Psych Paper Essays - DraftCarson Hill, , Term Papers

Psych Paper My Mom and Dad were divorced when I was one. Dad actually managed to sexually abuse me before the divorce. Karen and Janet, my two older sisters and I went to Dad's on Sundays where we had breakfast. We listened only to classical music, which we hated probably because it was Dad. We did not like him too much, he was different. I had no idea until after he was murdered that he was gay. Well, looking back he was flamboyant, wearing scarves and brooches. He was a gourmet cook and prided himself in the feasts he made for us. My favorite was the crepes drenched in butter and cinnamon sugar. He kept house meticulously, which mirrored his career, a famous art restorer. I never told him I loved him. We had an emotionally distant co-existence. One thing I have held dear like the person in Living through Personal Crisis by Dr. Ann Kaiser Stearns who saved all the clothes of their loved one is a small crystal Easter egg that he gave to me one Easter. It is a symbol of his love, and my valuing it. Mostly, he showed his love through things and outings to plays and musical recitals. Those times were sometimes fun sometimes tedious. But today, I have come to enjoy these types of cultural events. They have helped to shape who I am today. How do you grieve someone you hardly knew, but who is supposed to mean so much I have postponed the grief some what through alcohol and drug use and avoidance. He did mean something to me because when we came home from school, in seventh grade, that day in January, I was shocked when Mom declared, you're father is dead. What do you mean?! What happened?! What do you mean he's dead?! Then the tears started to come and the oh my God's- the utter shock. They told me it was a burglary but that is not what happened. The truth was withheld from me. He was actually taking advantage of two young male prostitutes. Risky behavior, that's for sure. What do you mean male?! What do you mean prostitutes?! I was humiliated! It was years later that I got this news. The whole scene was embarrassing. I thought everyone knew from the newspaper but the whole story was not in the newspaper due to plea bargaining. Back to the seventh grade when this occurred, I was supposed to give a speech dressed as Pocohontas in social studies. Needless to say I missed that one, and subsequently almost failed out of McDonogh that semester. People really don't give enough time for grieving in this society. I needed more time. You would not believe how many times I heard I'm sorry from acquaintances at school. It was too much. It did not help me at all to feel better. No one knew how to listen or even wanted to listen. One girl did ask me how many times he was stabbed. That was really ignorant. I would not have known what to say if someone had listened. But I'm sorry is really useless in helping a person in mourning. Not having any close friends during this time caused me to push my anger down. This began years or depression and suicidal thoughts. An awful lot can happen when one does not deal with pain and loss. My best friend, Ramsey and I did not even talk about the loss of my Dad. However I did find one coping mechanism to further lengthen my grief. It was alcohol. My first drink was with Ramsey at her grandmother's house. It was sweet white wine from my Dad's wine seller. I had no empathic friends at this time in my life, to route for me and help me to talk about my feelings. In middle school, who really has that anyway? It seems that no one I knew talked about problems, nor supported each other except the cheerleaders! The importance of empathic friends in my life today is priceless. I would not do without the recognition of growth, warmth and affection, the reminders of strengths, and the respect of my courage and sense of determination along with all the

The Significance of Physical Therapy Professor Ramos Blog

The Significance of Physical Therapy What pops into one’s head when thinking of a doctor? Most people say a doctor is the person one goes to visit when they are sick and hands them medicine in order to feel better. What most people may not know is that a Physical Therapist is now required to accomplish a doctorate degree in order to officially become a Doctor of Physical Therapy. From healing the individuals that have broken, fractured or even to helping those with lifelong diseases. Perhaps one of the most important aspects included in this career is the patient. The outcome of whether or not therapy works fluently almost entirely relies on patient participation. Not only are Physical Therapists greatly compensated for their work, but the patient outcome of regaining the strength they once had is perhaps the greatest reward.   Six to eight years is typically what this career entails. Completing such degrees as a Bachelor’s, Master’s as well as a Doctorate. After completing the doctorate degree, one now has the honor of being a Doctor of Physical Therapy (DPT). As well as the education aspect of being a participant of this career path, after completion, one must go through a series of state and federal certification as well as taking a state exam in order to get a state license. Along with the certifications and state license, a national exam is required in order to be a recognized PT. The national exam is called by the Federation of State Boards of Physical Therapy (â€Å"Physical Therapist†¦Ã¢â‚¬ ). After completion of the education required, a new doctor is born. After years of experience, some physical therapists choose to become a board-certified specialist offered by The American Board of Physical Therapy Specialities. A board-certified specialist can specialize in one of nine dif ferent specialties which include sports, orthopedics, and geriatrics. The compensation PT’s receive is quite large considering they are a type of doctor. Physical Therapists usually get paid a median of $91,541 a year. The highest quantity of payment would be as high as $104,437 in the Inglewood, California area (â€Å"Physical Therapist in†¦Ã¢â‚¬ ). Higher compensation would be determined by the wealth class of the area one is working in.   Often times, therapy is thought to treat the injured or hurt. Physical Therapists treat a lot more people than one may think. No one goes without the equal attention from a PT; from the elderly to the hurt to the medically disabled even to individuals with body affecting diseases. The elderly seem to need the most aid from a PT, due to their rapid loss of strength and ability. Regaining strength and muscle is a major part in the rehabilitation process. A patient walking through therapy often times needs more help and support regaining strength than anything else. Most hear or see an individual going to therapy because of something they suffered. Unlike an injury or fracture, a stroke is both serious and harmful event that can cause lifelong defects, or in most cases, the worst punishment of all, death. Individuals with strokes and or minor heart attacks visit a DPT’s office daily. The loss of strength, movement, and guidance often come with a stroke. Strokes are the leading ca use of disability. 75% of the 550,000 individuals who survive a stroke go on to live with varying degrees of impairment or disability (â€Å"Analysis of the Relationship†¦). Perhaps what most of the career consists of is patient participation. â€Å" The goal of a physical therapist is to promote the patients ability to move, reduce pain, restore function, and prevent disability† (Ross). However, This cannot happen if the patient does not go through with his part of the deal. The patient is not only the person who gives the PT work but also is the most important factor when determining the success of the treatment. The experience one has at a PT office does not depend so much on the DPT as it does on the patient. Participation of the patient very often determines the length of the stay, the effectiveness of the stay and the experience of the stay (â€Å"Significance of†¦Ã¢â‚¬ ). Whether it be a good or bad experience the therapists cannot do much for an individual if they do not participate. According to recent studies done by the US Bureau of Labor Statistics, Physical Therapy is in good hands in terms of future jobs. Between 2014 and 2024, Physical Therapist jobs will skyrocket by 34% . Approximately 210,900 licenced PTs are currently employed. That number will increase to an astonishing 282,700 by the year 2024. (Ross) Physical Therapy is not only well recognized for their work in the field of medicine, but has also been recognized nationally by mainstream media. Big names such as Forbes and CNN took some time to polish up the career of Physical Therapy in the media. â€Å"Forbes ranked physical therapists as having 1 of The Ten Happiest Jobs, according to articles published in 2013 and 2011. CNNMoney.com gave physical therapists a grade of â€Å"A† in Personal Satisfaction in 2012, as well as in its â€Å"Benefit to Society† categories.† As if the media polishing was not enough, more than three quarters of Physical Therapists polled to be â€Å" very satisfied† with their occupation (Ross). However, according to DPT Peter Christakos expresses his opinion towards the rapidly increasing profession. He describes the altering of PT class sizes in order to fulfill the fast growing student clusters. Christakos goes on to compare the profession of Physical Therapy to a bubble. The significance of a larger class size to the ongoing growth class sizes comes without saying. However, Peter does give a valid point when expressing that Physical Therapists hold the future of the profession in their hands. The supply and demand curve of future jobs in the field is meant to be untouched by PTs (Christakos). By increasing class volumes, the supply demand would be shooting up, leaving demand to catch up by itself. Christakos sketches the bubble of the profession,and asks â€Å"Will we [PTs] let it burst?† (Christakos) Having the opportunity to change one’s life go many ways. Physical Therapists aid those in need to positively impact their life. The hefty compensation goes without saying when speaking in terms of the patient’s progress and accomplishments during the rehabilitation process. The outcome does in fact affect the outcome of the treatment. Unlike other occupations, PTs can not do much for an individual if the patient does not cooperate. A Doctor of Physical Therapist plays a major part in the world of health care. The regaining of strength and ability of an individual who was once as strong as an ox   could not be done without a DPT. Christakos, Peter. â€Å"When Will the Bubble Burst?† PT in Motion. http://web.a.ebscohost.com/ehost/pdfviewer/pdfviewer?vid=5sid=1241b402-b590-43cd -ade4-b3de755e27db%40sdc-v-sessmgr03 . 23 July 2019 K, Janet. â€Å"Analysis of the Relationship Between the Utilization of Physical Therapy Services and Outcomes for Patients With Acute Stroke.† OUP Academic, Oxford University Press, 1  Oct. 1999, www.academic.oup.com/ptj/article/79/10/906/2842426 . Accessed 23 July 2019 â€Å"Physical Therapist Salary in Inglewood, CA.† Salary.com,  www.salary.com/research/salary/benchmark/physical-therapist-salary/inglewood-ca?personalized. Accessed 23 July 2019 â€Å"Physical Therapists : Occupational Outlook Handbook:† U.S. Bureau of Labor Statistics, U.S.  Bureau of Labor Statistics, www.bls.gov/ooh/healthcare/physical-therapists.htm. Accessed 23 July 2019 Ross, Libby. â€Å"Benefits of a Physical Therapist Career.† APTA,  www.apta.org/PTCareers/Benefits/. Accessed 23 July 2019 â€Å"Significance of Poor Patient Participation in Physical and Occupational Therapy for Functional  Outcome and Length of Stay.† Archives of Physical Medicine and Rehabilitation, W.B.   www.sciencedirect.com/science/article/abs/pii/S0003999304004307. 23 July 2019

Did Moses Write the Pentateuch or the Book of Moses in the Bible Research Paper

Did Moses Write the Pentateuch or the Book of Moses in the Bible - Research Paper Example Pentateuch contain the laws and instructions of God given to the people of Israel through Moses, hence Pentateuch’s other name â€Å"Book of Moses†. In the Pentateuch, the Israelites were appointed as the chosen people of God and the beneficiary of the Ark of Covenant and laid down the foundation of the coming of the Messiah in the presence of Jesus Christ. II. Passages in the Bible that suggests Moses authorship of the Pentateuch There are several passages in the Pentateuch and the Bible that led to the initial conclusion that indeed Moses wrote the entire body of the Pentateuch. ... .'" Matthew 22:24  "Moses said, 'If a man dies without children...'" Mark 7:10  "For instance, Moses gave you this law from God..." Mark 12:24  "...haven't you ever read about this in the writings of Moses, in the story of the burning bush..." Luke 24:44  "...I told you that everything written about me by Moses and the prophets and in the Psalms must all come true." John 1:17  "For the law was given through Moses..." John 5:46  "But if you had believed Moses, you would have believed me because he wrote about me. And since you don't believe what he wrote, how will you believe what I say?" John 7:23  "...do it, so as not to break the law of Moses..." Acts 26:22  "...I teach nothing except what the prophets and Moses said would happen..." Romans 10:5  "For Moses wrote..." III. Was the Pentateuch a work of a single author (by Moses) or an anthology of diverse material? It is easy to conclude that the first five books of the Bible were written by Moses given the above Bi blical passages suggestion that Moses wrote the entire Pentateuch. Also, the Books were attributed to him not to mention that he was a central figure to it. A close examination on the Pentateuch by scholars beginning in the eighteenth century however led them to conclude that the Pentateuch is not written by a single author, or by Moses alone as the traditional thinking suggests, but rather an anthology of diverse materials. Evidences that Pentateuch is not written by a single author When critical literary analysis was applied to the Pentateuch, it was found that the five books contained numerous duplications, broad diversity of writing style and even contrasting view points. The discovery of the duplication of the texts in the body of Pentateuch led scholars to study that the first five

Qualitative Research in management Essay Example | Topics and Well Written Essays - 2500 words

Qualitative Research in management - Essay Example This paper will begin with An Overview of Qualitative Research. There are generally two types of researches i-e., quantitative and qualitative research. Quantitative research is structured methods aiming at quantifying the data using the statistical method. They designed to prove reliability, generalizability, and objectivity. Qualitative research on the other hand, is unstructured methods seeking to give insights and understanding of problems. These two types of research are based on different concept. For instance, qualitative research is based on social sciences trying to understand and explain behaviors in particular situations while quantitative research evolved in natural since seeking to find commonly laws, which show the relationship of cause and effect. Qualitative research is a method of social study that focuses on how people think, live, and behaves. It is used in different academic disciplines as well as in social science. In addition, it is also used to gain a depth und erstanding of people attitudes, culture, feelings, values and interests and their social reality as individuals or groups. Marshall and Rossman define qualitative research as â€Å"a form of social inquiry that focuses on the way people interpret and make sense of their experiences and the world in which they live. The decision to use qualitative or quantitative research depends on the nature of issue under investigation. For example, if research aims to investigate the effect of credit supply shocks on firms financial and investment decision, then quantitative research would be more appropriate.... Marshall and Rossman (1998) define qualitative research as â€Å"a form of social inquiry that focuses on the way people interpret and make sense of their experiences and the world in which they live. The decision to use qualitative or quantitative research depends on the nature of issue under investigation. For example, if research aims to investigate the effect of credit supply shocks on firms financial and investment decision, then quantitative research would be more appropriate. However, if the objective were to explore how people respond to government announcement of cutting jobs, then qualitative research would be the best in that case. Therefore, the question of which approach is good for the study depend on the nature of the subject. Although both qualitative and quantitative research has advantages and disadvantages but qualitative research is believed to provide very rich data for analysis. The study by Punch (2005) highlights that qualitative research has advantages of be ing explorative in nature. It is because it allows researchers to explore new ideas, concepts and get new insights. There is also consensus among researchers that it helps in gathering the data in natural and reliable setting, which is not possible in quantitative research. In addition, as qualitative research focus on individuals, group etc., therefore, it helps to gain detailed and complex information about the phenomena under study. It may be because of these advantages that lead researchers to pursue qualitative research especially in social science or when the subject of study is human being (Mack et al, 2005). As mentioned earlier, that qualitative research

The buying back of shares is a dangerous financial strategy as it Essay

The buying back of shares is a dangerous financial strategy as it increases the company's capital gearing. Evaluate this - Essay Example There are different motives that would attract the companies to buy back the shares and there are different techniques that can be used to go through the process of stock repurchase. Different techniques that can are used by the companies for their stock buy-back are as follow: Company offers to purchase the shares from their shareholders at a premium price thus it gives value to them and extra return over price they actually had paid for the shares when they were bought. Companies often buy back their shares from the open market like an ordinary investor purchasing shares and making investment. It is often seen that the market and shareholders perceive the decision of the company to buy back the shares as a positive move and shareholders expecting higher returns stimulates stock price of the company (Larry, 1981). Motives for stock buyback Different circumstances and requirements of business conditions can influence management of share repurchase. Such motivating factors along with their reasons are discussed below: Market perception It is the perception of the shareholders and potential investors that exists in the market matters for future of company. Company is believed to use capital or extra finance available to them to buy back its shares thus giving the perception in market that there shareholders would be valued as they are provided the opportunity to trade possessed shares at the premium price (Udo & Richard, 2003). Thus removing any negative market perceptions that the stock price of the company has fallen and they have low future expectancy that what effects dealing of shares in market. It is often due to low earnings reported by the company in past some period, its operations effected by some scandal or lawsuit thus the share buyback is used as an option to remove any negative perceptions that are prevailing regarding the company in the market (David, et al., 1995). It is becomes necessary for the company to make the share buyback as market due to such instances and incidents might value the share price way low and shares are being traded at value that is below the expectancy of company thus in order to keep a standard for their shares in market and keeping value for their shareholders alive however it is believed that hike in share prices through this approach is of nominal period (Mansor, et al., 2011). Financial Ratios It is a usual practice in the market adopted by the investors before making any investment they make decisions on the basis of research and evaluation of the companies that are seem potential for the investment. Financial ratios of the company are most basic and foremost results that are used for the evaluation of the company. It is part of rational decision making of the investor as they evaluate their choice of investment before making the final decision (Amy, 2000). Thus share buyback can be the part of an accounting technique to get the desired results for the company as however it is the personal financ e of the company that they utilize to buy-back the shares thus it is confidence that the companies have on their abilities that makes them repurchase the outstanding shares that are either absorbed or turned to treasury stock. Thus the purchase reduces assets of company as it is the cash that is being paid for purchase of the shares therefore one of most important

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

Business Plan †Tfbg Essay

Product The Functional Beverage Group, Inc. has designed and is now developing a line of enhanced water products using a micro-targeting strategy. Consumers will be able to choose from a diverse, yet highly specific product offering based on their supplemental dietary or hydration needs. Each product will be optimized for vitamin content, electrolyte content, caloric content, and energy boost. We are currently in the process of developing three (3) of the targeted formulations. What makes our enhanced water products so unique is that all of these products will contain levels of Vitamin D3. Our major competitors – from Sobe, to VitaminWater, to Propel, and the rest – do not have enhanced waters that contain Vitamin D3. Because of the amounts of research data available, we may be able to make health claims concerning our formulations – claims that the other functional waters can’t make. Currently, there is no major marketer of a functional water product containing Vitamin D3. Why Vitamin D3? – Over the last two years, there has been a rash of research emerging concerning the lack of Vitamin D in our diets. Many physicians agree that the levels of Vitamin D suggested by current U.S. guidelines are insufficient. The lack of Vitamin D in the diet is beginning to gain notoriety by obstetricians, gynecologists, oncologists, pediatricians, and orthopedists across the country giving rise to what is being labeled as a new â€Å"epidemic† – Vitamin D deficiency. Our Technology – Vitamin D has chemical properties which causes it to be virtually insoluble in water. Therefore, a beverage company would need to develop the technology to dissolve Vitamin D3 into a water product using food grade ingredients while at the same time making a product that is pleasing in both taste and appearance. The Research and Development Team of The Functional Beverage Group has developed the technology to accomplish these goals. We are now seeking raise capital in order to finalize our formulation development and bring these product formulations to market. Investment Opportunity A $500,000 initial investment (available in units of $10,000 each) provides an equity position in The Functional Beverage Group, Inc. This funding will allow the FBG to complete initial development of its product line, develop informational web-site, and cover the legal fees and other expenses related to the completion of the second round of funding for the development of the operating company – Functional Foods & Beverages, Inc. Exit Strategy Our research has shown that most beverage companies are in the acquisition and/or partnering mode. Recently, many small beverage makers have been purchased by larger entities such as Coke, Pepsi, and Dr. Pepper/Snapple. Some of the more recent purchases include Coca-Cola’s purchases of Glaceau’s VitaminWater and SmartWater brands ($4.1 billion), Fuze Beverage ($327 million), Agua Brisa ($92 million), and Jugos del Valle ($456 million). Of more interest to The Functional Beverage Group is the recent investment of approximately $5 million the Dr. Pepper/Snapple Group made into Hydrive Energy, LLC. The Functional Beverage Group believes that our functional waters containing D3 will be a good fit for any of those organizations and therefore we can offer an attractive exit plan for our investors. In an otherwise sluggish merger-and-acquisitions market, successful beverage firms are still the darlings of Wall Street deal makers. According to the December 9, 2009 edition of the Wall Street Journal, November was the biggest month in over a year for deals involving consumer products and food and drinks firms with $12.54 billion in acquisitions. One of those companies for sale is Cliffstar Corp., a New York based fruit-juice and sports-drink maker. Cliffstar has hired Morgan Stanley to conduct an auction and has entered a second round of bidding, said several people familiar with the matter. Closely held Cliffstar has annual earnings around $75 million and is seeking seven to eight times earnings, which would put it a sales price at $500 million to $600 million, according to the article. Budget Statement Our revenue and expense projections are based on exhaustive industry research based on the cost to manufacture and market a new beverage product. In estimating revenues, we look at three products currently on the market: 1) Wal-Mart’s Acai-based Energy Drink, 2) Hy-Drive Energy Drink, and 3) DRANK Relaxation drink. These products are thought to be some of the most innovative products at the time of their introduction. Our revenue projections are conservative. If we can achieve early adoption into the major retailers like Wal-Mart or Target, we can far exceed those revenue projections. Our initial investors will become members of The Functional Beverage Group, Inc – an intellectual property development organization. Because The Functional Beverage Group, Inc will have few expenses and we expect to become profitable by Year 2. Most of these profits will be distributed as dividends to our shareholders. Figure 1. The Functional Beverage Group, Inc – 5 Yr Revenue Projections [pic] The Functional Beverage Group, Inc will maintain an approximate 40% stake in Functional Foods & Beverages, Inc (FFBI). FFBI will have the primary responsibility of manufacturing and market products licensed from The Functional Beverage Group, Inc. Figure 2. Functional Foods & Beverages, Inc – 5 Yr Sales Projections [pic] 2. The Functional Beverage Group, Inc. The Functional Beverage Group, Inc (The FBG), an Illinois Corporation was established in 2009 with a one core purpose – to become the preeminent supplier of functional or enhanced water products. The FBG is developing a line of functional water products based on the diverse needs of the functional water consumer. The consumer will be able to choose from a diverse yet highly specific product offering for their supplemental dietary or hydration needs. Each product is optimized for vitamin content, electrolyte content, caloric content, and energy boost. Our marketing will focus on grass roots efforts as well as forming alliances, partnerships, and promotional agreements with A-List celebrities to produce other unique marketing angles. Our business model will be split into three separate entities: 1) The Functional Beverage Group, Inc – an intellectual property organization responsible for the development and licensing of proprietary enhanced water products and other beverages to be produced and marketed by its subsidiary operating company, Functional Foods & Beverages, Inc. 2) Functional Foods & Beverages, Inc – the operating company responsible for the manufacturing of products developed by The Functional Beverage Group, Inc. Functional Foods & Beverages, Inc will have the exclusive right to manufacture and market products developed by The Functional Beverage Group, Inc. Functional Foods & Beverages will be managed by individuals with food and beverage industry experience. Although this organization will be managed by beverage industry professionals, selected members of the Functional Beverage Group, Inc will act as consultants to the organization. 3) Functional Beverage Real Estate Holdings, LLC – a real estate holding company responsible for acquiring any land and buildings associated with the manufacturing and distribution of products sold by Functional Foods & Beverages, Inc. The Functional Real Estate Holdings, LLC will seek to locate facilities in areas where they can take advantage of incentives such as TIF financing, property tax concessions, and vacant or unused property incentives. [pic] Figure 3. Proposed Operating Structure 3. Management Team Our core management team consists of: Shelby Parchman, President – MS Chemistry, Illinois Institute of Technology. Mr. Parchman has worked in new product development in the pharmaceutical and nutrition arenas for both Baxter Healthcare Corporation and the Amoco Corporation (Now BP). Mr. Parchman has years of experience working in the manufacture and formulation of analogs of Vitamin D3. In addition, he has a 15-year track record of success in working with start-up and entrepreneurial organizations. Mr. Parchman’s background in product development and nutrition has been instrumental in developing the unique features and formulations of our product mix. Edward A. Williams, Corporate Treasurer – JD, DePaul University School of Law, CPA (Licensed in IL & IN). Mr. Williams specializes in legal matters in the following practice areas: Tax Law, Tax Planning, Tax Litigation, Civil Practice, and Federal Taxation. Mr. Williams has represented several notable clients including the late Bernie Mac. Marvin Rux, Business Organization and Management Consultant – JD North Carolina Central University School of Law, MBA University of Chicago Booth School of Business, Mr. Rux practiced law for more than 20 years, specializing in the following practice areas: Real Estate Law and Taxation, Business Law & Development, and Estate Planning. Mr. Rux, no longer actively practicing law, provides consulting services to business development and real estate investment clients. Christopher McGruder, VP of Marketing – BA Business Administration, Barrington University. Mr. McGruder has extensive Marketing, Public Relations and Executive Assistance experience via Edelman PR Worldwide, Merck & Company Pharmaceuticals and Morgan Stanley. His clients’ list includes several Fortune 100 Companies such as: Micro-Soft, Sears, Wrigley’s, KFC, Unilever, Kobel Champaign, Mike’s Hard Lemonade, Cub-Cadet, and Axe Body Spray. He was instrumental in the capabilities development and promotions, and execution of product initiatives and national campaigns. Charles Moss, Marketing and Promotions – BA Communications, Southern Illinois University, Mr. Moss has years of experience in the entertainment and recording industries. Through his organization, Chuck Moss Presents, he has worked with various recording artists in all aspects of management, marketing and promotions. Because his reach stretched from Los Angeles to New York, he has been able to develop a valuable network of celebrities in both the music and sports industry. Terrence Seaphus, Marketing Consultant – MS Marketing/Advertising, Northwestern University Medill School of Journalism. Mr. Seaphus is an individual who can conceptualize a project and follow through to completion. His experience at M&M Mars along with his Northwestern University Graduate School tenure set the foundation that gave him the tools to succeed in marketing, advertising, diversity training and sales. His understanding of how to take new products through different channels including distributors, retailers, wholesalers, and finally, the end-consumer requires a 21st Century integrated marketing effort which happens to be his background. Michael Vick, Marketing Consultant – Pro Football Player, Virginia Tech (College), Atlanta Falcons, Philadelphia Eagles. In addition to being an outstanding football player, Mr. Vick has a keen sense of marketing and salesmanship. In addition to being a partner, Mr. Vick has expressed interest in being our first signed celebrity endorser. In addition, Mr. Vick has a list of contacts who have expressed an interest in investing in our endeavor. Mr. Vick still has numerous fans and followers. His jersey is still a best seller in the NFL – a good testament to his marketing potential. Pamela Williams, Manufacturing Consultant – MS Chemical Engineering, Washington University. Ms. Williams is a dynamic leader with extensive experience in project management, process and mechanical equipment design, and manufacturing start-up. Her broad technical expertise and demonstrated ability to learn technology quickly will enable us to complete project milestones at a fast pace. Additionally, Ms. Williams has over 12 years of experience working in global manufacturing at Proctor and Gamble. Larry Williford, Project Management – MBA, MPM, Keller Graduate School of Business. Mr. Williford has extensive experience in project management. He is skilled at working with business units to create sound business strategies, as well as supporting technology strategies. Mr. Williford worked in the IT departments of the McDonald’s Corporation, CNA Financial Services, and the Motorola Corporation before starting his own IT Consulting Business – Premier Project Management, Inc. 4. Introduction Functional Waters The bottled water industry has experienced phenomenal growth over the last ten years. Although low cost tap water is readily available, there is still 71 million bottles of water consumed per day. In 2007, bottled water sales reached $15 billion. What’s fueling the demand for bottled water? Bottled water demand is powered by the health and fitness craze. Consumers are being told that drinking bottled water is healthy and they have responded to the call by increasing their consumption of bottled water on a year over year basis. As the consumer becomes even more health conscious, there is an increased demand for enhanced and functional waters. These enhanced and functional waters contain added ingredients such as vitamins and minerals that allow the manufacturer to claim health benefits related to these waters. Therefore, functional waters have a greater product distinction. Demographically, these enhanced waters are especially popular with 18-35 year olds. Industry Trends According to beverage industry experts, the beverage industry has been trending towards lighter, lower calorie beverages with an emphasis on taste, refreshment, and function. Functional or enhanced beverages have seen phenomenal growth for the years 2006-2009 where the industry saw sales of enhanced waters and sports drinks up by 36% and 16% respectively for the period. Sales growth has been modest (approximately 3% from Jan 2009 to May 2010) during the current recession. However, according to Coca-Cola and Pepsi, sales of the enhanced waters have kept overall beverage sales in the black. Figure 4. Beverage Industry Growth [pic] Source – Beverage Spectrum, June 23, 2010 Factors for Success of the Product According to Michael Bellas of the trade publication Beverage World (www.beverageworld.com), there are some key factors in making a new beverage product successful. These factors are: 1) Make product exciting for the younger consumer, 2) Let the label tell a good story – convince the consumer, 3) Create great and exciting flavors, and 4) Create added value and credibility. We took these factors into account as we designed our initial product offerings. 5. Product Plan Our initial product line is designed to address three relevant issues concerning vitamin supplements, obesity, and water quality. The three main product qualities are: 1) Fortified with Vitamin D3, 2) Natural, no-calorie natural sweeteners, and 3) Certified pharmaceutical free. 1. Fortified With Vitamin D3 Over the last two years, there has been a rash of research emerging concerning the lack of Vitamin D in our diets. Many physicians agree that the levels of Vitamin D suggested by current U.S. guidelines are insufficient. The lack of Vitamin D in the diet is beginning to gain notoriety by pediatricians and bone doctors across the country giving rise to a new â€Å"epidemic† – Vitamin D deficiency. The Functional Beverage group has designed a line of â€Å"Health Waters† that include levels of Vitamin D3. We will design our marketing campaign around the concerns for the lack of Vitamin D in the diet along with the health benefits of supplementing Vitamin D in the diet. Because there is not a â€Å"one-size-fits-all† recommendation for the amount of Vitamin D that should be supplemented in the diet, we have designed different formulations for targeted groups. This keeps in line with our strategy of micro-targeted waters. Therefore, in addition to optimizing our formulations for taste, other vitamins, sugar content, etc, we will also optimize for the levels of Vitamin D suggested for our targeted groups. 2. Stevia – The Natural, No-Calorie Sweetener The Functional Beverage Group has chosen an extract of the Stevia plant as the primary sweetener in our enhanced water products. A recent article in the Wall Street Journal highlighted Pepsi’s and Coke’s development of products using the Stevia plant (see WSJ, July 31, 2008 – Beverage Wars Take on New Flavor). Massimo d’Amore, chief executive of PepsiCo’s beverage business in the Americas states that – â€Å"This is probably the biggest change in the formulation of beverages since the initial days of artificial sweeteners.† 3. Certified Pharmaceutical Free As evidence mounts of contaminants in some public water systems, unease about the water supply is growing. As detection technology improves, utilities are finding more contaminants in water systems. In early 2008, media reports of trace amounts of pharmaceuticals in water across the country drew attention from U.S. Senators and environmental groups, who are now pushing for regulations of these substances in water systems. Health concerns extend to bottled waters according to the National Defense Research Council. A lot of bottled water is actually tap water. Consequently, there is no assurance that what is coming from the bottle is any safer than what is coming from the tap, according to their studies. The Functional Beverage Group will certify each lot of water to be free of all pharmaceutical compounds. These results will be verified and/or tested by independent testing laboratories. In order to insure water of the highest purity, we will start with purified spring water. If necess ary, we will process/polish our feed water to a level of high purity utilizing industry standard methods. 6. Initial Product Design â€Å"†¦beverage marketers may be best served – and this is the key point – by classifying products according to the new evolving need states that define our consumer.† – Michael Bellas â€Å"Barrington’s [School District 202] dairy dilemma is an example of a discussion playing out across the country, as educators try to reconcile two concerns: childhood obesity and insufficient calcium intake. Even some experts have trouble coming up with a satisfying answer.† – Chicago Tribune, Nov. 19, 2009 Formulations We will formulate and bottle our products using purified Wisconsin spring water. Our initially proposed products are: 1) Infant Water, Certified Pharmaceutical Free (CPF) – This product is the same as any nursery water sold on the store shelves today. However, each bottle will contain a CPF label stating that we have tested the water and certified it to be free of any detectable levels of pharmaceuticals. What concerned mother wouldn’t choose our product over one that has not been certified? 2) X-Y-Teen (Young G) Formula – The target market for this formula will be children in grades K-12. This formula, containing Calcium, Vitamin D3, protein, and natural sweeteners will be marketed directly to school nutritionists/dieticians as a suitable alternative to milk. According to an article in the November 12, 2009 edition of the Chicago Tribune, there is a discussion playing out across the country as educators try to reconcile two concerns: childhood obesity and insufficient calcium and Vitamin D intake. According to the article, even some experts have trouble coming up with a satisfying answer. This product is the satisfying answer. 3) Women’s Formula – Designed to supplement nutritional requirements of women especially those of childbearing age. Our formulation will contain Calcium, Vitamin D3, and other vitamins and minerals important to women’s health. In addition, emerging research suggests the daily consumption of 1,000 IU of Vitamin D3 is associated with the support of breast health. A claim we can make in the marketing of our product. 4) General (Active Adult) Formula – A formula for the masses that contain low levels of Vitamin D3, Calcium, and other electrolytes. This formula is designed for the consumer to drink multiple bottles per day, hence the lower levels of vitamins and minerals. This formula will compete with the more mainstream â€Å"vitamin enhanced† water products and is targeted to replace the ever decreasing carbonated soft drink market. 5) Extreme Sports Formula – This product is designed for professional athletes and amateurs who participate in endurance sports or multiple bouts of intense exercise. The product contains Calcium and Vitamin D3 for stronger bones as well as increased amounts of electrolytes for more complete hydration. This formula is designed for the rigors of professional sports and can have variations for other professional sports endorsers. The target market consists of professional athletes and amateurs who participate in endurance sports or multiple bouts of intense exercise. We are designing an MV-7 formulation of the Extreme Sports formula for Michael Vick’s comeback to the NFL. This formulation is to be sold in markets where Michael Vick has a strong marketing and brand recognition presence. Additionally, we are in discussions with Pierre Thomas of the New Orleans Saints to come aboard as an endorser. Our future product offerings may include: 1) Winter Formula – This formulation will include higher levels of vitamin D for the winter months to address the lack of sunlight available in winter months. 2) Acai Berry Formula – Acai berries, found in the Amazon, are believed to have some very healthy qualities. Wal-Mart has recently entered the market for Acai Berry Juice and sold approximately $40 million worth of the juice within the first 90 days. 3) Baby Boomer’s Formula – A formulation designed for active adults who are ages 45 and older. The target demographic has a keen awareness of health related issues and an above average amount of disposable income. 4) Other Formulas – These can include energy drinks, other enhanced water formulations, natural juices, and alcohol based beverages. Container Design Because Vitamin D is sensitive to both light and oxygen (air), the traditional plastic bottle is not suitable for our formulation designs. We look at that being an added bonus because it forces us to use a newer, up-scale, and more hip package design – the aluminum bottle. The use of this packaging further differentiates our beverages from the typical bottled water and vitamin waters. An added advantage to using the aluminum bottle is the ability to added extremely artistic graphics to the outside of the packaging – adding even more product distinction – without the expense of a separate label. According to CCL Container, manufacturer of an aluminum bottle product, the aluminum bottle offers distinct advantages, including the ability of top-to-bottom shaping, chill-retention, re-sealability and durability. The use of the aluminum bottle has added significance over the plastic bottle as well when it comes to the environment. Because there are more â€Å"green† initiatives implement by both federal and local environmental concerns, it is important that product packaging is forward looking in terms of meeting any new environmental regulations. According to the Recycling Revolution web site (www.recycling-revolution.com/recycling-facts.html), these facts, among others, are worth considering about the use of aluminum for packaging: 1. A used aluminum can is recycled and back on the grocery shelf as a new can, in as little as 60 days – a process known a closed-loop recycling. 2. Because so many of them are recycled, aluminum cans account for less than 1% of the total U.S. waste stream – according to EPA estimates. 3. Americans use 2,500,000 plastic bottles every hour with most of them being thrown away. After considering product stability, costs, and environmental issues, we have concluded that the aluminum bottle is the perfect packing for our product design. 7. Trademarks, Patents, Copyrights, Licenses, Royalties We will seek trademark protection for all of our product brand names, designs, logos, and relevant phrases. In addition, we may patent some of our formulas and processes. However, we feel that keeping our formulations and processes a trade secret will offer better protection that securing a patent for the these items. We will review each situation on a case-by-case basis, in consultation with our legal team, as we make decisions on whether or not to pursue patent protection for any of our formulations or processes. 8. Government Approvals The United States Food and Drug Administration (FDA) regulates bottled water as a food product. The FDA has established specific rules for bottled water, including Standard of Identity Regulations that define different types of bottled water, and Standard of Quality Regulations that establish minimum levels for contaminant (microbial, chemical, and radiological). The FDA has also established Good Manufacturing Practices (cGMP) regulations for the processing and bottling of drinking water. These rules require that bottled water must be safe as well as processed, bottled, held and transported under sanitary conditions. Processing practices addressed in the cGMP regulations include protection of the water source from contamination, sanitation at the bottling facility, quality control to assure the bacteriological and chemical safety of source water, and sampling and testing of source water and the final product for microbiological, chemical, and radiological contaminants. Our bottling group will be required to maintain source approval and testing records in the event of any government inspection. Our bottling group may be subject to additional inspection by state and local licensing agency, health agencies, and/or environmental agencies. Procedures and protocols will be in place to ensure full compliance with all federal, state, and local rules and ordinances. In addition, all of our ingredients, including Vitamin D3, are on the FDA list of ingredients that are approved as GRAS (Generally Recognized as Safe). Consequently, no approvals are required for adding these ingredients to bottled water. However, there may some restrictions on how much can be added to the bottled water product. Our formulations will be well below those limits. 9. Product Liability We will purchase product liability insurance and/or an umbrella policy in addition to the product liability insurance coverage that is held by any of our suppliers. We are depending on our legal team to give us further guidance on the types and amounts of insurance we should obtain in order to protect the organization from any product liability or other claims. 10. Production All production will be performed by our subsidiary operating company Functional Foods & Beverages, Inc. In addition, we will qualify contract bottlers to ensure a continuum of production in the event our primary production facility is out of service or in the event we would need excess production capacity in order to meet unanticipated product demand. 11. Marketing Plan – Fortified Beverages â€Å"†¦beverage marketers will open new vistas for growth. Their size and growth opportunities will be different; their product positioning will be more specific.† – Michael Bellas (Beverage World) Three simple goals As we market our products and create brand awareness, we have three simple goals we look to accomplish: 1) Convert non-bottled water drinkers to enhanced bottled water drinkers, 2) Convert bottled water drinkers to enhanced bottled water drinkers, and 3) Convert others from competitor’s products. Our marketing plan is designed to efficiently accomplish these goals. A multi-prong approach We are devising a multi-prong approach to our marketing efforts. We will develop a sales force to create relationships and alliances with people and organizations of influence in our target markets. Figure 6. Marketing Plan [pic] Target Market – School Districts Across the Nation One of the first formulations the FBG will design and develop will be the Young G formulation. This formulation which contains Calcium, Vitamin D3, protein, and reduced sugars, is an excellent alternative to milk. Children need about 32 ounces of milk daily just to get the recommended allotment of vitamin D. It is difficult getting children to drink eight ounces of milk, let alone 32 ounces. Our Vitamin D3 fortified Young G formulation is the drink for them. Having no fat and fewer calories than 2% milk also makes this an attractive product to highlight in First Lady Michelle Obama’s new Childhood Obesity Initiative. The size of this market is enormous. If we count only the children receiving subsidized lunches in the school system, we have a market that is 31 million children strong in more than 100,000 schools. Target Market – Sports Fans We are very fortunate to have professional football player Michael Vick as a member of our founding group. Mr. Vick immediately saw the potential of our proposed formulations and did not hesitate to come on board. Another formulation in the stages of development is our MV-7 formulation. This formulation will be marketed as the drink developed for his return to the NFL. Having Mr. Vick on board establishes immediate brand recognition and credibility for our products. Currently, he is receiving tons of media attention every time he hiccups. This media attention is invaluable. For example, experts estimate that last year’s giveaway of free Grand Slam breakfasts by Denny’s generated roughly $50 million through free advertising. We look forward to cashing in on this media attention as well. Additionally, we are looking to sign additional celebrity endorsers from both the sports and entertainment arenas. We are currently in discussions with Pierre Thomas of the New Orleans Saints to bring him aboard as another celebrity endorser from the sports world. 12. Competition Profile There are numerous competitors in the market for enhanced water products. Even with numerous products on the market, new brands can be highly successful. It is a matter of carving out a position in the market where your product has the perception that it does something the others are not doing. As shown in Figure 6 below, there is no huge product distinction from the major functional water brands. Propel Fitness Water includes calcium for â€Å"stronger bones,† however Vitamin D is required in order for the human body to absorb calcium. While it may be obvious to consider our major competitors to be other â€Å"vitamin† water products, we beg to differ. We feel that our major competitors and target market would be those who drink milk or use some other form of Vitamin D fortified consumer product. These products include cereals, cereal bars, and yogurts. Because of extensive research into Vitamin D deficiency, these products can make specific claims on their labels – claims that the vitamin water products cannot make. Because our products are fortified with Vitamin D, we can make these same health claims. As a result, we can make this product stand well above the vitamin water products on the market. In the article Chocolate Milk Lovers Have a Cow About Bans, Chicago Tribune, November 12, 2009, it has been noted that children are not drinking white milk and that chocolate and strawberry milk products are too high in calories. The article goes on to express parents’ concerns that children are not getting enough Calcium because they are not drinking milk. The conclusion is that there is no suitable alternative to milk in the schools. We conclude then that milk is indeed our main competitor because we have designed the suitable alternative. Table 1. Competitive Comparison |Advantages |Drawbacks | |Milk | | |Well known source of Vitamin D & Calcium |Lactose intolerance in many individuals | |Source of Protein and essential fats |Not very portable – needs refrigeration | |Strong marketing campaign USDA subsidized in schools |Concerns about hormones | |$0.50 per 8 oz. serving |Flavors are high in calories | | |Limited shelf life | |Vitamin Waters | | |Brand recognition |Flavors are weak or medicine-like | |Large marketing budgets |No true â€Å"function† | |Moving towards healthier product lines |Product choices can be overwhelming | |Lower calories |Some have high sugar content | |Natural flavors |Not directly marketed to younger generation (target 18-35 year olds) | |$0.60 per 8 oz. serving | | |Functional Foods | | |Alternative sources of Vitamin D & Calcium |Some products are dairy ( lactose | |Contained in mainstream food items |Usually breakfast specific | |Some are portable |Some are not portable | |Brand recognition |Perishable | |Cost per serving varies | | |Aqua-D from the FBG, Inc | | |Designed as a great tasting, low calorie direct replacement for milk |No product history | |Vitamin D and Calcium containing alternative to more popular enhanced |Major competition from Coke and Pepsi Products | |waters e.g. Vitaminwater |Limited marketing budget | |Smaller bottles w/ lower price point (