Study On Term Structure Of Interest Rates Finance Essay - Free Essay Example

Sample details Pages: 6 Words: 1753 Downloads: 6 Date added: 2017/06/26 Category Finance Essay Type Research paper Did you like this example? The term structure of interest rates is an extremely important element in Finance. It is one of the most important indicators for pricing contingent claims, determining the cost of capital and managing financial risk. Interest rates may be used in an extensive variety of applications; such as investments, long term debt, determination of the cost of capital, measurement of credit risk, valuation of contingent claims as well as pricing, hedging and managing the risk of interest rate derivatives. Don’t waste time! Our writers will create an original "Study On Term Structure Of Interest Rates Finance Essay" essay for you Create order Furthermore; interest rates are used in the establishment of fiscal and monetary policies. Maturity plays also an important role as a determinant on interest rates; since this factor determines the length on a loan. Longer term loans imply higher interest rates than shorter term loans since a longer term implies higher future uncertainty of expected outcomes. Financial theory and asset pricing models state that as maturity increases the risk involved or assumed by investors is higher. Therefore; the expected returns should be greater. Consequently; investors would be interested in knowing elasticity estimates according to specific frequencies. As maturity increases the mean increases accordingly suggesting the existence of a term premium built on the term structure. Interest rates are frequently used in several additional applications; such as fixed income securities and interest rate derivatives. In both cases interest rates play a key role; since this component is utilized to determine the present value. Within the area of financial risk management, it is important to determine how a change in the level of interest rates will affect a specific asset. Interest rate derivatives allow for the possibility of hedging risk as a result of unpredictable shocks. Financial instruments are widely applied since they are able to explain how risk management maximizes shareholders wealth. Interest rate fluctuations create one of the most important determinants on bond prices. As interest rates fluctuate; bondholders are exposed to capital losses and gains. However; this exposure is only experienced when bondholders hold bonds only for a determined period of time. In the case when bonds are hold until maturity; there is no exposure to risk. In addition; it has been shown empirically that long term bonds are more sensitive to interest rate movements than short term bonds. THEORY AND LITERATURE REVIEW The price of a bond depends on the stochastic behavior of the current and future spot rates in the economy. As a result; bond prices must be a function of the current and future spot rates. Additionally; interest rates can not be constant, since that would imply predictability on bond prices. Moreover; constant interest rates may imply no volatility on the underlying assets. Consequently; the demand for any interest rate derivatives would reduce completely since all possible risk could be vanished. Therefore it is important to model the term structure of interest rate. Theories of Term Structure In order to be able to evaluate and understand correctly the term structure of interest rates; it is important to comprehend the different theories involved. It is required to understand how the spot rates or discount factors are determined; as well as to comprehend the explanations that determine the shape of the term structure of interest rates. According to Nelson (1972); the term structure of interest rates is determined mainly by two different theories, which are the liquidity preference theory and the preferred habitat theory. Moreover; Gibson, Lhabitant and Talay (2001) agree that the term structure of interest rates is mainly explained by three theories which analyze the relationship between interest rates of various maturities and the value of the term premium. These theories include the expectations hypothesis, the liquidity preference theory and the segmented market hypothesis. Liquidity Preference Hypothesis This theory was developed by Hicks. It predicts that a term premium may be obtained by capital invested in long term bonds because bond holders will require compensation for exposure to capital fluctuations. (Nelson; 1972) According to the liquidity preference theory, investors are risk averse, prefer short term maturities and will require a premium in order to commit in long term securities. Liquidity Preference Theory admits the importance of expected future spot rates but gives more importance to the effects of the risk preferences of market participants. This hypothesis states that risk aversion will cause forward rates to be greater than expected spot rates by an amount which increases with maturity. The term premium is the increment given to investors in order to hold longer term securities since those imply higher risk. Expectations hypothesis This theory gives increasing importance on the expected values of future spot rates. This theory states that bonds are priced so that the implied forward rates are equal to the expected spot rates. This hypothesis is characterized by two propositions. The first proposition states that the return on holding a long term bond to maturity is equal to the expected return on repeated investment in a series of short term bonds. On the second proposition; it is mentioned that the expected rate of return over the next holding period is the same for bonds of all maturities. According to the expectations theory, it is argued that the term structure of interest rates is driven by the investorsacirc;â‚ ¬Ã¢â€ž ¢ expectations on future spot rates; where the forward rate is an unbiased estimator of the future spot rate. The rate of return on a bond maturing at time should be equivalent to the geometric average of the expected short term rate from t to T. Preferred habitat theory This theory was developed by Modigliani and Sutch (1966). It states that market participants are assumed to have preferred maturity ranges but will decide to change their selected habitat if a enough term premium is offered. (Nelson; 1972) According to the preferred habitat theory, investors and borrowers have different specific time horizons .The institutional investors have different maturity needs that lead them to confine their security selections to specify maturity segments. This theory contends that the business environment along , with the legal and regulatory limitations tends to direct each type of financial institutions to allocate its resources to particular types of bonds with specific maturity characteristics. DATA CONSIDERATION For determining the term structure of interest rates we have taken most actively traded wholesale bond market data from NSE website using the bhavcopy. The data was taken from 9th August, 2010 to 23rd August, 2010. Firstly we have taken all the bonds the bonds from bhav copy of WDM from NSE website. This comprised of around 4300 bond list. Then we excluded all those bonds which have not been traded in last 15 days. The bonds have improper or incomplete data have also been removed. We were left with 132 different bonds which have been included in our study. Then those observations which have been found as outliers are further removed from our data sample. The final sample after removing outliers was of 99 bonds. METHODOLOGY Yield to maturity of all these government Coupon paying bonds is calculated. The term to maturity is also calculated. This is done by using the acirc;â‚ ¬Ã…“yieldacirc;â‚ ¬Ãƒâ€šÃ‚  function of excel. The term to maturity is calculated using the Day360 function of excel. Test for Normality was done for both YTM and TTM series. The Jacques Bera statistics was used to check the normality of data. Cooks distance is a commonly used estimate of the influence of a data point when doing least squares regression. Cooks distance measures the effect of deleting a given observation. Data points with large residuals (outliers) and/or high leverage may distort the outcome and accuracy of a regression. A large Cooks D indicates that excluding a case from computation of the regression statistics changes the coefficients substantially. There are different opinions regarding what cut-off values to use for spotting outliers: A simple operational guideline of Di gt; 1 has been sug gested. All values greater than 4/n where n is the number of our data sample can be removed as outliers. This method is used to remove the outliers in our regression. The outlier was removed using the SPSS software. (Files attached) The regressions using various models have been run between yield to maturity data and time to maturity data. The dependent variable was Yeild to maturity and independent variable was time to maturity. This was done in EVIEWS. (Files attached ) ANALYSIS Model Equation R2 White hetroscadacity Test Residual normality Linear Y = b0 + (b1 * t) 0.357 0.017 0.008 Log Y = b0 + (b1 * ln(t)). 0.553 0.28 0.034 Inverse Y = b0 + (b1 / t). 0.377 0.011 0.057 Quadratic Y = b0 + (b1 * t) + (b2 * t**2). 0.57 0.34 0.023 Cubic Y = b0 + (b1 * t) + (b2 * t**2) + (b3 * t**3). 0.57 0.607 0.024 Power ln(Y) = ln(b0) + (b1 * ln(t)) 0.545 0.078 0.001 Growth ln(Y) = b0 + (b1 * t). 0.34 0.01 0.00047 Sqrt YTM Y1/2 = b0 + (b1 * t) 0.35 0.013 0.0009 Sqrt TTM Y = b0 + (b1 * t1/2) 0.47 0.111 0.0275 Analysis Cubic and quadratic models both have an R2 of 0.57 and the power and log model have an R2 of 0.55. Quadratic model has white heteroscedasticity value of 0.34, cubic has 0.607 and log has 0.28. Considering the R2 and white heteroscedasticity, the best model is cubic model.The equation found out to be as: YTM = 0.06-0.0028*ttm+0.015*ttm^2+0.00014*ttm6^3 RESULT The equation of term structure of interest rates can help us to determine the coupon interest of new bonds which are to be raised by issuing authorities. This can also help us to compare and estimate the coupon payments for other corporate bonds by adding the additional risk premium to the ytm at that maturity. This also helps us to get a better idea of which all bonds needs to be used for investment portfolio. GRAPHS AND PLOTS Scatter Plot Linear Model Logarithmic Model Power Model Quadratic Model Cubic Model Power 4 Model LIMITATION Inflation rate, volatility, mean, spread between long and short term rates could have a significant impact on the term structure equations but we have considered that the price of bond have included all these effects, which can be further debated. There is no common and unified frame-work which could nest all available equations. The high end models like Nelson Siegel etc were tough to implement due to knowledge and exposure constraints. Corporate bonds though have been considered to have a certain risk premium over and above the government bonds which we have included in our study but this can be a further explored. SCOPE FOR FURTHER IMPROVEMENT The term structure for Interest rates equation can be improved using Splines and Knots. We have done some work on Splines in SAS but due to constraints of knowledge, the scope of improvement remains. There are few other models like Nelson-Seigel Model and Cox-Ingersoll-Ross model which can help us determine these equation better can also be implemented.

Protests Against the Vietnam War - 996 Words

James A. Baldwin once said, â€Å"The most dangerous creation of any society is the man who has nothing to lose† (BrainyQuote.com). In the 1960s, â€Å"the man† was youth across the country. The Vietnam war was in full force, and students across the country were in an outrage. Society needed an excuse to rebel against the boring and safe way of life they were used to; Vietnam gave them the excuse they needed. Teenagers from different universities came together and formed various organizations that protested the Vietnam war for many reasons. These reasons included protesting weapons and different tactics used in the war, and the reason the U.S. entered the war in the first place. These get-togethers had such a monumental impact on their way of†¦show more content†¦A capsule was drawn by Congressman Alexander Pirnie, any man born between 1944 and 1950 has their name in the capsule and if drawn, must participate in the war. This angered Americans because it was a gainst their will, and they felt as if the government was controlling every aspect of their life. Another reason American adults were against the war was because of the weapons and strategic tactics used in the war. As stated in â€Å"Weapons of the Vietnam War†, Weapons used in the Vietnam War were more mortifying than in any other war. The communist side (the Soviet Union) used not only your standardized weapons, but they also used toxic chemicals and explosives (History.com). South Vietnam was in real trouble, the American-manufactured weapons were no match to the devastating weapons that the communists used. Back at the homefront, people were horrified when they caught wind of what was happening out in battle, this egged on more protests. In accordance with â€Å"Vietnam War Protests†, The SDS organized more Anti-war marches and other protests after the United States retaliated on North Vietnam by beginning to bomb them (History.com). The cost of materials were goi ng up and it was getting more expensive to make the bombs and other weapons, the U.S. was putting a whole $25 billion a year into manufacturing these supplies. This upset Americans not just on a moral level anymore, but also on an economic level; the governmentShow MoreRelated The Vietnam War and the Protest Against It Essay3560 Words   |  15 Pagesboth in the Vietnam War and in the struggle to stop it. I learned that patriotism includes protest, not just military service.† The Vietnam War was a conflict that lasted from 1956-1975 which the United States participated in along with the South Vietnamese who fought against the Communist North Vietnamese. Many Americans strongly disapproved of the war which caused many protests and riots. The war lasted 25 years killing many people and eventually the North Vietnamese won. 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Many incidents triggered the Anti-War movement and the Hippie counter culture such as the growing United States involvement in Southern Vietnam, the gruesome images that the evening news showed uncensored, the draft that caused many thousands of men to lose their lives and their minds as the end result of the war. This war triggered a great sense of whatRead MoreEssay on Johnsons War: The Domino Effect1031 Words   |  5 PagesSpecial Forces in South Vietnam but President Johnson made the decision to engage in full warfare in the region. Because Johnson decided to engage in full warfare, it is fair and truthful to dub the Vietnam conflict, â€Å"Johnson’s War.† After President Johnson finished JFK’s term, he was in a bit of a â€Å"pickle.† Johnson wanted to stay the course in Vietnam but he feared that a military setback in the region would tarnish his image for the upcoming election. Johnson campaigned against Arizona Senator Barry

Intertestament Period Free Essays

Exploring the Bible 3 October, 2011 Inter-Biblical Period: 400 Years The Old Testament focuses on God’s covenant with his people and the stories of men of great faith and also men of prophecy, foretelling Christ coming. The New Testament, however, focuses on the redemption side. The Redemption side is Christ’s story here on Earth and his ministry to other people. We will write a custom essay sample on Intertestament Period or any similar topic only for you Order Now Malachi, the last book written in the Old Testament, was written around 424 B. C. Then 418 years after, the book of Matthew, the first book of the New Testament, was written. The Intertestamental Period is the period of history between the two testaments. Since God did not speak to his people directly through prophets, this period is also known as the 400 years of silence. Now, what happened in those four hundred years? The Intertestamental Period was a time where many empires came along, new religious groups formed, and where theological and literature pieces were developed that molded Israel going into the time of Christ. Politics in a nation help dictate and run the people, in Israel’s case, they had to deal with many empires coming in. During the Intertestamental Period, they had five key periods of leaders and kingdoms. The Persian Empire arrived around 430 B. C. and they ruled until 332 B. C. The Persian rule was recorded as being mild and tolerant. (Scott, 1783) The Persians were taken over by the Greeks. The Greek period went from 331 B. C. to 167 B. C. (Scott, 1783) Alexander the Great, son of King Philip of Macedonia, was given the control of the Greek army around the age of 20. (Halley, 402) With the control of the army, he was able to sweep over and take over Egypt, Assyria, Babylon, and Persia. Alexander the Great was very compassionate towards the Jews and he spared the city of Jerusalem. He established Greek cities in his conquered places and he did it with the plan to spread Greek culture and language throughout the world including Israel. After Alexander’s death, his empire was separated to his four generals. (Halley, 402) Egypt and Palestine was given to Ptolemy and under him the conditions of the Jews were at a peaceful state. In Egypt, Alexandria was the influential center of Judaism. In 167 B. C. was the beginning of the Period of Independence also known as the Maccabean period. Mattathias was a priest and he was upset at Antiochus motivation to destroy the Jews, so he gathered Jews and raised a revolt. Mattathias had five sons, Judas, Jonathan, Simon, John, and Elezar. (Halley, 404) The Maccabean period lasted until 63 B. C. and the Romans followed after. Palestine was conquered by the Romans under Pompey. Idumean was the first to be appointed ruler of Judea. His son, Herod the Great, succeeded him. (Halley, 404) Herod was a shrewd politician who wanted to get good with the Jews. He was very cruel and brutal towards his people. Politics and leaders are key roles in establishing a nation. In this case, these five empires helped develop rules and guidelines that led the people and that eventually grew and prepared Israel for the coming of Christ. During the 400 years of silence, religion was another area that grew in Israel. During this time, the religion was not set up was polytheistic or monotheistic but instead it was groups of people. For example the four main groups of the religions groups or parties are Pharisees, Sadducees, Zealots, and Herodians. These four groups followed what they believed and chose to do whatever they wanted to do. The Pharisees is the group most people probably know because of their role in the Gospels and the fact Paul was one. They took the Law and believed it was their job to take it and to put into new conditions. (Hester, 325-326) The accepted both the Torah and tradition. The Pharisees rejected anyone who didn’t live by the standards they did. On the opposite side were the Sadducees. They were the second main group and they had more power than the Pharisees until 70 A. D. when their temple was destroyed. (Hester, 325-326) The Sadducees consisted of the wealthy priests. They were a conservative group and they didn’t try to take the Law and put into a new situation but they instead took and limited themselves to the five books of Moses. After 70 A. D, the Pharisees were the leaders of the Jewish people by giving them a religious life aside from the temple. The other two parties were more political than religious groups. The Zealots were a nationalist group that opposed the Romans. Simon, one of Jesus’ disciples, was a Zealot. The other group, the Herodians, basically supported Herod and his dynasty and supported what he did for the nation. These four groups are the religious groups that developed the main teachings and guidelines people believe until Christ’s ministry began. Even though religion and politics are a big part of a civilization, another key role is the literature and writing of a nation. Literature and writing in Israel or any nation is an influential part because it is what the people follow and speak. In Israel, Hebrew was the language of the Old Testament. This was the main language of religion. Latin was the language of Roman and it was commonly spoken among the people. Greek was another language and it was the language that tied the Roman Empire together. The most common language of Palestine in Jesus’ day was Aramaic. (Halley, 410) Most writings are believed to have been written in Aramaic and translated into Greek. (Halley, 410) The Old Testament was written in Hebrew but was spoken in Greek. Septuagint is a translation of the Old Testament into Greek. The Torah was translated first. It was called the Septuagint because of the 70 translators and Septuagint means 70 in Greek. (Halley, 409) Another type of translation was Targums and they are translations of the Old Testament into Aramaic. They were first oral translations, paraphrases, and interpretations these types of languages and writing were influential in the development of the social status during the Intertestamental Period. Even though writing is important the question is what was the theology being taught during this period? Theology is important because it is what the people studied and how they viewed God. The Apocrypha, is writings which the writer assumed the name of a hero long since dead, and rewrote history in terms of prophecy. (Halley, 406) Some of this included, Books of Enoch, Assumption of Moses, Ascension of Isaiah, Book of Jubilees, Psalms of Solomon, and more. These books are the books that were written by people in the period of the 400 years of silence, and they preached about the prophecies that the prophets spoke and also the birth of Christ and the end times. This theology is the closest literature that the people had to connect to God and the prophecies that was spoken. All of these books spoke of Christ coming and his ministry that he will live for and preach. The Intertestamental Period consisted of political powers overtaking each other, religious groups, and theological books and literature that preached Christ coming and that developed the nation of Israel. The political side consisted of Persian, Greek, Egyptian, the Maccabees, and the Romans. The eligious side had the Pharisees, Sadducees, Zealots, and Herodians and they all had different views and theories. And the language part consisted of Latin, Greek, Hebrew, and Aramaic. The theology piece was the Apocrypha, which re-emphasized the prophets foretelling. All these pieces and parts put together made up the Intertestamental Period and it formed Israel and it carried over into the ministry of Jesus. The 400 years of silence at last was broken, and God sent his son Jesus Christ t o testify the truth and overcome the world. Work Cited Scott, J. Julius Jr. â€Å"Time Between the Testaments. † ESV Study Bible: English Standard Version. Wheaton, IL: Crossway Bibles. 2008. 1783-1789. Print. Halley, Dr. Henry H. Halley’s Bible Handbook: with New International Version. Grand Rapids, Michigan. Zondervan Publishing House. 2000. 402-412. Print. Hester, H. I. The Heart of Hebrew History: A Study of the Old Testestament. Liberty, Missouri, The Quality Press, Inc. 1962. 313-330. Print. How to cite Intertestament Period, Essay examples