Musical History And Societal Influences Music Essay

Musical History And Societal Influences Music Essay The definition of music is defined in many ways; Websters definition is as follows an art of sound in time that expresses ideas and emotions in significant forms through the elements of rhythm, melody, or harmony. There are many theories regarding when and where music formed. Many agree that music began even before man existed. Researchers point out that there are six periods of music and each period has a certain style of music that made what music is today. Here are some resources for you to better understand the history of music. (Estrella 2001) Music is traced back as far as ancient Israel a thousand years before Christ; King David composed and sang hundreds of songs called psalms. A few of them are written in the old testament in the book of Psalms. But music as we know it now, as having structure and form, may have begun in the 10th century with the Gregorian chants. These chants were organized and detailed with soloists and small groups singing distinctive parts. The music we are more in common with began around the year 1200 and soon after, troubadours singing folk music starting to appear in parts of Europe. In the 14th century, sacred music (church music and hymns) was quite common (but secular music had begun to take hold as well). During the renaissance (around the year 1500) one of the most significant events occurred-the birth of the composer. The appearance of composers, of course, spawned instrumental music and the creation of the instruments such as the piano and lute. (Ezine Articles 2005) The years 1750 to 1820 is considered the Classical period with the piano being a composers instrument of choice. During this time, Mozart wrote his first symphony, Bach performed in London, and Beethoven was born. Many of the symphonies we enjoy today were written during this time. Music has truly evolved since this period though. By 1900, a man named Scott Joplin had composed and published the Maple Leaf Rag, an event many see as the beginnings of the music we know today as popular music. Soon after, new musical forms were taking hold. Jazz in the 1930s (Louis Armstrong, Billie Holiday), big band music in the 1940s (Tommy Dorsey, Duke Ellington), and rock-and-roll (Elvis Presley, Chuck Barry) in the 1950s. Other countries (most notably France and Spain) were creating their own popular music during this time. (Ezine 2005) The three time periods I want to focus on is Medieval, Renaissance, Baroque, Classical, Romantic, and Contemporary. This is all known to us to day as Opera, RB, Rock, Hip Hop, Soul, etc. Music has been around for years and can be broken down into many stages or cycles. People everywhere all over the world make their own style of music. Ever genre, sound, melody is different in some way. When we look at the medieval music, we are dealing with the longest and most distant period of musical history. Saint Gregory is credited with organizing the huge repertory of chant that developed during the first centuries of the Christian church, hence the term Gregorian chant. He was pope from 590 to 604, and the medieval era continued into the 1400s, so this period consists of almost a millenniums worth of music. One of the principal difficulties in studying medieval music is that a system for notating music developed only gradually. The first examples of musical notation date from around 900. For several centuries, notation only indicated what pitch to sing. The system for notating rhythm started in the 12th or 13th century. Gregorian chant is monophonic, meaning music that consists of only one melodic line without accompaniment. The beauty of chant lies in the serene, undulating shapes of its melody. We do not know who wrote the melodies of Gregorian chant. Like folk melodies, the music probably mutated as it was passed down through generations and eventually reached its notated form. Polyphony, music where two or more melodic lines are heard simultaneously, did not exist (or was not notated) until the 11th century. Unlike chant, polyphony required the participation of a composer to combine the melodic lines in a pleasing manner. Although most medieval polyphonic music is anonymousthe names of the composers were either lost or never written down at allthere are composers whose work was so important that their names were preserved along with their music. (Ezine 2005) Renaissance is reflected by the changing role of the composer in society. Unlike most of their medieval times, the great masters of the Renaissance were created in their own lifetimes. The technique of printing music, while slow to evolve, helped in the preservation and distribution of music and musical ideas. Sacred music was still predominant, though other music became more prevalent and more sophisticated. The repertory of instrumental music also began to expand significantly. New instruments were invented, including the clavichord and virginal and many existing instruments were improved. Masses and motets were the primary forms of sacred vocal polyphony. Other vocal forms included motets, madrigals and songs (generally accompanied by lute or a small instrumental ensemble or consort). Instrumental pieces were usually short polyphonic works or music for dancing. (Ezine 2005) Compared with the medieval style, Renaissance polyphony was lush and sonorous. The era between Josquin Desprez and Palestrina is known as the golden age of polyphony. Imitationwhere one melodic line shares, or imitates the same musical theme as a previous melodic linebecame an important polyphonic technique. Imitation was one method composers used to make complex music more easily comprehensible and give the listener a sense of structure. Imitative polyphony can be heard in the masses and motets of composers from Josquin onward and is featured in instrumental music by Byrd, Gibbons, and the Gabriellis. Baroque music is often highly ornate, colorful and richly textured when compared with its predecessors. Opera was born at what is considered to be the very beginning of the Baroque era, around 1600. This unique form combines poetry, theater, the visual arts and music. It came about because a group of Italian intellectuals wanted to recapture the spirit of ancient Greek drama in which music played a key role. The first great opera was Orfeo, by Claudio Monteverdi, first performed in 1607. Musics ability to express human emotions and depict natural phenomenon was explored throughout the Baroque period. Vivaldis famous set of concertos, The Four Seasons, is a famous example. Although imitative polyphony remained fundamental to musical composition, homophonic writing became increasingly important. Homophonic music features a clear distinction between the melody line and a subsidiary accompaniment part. This style was important in opera and other solo vocal music because it focused the li steners attention on the expressive melody of the singer. The homophonic style gradually became prevalent in instrumental music as well. (Ezine 2005) Many Baroque works include a continuo part in which a keyboard (harpsichord or organ) and bass instrument (cello or bassoon) provide the harmonic underpinning of chords that accompanies the melodic line. New polyphonic forms were developed, and as in the Renaissance, composers considered the art of counterpoint (the crafting of polyphony) to be essential to their art. Canons and fugues, two very strict forms of imitative polyphony, were extremely popular. Composers were even expected to be able to improvise complex fugues on a moments notice to prove their skill. The orchestra evolved during the early Baroque, starting as an accompanist for operatic and vocal music. By the mid-1600s the orchestra had a life of its own. The concerto was a favorite Baroque form that featured a solo instrumentalist (or small ensemble of soloists) playing against the orchestra, creating interesting contrasts of volume and texture. Many Baroque composers were also virtuoso performers. For example, Archang elo Corelli was famous for his violin playing and Johann Sebastian Bach was famous for his keyboard skills. The highly ornamented quality of Baroque melody lent itself perfectly to such displays of musical dexterity. (Grieg 2002) The word Classical has strong meaning, mixed with the art and Philosophy of Ancient Greece and Rome, along with their ideals of disciplined expression. The late Braque was complex and melodically different. The composers of the early Classical period changed direction, writing music that was much simpler to understand. Homophony music, another part of classical music in which melody and charm are distinct, and has dominated the Classical style is another form of classical music. New forms of composition were developed to accommodate the transformation. Santana Form is the most important of these forms, and one that continued to evolve throughout the Classical period. Although Baroque composers also wrote pieces called sonatas, the Classical sonata was different. The essence of the Classical Sonata is difficult to understand. A highly simplified example of such a conflict might be between two themes of contrasting character. (Grieg 2002) This contrast would be found during the course of the sonata, and then resolved. Sonata form allowed composers to give pure instrumental music recognizable dramatic shape. Every major form of the Classical era, including the string quartet, symphony and concerto was molded on the dramatic structure of the sonata. One of the most important developments of the Classical period is the growth of the public concert. Although the aristocracy would continue to play a significant role in musical life, it was now possible for composers to survive without being the employee of one person or family. This also meant that concerts were no longer limited to palace drawing rooms. Composers organized concerts featuring their own music, and attracted large audiences. The increasing popularity of the public concert had a strong impact on the growth of the orchestra. Although chamber music and solo works were played in the home or other intimate settings, orchestral concerts seemed to be naturally designed for big public spaces. As a result, symphonic music composers gradually expanded the size of the orchestra to accommodate this expanded musical vision. (Grieg 2002) Just as the word Classical conjures up certain images, Romantic music also does the same. Whether we think of those romance novels with the Romanticism implies fantasy and sensuality. The Classical period focused on emotional restraint. Classical music was expressive, but not so passionate that it could overwhelm the work Beethoven, who was in some ways responsible for igniting the flame of romanticism, always struggled (sometimes unsuccessfully) to maintain that balance. (Greig 2002) Many composers of the Romantic period followed Beethovens model and found their own balance between emotional intensity and Classical form. Others reveled in the new atmosphere of artistic freedom and created music whose structure was designed to support its emotional surges. Musical story-telling became important, and not just in opera, but in pure instrumental music as well. The tone-poem is a particularly Romantic invention, as it was an orchestral work whose structure was entirely dependent on the scene being depicted or the story being told. Color was another important feature of Romantic music. A large palette of musical colors was necessary to depict the exotic scenes that became so popular. In addition to seeking out the sights and sounds of other places, composers began exploring the music of their native countries. Nationalism became a driving force in the late Romantic period and composers wanted their music to express their cultural identity. This desire was particularly intense in Russia and Eastern Europe, where elements of folk music were incorporated into symphonies, tone-poems and other Classical forms. (Wagner 1999) The Romantic period was the days of the virtuoso. Gifted performers and particularly pianists, violinists, and singers became enormously popular. Liszt, the great Hungarian pianist/composer, reportedly played with such passion and intensity that woman in the audience would faint. Since, like Liszt, most composers were also virtuoso performers, it was inevitable that the music they wrote would be extremely challenging to play. The Romantic period witnessed a glorification of the artist whether musician, poet or painter that has had a powerful impact on our own culture. (Wagner 1999) This style of music became known as being romantic. The evolution of music is at least partly shaped by the influence one composer has on another. These influences are not always positive, however. Sometimes composers react against the music of their recent past (even though they might admire it) and move in what seems to be the opposite direction. For example, the simplified style of the early Classical period was almost certainly a reaction to the extreme intricacies of the late Baroque. The late Romantic period featured its own extremes: sprawling symphonies and tone-poems overflowing with music that seemed to stretch harmony and melody to their limits. It is certainly possible to view some early 20th century music as an extension of the late Romantic style, but a great deal of it can also be interpreted as a reaction against that style. 20th century music is a series of isms and neo-isms. The primal energy of Stravinskys Rite of Spring has been called neo-Primitivism. The intensely emotional tone of Schà ¶nbergs early music has b een labeled Expressionism. The return to clearly structured forms and textures has been dubbed neo-Classicism. (R. Strauss) These terms have been employed in an attempt to organize the diversity of styles running through the 20th century. Nationalism continued to be a strong musical influence in the first half of the century. The study of folk songs enriched the music of numerous composers, such as Ralph Vaughan Williams (England), Bela Bartok (Hungary), Heitor Villa Lobos (Brazil) and Aaron Copland (USA). Jazz and popular musical styles have also been tremendously influential on classical composers from both the United States and Europe. Technology has played a increasingly important role in the development of 20th century music. Composers have used recording tape as a compositional tool (such as Steve Reichs Violin Phase). Electronically generated sounds have been used both on their own and in combination with traditional instruments. More recently, computer technology has been used in a variety of ways, including manipulating the performance of instruments in real time. (R. Strauss) So as you can see, music has been around for centuries. Many people have helped music evolve over the years. The six long periods of music that were discussed above really helped music become what is today. Although each individual listen to various types of music they all started the same, with either a rhythm or beat. Music was originated long before humans even existed and grew from there. Music in general has made the world a better place. It gives people a way to express themselves. Music has been called The International Language; a very simple thought with much meaning behind it. Even if you cant speak the language of a country, you can move, sway, dance and most of all enjoy the music of the country. We may not understand the words of a musical selection but we do understand the beauty. (Ruth 2008) Musics interconnection with society can be seen throughout history. Every known culture on the earth has music. Music seems to be one of the basic actions of humans. However, early music was not handed down from generation to generation or recorded. Hence, there is no official record of prehistoric music. Even so, there is evidence of prehistoric music from the findings of flutes carved from bones. The influence of music on society can be clearly seen from modern history. Music helped Thomas Jefferson write the Declaration of Independence. When he could not figure out the right wording for a certain part, he would play his violin to help him. The music helped him get the words from his brain onto the paper. In general, responses to music are able to be observed. It has been proven that music influences humans both in good and bad ways. These effects are instant and long lasting. Music is thought to link all of the emotional, spiritual, and physical elements of the universe. Music can also be used to change a persons mood, and has been found to cause like physical responses in many people simultaneously. Music also has the ability to strengthen or weaken emotions from a particular event such as a funeral. People perceive and respond to music in different ways. The level of musicianship of the performer and the listener as well as the manner in which a piece is performed affects the experience of music. An experienced and accomplished musician might hear and feel a piece of music in a totally different way than a non-musician or beginner. This is why two accounts of the same piece of music can contradict themselves. (ODonnell 2001) According to The Center for New Discoveries in Learning, learning potential can be increased a minimum of five times by using this 60 beats per minute music. For example, the ancient Greeks sang their dramas because they understood how music could help them remember more easily). A renowned Bulgarian psychologist, Dr. George Lozanov, designed a way to teach foreign languages in a fraction of the normal learning time. Using his system, students could learn up to one half of the vocabulary and phrases for the whole school term (which amounts to almost 1,000 words or phrases) in one day. Along with this, the average retention rate of his students was 92%. Dr. Lozanovs system involved using certain classical music pieces from the baroque period which have around a 60 beats per minute pattern. He has proven that foreign languages can be learned with 85-100% efficiency in only thirty days by using these baroque pieces. His students had a recall accuracy rate of almost 100% even after not r eviewing the material for four years. The article above discusses how the history of music not only helped human beings but impacted their lives greatly to where we learn better and think better. (ODonnell 2001)

When people become very angry, they are said to be operating from their `dinosaur brain`

It has been said that the thing that sets human beings apart from all the other creatures in the animal kingdom is the fact that human beings have the ability for discernment and for logical thinking. In times were animals would be ruled by impulse and instinct, human beings are able to control these urges to a certain extent. As beings capable of suppressing baser instincts and impulses, human beings are expected to be above such primal instincts.It is for this reason that people who are very angry or emotional and give in to such baser instincts are said to be operating from their â€Å"dinosaur brains. † It is not to say of course that operating from one’s dinosaur brain means that one is also capacitated with the same intellectual capacity as that of those prehistoric animals. Dinosaurs were creatures that had smaller brains than today’s creatures and as such their thinking had not evolved to the same extent.This means that these animals only followed the bas ic instincts such as eating, mating and sleeping, offshoots of which are aggression in certain cases in order to preserve and protect. Therefore, any person who is operating from their dinosaur brain is simply exercising the functions that dinosaurs used to use in the underdeveloped brains. Feelings such as anger and hunger become the ruling considerations and logic is never part of the equation.

The History of Deodorants and Antiperspirants

Mum deodorant is generally recognized as being the first-ever commercial deodorant... but we dont actually know who invented it.    Mum Deodorant Before the advent of deodorant, people generally battled their offensive smells by masking them with perfumes (a practice dating to the Ancient Egyptians and Greeks).  That changed when Mum deodorant came onto the scene in 1888. Unfortunately, we dont actually know whom to thank for saving us all from our stink, as the inventors name has been lost. All we know is that this Philadelphia-based inventor trademarked his invention and distributed it through his nurse under the name of Mum.   Mum also had very little in common with the deodorants found in drugstores today. Unlike todays roll-on, stick or aerosol deodorants, the zinc-based Mum deodorant was originally sold as a cream applied to the underarms by the fingers.    In the late 1940s, Helen Barnett Diserens joined the Mum production team. A suggestion by a colleague inspired Helen to develop an underarm deodorant based on the same principle as a newfangled invention called the  ballpoint pen. This new type of deodorant applicator was tested in the USA in 1952, and marketed under the name of Ban Roll-On. The First Antiperspirant Deodorants can take care of smells, but theyre not as effective at taking care of excessive sweating. Fortunately, the first antiperspirant came onto the scene just 15 years: Everdry, which launched in 1903, used aluminum salts to block pores and inhibit sweating. These early antiperspirants caused skin irritation, however, and in 1941 Jules Montenier patented a more modern formulation of antiperspirant that reduced irritation, and which hit the market as Stopette. The first antiperspirant aerosol deodorant was launched in 1965. However, antiperspirant sprays lost popularity due to health and environmental concerns, and today stick deodorants and antiperspirants are most popular.

Predicting Fall Color and Autumn Leaf Display

University of Georgia silvics professor, Dr. Kim Coder, suggests there are ways to predict how beautiful a fall color and autumn leaf display will be. Key predictors are used along with a good mix of common sense and can forecast the quality of a viewing season with surprising accuracy. Leaf Volume The fall season should start with substantial leaf volume. The more leaves attached to trees entering the color season means more to look at. Droughty summer weather conditions can limit that volume but a wet summer can set up disease and insects. You hope for a moderately dry summer. Health Healthy leaves not only present quality viewable leaf surfaces to look at but vigorous leaves stay attached to trees longer. Pest and environmental problems can damage and disrupt leaf surfaces so much that they can actually detract from a quality viewing season. Increased pests can be a factor of both weather and temperature during the summer growing season. Temperature and Precipitation Cool night temperatures with no freezes or frosts and cool, bright, unclouded sunny days will enhance the leaf color change. Slightly dry conditions in the last half of the growing season and on into the fall have a positive effect. Here are the conditions Dr. Coder says contribute to a poor season: Fall rain fronts and long overcast periods diminish color presentation. So do strong wind storms that blow the leaves from the trees. Wet and humid growing seasons lead to many leaf infections and premature leaf abscission. Freezing temperature and hard frosts stop color formation dead. Get Organized A true leaf-peeper will keep accurate annual records of peak color days over the past decade. Peak color day dates tend to repeat themselves over time.

Obesity A Major Problem Today Society Within The United...

Obesity is a major problem in today’s society within the United States. To be more specific, childhood obesity. Childhood obesity is becoming worse, and the adults don’t realize the impact it has on the rest of the child s life. According to Americas Let’s Move initiative the definition of Obesity is, â€Å"excess body fat. Because body fat is difficult to measure directly, obesity is often measured by body mass index (BMI), a common scientific way to screen for whether a person is underweight, normal weight, overweight, or obese ( Obama). According to Jean Cowie, â€Å"obesity is caused by an imbalance in equilibrium between energy intake and energy expenditure† (Cowie). Metabolism plays a huge role in the upcoming stages of becoming obese. One of†¦show more content†¦The complications can range from heart disease, type 2 diabetes, asthma, high cholesterol levels, high blood pressure, and even sleep apnea. These health complications lead to many social complications. Social complications that can be linked to things such as bullying. According to Americas Let’s Move initiative, â€Å"overweight and obese children can often be targets of early social discrimination†. â€Å"Numerous studies have documented harmful weight-based stereotypes that overweight and obese individuals are lazy, weak-willed, unsuccessful, unintelligent, lack self-discipline, have poor willpower, and are noncompliant with weight-loss treatment (Obama). This being stated allows for psychological stress in an individual which can also lead to lower self-esteem. With lower self-esteem comes self-image problems. Self-image is becoming a major problem in today’s society because of the pressure that is put on both males and females to look a certain way in order to be portrayed as â€Å"beautiful†. At this point in the obese stage, it can cause the child to begin to go into a depressed state. Depression can have lifelong circumst ances such as poor health, poor living conditions, no motivation, and with these individuals tend to become obese. Along with depression, there are many other lifelong complications that can evolve from being obese from a young age. Self-image is a huge problem in obese children and can make an

Power Utility Consumption Capm in Uk Stock Markets Free Essays

string(114) " for values of risk aversion \(\? \) between 0 and 10 and values of the beta coefficient \(\? \) between 0 and 1\." Pricing of Securities in Financial Markets 40141 – How well does the power utility consumption CAPM perform in UK Stock Returns? ******** 1 Hansen and Jagannathan (1991) LOP Volatility Bounds Volatility bounds were first derived by Shiller (1982) to help diagnose and test a particular set of asset pricing models. He found that to price a set of assets, the consumption model must have a high value for the risk aversion coefficient or have a high level of volatility. Hansen and Jagannathan (1991) expanded on Shiller’s paper to show the duality between mean-variance frontiers of asset portfolios and mean-variance frontier of stochastic discount factors. We will write a custom essay sample on Power Utility Consumption Capm in Uk Stock Markets or any similar topic only for you Order Now Law of one price volatility bounds are derived by calculating the minimum variance of a stochastic discount factor for a given value of E(m), subject to the law of one price restriction. The law of one price restriction states that E(mR) = 1, which means that the assets with identical payoffs must have the same price. For this constraint to hold, the pricing equation must be true. Hansen and Jagannathan use an orthogonal decomposition to calculate the set of minimum variance discount factors that will price a set of assets. The equation m = x* + we* + n can be used to calculate discount factors that will price the assets subject to the LOP condition. Once x* and e* are calculated, the minimum variance discount factors that will price the assets can be found by changing the weights, w. Hansen and Jagannathan viewed the volatility bounds as a constraint imposed upon a set of discount factors that will price a set of assets. Therefore, when deriving the volatility bounds, we calculate the minimum variance stochastic discount factors that will price the set of assets. Discount factors that have a lower variance than these values will not price the assets correctly. Furthermore, Hansen and Jagannathan showed that to price a set of assets, we require discount factors with a high volatility and a mean close to 1. After deriving these bounds, we can use this constraint to test candidate asset pricing models. Models that produce a discount factor with a lower volatility than any discount factor on the LOP volatility can be rejected as they do not produce sufficient volatility. Hansen and Jagannathan find evidence that using LOP volatility bounds, we can reject a number of models such as the consumption model with a power function analysed in papers such as Dunn and Singleton (1986). 2 Methodology To test whether the power utility CCAPM prices the UK Treasury Bill (Rf) and value weighted market index returns, we first calculate the LOP volatility bounds. The volatility bound is derived by calculating the minimum variance discount factors that correctly price the two assets for given values of E (m). The standard deviations of the stochastic discount factors are then plotted on a graph to give the LOP volatility bound shown in figure one. Figure 1 here The CCAPM stochastic discount factors are then calculated for different levels of risk aversion. The mean and standard deviation of these discount factors are then plotted on the graph and compared to the LOP discount factor standard deviations. Pricing errors can then be calculated and analysed to see whether the assets are priced correctly by the candidate model. To accept the CCAPM model in pricing the assets, we expect the stochastic discount factors variance to be greater than the variance of the LOP volatility bounds. It is also expected that pricing errors and average pricing errors (RMSE) will be close to zero. These results will be analysed more closely in the later questions. 3 Power Utility CCAPM vs LOP Volatility Bounds In order for the power utility CCAPM to satisfy the Law of One Price volatility bound test at any level of risk aversion, the standard deviation f the CCAPM stochastic discount factor at that level of risk aversion must be above the Law of One Price standard deviation bound for the mean value of the CCAPM stochastic discount factor at the same level of risk aversion. This is the null hypothesis and if it is accepted then the model satisfies the test. The alternative hypothesis is that it the stand ard deviation of the stochastic discount factor is below the Law of One Price standard deviation bound for the mean value of the stochastic discount factor. If the null hypothesis is rejected and the alternative hypothesis is accepted then the model does not satisfy the test. Table 1 here Figure 2 here Figure 2 shows LOP volatility bounds and the standard deviations and means of the CCAPM stochastic discount factors for levels of risk aversion between 1 and 20. It is obvious the standard deviations (Sigma(m)) of the CCAPM stochastic discounts factors are much lower than the LOP volatility bounds corresponding to the means (E(m)) of the CCAPM stochastic discount factors. This is true for any level of risk aversion, because the entire CCAPM (green) line lies below the LOP volatility bounds (dark blue) line. Table 1 shows the standard deviations of the stochastic discount factors and the precise LOP volatility bound values, corresponding to the stochastic discount factor means so that the CCAPM can be formally tested. All of the standard deviations are lower than their respective volatility bound values. Therefore the null hypothesis is to be rejected and the alternative hypothesis is to be accepted for all levels of risk aversion between 1 and 20. Furthermore it would take a risk aversion of at least 54 to accept the null hypothesis. Therefore the power utility CCAPM stochastic discount factor does not satisfy the Law of One Price volatility bound test. These results are consistent with the equity premium puzzle study by Mehra and Prescott (1985). The study examines whether a consumption growth based model with a risk aversion value restricted to no more than 10 accurately prices equities. They have found that according to the model equity premiums should not exceed 0. 5% for values of risk aversion (? ) between 0 and 10 and values of the beta coefficient (? ) between 0 and 1. You read "Power Utility Consumption Capm in Uk Stock Markets" in category "Papers" However the average observed equity premium based on the average real return on nearly riskless short-term securities and the SP 500 for the period 1989-1978 was 6. 18%. This is clearly inconsistent with the predictions of the model. In particular if risk aversion is close to 0 and individuals are almost risk neutral, the model fails to explain why the sample’s average equity returns are so high. If risk aversion is significantly positive the model does not justify the low average risk-free rate of the sample. The results of Mehra and Prescott’s (2008) empirical study are consistent with our results, because the power utility CAPM did not satisfy our empirical tests. 4 Kan and Robotti (2007) Confidence Intervals The Law of One Price volatility bounds calculated in part 2 are subject to sampling variation. We have calculated point estimates of the volatility bounds, but we did not take into account that our results are based on a finite sample of Treasury Bill and market returns. To more accurately test whether the power utility CCAPM passes the LOP volatility bounds test, we need to identify the area in which the population volatility bound may lie. The area used is that between the upper and lower 95% confidence intervals for Hansen-Jagannathan volatility bounds obtained by Kan and Robotti (2007), shown in table 2. If the standard deviations of the CCAPM stochastic discount factors lie below that area for values of risk aversion between 1 and 20, then the power utility CCAPM model is to be rejected according to this test. Table 2 here Figure 3 here Figure 3 contains point estimates of the LOP volatility bounds, the standard deviations and means of the CCAPM stochastic discount factors for levels of risk aversion between 1 and 20 and the 95% confidence intervals for the volatility bounds. All of the standard deviations are below the area in between the upper and lower confidence intervals for the volatility bounds. This indicates that at a 95% certainty the CCAPM does not satisfy the LOP volatility bound test even when sampling errors are taken into account. Performance of Power Utility CCAPM In recent academic literature on the subject of asset pricing models a common formal method of evaluating model performance is to calculate the pricing errors on a set of test assets. In this report the test assets are the Treasury Bill and Market Index quarterly returns from Q1 1963 to Q4 2009. The pricing error is calculated as [pic] Where [pic], [pic] Treasury Bill and Market Index returns, and [pic] is the pri cing errors. Table 3 here For a model to correctly price an asset it would require that the pricing errors are as close to zero as possible since the pricing error is a measure of the distance between the model pricing kernel and the true pricing kernel. From Table 3 we can see that the pricing errors for the different values of risk aversion are not close to zero and the size of the errors actually increases with the level of risk aversion. We can also see that the Route Mean Square Pricing Error (RSME) which measures the average distance from zero of the pricing errors is not as close to zero as we would hope and also increases with the level of risk aversion. If we note the case for a risk aversion level of 20 then the RSME is 6. 76%, since this is quarterly data this works out to an annual RSME of approximately 27%. With such large pricing errors we would not expect this model to perform strongly. Hansen and Jagannathan (1997) found that for different levels of risk aversion the pricing errors do not vary greatly. As noted above, this is not the case in our sample in which the error increases with the level of risk aversion, thus creating an ever wider dispersion of pricing errors. This is counterintuitive to what we would usually assume as with increased levels of risk aversion the consumer is only willing to accept a certain level of return for lower and lower levels of risk, therefore we would expect at some point that the mean variance level would pass the volatility bounds and therefore correctly price the assets. Conforming with this report Cochrane and Hansen (1992) found that in order to satisfy the levels of variance necessary to surpass the volatility bounds a risk aversion level of at least 40 was necessary. It should be noted that in reality this is quite unreasonable and also that for this level of variance to be attained the expected return might also have to drop below the level necessary to surpass the volatility bounds. Table 4 here From Hansen and Jagannathan (1991) we know that in order to price a set of assets correctly the stochastic discount factor (SDF) should be close to one and have high levels of volatility. Table 4 shows that SDF’s at low levels of risk aversion are relatively close to one but have very low levels of volatility. When the level of risk aversion increases the SDF’s get further and further away from one yet the volatility also increases. Therefore it seems reasonable to conclude that we would not expect any of these SDF’s to price the assets correctly. The results illustrated above are consistent with the earlier analysis and point to the conclusion that the power utility CCAPM does not do a good job in pricing the two test assets and thus does not perform well in UK stock returns. Cochrane and Hansen (1992) agree with this conclusion but Kan and Robotti (2007) find the opposite. The reason for this could be the use of sampling error in the Kan and Robotti paper and the different data used the in the analysis. This report illustrates that there exists not only an equity premium puzzle but also a risk free rate puzzle. This risk free rate puzzle as noted by Weil (1989) states that if consumers are extremely risk averse, a result of the equity premium puzzle, then why is the risk free rate so low. Weil cites market imperfections and heterogeneity as the probable causes of this puzzle; however, this is not the explanation that Bansal and Yaron (2004) find. Using a model that accounts for investor reaction to news about growth rates and economic uncertainty they are able to go some way to resolving not only the risk free rate puzzle but also the equity risk premium puzzle. One method that could be used to improve the performance of the power utility CCAPM would be to construct the model using conditioning information; this would enlarge the possible payoff space available to investors. Kan and Robotti (2006) find that including conditioning information in models reduces the pricing errors by allowing the prices of volatility to move in line with the market. Although as Roussanov (2010) finds, conditioning information does not necessarily improve model performance and may actually exacerbate the problem. 6 Sampling Error in the Volatility Bounds When using the volatility bounds as specified by Hansen and Jagannathan (1991) to test asset pricing models we must be wary of sampling error in the bounds. As noted previously if a model does not lie within the Hansen and Jagannathan volatility bounds then we can conclude that it does not price the test assets correctly. However, Gregory and Smith (1992) and Burnside (1994) first noted that this test does not take into account significant sampling variation and could therefore reject models that price assets correctly. Burnside (1994) uses Monte-Carlo simulation to illustrate that over repeated samples if sampling error is ignored the volatility bounds test performs poorly. Gregory and Smith (1992) state that the sampling error could be due to large variability in the estimated bounds or the use of sample data in the analysis. Kan and Robotti (2007) derive the finite sample distribution of the Hansen and Jagannathan bounds in order to take account of this sampling error. They argue that confidence intervals that take into account the variation can be constructed and used to test asset pricing models. The importance of this new method of testing cannot be underestimated as it could affect the decision to reject an asset pricing model or not, this is best illustrated with reference to examples. Kan and Robotti test the equity premium puzzle using data from Shiller (1989) to show the implications of taking into account sampling error. Through constructing the 95% confidence intervals for the Hansen and Jagannathan volatility bounds they are able to show that the time-separable power utility model being tested may not be rejected at low levels of risk aversion. This is in stark contrast to the findings when sampling error is not taken into account where the model is strongly rejected except for unfeasible levels of risk aversion. From Figure 3, as noted earlier, even when sampling error is taken into account for the model tested in this report it does not fall within the volatility bounds. However, it does decreases the distance between the model and the volatility bounds which is the major consequence of the Kan and Robotti paper. This new method goes some way to solving the problem noted by Cecchetti, Lam, and Mark (1994) who found using classical hypothesis tests that the Hansen and Jagannathan bounds without sampling error rejected true models too often. Again, an extension here could be to use conditioning information to improve the volatility bounds by using the methods of Ferson and Siegel (2003) and as a result hopefully reduce the sampling error in the bounds. References Bansal, R. and A. Yaron, 2004, Risks for the long run: A potential resolution of asset pricing puzzles, Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, 08. Burnside, C. , 1994, Hansen-Jagannathan Bounds as Classical Tests of Asset-Pricing Models,† Journal of Business Economic Statistics, American Statistical Association, vol. 12(1), pages 57-79 Cecchetti, S. G. , P. Lam, and N. C. Mark, 1994, Testing Volatility Restrictions on Intertemporal Marginal Rates of Substitution Implied by Euler Equations and Asset Returns, Journal of Finance, 49, 123–152. Cochrane, J. H. and L. P. Hansen, 1992, Asset Pricing Explorations for Macroeconomics, NBER Chapters, in: NBER Macroeconomics Annual 1992, Volume 7, pages 115-182 National Bureau of Economic Research, Inc. Dunn, K. , and K. Singleton, 1986, Modelling the term structure of interest rates under Non-separable utility and durability of goods, Journal of Financial Economics, 17, 1986, 27-55. Ferson, W. E. , and A. F. Siegel, 2003, Stochastic Discount Factor Bounds with Conditioning Information, Review of Financial studies, 16, 567–595. Gregory, A. W. and G. W Smith, 1992. Sampling variability in Hansen-Jagannathan bounds, Economics Letters, Elsevier, vol. 38(3), pages 263-267. Hansen, L. P. and R. Jagannathan, 1991, Implications of Security Market Data for Models of Dynamic Economies, Journal of Political Economy, Vol. 99, No. 2 (Apr. , 1991), pp. 225-262   Hansen, L. P. and R. Jagannathan, 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 591-607. Kan, R. , and C. Robotti, 2007, The Exact Distribution of the Hansen-Jagannathan Bound. Working Paper, University of Toronto and Federal Reserve Bank of Atlanta. Mehra, R. , and E. C. Prescott, (1985), The equity premium: A puzzle, Journal of Monetary Economics 15, 145-161. Roussanov, N. , 2010, Composition of Wealth, Conditioning Information, and the Cross-Section of Stock Returns, NBER Working Papers 16073, National Bureau of Economic Research, Inc. Shiller, R. , 1982, Consumption, Asset Markets and Macroeconomic fluctuations, Carnegie–Rochester Conference Series on Public Policy, Vol. 17. North-Holland Publishing Co. , 1982, pp. 203–238. Shiller, R. J. , 1989, Market Volatility, MIT Press, Massachusetts. Journal of Economic Behavior Organization, Elsevier, vol. 16(3), pages 361-364. Weil, P. , 1989, The equity premium puzzle and the risk free rate puzzle, Journal of Monetary Economics 24. 401-422. Appendix [pic] Figure 1 LOP Volatility Bounds. The figure shows the LOP volatility bounds (dark blue line) which were found by using Treasury Bill and market returns as test assets. [pic] Figure 2 LOP Volatility Bounds with CCAPM. The figure shows the LOP volatility bounds (dark blue line) which were found by using Treasury Bill and market returns as test assets. It also shows the means and corresponding standard deviations of the CCAPM stochastic discount factors (green line) for values of risk aversion between 1 and 20. [pic] Figure 3 LOP Volatility Bounds with CCAPM and Confidence Intervals. The figure shows the LOP volatility bounds (dark blue line) which were found by using Treasury Bill and market returns as test assets. It also shows the means and corresponding standard deviations of the CCAPM stochastic discount factors (green line) for values of risk aversion between 1 and 20. The figure contains the confidence intervals, with a 95% level of confidence, estimated by Kan and Robotti (2007) for E(m) between 0. 97 and 1. 0082 for the Law of One Price volatility bounds for their first set of test assets. The light blue line shows the upper bounds of the confidence intervals and the red line shows the lower bounds of the confidence intervals. Table 1 CCAPM stochastic discount factors’ means and standard deviations and corresponding LOP volatility bounds CCAPM |LOP volatility bounds |CCAPM | | |means | |st. dev. | | |0. 985121 |0. 82806186 |0. 011749 | |0. 980404 |1. 2067111 |0. 023503 | |0. 975849 |1. 57451579 |0. 035275 | |0. 971456 |1. 93015539 |0. 04708 | |0. 967223 |2. 27320637 |0. 58934 | |0. 963151 |2. 60350158 |0. 070853 | |0. 959239 |2. 92096535 |0. 082854 | |0. 955486 |3. 22555764 |0. 0 94953 | |0. 951893 |3. 5172513 |0. 107169 | |0. 94846 |3. 7960217 |0. 11952 | |0. 945187 |4. 06184126 |0. 132027 | |0. 942074 |4. 31467648 |0. 14471 | |0. 939121 |4. 5448604 |0. 15759 | |0. 93633 |4. 7812196 |0. 17069 | |0. 933701 |4. 99481688 |0. 184033 | |0. 931234 |5. 19520693 |0. 197645 | |0. 928931 |5. 38230757 |0. 211552 | |0. 926792 |5. 55602479 |0. 225781 | |0. 92482 |5. 71625225 |0. 240361 | |0. 923016 |5. 8628708 |0. 255322 | This table shows the means of the CCAPM stochastic discount factors for levels of risk aversion between 0 and 20, the corresponding LOP volatility bounds and the standard deviations of the CCAPM stochastic discount factors. Table 2 95% confidence intervals for E(m) between 0. 97 and 1. 0082 E(m) Lower Upper 0. 9700 3. 1823 5. 2069 0. 9710 2. 9385 4. 8383 0. 9719 2. 7038 4. 4830 0. 9729 2. 4781 4. 1411 0. 9738 2. 2617 3. 8125 0. 9748 2. 0544 3. 4974 0. 9757 1. 8565 3. 1959 0. 9767 1. 6680 2. 9080 0. 9776 1. 4890 2. 6337 0. 9786 1. 3195 2. 3731 0. 9795 1. 1597 2. 1262 0. 805 1. 0097 1. 8931 0. 9815 0. 8696 1. 6739 0. 9824 0. 7394 1. 4685 0. 9834 0. 6194 1. 2770 0. 9843 0. 5096 1. 0993 0. 9853 0. 4101 0. 9356 0. 9863 0. 3212 0. 7857 0. 9873 0. 2429 0. 6497 0. 9882 0. 1755 0. 5275 0. 9892 0. 1190 0. 4192 0. 9902 0. 0736 0. 3248 0. 9912 0. 0393 0. 2445 0. 9922 0. 0160 0. 1784 0. 9931 0. 0030 0. 1275 0. 9941 0 0. 0938 0. 9951 0 NaN 0. 9961 0 0. 0938 0. 9971 0. 0029 0. 1279 0. 9981 0. 0159 0. 1798 0. 9991 0. 0395 0. 2474 1. 0001 0. 0745 0. 3302 1. 0011 0. 1212 0. 280 1. 0021 0. 1796 0. 5408 1. 0031 0. 2498 0. 6689 1. 0041 0. 3317 0. 8123 1. 0051 0. 4255 0. 9714 1. 0061 0. 5309 1. 1461 1. 0072 0. 6481 1. 3368 1. 0082 0. 7769 1. 5437 This table shows the upper and lower bounds of the 95% confidence intervals Kan and Robotti (2007) calculated for the volatility bounds for their first set of test assets. The confidence intervals presented are for values of E(m) between 0. 97 and 1. 0082. Table 3 Pricing errors for the Treasury Bill (Rf) and the value weighted UK market index (Rm), and the Root Mean Square Pricing Error (RSME) for each level of risk aversion Level of Risk Aversion |Error Rf |Error Rm |RSME | |1 |-0. 0104 |0. 0047 |0. 0080 | |2 |-0. 0152 |-0. 0001 |0. 0107 | |3 |-0. 0199 |-0. 0049 |0. 0144 | |4 |-0. 0244 |-0. 0094 |0. 0184 | |5 |-0. 287 |-0. 0138 |0. 0225 | |6 |-0. 0329 |-0. 0180 |0. 0265 | |7 |-0. 0369 |-0. 0221 |0. 0304 | |8 |-0. 0408 |-0. 0260 |0. 0342 | |9 |-0. 0445 |-0. 0297 |0. 0378 | |10 |-0. 0480 |-0. 0333 |0. 413 | |11 |-0. 0514 |-0. 0367 |0. 0446 | |12 |-0. 0546 |-0. 0399 |0. 0478 | |13 |-0. 0577 |-0. 0430 |0. 0508 | |14 |-0. 0606 |-0. 0459 |0. 0537 | |15 |-0. 0634 |-0. 0487 |0. 0564 | |16 |-0. 660 |-0. 0513 |0. 0590 | |17 |-0. 0684 |-0. 0537 |0. 0614 | |18 |-0. 0706 |-0. 0560 |0. 0636 | |19 |-0. 0727 |-0. 0580 |0. 0657 | |20 |-0. 0747 |-0. 0600 |0. 0676 | | | | | | The pricing errors above are calculated as [pic], where [pic], [pic] Treasury Bill and Market Index returns, and [pic] is the pricing errors. The RSME is simply the average pricing error of the stochastic discount factor for each level of risk aversion. Table 4 Summary Statistics for power utility CCAPM stochastic discount factor |Level of Risk Aversion |Average |St Dev |Min |Max | |1 |0. 9851 |0. 0117 |0. 9551 |1. 0436 | |2 |0. 804 |0. 0235 |0. 9214 |1. 1000 | |3 |0. 9758 |0. 0353 |0. 8889 |1. 1595 | |4 |0. 9715 |0. 0471 |0. 8575 |1. 2223 | |5 |0. 9672 |0. 0589 |0. 8273 |1. 2884 | |6 |0. 9632 |0. 0709 |0. 7981 |1. 3581 | |7 |0. 592 |0. 0829 |0. 7699 |1. 4316 | |8 |0. 9555 |0. 0950 |0. 7428 |1. 5090 | |9 |0. 9519 |0. 1072 |0. 7166 |1. 5906 | |10 |0. 9485 |0. 1195 |0. 6913 |1. 6767 | |11 |0. 9452 |0. 1320 |0. 6669 |1. 7674 | |12 |0. 421 |0. 1447 |0. 6434 |1. 8630 | |13 |0. 9391 |0. 1576 |0. 6207 |1. 9638 | |14 |0. 9363 |0. 1707 |0. 5988 |2. 0701 | |15 |0. 9337 |0. 1840 |0. 5777 |2. 18 21 | |16 |0. 9312 |0. 1976 |0. 5573 |2. 3001 | |17 |0. 9289 |0. 116 |0. 5377 |2. 4245 | |18 |0. 9268 |0. 2258 |0. 5187 |2. 5557 | |19 |0. 9248 |0. 2404 |0. 5004 |2. 6940 | |20 |0. 9230 |0. 2553 |0. 4827 |2. 8397 | This table shows the average value, standard deviation, minimum and maximum for the stochastic discount factor at each level of risk aversion. ———————– 24th November 2011 How to cite Power Utility Consumption Capm in Uk Stock Markets, Papers

Hospital Sleeping free essay sample

Even today I study Douglass sleeping face. Eleven years old, sleeping late onSaturday mornings, he rarely sleeps in his own room with its crooked Snoopydecorations. A boy could live forever with the Peanuts gang. Ive watched himsleep since he was six months old after his lengthy hospital stay fordehydration. The way ghosts float around in hospital air, with itsheavy and sanitary stench, has always amazed me. I have not always seen thephantoms: When Doug was admitted, my only frame of reference of hospitals hadbeen visits for routine physicals. I thought the doctors office was pee ina cup and a finger pin-pricked. These illusions were swept away, andreplaced with the notion that dreams are merely a function of something greater:sleep. After three days in the hospital, Douglas was doing worse. Thedoctors had said he would be in and out of the hospital, but now hewouldnt accept food and had to be sedated and fed intravenously. We will write a custom essay sample on Hospital Sleeping or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page In hisroom, my brother lay still in a crib, mobile overhead. I stared at him frombehind my parents. He looked like an albino imp, half-naked and sleeping. The IVdangled above his head, entering his arm. So that he would not remove the needle,his arm had been bound to the crib. In his sleep, he shook a bit, spasming as onedoes after a long time outside in the snow without mittens. Close to the door, aTV hung from the ceiling. Later that night, my father would watch CNN, and thenight after my mom would watch the local news. They took turns staying to watchthe baby sleep. After a week, the doctor finally released my brother. Hehad to rest for the first few days home, an order I found irritating: if he weretruly better, shouldnt he be able to act his usual self? Somehow, Iloved him more after his rehabilitation. While he slept, I would peek at him. Itmust have been strange that my youngest brother was the focus of so much of myattention, but I hardly cared. When my brother sleeps, he always makes this face:His eyes are loosely shut, as to make the eyelids nearly translucent. His mouthinvariably remains half-open with his top row of teeth pensively suspendedmillimeters above the bottom lip. It looks as if he is in heated conversation,waiting patiently for a break in the dialogue so he can explode the revelationthat rocks nervously on his pursed lips. My brother goes to therapy for anauditory processing problem. I frequently become frustrated with his inability toarticulate: Doug, where is Mom? No response; he sits andstares as if in suspended animation, his head tilted slightly to theright. Doug, where is Mom? Where did she go? Noresponse. Douglas! What? I couldnt hearyou! he awakens. Have you been listening? Perhapsit is only when he is asleep that this impediment washes away, and he listens sowell that his discourse develops at the utterance of a syllable. One day, I wantto feel that I live on the brink of explosion: I will be so involved in thedialogue of the world that I will be incapable of restraining myself. Ioften fear that when Douglas grows up, no one will understand when hes havingtrouble listening. I wonder what he will be like, and what hell be. The acuityand compass of his memory are so well developed, but where will that take him? Heonce memorized a book on dogs and could recite the average weight and lifeexpectancy of any breed after only a moments hesitation. Douglas whats a French Bulldog? Years orsize? Size. Um, 14 to 16pounds Sometimes I wonder so much about my brother and his futurethat I want to throw up my hands and yield to destiny. I want to beg the fates togive me the answer, to please let me stop guessing. I know now how awesome andfrightening uncertainty is, but Ive learned so much from watching him sleep. Iknow now the importance of living in the moment and actively participating in thepresent. The rest of lifes demands hardly matter. Right now I need only bepatient, and watch Douglas sleep.