Odwalla Case Essay

Odwalla Incorporate is known for high quality products and it takes pride in the way the juices are made. However, with E. coli crisis it has become extremely difficult to maintain that standard unless Odwalla designs a proper strategy to counter the effect. I will help you design a communication strategy for each stakeholder to emerge from this crisis, regain loyalty and improve brand image. Odwalla must take full ownership of this crisis and communicate to its stakeholders about the recall process, quality assurance policies and steps taken to resolve the issue. The timing and the process is extremely important to communicate effectively. Below are the list of key issues and the communication strategies for each stakeholder that will help get through this crisis. KEY ISSUES Some of the key issues that Odwalla face because of the E. coli breakout are: †¢Determining communication strategy to respond in the crisis †¢Identifying pasteurizing methods to maintain the same taste and quality †¢Maintaining current core competency – use of minimal production processes to deliver superior taste and nutritional values †¢Researching side effects of adding chlorine, as suggested by a quality assurance manager †¢Identifying ways to provide safe products in future †¢Identifying ways to maintain the customer loyalty †¢Identifying strategy to regain stakeholders’ faith †¢Handling lawsuits from affected consumers These issues will affect the company’s future business operations. Therefore, Odwalla must take immediate action to contain the breakout and find solution to avoid re-occurrence in future. COMMUNICATION STRATEGIES FOR EACH STAKEHOLDER Odwalla must communicate with all of its stakeholders. The following are the communication strategies for the nine most important Odwalla stakeholders – the affected customers, the public, the employees, the crisis management committee, the distributors, the retailers, the suppliers, the officials, and the shareholders/investors. Affected Customers †¢Apologize immediately and take full responsibility for the crisis to the affected consumers by contacting them by phone or paying a visit †¢Guarantee appropriate measures will be taken to fix the issue †¢Send condolences letters to all consumers who are affected by consuming the Odwalla juice and compensate them for medical costs and hardship Public †¢Launch TV, Radio and Internet advertisements to inform everybody about the crisis and seek apology †¢Regain consumer’s confidence by assuring that this issue will be resolved soon †¢Arrange factory tours for public assurance Employees †¢Call in for all-employee meeting to explain the crisis and ask employees for ideas to pasteurize the products by maintaining same taste †¢Send out a memo to all employees requesting them to contact crisis management committee with ideas and inquiries †¢Instruct all employees to direct any questions or inquiries from media to Internal communication department Crisis management committee †¢Identify the batch numbers of the affected products †¢Quarantine all the affected products †¢Develop the recovery plan and review with officials before implementation Distributors †¢Send memos to distributors with batch numbers and ask them to recall the products and freeze any supply going to the retailer †¢Tell distributors to dispose all the products matching the batch numbers given to them Retailers †¢Send memos to retailers with batch number and ask them to recall the affected products. †¢Work with retailers for any customer re-funds requests Suppliers †¢Suspend receiving of all the supplies from the suppliers †¢Ask suppliers to look for E. coli in their supplies and urge them to take appropriate actions †¢Discuss with supplier for ideas and methods to avoid any contamination even before the products get to Odwalla facility Officials †¢Communicate openly with the health agencies and law officials by cooperating with the investigation process †¢Explain the recovery plan developed by crisis management committee †¢Get certified for the process from the health agencies Shareholders/Investors †¢Call for immediate Board of director meeting and explain the crisis, recovery plan and cost of fixing the crisis NEXT STEP Odwalla must take immediate action to avoid damage to customer’s confidence level and lose faith in stakeholders. In order to resolve the issue quickly Odwalla must take following important steps: †¢Identify the contaminated batch numbers †¢Quarantine the contaminated products †¢Communicate with all stakeholders †¢Find the root-cause of contamination †¢Implement the solution from root-cause analysis †¢Get approval from health agencies †¢Keep consumers updated via advertisements – TV, Radio, Newspapers and Flyers †¢Organize factory tour for customer satisfaction FINAL WORDS Odwalla must communicate immediately by enforcing the communication strategies. The consequences for not communicating effectively are worse and will affect from losing customers to long lawsuits and filing bankruptcy. It will be very challenging to find a solution that will maintain the same taste and not to have pasteurized the products. However, you will find smart and effective ways of communicating with stakeholders in this memo that will not only help Odwalla regain the lost glory but also avoid any adverse implications. With every Core Competencies, there are rewards and crisis. Odwalla must embrace this crisis as a lesson learned and use this experience to come up with new tools and technologies for production process and live up to its vision: â€Å"Odwalla’s vision has always been to nourish people everywhere with the ineffably honest art and rhythm of nature’s offerings. We live on the principle of respect for our consumers who rely on us for consistent quality in taste and nourishment and respect for the earth on which we rely for holistic nourishment† I would like you to consider my communication strategies and be calm and patient in handling the crisis. Please feel free to contact me for any questions you may have.

Shotgun vs Rifle

Compare & Contrast All guns serve different purposes. Guns have been a part of American history for many years. Many different kinds of guns have been used for many different types of jobs. Just as police use guns for law enforcement, hunters use guns to harvest game and they have different guns for different game. The two most commonly used firearms of hunters, are the rifle and the shotgun. One of the great things about having a well-made shotgun is that they are not very expensive and will usually last you a long time. They are very easy to take care of and you can put many rounds threw them before they need to be cleaned.When you do need to clean them, it is very simple because a shotgun does not have a lot of working parts. So, it is very easy to get a cleaning tool in all parts. A couple of down falls to a shotgun is that your range is minimized to how far you can actually shoot accurately and kill game, (you can shoot slugs threw them around 100 yards, but there are not always accurate and when harvesting game you always want a clean kill). So the typical ammo is bird shot or steel shot, shooting birds from ten yards all the way up to forty yards. A rifle is an amazing weapon.There are tons of things you can do with a rifle and so many different kinds of calibers that you can shoot. Anything from a . 22 caliber bullet all the way up to a . 50 caliber bullet, this will shoot well over a mile. Rifles are used far more by hunters than any other gun out there. The rifle can take all kinds of game and is also very accurate with really long distances. With the rifle, you have a better chance at a good, clean kill because of its accuracy. When learning how to shoot rifles, it takes a lot of practice and patience when shooting because the slightest twitch will send your bullet off target.Another important thing to remember is if you use a scope, you will always have to be very cautious to not to bump your gun into anything or drop it because it is very easy to k nock your scope out of alignment and once you do that you will not be able to harvest a game. Rifle and shotguns are both awesome guns, and there are many different ways they are used for depending of the person, for example hunting, competition shooting, and they are used for law enforcement. Personally, shooting and guns in general are some of my passions along with hunting. I use this time to get out in the woods, relax and have a good time with friends.

An Old Woman.

The poem is highly symbolic and very common placed in it's subject matter. The poet was impressed by the temple of Kandoba at Jajori and the poem is thus against this setting. â€Å"An Old Woman† is a graphic picture of a beggar woman. Having lost the promises of her past, she is reduced to her present state. As the speaker views her squarely, he, in a sort of ‘revelation', becomes aware of the decay which has set in her person and which is extended to the decaying tradition symbolized by the hills and the temples. Without using many words, the old woman forces the narrator to look at her from closed quarters.It is then that he realizes the hypocrisy of society and the decadence of the social system that has ruined the old woman to a beggar. he finds that the social fabric is destroyed, architectural features go into ruins. Human values are forgotten. The old woman's condition reduces the narrator to a small status when he feels as insignificant as that small coin in her hand. This poem humbles us to remember our responsibility to society. It reveals the callousness, a failure on our part to take care of the elderly, protect our heritage and preserve our values.In the rush of materialism and the desire to achieve, one takes all that one can from society, but giving the same back is largely forgotten. So the cracking hills, crumbling temples, crumbling of social order is directly a result of our negligence, our failure to act responsibly. Somewhere, the materialistic world has made man selfish, trapping him in a race to accumulate. When society has to face this onslaught, cracks appear, but selfish man forgets to repair the cracks, forgets to salvage lost values, thereby creating a dilapidated social fabric†¦.

Incident manegment process at Catholic University of America Essay

Incident manegment process at Catholic University of America - Essay Example This could include the use of a service desk which acts as a link between the end users and the technical staff diagnosing the incident. The service desk updates the users on the progress of issue being resolved. Incident Management Cycle Incident life cycle involves discovery and listing, grouping and preliminary intervention, inspection and analysis, solution and revival, incident closure, incident ownership, follow up and evaluation, tracking and communication. To avoid IT business disruptions as a result of system failures, it is important to plan and implement programs to optimize IT service management. This begins with the analysis and alignment of the current and future business requirements and appropriate IT services provided. More serious incidents must be given precedence/priority where there are a number of incidents to be dealt with at the same time, where the user must be consulted and reference made to the Service Level Agreement (SLA). To prioritize, urgency and impac t of the incident to the user and the business must be evaluated (Office of Government Commerce 31). An incident that may not be resolved by first line support staff should be escalated to more expertise or authority. This could be either functional (horizontal) or Hierarchical (vertical) escalation. 1. Listing of Accepted Incidents Any section of the IT infrastructure may cause incidents to happen including computer operations, networking, service desk itself, procedures etc but these are usually reported by users. Detection systems can however be used to trap events taking place with the IT infrastructure. Incident management is related to other processes such as configuration management, problem management, change management, service level management, availability management, and capacity management (Office of Government Commerce 33). 2. Incident Grouping and Preliminary Intervention This involves grouping the incidents in some identified criteria. Services related to the inciden t are identified with due regard to the SLA. A support group is selected if support staff cannot resolve the incident issue; a support group is determined as part of functional escalation and based on incident categorization. An aspect of timelines here is critical involving informing the affected business user about the estimated amount of time expected to resolve the issue, with due updates on progress also provided. Incidents are also matched to determine whether similar ones occurred previously, thus helping on diagnosis and solution turnaround. 3. Solution and Revival Following an incident resolution, a record is made in the system for a Request for Change (RFC) submission to change management where necessary or/and appropriate. The RFC should usually lead to a solution (Office of Government Commerce 35). 4. Closure With a solution in place, the incident is routed back to the service desk by the support group. Service desk then informs the user to check if indeed the incident h as been resolved thereby closing the incident and incident record updated to show final category and priority, affected users and components which have been identified as causes of the incident. If user is not comfortable with the solution, the process can be reinitiated at the appropriate stage. 5. Incident Monitoring and Evaluation Service desk

Video Games in America Research Paper Example | Topics and Well Written Essays - 1250 words - 22

Video Games in America - Research Paper Example These critics also argue that playing video games encourages violence and leads to addiction even though these allegations do not have any particular basis and evidence. Numerous research on if video games encourage violence has been unsatisfactory and has focused only on the short-term impact. During the periods when playing video games has become a commonplace occurrence in America; the rate of violent crimes has decreased by almost a half. If the games made people become violent, this tendency should be exhibited in the figures considering that half of the American people play either computer games or video games as demonstrated by the graph (Adam 2009). According to research, only three percent of people who play video games play alone as most of them engage in multi-player games in the same rooms or through online connections. It has also been suggested that gaming can be a topic of discussion for both children and adults which creates a foundation for friendships. This social attribute of gaming is demonstrated through teamwork and the sense of collaboration that is evident between the super players and their fans. The professional player's stream videos of their playing through online sites in order to assist other people who wish to play the games to learn and view various techniques. Video games are important in relieving stress as playing involves undivided attention.

Responsible Corporate Governance Ayuso and Argandona (2007) Assignment

Responsible Corporate Governance Ayuso and Argandona (2007) - Assignment Example Evaluation criteria marking are marked on a scale of 0-10 where 9-10 is excellent, 7-8.9 is notable, 5-6.9 is passed and 0-4.9 failed. Coca-cola Company has been awarded 9 in the scale of marking criteria due to its global market existence and recognition. Coca-cola has established its roots in many countries in almost all the continents. Coca-cola has most consumers and recognition compared to most of the existing soft drinks globally. The company has created great employment opportunities due to its establishment in many countries. 1. Evaluation criteria marking assist an organization to know its category and performance according to the provided scale. This will help a company to set objectives on how to improve or maintain their position. 1. Companies which find out that they are marked high on the scale may embrace laxity tending to maintain their daily practices while modern methods of management emerge on daily basis. This may have a negative impact in future. Coca-cola company is a global manufacturer and retailer of beverage based in Georgia, united states. The coca-cola company comprises many brands and products but the core product is the coca-cola drink. Various types of media are used in order to advertise the coca-cola brand in general and coca-cola drink in particular. These types of media include visual and published media. This has helped the brand to reach global markets which is considered as a huge success. The company aims at profit maximization and all efforts of the company are directed towards the achievement of this primary objective. The company has been able to expand its roots in various countries. The companies have their specific objective which one of them is to create awareness of the product to each and every person thus resulting to great sales of the product. This is the selection of different ways used for the evaluation process. Evaluation

Amistad Essay Example | Topics and Well Written Essays - 1000 words

Amistad - Essay Example The Spanish colonies of Cuba and Puerto Rico would continue to tolerate the outlawed slave trade until the 1860s, but eventually outlaw slavery by the end of the 1870s2. By the time of the Amistad incident, the feeling in America towards slavery had polarized. Feelings ran the gamut from the abolitionists that called for an immediate ban on slavery, to the people that felt a constitutional amendment was long overdue, and included the advocates that argued slavery was a states' issue and wished to prolong the practice, primarily in the rural South for economic reasons. In the Northern States, "the rising voices of black, as well as white, abolitionists are partly responsible for ending slavery in the Northern states during the first part of the nineteenth century"3. According to Jackson, "if many were sympathetic to the Africans, there were plenty of others among the American press and public with only contempt for them", and Cinque, the leader of the mutineers, was described by one journalist to be "as miserably ignorant and brutalized a creature as the rest"4. Many people such as "Lewis Tapan, a prominent New York businessman, Joshua Leavitt, a law yer and journalist who edited the Emancipator in New York, and Simeon Jocelyn, a Congregational" could sense the coming of the civil war over this unresolvable issue and "decided to publicize the incident to expose the brutalities of slavery and the slave trade"5. In 1839, the nation was deeply divided over the slavery issue and many people were willing to take a hard stance either for or against it. C. Legal aspects of the Supreme Court's decision. Though there was significant political and emotional pressure placed on the court, the eventual decision was a correct legal finding. The case rested on three principles; jurisdiction, the mutineer's status as slaves, and the concept of slaves as property. "The Spanish minister pointed out that the Amistad mutiny took place on a Cuban vessel traveling between Cuban ports and was thus beyond the jurisdiction of American courts"6. The court ruled that the mutineers were "kidnapped and free Negroes, the treaty with Spain cannot be obligatory upon them; and the United States are bound to respect their rights as much as those of Spanish subjects"7. The court rightfully found that they had been kidnapped, since they had been taken in violation of international agreements, and since they were being held as kidnapped captives, the Supreme Court upheld the lower court's decision. "The court declared that the blacks had never been lawful slaves and that they were kidnapped and illegally transp orted to Cuba. Their mutiny was an act of self-defense"8. Adams challenged the Court to find a more sweeping decision "on the basis of natural rights doctrines found in the Declaration of Independence"9. However, the majority opinion "found slavery repugnant and contrary to Christian morality, he supported the laws protecting its existence and opposed the abolitionists as threats to ordered society. Property rights, he believed, were the basis of civilization"10. D. Impact of the Amistad incident on slavery. The impact of the Amistad incident gave the abolitionists a social and political boost that would continue to echo into the future. "The importance of the Amistad case lies in the fact that Cinque

Business Plan For A Company In The Food Industry. Ricer Essay

Business Plan For A Company In The Food Industry. Ricer - Essay Example The services will be based cash on delivery and cash with order. Ricer’s services will be commonly known as Ricer Vending Units. The original trial was conducted in October 25th, 2012 which was highly applauded by most residents within the city and projected to be a success once it will be launched. The business intends to expand gradually through franchises to other cities and states in the next ten years. Market Analysis The business is projected to be worth  £ 250,000 which will serve the local markets that are vast and well segmented. The population consists of 50.6% of female and 49.4% of men while the median age is around 34.8 years and the entire working population is 311,300 and the residential population goes at 506,800 according to statistics done in mid 2009. The City has a higher young age profile which will form an essential market for the Ricer’s products. This profile of the population reveals that the target consumers will most likely be the young and vibrant students and the working group. Thus the products will be distributed near colleges and University campuses, weekend markets and other convenient places such as leisure parks (Daniels, 2002, p. 53). Strategy and Implementation Ricer aims to create a brand recognition using its Ricer vending Units through positioning strategically in the entire business district within the city. Upon achieving the brand recognition, the services will be provided and eventually they will be available in major superstores and supermarkets (Stokes and Wilson, 2010, p. 3). Moreover, Ricer will then provide franchises to foster further expansion. 1.5 Management The Ricer will be owned by two ladies with massive experience in the business management, product promotion and hospitality industry. The pioneers are based from two different diversities which include; Chinese culture and the English culture. They were previous staff of a renowned restaurant in the world having worked for about ten years. They intend to employ other staff to help them in the preparation and distribution of food to the target market in the streets. 1.6 Financial Plan Ricer is projected to have a formidable starting financial base even though it will need extra funding to accomplish its goals and objectives. According to the analysis of the forecasts the revenue from the business is expected to grow to ? 7.5 million by year 5 and subsequently to ? 15.75 million by year 10 with an EBITDA amounting to ? 5 million by year 5. An initial survey from the streets it was determined that the firm would need to sell 75 meals to breakeven. The profound financial strategy ascertains that the firm will be more favorable as an acquirement for exit (Bhide?, 2000, p. 5). 1.7 Start-up funds and expenses This business plan will attract the following start up funds and start-up expenses. Start-up Expenses Legal ? 250 Marketing consultants ? 750 Design costs ? 2,500 Payroll expenses ? 12,000 Fuel costs ? 2,500 Business and Liability cover policy ? 5000 Total Expenses ? 23000 Start-up Assets Cash needs ? 250,000 Start-up Inventory ? 50,000 Other Short term assets ? 25,000 Total Short Term Assets ? 25,000 Non-current Assets ? 50,000 Total Assets ? 400,000 Start-up Funding for the fast food firm Investment for the business Rickrosly ? 150,000

Edit Essay Example | Topics and Well Written Essays - 250 words - 1

Edit - Essay Example The second step was that he brought forth early wins which were evident and visible to all employees of the company. This included reduction in number of hierarchies and introduction of two initiatives which particularly aimed at bringing openness, simplicity, self-confidence, and increasing operational speed. The next step was to develop ownership amongst the employees. For this he developed an initiative called â€Å"work out† which created space for open interaction with different level of employees. Thus he ensured that the company had a strong foundation before further global expansion. Moreover, every employee felt connected with every management policy and action. Fourthly, Welch incorporated wins easy to achieve with least capital. This included the policy that every GE initiative must acquire a number one or 2 positions in the market or else fix it, sell it, or close it. The sale of non-performing initiatives created capital for further investment amounting upto $21billion. He abolished strategic planning system and established a real time planning process which involved fourteen key business heads occasionally developing competitiveness strategies. These served as wins that speak to powerful players to receive their

Given the dynamism of today's market and the ever increasing degree of Assignment

Given the dynamism of today's market and the ever increasing degree of competition globally, produce a critical assessment of - Assignment Example In regard specifically to the business sector, the involvement of certain business tools and frameworks in the promotion of globalization seems to be extended. Reference can be made, for example, to the information systems, in all their forms. Information systems are highly related to globalization. Moreover, these systems are likely to be used by business worldwide as a tool for acquiring competitive advantage. The above role of information systems is presented in this paper. The Porter Five Forces model is used for explaining the involvement of information systems in the increase of business competitiveness, both locally and globally. Table of contents Executive Summary 2 1. Introduction 4 2. IT and competitive advantage 4 2.1 Effects of globalization on business – information systems and their relationship to globalization 4 2.2 Business processes and their relationship to information systems 7 2.3 Evaluation of the use of information systems as tools for increasing busines s competitiveness – Porter’s Five Forces model 10 3. Conclusion 12 References 14 Appendix 15 1. Introduction Aligning business processes with organizational objects is one of the most critical challenges that organizational leaders worldwide have to face. On the other hand, business processes are not standardized. Rather, they have to be changed continuously so that they can keep the organizational competitiveness high. Information systems can be considered as a tool that help business processes to achieve the above target. In practice, the use of information systems in organizations has been related to globalization. This view can be considered as justified if taking into consideration the following fact: information systems have been expanded across business activities of all sectors mostly because certain businesses have emphasized on the particular systems. Since the role of information systems in enhancing organizational profits and improving businesses processes has been made clear, the popularity of these systems worldwide has been increased. The relationship between information systems and globalization is examined in this paper. Particular emphasis is given on the potential use of information systems for achieving competitive advantage. It is proved that, indeed, information systems can play such role. However, it is necessary for the involvement of these systems in organizational activities to be carefully planned and monitored, otherwise the relevant plan will be led to a failure, either in the short or the long term. 2. IT and competitive advantage 2.1 Effects of globalization on business – information systems and their relationship to globalization. The high value of information systems for the development of business activities cannot be ignored. In order to understand the involvement of information systems in modern organizations it would be necessary to refer primarily to the effects of globalization on businesses; then, th e role of information systems in supporting business activities could be understood. Modern market is characterized by a ‘global integration’ (Walker 2004, p.171). This means that a firm can survive in the global market only if it is able to strengthen its processes so that they can secure the firm’s competitiveness towards its rivals (Walker 2004, p.171). At the same time, Doole and Lowe (2005) that globalization has set a new challenge for all businesses: instead of trying to keep their existing market position,

New Media Technologies And News Production Essay

New Media Technologies And News Production - Essay Example On the other hand, families saw the need of sitting and watching the television after a day’s work rather than reading newspapers to acquire information. Additionally, the advancement in to the World Wide Web era gave birth to personalized consumption of information since it a was faster and more detailed way of news reporting. News production and the internet Moreover, the information transmission through the internet led to great cultural diversifications in the way of consuming news. The internet is a platform of free culture in that the information provided costs less or is free. Sequentially, the newspapers in the developed nations are unable to compete with the internet in terms of revenue accumulation. Undoubtedly, journalists who find themselves on the receiving end of losing their jobs because of the financial strain in the world today have implemented the use of blogging sites on the internet (Schubert, 2011:5). These blogging sites provide an avenue for the airing o f their views through cheap and reliable means (Stuart 2003:36). They do not find themselves answerable to any one except authorities of their lands of origin. Therefore, the internet has offered a way of bridging the professional gap from that of being unemployed to that of independence for practicing journalists across the globe. On the contrary, citizens have also had their fair contribution in reporting, as the internet offers a platform for posting photographs and amateur video footage on happening events. This is what citizen journalism entails (Greer & McLaughlin, 2010:1045).Once these pictures find their way to the internet, they give room for research where the researching on more facts surrounding the developing story may get to the public domain... This essay stresses that the media has a way of portraying protests and demonstrations by the public in a violent and the non-attractive way. Usually, they portray the demonstrators as those who have high traits of anarchy. This depicts the influence of the media in explaining the actual state happening events. However, governments have emphasized the need for positive reporting rather than negative reporting through the showing of disturbing images. Ideally, negative reporting may affect a country’s economy in that it may bring down a country’s attractiveness to potential investors. Modern day media forms should act as public relations features rather than weapons of ruining public image. Therefore, the media has a role to play in restoring public trust in institutions like the police force that have had the repute of violence and brutality to the public. This paper makes a conclusion that The transformed media has a critical place in the present society because many use it as a matter of the need to feel informed. In this regard, responsible journalism should be the foundation for any coverage of information intending to reach the public domain. Ideally, the media is a tremendously powerful tool that which can influence the society either negatively or positively. Subsequently, the transformed media should ensure that it is impartial and steers the society towards the right direction. Finally, the transformed media forms have defined the standards of living for many of the urban citizens since the reception and production of news is immense quality and class.

The Issue of Internet Addiction Syndrome Essay Example for Free

The Issue of Internet Addiction Syndrome Essay The phenomena of Internet Addiction Disorder/Syndrome (IAD/IAS) are not new phenomena that are really not new when one stops to think about the underlying aspects of it. It is simply a new variant on traditional Obsessive Compulsive Behavior (OCD) and addictive personalities. For those unfamiliar with the term IAD, it refers to an obsessive compulsive behavior approach to the internet where one invests significant amount of time â€Å"socializing† online or even performing academic pursuits or isolated leisure pursuits such as reading online to such a degree that other aspects of interaction – personal or interpersonal – are completely excluded. This behavior becomes so absorbing that the person can not pull him or herself way from the computer despite the fact that there are negative consequences that can result. Hence, the continuation of a particular behavior despite the fact that there are negative repercussions that may result is a textbook definition of the term addiction and, to a certain extent, I, myself, have suffered certain IAD type behavior patterns.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In general, an article written by Lisanne Carothers effectively describes the behavioral patterns of individuals who embody the traits of this condition:   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   â€Å"A recent study of [a multitude of] participants conducted revealed obsessing over   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   e-mail and the Internet [has the potential to severely damage common] daily   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   relationships and work performance. Those suffering from IAD most often have     Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   [lacking relationships in the real world] and†¦develop a new persona, play out   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   sexual fantasies or have instant access to [new people, places and experiences].   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   For myself, my own compulsive behavior manifested in the form of message boards that dealt with personal interests of mine. This may not seem like a â€Å"big deal† to some, but the reason I eventually curtailed my own personal ‘time-wasting’ in this pursuit was because it was getting to be, well, addictive and compulsive. For example, for a period of time in my life I developed a passing interest in videogames. In an attempt to learn more about videogames I would frequent message boards for more information. Eventually, this led to me writing questions on message boards and then reading the answers that were provided. This may seem benign and, to a great degree, it was. My Own Experience   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In time, I began to interact more and more with people in the message boards and this became somewhat of a social function. This social interaction started to become somewhat repetitive on my part and, honestly, started to become frequent enough that the patterns bordered on compulsive. At this point, I became somewhat uneasy about my own behavior and simply stopped spending the amount of time that I previously spent on the project. This never manifested itself in me into any sort of serious problem. For others, however, the addiction to this new world of the internet becomes so severe that they lose perspective and do not pull themselves out of it. As such, their compulsions become debilitating. The Potential Damage   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Is there anything wrong with all this? Is it really such a bad thing to have to deal with? To a great extent, the answer is yes although most people do not realize this. The reason they do not realize it is because: The joy that they receive from the internet clouds their judgment. They do not realize how much damage is occurring do by their time commitment   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   The Issue of Internet Addiction Syndrome – Page 3 Obsessing over fantasy personas and their online experiences keeps them out of the real world.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Consider the following notion in regards to this:   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   [The real world ceases to be important for them. even common everyday things    such as] food, personal cleanliness, relationships, even [something as critically   Ã‚   important for health such as] sleep are forgotten in the world of †¦the Internet.     Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   More and more of their conversations, social activities and even personal   Ã‚  Ã‚   relationships [develop through the origination point of electronic mediums    rather             then anything] face to face. (Watkins) Clearly, this is not the best way to go about life. This is something that I realized early and quickly divested myself of the problem. I have, however, noticed the prevalence of this problem in other people and it is not a good path that they are on. The reason for this is that when people opt to create a life for themselves that is one of â€Å"virtual reality† as opposed to absolute reality, there will be an instance where they must confront absolute reality sooner or later. Often, if they invest too much time in their online interactions, they will be at a severe disadvantage in the proverbial real world. Public Opinion   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Also, I find it troubling that many do not even believe a condition such as Internet Addition Syndrome even exists. Like many issues of mental health and stability, the public will often take a dismissive attitude towards the subject matter and instead label the problem a character flaw or weakness. This is unfortunate because it does not allow the person to receive the proper counseling, treatment or advice they need. This causes the condition to perpetuate and, possible, get worse. Hopefully, as the awareness level of this condition continued to expand more and more people will take the condition serious and those in need of help will receive the help they need before the condition becomes overwhelming.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   As noted by Robert Purdy in his essay â€Å"Internet Addiction,† the best way to treat this condition is to slowly and gradually reduce one’s time on the internet. I, myself, however, was more abrupt in my discontinuation of the vast majority of my internet time, but this is due in great part to the fact that I was not as obsessive as others are. For those who are struggling with more severe forms of Internet Addiction Syndrome, a gradual reduction would be well advised. Bibliography Carothers, L. â€Å"Internet Addiction.† 1 December 1997 Retrieved 24 September 2007 From     Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   http://www.bcmag.com/features/9609net.html. Stonecypher, L. Are You Addicted to the Internet? 2004 Retrieved 25 September 2007   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   From http://www.kudzumonthly.com/kudzu/jul01/addiction.html Purdy, R. â€Å"Internet Addiction.† Date Unknown Retrieved 24 September 2007 from   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   http://iml.jou.ufl.edu/projects/students/purdy/addiction.htm Purdy, R. â€Å"The Internet: Boon or Detriment to Society?† Date Unknown Retrieved 24   Ã‚   September 2007 from http://iml.jou.ufl.edu/projects/students/purdy/index.htm Watkins, R. â€Å"Geek Speak.† 1998 Retrieved 25 September 2007 From   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   http://ourworld.compuserve.com/homepages/geekspeak/Addict.htm

Counselling Rape Survivors

Counselling Rape Survivors According to the Home Office findings, Rape is defined as ‘forced to have sexual intercourse (Vaginal or anal penetration)’. The legal definition stipulates it to be ‘penile’. In general terms, rape is an act of aggression and violence against another; it is not an act of sex but is one of specifically dominance and power. Key points of the findings of the Research, Development andStatistics directorate of the Home Office published in 2002 are listedbelow. 0.4% of women aged 16 to 59 in England and Wales said they hadbeen raped in the year preceding the 2000 BCS, an estimated 61,000victims. 0.9% of women said they had been subject to some form ofsexual victimization (including rape) in this period. Around 1 in 20women (4.9%) said they had been raped since age 16, an estimated 754,000 victims. About 1 in 10 women (9.7%) said they had experiencedsome form of sexual victimisation (including rape) since age 16. Age is the biggest risk factor for experiencing sexual victimisation; women aged 16 to 24 were more likely to say they had been sexually victimised in the last year than older women. Women are most likely tobe sexually attacked by men they know in some way, most often partners(32%) or acquaintances (22%). Current partners (at the time of theattack) were responsible for 45% of rapes reported to the survey.Strangers were responsible for only 8% of rapes reported to the survey.18% of incidents of sexual victimisation reported to the survey came to the attention of the police; the police came to know about 20% of rapes. 32% of women who reported rape were ‘very satisfied’ with theway the police handled the matter, 22% were very dissatisfied. Lessthan two-thirds (60%) of female rape victims were prepared toself-classify their experience as ‘rape’ and less than three-quarters(70%) of women who self-classified themselves as having been victims of ‘attempted r ape’. Amnesty international reported that there were 14,000 recorded rapesin 2003 and 11,441 recorded rapes in 2002, representing a 8% increase.According to the Home Office, in the year ending March 2003, the totalnumber of sexual offences recorded by police in England Wales was 48,654, a 17% rise over the previous year. A victim of rape feels the fight or flight response that humans have built-in; which means that when the incident is over, one is leftwith a feeling of devastation, exhaustion, confusion, sadness, etc. The lingering psychological disorder is called Post Traumatic Stress Disorder (PTSD). The most effective therapeutic approach for long-term,severe PSTD appears to be talking treatment sessions with a clinicalpsychologist, in which the person is encouraged to talk through theirexperiences in detail. This may involve behavioural or cognitivetherapeutic approaches. Antidepressants may also be prescribed torelieve concurrent depression, a common feature in survivors, andenable the person to get the most out of any psychological treatment.Counselling may be helpful too in the early stages of recovery,particularly from counsellors experienced in the treatment of PTSD. Before we go into detail on counselling for rape survivors, it is essential to take into account the effectiveness of counselling in general. According to the Department of Health (2001), Counselling hasbeen defined as â€Å" a systematic process which gives individuals anopportunity to explore, discover and clarify ways of living moreresourcefully, with a greater sense of well-being †. The use ofcounselling as a means of responding to people in distress and turmoilhas been increasing rapidly in recent years. This has generated adebate on the effectiveness of counselling process itself. The methodsof evaluation of effectiveness is also highly controversial. Theconcerns in the qualitative and quantitative evaluation is discussed indetail later. Bondi summarises from her reports on controlled trials conducted inhealth care settings. They seem to indicate that counselling is aneffective intervention, clinically and economically. Its costs andbenefits are broadly comparable to those of antidepressant medication. Moreover, it seems to be a popular choice with many patients. Cautionis sometimes attached to the results of these trials. This may be dueto the fact that it only involves a small trial when compared to thelarge trial group of medication. Studies of counselling in othersettings indicate a high level of satisfaction among clients. Bondialso writes that there is good evidence to suggest that counselling hasa capacity to reduce demand on psychiatric services. This is becausecounselling prevents less serious problems from becoming more seriousand helps people to maintain reasonably good levels of mental health. Choice of treatment of survivors of rape has been one of increasing significance within health care and also highlights the need toconsider factors other than clinical and cost-effectiveness.Counselling is not the only form of talking treatment available. Otherforms of talking treatment include psychotherapy, cognitive behaviourtherapy, self-help groups and support groups. Counselling attaches a great significance to the autonomy of the victim and therefore it cannot be administered to the unwilling. The success of counselling, therefore, depends on active participation. For counsellingof rape victims, feelings caused by abuse may be quite overwhelming and difficult to deal with. The Department of Health (2001) has recommended counselling as one of the types of psychological therapy for depression, anxiety, panic disorder, social anxiety and phobias andpost traumatic disorders. These problems can be mainly related tosurvivors of rape. The National Center for Victims of Crime (2004) recommends that counselling can help cope with the physical and emotional reactions to the sexual assault or rape, as well as provide necessary information about medical and criminal justice system procedures. According to the reports by the Brunel University (2005) on sexual abuse and rape, sharing experiences in a safe, understanding and confidential setting may help to manage their feelings by being heard and taken seriously.   Counselling enables to make sense of the present, in relation to the past.   Some survivors of sexual abuse maybe plagued by memories in the form of distressing flashbacks, mental images or nightmares.   Talking about the images and memories while being heard and supported will often ease the problem.   It may beeasier to share incidents and feelings with a professional counsellorconfidential, rather than a friend. Some people prefer to talk to ahelpline so they do not have to face the person they are disclosing to.    According to Bondi’s summary of her studies on the effectiveness ofcounselling that sceptics often voice doubts of counselling because itappears to involve nothing other than one (or two people) â€Å"chatting† toa counsellor. However, in spite of these doubts, communication takesplace when counselling is effected, whereby a special kind ofrelationship is developed between the counsellor and the victim. Bondiattributes this to the fact that human beings are social creaturescapable of connecting with others. It is worth to note that allapproaches to counselling share a commitment to apply insights andunderstandings about the importance of these connections to offertherapeutically effective relationships. Impacts of counselling on rape survivors often depends on the development of a helpful working relationship between the counsellor and survivor.   According to the STAR findings, some women feel nervous and unenthusiastic about seeing a counsellor. Therefore, it is essential that they feel relaxed and comfortable to be able to talk freely. Setting up of a pace comfortable for the victim is important as it recognises the interlinked nature of people’s lives (Skinner andTaylor,   Home Office report 51/04).   According to Bernes (2005), effective counselling leading to a good counsellor-victim relationship follows the following dynamics. They are an emotionally charged, confiding relationship between the patient and therapist; warmth, support and attention from the therapist in a healing setting; a positive therapeutic alliance between patient and therapist; a new rationale or conceptual scheme offered with confidence by the therapist; the passage of time; installation of hope and expectancy and finally techniques consistent with patient expectation and efficacy. Common process strategies in counselling include gathering sufficient information, listening well and with understanding, helping the individual reflect and gain insight, helping in decision-making and goal setting, and providing options and ideas for client consideration (Korhonen). According to the Home Office reports on the STAR scheme, the data collected from the survey did not give any indications that anyone counselling technique works better than another.   Methods likedrawing or making lists of feelings, events, concerns and workingthrough them were found to be effective by some rape survivors. Some found making plans for the future, for example, symbolic moves such aschanging the dà ©cor of the room seemed to indicate a new phase in their lives.   Others indicated that a flexible integrated approach with respect, a respectful politeness, support and even the smiling face of the counsellors seemedto have helped them. The need for administering couna respectful, supportive and caring environment is also essential. Also, them cope development of a programme of work that enabled them to look at themselves in a logical, positive and respective manner athem cope with their emotions and move forward at their own pace is essential. The university of Dundee has introduced a computer counsellingtechnique called ‘ENHANCE’ for rape victims. Often, women who have been raped find it hard to talk about their feelings and research evidence shows that in sensitive and potentially embarrassing areas of human functioning, some people may find it easier to talk openly to acomputer. ENHANCE,   a computer based facility which includes a diaryfacility for free writing, a visualisation tool to describe feelingsand graphic manipulation and exploration, an information base to accessa range of supportive information, leaflets and contacts and the optionof what to destroy or save it for later reference. Further work is being done to develop ENHANCE and the researchers feel that their workcan be transferred to other agencies in future. Furthermore, it is inan early stage to be assessed for effectiveness. Computer counselling is, therefore, new and brings to attention to the fact there is very few online support avail able for rape survivors. This can be a good sourceof data for qualitative research as it reduces some of its ethical risks which are discussed in detail later.  Ã‚  Ã‚   It is very difficult to assess the effectiveness of counselling forrape survivors as due to the dilemmas in relation to the ethicalpractises of counselling, training and qualifications of counsellors and the evaluation of counselling and little published information.Counselling services are offered in a wide range of settings, which influences the kind of outcomes (Bondi). Bondi, in her review ofdifferent counselling orientations writes that similar effects may beusually reported. This is consistent with the argument that it is thequality of the therapeutic relationships offered by the counsellorswhich determine the effectiveness of counselling.   Effectiveness of rape counselling can be studied by either qualitativeor quantitative research. McLeod (2000) reports from his paperpresented at the 8th Annual International Counselling, University of Durham that counselling in Britain at the beginning of the twenty-first century does not have a clear vision of the role of research. It is worth mentioning that very few studies have focussed on research methods to measure effectiveness of counselling for rape victims. McLeod also reports that, in general, published studies of counsellingand therapy in dominated by quantitative research like up to 95%. Ingeneral, cultural assumptions are concerned with the development ofmethods that are valid and reliable.   Quantitative research reduceshuman experience and action to variables. Hypothesis are framed interms of the relationships between these variables, which can often beinterpreted a rational voice allowing no expression of feeling orpersonal experience (McLoad, 2000).   There has been no reports  relating to quantitative research on counselling for rape. Qualitative research has been used lately in the health care settingsand voluntary organisation for rape survivors. Qualitative research refers to research conducted in an interpretive or critical tradition. Research conducted in this tradition generally includes ethnographies, naturalistic observation or intensive interviewing studies, and usessome type of content analysis of words or texts to generate themes, which summarize the results of the study. The goals of qualitative research are not usually to generalize from the findings to some largertruth, but rather to explore or generate truths for the particular sample of individuals studied or to generate new theories. There is often an emphasis in qualitative research on perception or livedexperience.  There   are quite a few ethical concerns in qualitative research of assessing the effectiveness of counselling of rape victims.   Knapik (2002)in his paper summarises the ethical concerns of qualitative researchwhich mainly rev olve around an assessment of benefit versus harm,confidentiality, duality of roles, and informed consent   It is oftenassumed that qualitative data does not involve physical manipulation orintrusive procedures on victims. But it can pose certain risks to the victims.   Moleski and Kiselica (2005) highlight the dangers of a dual or multiplerelationships between the counsellor and victim. During research involving in-depth interviews or focus group discussions on such asensitive as rape, the researcher (generally a counsellor, but called aresearcher in this context as the data collected is for the purposes of qualitative research) develops a relationship of trust with the victim. The relationship may be misinterpreted by the participant as atherapist-client relationship. The data may be interpreted in waysunflattering or damaging to participants. It is therefore important toassess the harms and benefits in dealing with real clients. Secondly, risks to individuals participating in qualitative researchmay often not be anticipated. This is because the method and researchquestions are always evolving and changing from the various organisation’s approach to the case. These risks should be made clearto the participants from the beginning and also du ring the course ofthe experiment. Thirdly and most importantly, qualitative research   always generatesquestions on the ability to protect confidential information. Usually, names and personal data are excluded from published results, but quotations, cues from the publications can always identify theparticipant to those familiar with the research. Reasons for this maybe because of the nature of sensitivity of the rape abuse problem,  trial groups always being small and trials being conducted in smallcommunity structures. Reports were published by the Home Office on the ‘STAR young person project’ on assessing the counselling services offered to rape survivors. Young women primarily had a positive counselling experiencebut a small number reported some level of dissatisfaction.   One of the reasons were the short sessions of counselling, as they could not continue working with their counsellors on a long term basis. This indicated the issue of assess to a restricted number of sessions.  Another issue was the pace at which information is disclosed to thecounsellor, as a small percentage of the women disliked gettingstraight to the information or having to answer questions pertaining tothe incidents within a shorter period of contact between the victim andthe counsellor. This may be because a certain time span is needed toestablish a counsellor-victim relationship which varies from case tocase and depends on the severity of the case.       Another small percentage of the STAR participants felt that the counsellor was not equipped to work with areas of the case and thatthey were given unhelpful advise or irrelevant information or help in away which was not the one suited for the particular case. This throwslight on the training issues of counsellors, whether they are properly equipped for the job. Another percentage of the women, said that thecounsellor disapproved of them being late or related issues whichindicate an over-protective or over-controlling issue which can causenegative impacts on the counselling experience. The findings indicatethe need for a more flexible approach during counselling experiences, longer-term counselling and support by the counsellor, proper trainingfor counsellors and more research into counselling methods and theirevaluation.   According to the findings of the British Crime Survey (2002), it isdifficult to assess the level of support for victims of rape due to the small number of victims in year 2001. Also, the British Crime Survey(2002) reports that support services are under-funded, relative tosupport services dedicated to victims of domestic violence. In UK, therapy services for rape survivors are available from charity andlistening services, health services provided by the universities forstudents, NHS and   few religious movements.   In the NHS, there areusually long waiting lists sometimes up to a year for patients toaccess counsellor services. In voluntary and charity services there maynot always be round-the clock assistance for rape survivors. Telephone access is restricted to certain times of the day.   Findings of research on women rape victims are available in a varietyof forms and from a variety of places. Professional journals such as Violence Against Women, the Journal of Interpersonal Violence, Aggression Violence Behavior, Violence Victims, and the Journal of Family Violence include research conducted by psychologists, social workers, sociologists, advocates, and others. In addition to professional journals, findings of research are presented at domesticviolence conferences, described in the popular press, found on websites devoted to ending violence against women, and are available aspublications from government agencies like the Home Office, UK orprivate research organizations (various voluntary organisation’swebsites). Research reports published in scientific journals are subject to peer-review.   Research published in scientific journals thus gives thereader some confidence in the scientific credibility of the researchfindings. Scientific credibility, however, does not necessarily meanthat the findings represent â€Å"the truth†. Research released directlyfrom an organization sponsoring the research does not usually gothrough the peer review process. So there is a real need for independent qualitative research into the counselling services for rape victims in the UK. The UK Home Office should actively engage inindependent evaluation of counselling services for rape victims. The STAR project recommendations the following for future research. There is need for piloting and evaluating peer support systems. New research projects into contexts and circumstances of rape is requiredto throw new light on the academic and practitioner’s knowledge. More research is needed into the needs of victims from internet supportservices while reviewing the current internet support service toprovide guidelines for practise. More creative approaches in regards toservices for survivors were also required. It is also recommended that counsellors be given appropriate training to improve the services to rape survivors. According to Bernes (2005), there are five critical components forbecoming an effective counsellor. The counsellor should have aprofound, genuine and early draw to the field, a profound and genuinefascination to try to understand human nature, cognitive ability, arigorous and quality academic program and major field exposure. There is therefore a genuine need for efforts to be focussed in creating effective counsellors to deal with rape victims. More funding to develop therapy services is required. There is a need to establish infrastructure towards organisations involved in treatmentand care of victims. Further research into the effective processes ofvarious approaches of counselling is recommended. Detailed research isneeded into the qualitative analysis of effectiveness of thecounselling processes. Also, independent qualitative analysis in victimsupport is needed to verify the results. In general, in the UK, counselling for rape survivors have still a long way to go.

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