the similar steps as calculating VaRs using the normal-GARCH(1,1) model. 3.3.2.3. Parametric approaches under the normal distributional assumption of returns modified by the Cornish-Fisher Expansion technique The section 3.3.2.2 measured the VaRs using the parametric approaches under the assumption that the returns are normally distributed. Regardless of their results and performance, it is clearly that this assumption is impractical since the fact that the collected empirical data experiences fatter tails more than that of the normal distribution. Consequently, in this section the study intentionally employs the Cornish-Fisher Expansion (CFE) technique to correct the z-value from the assumption of the normal distribution to significantly account for fatter tails. Again, the question of whether the proposed models achieved powerfully within the recent damage time will be assessed in length in the chapter 4. 3.3.2.3.1. The CFE-modified RiskMetrics Similar

For my project I am going to design a new range of Alco-pop

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Appendix B Data Use Agreement Essay - 858 Words

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A stapler was passed around, and the participants were instructed to staple their demographics survey, recall sheet, and drawings together. The stapled sheets were then collected by the experimenters. The experimenters shuffled and marked each set of papers with a unique number between 1 and 23 in order to identify the resulting data whileRead MoreWriting The Results Section Is More Intimidating Than Writing Materials And Methods1271 Words   |  6 Pagesto use all your writing skills to objectively present your key findings in an orderly and logical sequence using illustrative materials and text. Your Results should be organized into different segments or subsections where each one presents the purpose of the experiment, your experimental approach, data including text and visuals (tables, figures, schematics, algorithms, and formulas), and data commentary. For most journals, your data commentary will include a meaningful summary of the data presentedRead MoreTiffany Co960 Words   |  4 Pagesw/ household incomes over $100,000 to grow by 20% (O) • Low cost manufacturing abroad Ââ€" China, Brazil (O) • High discretionary income of baby-boomers through credit card use (O) 2. Technology • Increased availability of Internet (O) • Increased use of E-Commerce (O) • New QAD MFG/PRO software to collect real-time data (O) 2. Political-Legal • Increase in free trade (O/T) • China s membership to WTO (O) • WTO Ââ€" World Trade Organization (O/T) • Tax benefits associated w/ ETI (O) Read MoreStarbuckss Marketing Plan For Starbucks1305 Words   |  6 PagesVerismo. All of the intricacies that make Starbucks a big success also offer challenges to the company that puts more weight on an effective strategic management process. Starbucks honors their responsibility, both socially and ethically, by trying to use dependably grown coffee and increase their fair trade coffee supplier (Starbucks Corporation, 2012). Starbucks began in 1971 as a sole coffee shop in Seattle, Washington and has become a complex, expanded business of stores, packaged goods, and productRead MoreGSBS6002 Assignment 2 Tri 2 20151335 Words   |  6 Pagescustomers. A member of your team has already collected data that can be used for this analysis. To collect this data, a simple random sample of 500 customers was selected. Of the 500 customers to whom surveys were sent, 420 responded. The survey used to collect this data is provided below and the survey responses have been collated in the CompleteCare.xls Excel file. You are required to write a report after performing an analysis on the data collected from the customers of Computers R Us. A member

Panera Bread - Free Essay Example

Sample details Pages: 3 Words: 755 Downloads: 8 Date added: 2017/09/25 Category Advertising Essay Type Argumentative essay Tags: Restaurant Essay Did you like this example? Panera Bread began in 1981 as Au Bon Pain Co. , a fast-casual bakery and cafe chain, founded by Louis Kane and Ron Shaich. Throughout the 1980s and 1990s, the chain grew along the east cost of the United States and internationally. It dominated in the bakery-cafe category. In 1993, Au Bon Pain Co. purchased Saint Louis Bread Company, which was founded by Kenneth Rosenthal. At this time, the Saint Louis Bread Company was in the midst of renovating its 20 bakery-cafes in the Saint Louis area. The concept’s name was ultimately changed to Panera Bread. By 1997, it became clear that Panera Bread had the potential to become one of the leading brands in the nation. In May 1999, to expand Panera Bread into a national restaurant, all of Au Bon Pain Co’s business units were sold, with the exception of Panera Bread. The company was then renamed Panera Bread. The company was operating 1,362 bakery-cafes in 40 states and 17 facilities that delivered fresh dough to the caf es daily. Panera Bread still operates under the name St. Louis Bread Company, with its headquarters in St. Louis. The St. Louis area has over 50 locations. In 2005, Panera Bread was recognized as one of Business Week’s â€Å"100 Hot Growth Companies†, earning $38. 6 million with a 42. 9% increase in profits. In 2006, Panera Bread was recognized as the top performer in the restaurant category for one, five, and ten year returns to shareholders, reported by The Wall Street Journal. In 2007, Panera Bread purchased a majority stake in Paradise Bakery Cafe, a Phoenix-based concept with over 70 locations in 10 states, the balance to be purchased in June of 2009. In 2008, Health magazine judged Panera Bread as the healthiest fast food restaurant. Also in 2008, Panera Bread began expanding into Canada, with Richmond Hill and Mississauga, both in the Toronto area. As of 2009, the restaurant was named most popular for eating on the go by the restaurant review service Zagat . They were also rated #1 for best salad, best healthy option, and best facilities among restaurants with less than 5,000 locations. Panera Bread now has 1,380 bakery cafes in 40 states and Canada, delivering fresh artisan breads, bagels, muffins, scones, sandwiches, as well as soups, salads, and specialty coffee drinks. By emphasizing nutritional value and quality, such as antibiotic free chicken and whole grain bread, this restaurant chain distinguishes its products from fast food restaurants such as McDonalds, Wendy’s, and Burger King. Panera also distinguishes itself from these other fast food chains by providing a longer dining experience, with more welcoming furnishings and free Internet access. As opposed to the concept of â€Å"fast food†, Panera is associated with the concept of â€Å"fast casual†. This is a combination of fast food with a casual dining experience. Panera targets consumers who seek meals of higher quality than they would find at t he traditional fast food chain, but don’t have the time to dine in or have a sit-down meal at a restaurant. Though there are many other restaurants who offer this same combination, they tend to be local and do not benefit from a national brand name with a large advertising budget. A key aspect of Panera Bread’s business that protects the company from direct competition in the fast food industry is their product niche, artisan fast food. Fast food chains are often criticized for offering unhealthy foods. But, Panera Bread focuses on a higher nutritional value in their products. Dine in restaurants are very susceptible to drops in consumer spending, so Panera Bread’s cheaper items, while still being healthier than your typical fast food chain, make it an attractive alternative to traditional eateries. All the same, the product niche allows Panera flexibility in raising menu prices because consumers recognize the products as high quality, especially in compar ison to the traditional fast food chains. The company’s marketing strategies focus on product merchandising, such as the promotion of new menu items, as opposed to product prices. The company also sponsors charitable events as a marketing tool. Since the founding of Panera Bread, the company has made efforts in giving back to local communities. Panera runs the Community Breadbox program, where they match cash donations from customers and distribute them to local non-profit organizations. Through the Day-End Dough-Nation program Panera Bread runs, unsold bakery products are packaged and collected at the end of each day and donated to local food banks and charities. The company also participates in the Scrip fundraising program, which invites non-profit organizations to pre-purchase $10 Panera Bread gift cards at a 9% discounted rate and resell them at full price to raise money. Don’t waste time! Our writers will create an original "Panera Bread" essay for you Create order

Economic Effects of Diabetes on the Elderly - 1751 Words

Economic effects of diabetes on the elderly Diabetes has been described, by doctors, as a metabolic disease in which the patient has high blood glucose (blood sugar), either because insulin production is inadequate, or because the body s cells do not respond properly to insulin. The overall management of diabetes for older adults would be the same as management for younger adults. Nutritional management is essential for older adults primarily to control malnutrition and the patient being underweight. For older adults, diabetes can not only be difficult for their overall health but also can cause financial hardship. I’ll discuss how Medicare and Medicaid help elevate some of the financial burden that†¦show more content†¦The idea is to give seniors a fixed value voucher and give them options while shopping for coverage in the private insurance market. The voucher system would help control health care cost by allowing seniors to shop for their coverage thus driving the insurance market to keep prices competitive and affordable for seniors. Health policy experts have concluded that if Medicare is to be saved for the next generation, small concessions must be made to allow the program to prosper into the future. Liberal groups argue that cutting entitlement programs such as Medicare may cause a health crisis to epidemic proportions. Liberal groups would rather raise taxes or end tax cuts for the wealthy in order to get the country’s economic crisis contained and Medicare Health policy experts have concluded that if cuts in Medicare occurs, many seniors may not receive basic healthcare. The notion that lawmakers would be asking seniors to tighten their belts while the Federal Government still gives huge tax breaks to millionaires and subsidies to oil companies is wrong and immoral. Critics of the voucher system warns that the system is flawed and would give more control to the insurance companies without supplying any guarantee that seniors could find a plan comparable to traditional Medicare. Replacing Medicare with vouchers for private insurance would shift costs to seniors and increase overall costs by allowing private insurance companies toShow MoreRelatedMalnutrition Among The Elderly : Malnutrition1681 Words   |  7 PagesMalnutrition in the Elderly The general objective of this research paper is to increase awareness about a mostly hidden epidemic among the elderly. Studies show one in every two older people are at risk for malnutrition. (Drewnowski Evans, 2001) Findings also show that hunger among the elderly is an enormous, far-reaching problem found in places across the globe, but the United States seems to be an unlikely place to find starvation where food is plentiful. Consequently, because of ineffectiveRead MoreThe Alcoholism And Substance Abuse978 Words   |  4 Pageshave a higher school dropout rate. Young adults to the elderly suffer from the misuse. â€Å"Though alcoholism and substance abuse rates are lowest among the elderly, access to habit-forming prescription drugs increases their risk of substance abuse† (Burkholder Nash, 2013, sec. 3.4.). There are many who suffer from unemployment, health issues, poor decisions etc. It is hard to become employed and to keep a job while under the influence. Diabetes , Liver disease, Heart disease and Kidney failure are onlyRead MoreSymptoms And Symptoms Of Diabetes Essay1457 Words   |  6 PagesDiabetes 1. Illness or Symptoms: The most common symptoms are fatigue, having to urinate more than feeling thirsty, distorted vision, and dry mouth. Type 1 diabetes symptoms are rapidly noticed with more severe symptoms verses type 2 diabetes, which have symptoms that usually are not as noticeable and develop at a slower rate. 2. Patients: Patients who are over 45 are more likely to get diabetes; the older you get the more of a risk you have. If the patient has a family background of type 2 diabetesRead MoreMedicare Funding Crisis1692 Words   |  7 PagesDonnie Tatar University of Michigan HSM544: Health Policy and Economics As the newly appointed chief of staff I have been tasked with responding to a proposal for reducing Medicare expenditures by enrolling participants in HMO. I understand that we have some key questions must be addressed and that we must justify our position on either economic efficiency or equity grounds. Outlined below are some of the questions that must be answered in order address this issue properly. Is Medicare inRead MoreObesity And Its Effects On Society1303 Words   |  6 PagesObesity and its Effects on Society ‘America is fat’, this statement repeated by numerous people in and out of healthcare profession and if someone don’t believe this statement, maybe the following statistic will change our mind. According to (CDC) Center for Diseases Control and prevention, obesity rate grew 65% between 1990 and 2002(Su). Still not convince? When most Americans read that statistics they have single question is ‘Why?’ How is the rate of obesity growing so fast? Is this the way weRead MoreGovernment Funding Is The Major Source Of Health Funding1376 Words   |  6 Pagesbudget impact and opportunity costs into consideration. BIA as an important part of comprehensive economic evaluation, assesses the impact of new interventions or drugs on national, regional or local health budget plan(41). Taking budget impact and opportunity costs into account will make the results more applicable to the reality. Country-specific CEA and subgroup Analysis are important Several economic evaluation studies applied UKPDS 34 to assess the cost-effectiveness in its domestic context suchRead MoreWeb of Diabetes Causation in the Elderly2549 Words   |  10 Pagesï » ¿Web of Diabetes Causation in the Elderly Web of Diabetes Causation in the Elderly Introduction Epidemiology is the study of environmental and genetic influences on the prevalence of disease and injury (Rossignol, 2007, p. 1). Environmental influences include pollution, lifestyle choices, health care access, care quality, social factors, and workplace hazards. These and other factors help to determine geographic, social, and economic differences in health quality. Epidemiology is therefore theRead MoreThe Prevalence And Incidence Of Type 2 Diabetes Essay1664 Words   |  7 PagesA. Statement of the Problem The prevalence and incidence of type 2 diabetes are increasing worldwide, particularly in devel-oping countries, in conjunction with increased obesity rates and westernization of lifestyle (In-zucchi et al., 2012). The economic burden for health care systems is skyrocketing, owing to the costs associated with treatment and diabetes complications. Type 2 diabetes remains a leading cause of cardiovascular disorders, blindness, end-stage renal failure, amputations, and hospitali-zationsRead MoreThe Retirement Of Elderly Today983 Words   |  4 PagesJun Hui Bae PHE 345U Jost Lottes 29 Nov. 2015 The Retirement of Elderly Today, the elders live longer than few decades ago. if the elderly age is before and today the same, today is a way healthier cause of development of medical. It means that elderly may work few more years after they retire and they should work longer because their drug bill is increasing. In fact, many workers are discovering that they are going to have to work longer than they originally anticipated - an adjustment that canRead MorePathophysiology And Pathophysiology Of Diabetes Mellitus Type 21474 Words   |  6 PagesPharmacology of Diabetes Mellitus Type 2 Type 2 Diabetes is a chronic condition that millions of people around the world suffer from. It is related to the hormone insulin, which is secreted by islet of Langerhans cells in the pancreas, it regulates the level of glucose in the bloodstream and supports the body with breaking down the glucose to be used as energy. When people have diabetes, the body doesn’t produce enough insulin or cells don’t respond to the insulin that is produced. Type 2 diabetes is one

Economics †What does overall supply of labour depend upon Free Essays

1.) What does overall supply of labour depend upon? The overall supply of labour is affected in several different ways. First of all, the working population is considered to be in between 16 and 65 years of age. We will write a custom essay sample on Economics – What does overall supply of labour depend upon? or any similar topic only for you Order Now The inactive population is therefore those younger than 16 and those over 65 years. If there was a huge baby boom in the foreseeable future then the benefits of this would not be felt until some years later when they would become part of the working population. However, in order that the government can gain maximum tax revenue is if more people are in full time education and higher education with the prospect of working in a high paid job. Initially, this would be quite difficult but it would relieve the pressure placed on by the dependency ratio. Other factors that affect the supply of labour are that the death rate is always decreasing therefore the population is increasing. The current health service is going to be put under even more sustained pressure as the more people get older and live longer. This also adds to the increasing dependency ratio. Many people who immigrate to Britain will then, on the whole, add to the overall supply of labour. Another very important factor is that women are getting married later on in life so that they can pursue a career. Also read this  Cheating in a Bottom Line Economy 2.) How do you account for the increase in inactive males in recent years? There are many reasons that men become increasingly inactive in recent years. One reason is, in recent years the primary industry has decreased substantially and the tertiary and services sector has grown considerably. Many men were involved in the primary sector such as factory, coal mining, and farming. Over the last few decades those manufacturing industries have slowly reduced and more tertiary and services have been growing. The tertiary and services sector have a tendency to employ more women, possibly because they are more ‘approachable’ than men. One could think of this as sexual discrimination perhaps. Those men who worked in low skilled jobs also found it difficult to adjust to a new job as those low skilled jobs are not readily available. However, the younger male population tend to stay in education additional to compulsory education. 3.) What has been the economic impact of migration both into and out of the British economy over the past 40 years? The impact of migration had many advantages as well as disadvantages. Over the last 40 years migration, in some cases, has severely affected the working population. For example, in the 1960’s and 1970’s many people chose to migrate to another country so the working population would decrease. The cost of the decrease was a net fall in output. More higher qualified professionals e.g. Doctors, Teachers chose to work away from the UK. This may have a bearing on why there is a shocking lack of teachers around today. Anyway, due to this problem, many people from other parts of the world like Australia, New Zealand, India, South Africa were persuaded to come and work in the UK. 4.) Why are more women becoming more economically active? More women work and have become economically active because of changes in the law forcing firms to have a certain proportion of women in their company. Equal Pay Legislation and Maternity Provision was at the forefront of gaining equal opportunities. Nowadays, many women do not marry when they are in their early 20’s but they may do after they turn 30. Theoretically, these women would choose not to have a baby as they would then be tied down and cannot pursue their career. Formerly, women tended to be house wives, they used to all the house work but because of technological advances time taken to do all the housework shortened leaving the women nothing to do for the rest of the day. The other reason is that women are more flexable with their work hours, they tended to work more part-time. The demand for women workers has sharply risen with the increase in tertiary and services sector. More employers are looking for women to improve the appearance of the company. 5.) To what degree has changing the nature of employment within U.K. affected participation ratios of men and women? Over the last few decades, due to the decline in manufacturing industries and the incline of tertiary industries we can conclude that there has been extensive. This is because as manufacturing industries declined many men found it difficult to learn new skills as well as employers preferred to train younger people. The ratio’s show this by male inactivity slowly rising as female inactivity fell. How to cite Economics – What does overall supply of labour depend upon?, Papers

Genetic Transformation

Question: Describe about the Genetic Transformation? Answer: The field of microbiology deals with the study of the microorganisms like bacteria, virus, fungi, protozoa and archaea. The research on these micro organisms involve the biochemical, physiological, cellular, ecological, clinical and evolutionary aspect also. In order to identify the microorganisms, the very first techniques employed in microbiology lad is the streaking and plating of the bacteria, so that pure colonies of the bacteria are obtained and it is easier to identify the species. The series of methods followed after this are the serial dilution and then plating. Following this, the transformation of bacteria can be carried out so that the gene of interest can be inserted into the genome of the bacteria. The ability of the bacteria to take up genes of different origins, have made it possible to clone many genes including the genes of the humans (Moran et al. 2012). After the transformation process, it is important to observe the bacterial cells under the microscope so that th e efficiency of transformation and the success rate. The present report also deals with the analysis of the tolerance capacity in the bacterial biofilms vs. the planktonic cells. Introduction: Microbial inhabitants have evolved to survive in a variety of ecological niches and growth habitats. Some grow rapidly, some slowly. Some can replicate with minimal number of nutrients present, whereas others require enriched nutrients to survive. Variation exists in atmospheric growth conditions, temperature requirements, and the cell structure. This diversity is also found in the micro-organisms that inhabit the human body as normal flora, as opportunistic pathogens, or as true pathogens. Each microbe has its own unique physiology and metabolic pathway that allow it to survive in a particular habitat (Relman, D. 2012). One of the main roles of a diagnostic or clinical microbiologist is to isolate, identify and analyse the bacteria that causes disease in humans. Knowledge of microbial structure and physiology is extremely important to clinical microbiologists in three areas: Culture of organisms from patient specimens Classification and identification of organisms after they have been isolated Prediction and interpretation of antimicrobial susceptibility patterns The main aim of the techniques of microbiology is to isolate and identify the micro organisms and use them for various biotechnological applications. The purification of bacteria is carried out with the help of the streak plate technique which enables the isolation of the pure colonies from inoculums by creation of areas that have increasing dilution on the single plate of agar (Gudina et al. 2012). In natural habitats microorganisms usually grow in complex, mixed populations containing several species. This presents a problem for the microbiologist because a single type of microorganism cannot be studied adequately in a mixed culture. One needs a pure culture, a population of cells arising from a single cell, to characterize an individual species. Pure cultures are so important that the development of pure culture techniques by the German bacteriologist Robert Koch transformed microbiology. Within about 20 years after the development of pure culture techniques most pathogens responsible for the major human bacterial diseases had been isolated (Tortura, P, Funke, B and Case, C. 2013). In this report the major organism on which the focus is laid is Pseudomonas fluorescens, which is a non pathogenic saprophyte that colonizes water, soil and even the plant surface. This microbe suppresses the plant diseases by producing a number of secondary metabolites like antibiotics, siderophores and hydrogen cyanide. This microbe has the ability to enter into the plant vascular system and reach various parts of the plant and act like a systemic bio control agent against various bacterial and fungal diseases (Dr. Ranjan Laboratories 2008). Another component of this report is to determine the level of antibiotic resistance in the bacterial culture. The antibiotic resistance is said to occur when the bacteria undergoes change in some way such that there is reduction or elimination of the efficacy of the drugs/ chemicals or the agents that aim at curing or preventing infections. Antibiotic resistance occurs when the antibiotic has lost its efficacy in killing the bacteria or fighting the infection. If the bacterial strain, against which the antibiotic is being used, develops the resistance, then even the high dose of antibiotic would not harm the bacteria and it will keep on growing. Whenever the studies need to be performed for research purpose, the use of E. coli bacteria is preferred. This is because the observation of the outgrowth of the members of the Enterobacteriaceae family (including E. coli) is easier as they are facultative anaerobes rather than obligate anaerobes (Mueller, K 2013). In this experiment, the procedure of plating and transformation of the E. coli cells is carried out. The aim of the experiment is to isolate the transformed colonies of bacteria and observe them for antibiotic resistance. In the second part of the experiment, the aim is to identify which has better antibiotic resistance- planktonic cells or the biofilms produced by the bacteria. Materials and Methods: Practical 1 Purification of bacteria was done by the streak plating technique that creates areas with increased dilutions such that every bacteria is far off from other bacteria and spread on the plate individually. Agar plates were prepared with 1.5% agarose and were incubated. The culture was streaked on the plates with the help of the inoculum loop. The plate is streaked sector wise (four quadrants). Following this, the serial dilution of the bacterial culture is prepared by making a serial 10 fold dilutions starting from 10-9. The aliquots of 1 ml bacterial culture to 9 ml of PBS (phosphate buffer saline) are added. A loopful from each of the dilutions is then spread on the agar plates individually. The next technique is the genetic transformation of the bacteria using the pGLO plasmid DNA. The aim of this method is to incorporate two genes into the E coli cell line- one that codes for the GFP (green fluorescent protein) and th eother that provides resistance to ampicillin antibiotic. The pr ocess is carried out in the presence of calcium chloride solution and the plasmid DNA of pGLO plasmid. A small loopful of the bacterial cells is added to tubes labeled as +pGLO and pGLO and the transformation solution (CaCl2) is also added. In +pGLO tube, 10 ul of pGLO plasmid is added and in the pGLO tube no plasmid is added and it is taken as the control. The tubes are incubated and post incubation, heat shock is given to break the cell wall so as to allow the penetration into the nucleus. Practical 2 The first step in this practical was to determine the observation and other records from the previous pratical and then carry out Gram staining to characterize the bacteria. The protocol starts with the preparation of smear of the bacterial culture and then adding crystal violet. The glass slide is then gently washed with water and then grams iodine is added, kept for 60 seconds and then washed with distilled water. The decolorizing solution is then added and the blue dye flows out. The solution is made up of 95% ethanol. The decolorizing solution is again washed off with water and counterstain Grams safranin is then added and kept for 60 seconds. The slides were then observed under the microscope and the gram negative and gram positive bacteria were analysed. The next protocol was that of preparation of E. coli cultures of biofilms. Practical 3 The aim of this experiment was to analyse the strength of the biofilms against the antibiotics and then comparison of the resistance with the resistance to the planktonic cells of the same species. The protocol was carried out by preparing the dilutions of the biofilm culture and then treating them with the specific volume of antibiotic and then preparing the dilutions of planktonic cell culture and again treating them with the antibiotic. The number of cells that survived was seen/ observed with the help of the microscope and the total surface covered by the dead and live cells was evaluated. Results: The microbiological experiements were done to identify and analyse the rate of success of transformation of the pGLO plasmid into the genome of the E. coli bacteria and also the analysis of rate of successful development of antibiotic resistance in cell culture biofils and against the planktonic cells of same species, was also observed. The experiment was successful to a certain extent. The (+) LB/amp/ara plate contained a number of colonies of cells, which when exposed to the UV rays, fluoresced. On the contrary, the (-) LB/ amp/ ara plates contained no colonies. This concluded that the colonies in the former case were the transformed bacteria that had incorporated the GFP gene and the antibiotic resistant gene (derived from the pGLO plasmid). While in the latter case, the transformation was not successful and hence, the original bacterial cells did not survive in the presence of the antibiotic ampicillin. However, negative results were obtained on the (-) LB/amp plate and these col onies glowed under the UV light. Moreover, there were no signs of any colonies on the (+) LB/Amp plate, which was a negative result. Probably, the transfer of the colonies via loop on the plate was error prone and this might have led to loss of accurate data. The results of the third practical are demonstrated in the appendix section. The graphical analysis of the antibiotic resistance in planktonic cells and biofilm was done and Fischer two tailed test was carried out to determine the statistical significance of the categorical data that was obtained. The exact hypergeometric probability of the Fisher test was found to be 0.0003693, which is significant enough to reject the null hypothesis and provides the evidence that significant difference exists between the two groups. The t test score of 0.008857 is also significant and can be used in determination of p value which will further prove if the null hypothesis is correct or wrong. The two tailed probability is used when the direction of the difference between the two entities is not specified. The score obtained corresponds to a very significant value and therefore there exists a significant difference between the number of dead and live cells in planktonic and biofilm, with and without the antibiotics. In the comparative graphical analysis of the number of dead cells in the control plate and the antibiotic treated plate, varying results were obtained. Graph 1: Comparative analysis of the number of dead cells in biofilm with antibiotics and planktonic with antibiotics. The graph shows that the number (percentage) of dead cells in the plate of planktonic cells that were treated with antibiotics, was more than the percentage in the biofilm plate. Graph 2: Comparative analysis of the number of dead cells in planktonic control plate and planktonic cells incubated with antibiotic The graph shows that the relative number of dead cells in the control were less as compared to the number of dead cells found in the antibiotic treated plate. Graph 3: Comparative analysis of the number of dead cells in Biofilm control plate and biofilm cells incubated with antibiotic. The graph shows a deviated result because the number of dead cells in the control plate are found to be more than the number of dead cells in the antibiotic treated plate. Discussion: The very first step in any microbiological experiment related to the isolation and identification of the bacteria, is the proper streaking and plating technique. The experiment of streaking and plating was done successfully and colonies of pure culture were also obtained. In the next step of transformation, there was successful transformation of the E. coli cells and this was determined by plating the inoculums on the LB agar plate that contained ampicillin antibiotic. The successful transformation was visualized under the UV rays and the colonies were found to be illuminated. The antibiotic resistance in planktonic bacteria is related to the inactivation of the antibiotic, thereby leading to the modification of the targets and eventually exclusion of the antibiotic. On the other hand, the biofilm is a result of increase in the resistance of the constituent microbes, to the stressors or the antibiotics. This biofilm acts as a protective environment and protects and helps the bacteria to survive by increasing the inherent resistance of the micro organism (Paraje, M. 2011). The result from the experiment of analyzing the resistance of planktonic bacteria vs the biofilm were consistent to certain extent. From the experiment is it quiet evident that the number of dead cells in the control is less than the treated bacteria and this is because not all the bacteria have resistance to the antibiotic to which they are exposed. However, in the third comparative analysis where the number of dead bacteria in the biofilm control are more than the dead bacteria in the t reated biofilm, there is some form of laboratory error that has led to wrong observations. The most common error is the wrong way of handling the samples and invading the sterile environment that is required for proper growth of the bacteria. Another most common error is that of accurate pipetting and media preparation. The pipetting error is often observed when the medium for plating is prepared or the inoculum is transferred on the plate. There are other possible errors that could have hampered the positive outcome of the results, like the use of wrong culture volumes, error in the serial dilution, etc (Schofield, C. 2006). Appendix: Analysis: Serial dilution Practical 1 Result of no of colonies counting Dilution No. of colonies Concentration of bacteria (CFU ml-1 ) 10-9 0 0 10-8 0 0 10-7 4 4 x 108 10-6 10 1 x 108 10-5 133 1.33 x 108 The formula used for the calculation of the concentration of bacteria is: Number of bacteria = (CFUs on plate (e.g. 27)/ CFUs ml-1 volume plated (e.g. 0.1 ml)) x Dilution factor (e.g. 1 x 105) Transformation Data The PGLO plasmid that is used for the transformation, codes for two genes. One gene produces the GFP protein that gives the inherent green fluorescent glow to the organism and the second gene produces resistance to ampicillin (Blaber, M. 2004). If the genetically transformed cells survive the antibiotic ampicillin, we can infer that the process of transformation has been successful and the genes from the plasmid have been transferred into the cells. The effect of Ampicillin on E coli cells is such that it penetrates through the outer wall of the gram negative bacteria and inhibits transpeptidase, which aids in formation of bacterial cell wall and eventually causes the lysis of the cell (Lawrence, K and Anthony, M 2013). Therefore, the normal (untransformed) cells of E coli are not resistant to ampicillin. So when, after transformation, the cells are grown on LB agar plate containing the antibiotic, only those cells survive and form colonies that have the gene which is resistant to ampicillin. And this can happen only when the transformation has been successful and the gene encoding the resistance against ampicillin has been transferred into the genome of the E. coli cells. Whats glowing? When the UV rays were shined on the negative pGLO plasmid DNA, there was nothing visible and thus, no significant change or observation was recorded. But when the UV rays were shined on positive pGLO plasmid DNA, the colonies of cells appeared in fluorescent green color. This concluded that the protein encoded by the GFP (Green fluorescent protein gene) was being expressed in the cells and because of this expression there was a characteristic green color. There are two sources of fluorescence that can be eliminated- the pGLO plasmid DNA and the original bacterial cells. From the result, it can be concluded that the source of fluorescence is the presence of the pGLO plasmid DNA. The pGLO plasmid produces a protein that encoded by the Green fluorescent protein gene. Expression of this protein gives the characteristic green color to the cells. The experiment was successful to a certain extent. The (+) LB/amp/ara plate contained a number of colonies of cells, which when exposed to the UV rays, fluoresced. On the contrary, the (-) LB/ amp/ ara plates contained no colonies. This concluded that the colonies in the former case were the transformed bacteria that had incorporated the GFP gene and the antibiotic resistant gene (derived from the pGLO plasmid). While in the latter case, the transformation was not successful and hence, the original bacterial cells did not survive in the presence of the antibiotic ampicillin. However, negative results were obtained on the (-) LB/amp plate and these colonies glowed under the UV light. Moreover, there were no signs of any colonies on the (+) LB/Amp plate, which was a negative result. Probably, the transfer of the colonies via loop on the plate was error prone and this might have led to loss of accurate data. The interaction between genes and environment No, it is practically not possible to determine and conclude about the bacteria being ampicillin resistant, simply by looking at them. This is because both, the non resistant bacteria as well as the ampicillin resistant bacteria.However, the comparison can be done by viewing the number of colonies on the two plates- one lacking the gene of ampicillin resistance (-pGLO LB plate) and the other with the gene for ampicillin resistance (+pGLO LB plate). The number of colonies on the +pGLO LB plate determine the number of bacteria that are resistant to ampicillin, while the number of colonies on the pGLO LB plate determine the number of bacteria that are not resistant to ampicillin. The environment of the bacteria was changed by adding ampicillin to LB plate. The bacteria that were resistant to ampicillin grew on this plate while the non resistant ones, were killed. To see the bacterial cells glow green, one of the factors that need to be present is the sugar arabinose in the agarose plate. The transformed cells appear white on the plates containing arabinose. Another factor contributing to the fluorescence of the bacterial cells is the UV light, which when falls of the GFP protein, excites the protein to emit a fluorescent glow and thereby appear fluorescent green in color. The arabinose sugar helps in turning on the expression of the GFP or the green fluorescent protein by binding to the regulatory protein that resides on the promoter region (Desai, T and Rao, C 2010). When the binding between arabinose sugar and the regulatory protein occurs, there is change of shape and this facilitates the transcription of gene by the RNA polymerase. The major advantage for any organism, if it is capable of turning on or off a particular gene, is that the genes can adapt to different conditions and thus, prevent the overproduction of the unnecessary proteins. Transformation efficiency calculation Total number of green fluorescent colonies growing on the LB/ amp/ ara plate= 240 Total number of pGLO plasmid DNA in the bacterial cells spread on the LB/amp/ara plate= 1 l= 0.08 g 10 l= 0.08 x 10 = 0.8 g of DNA Fraction of DNA used = 100/510 = 0.1961 pGLO DNA spread in g= 510 x 0.1961 = 99.99 g Transformation efficiency: No. of colonies on LB/amp/ara plate= 227 Microgrmas of DNA spread on the plates= 0.16 Transformation efficiency= 1.4 x 103 References: Blaber, M, 2004, Lecture 7: Genetic transformation (using bacteria and the pGLO plasmid), BCH 4053L Biochemistry lab, viewed on 18th April 2015, https://www.mikeblaber.org/oldwine/BCH4053l/Lecture07/Lecture07.htm. Desai, T and Rao, C, 2010, Regulation of arabinose and Xylose metabolism in Escherichia coli, appl. Environ. Microbiol., Vol. 76, no. 5, pp: 1524-1532. Ranjan Laboratories, 2008, Pseudomonas fluorescens, viewed on 29th April 2015, https://www.drrajanlaboratories.com/product1.html. 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