The Fun of the Hunt in Othello - Literature Essay Samples

In Shakespeares play, Othello, the men hunt the women, as a human hunts animals in the wild. The man exerts dominance and expects the woman to accept her submissive role in relation to his dominance. The central couples involved in showing this type of male-female relationship are Othello and Desdemona, Iago and Emilia, and Cassio and Bianca. Shakespeare illustrates the hunt in the sexual encounters, the marriages/ relationships, and the murders exhibited by these characters during the play. Simultaneously, the way the men hunt the women in the play is mirrored by the way Iago hunts all of the characters. The hunting which is displayed throughout Othello is reinforced by the plethora of animal images Shakespeare uses in the language of the play.Emilia clearly sees, and articulates, the nature of the hunter-hunted male-female relationship. She shows this understanding when she says what is it that [men] do when they change us for others? Is it sport? I think it is (IV,iii,107 ). Emilia is examining the inclination of men to sleep around. She explains it by saying that men do not see women as humans, but rather as animals who are fun to chase, but once conquered, lose some of their intrigue and the men want to move onto other women. Iago shows that he has this opinion of women when he says that Desdemona and Emilia are wildcats in their kitchens who rise to play and go to bed to work (II,i,123,129). Iago is saying that his vision of women is that when they are not in bed they are just playing. This goes along with the definition that The American Heritage Dictionary gives of sport that it is a type of game with a certain set of rules (a hunt, for example). Similarly, the use of the word wildcats to describe them again calls up the sport (of hunting) image. It is a game for men to get the women from the kitchens into bed. Then, when the women are in bed they simply fulfill their duties to their husbands to sleep with them. Once they are in bed (h aving sex), the game has ended. Othello also makes reference to women as inhuman prizes when he calls Desdemona honey (II,i,225), although this reference is unintentional on his part. By calling her honey he is utilizing a common term of endearment, calling a woman honey is like calling her sweet because honey is sweet. However, the term also has a flip side of meaning to it which affirms the way men hunt women in order to get them into relationships or into bed. This side is that humans must break through the protecting barrier of bees to achieve honey. To achieve his honey (Desdemona) Othello must get her to fall in love with him, in other words, break through her defenses and get into her heart. The reader is not privy to that portion of Othello and Desdemonas relationship in the play, that part takes place before the action of the play begins, but it can be inferred. The sport that Emilia talks about is the hunt of women.Seduction, which is the starting point of a male-fe male relationship, is portrayed as having certain rules, as does a hunt (a type of a game/sport), in Othello. The rules are often established societally. Roderigo attempts to abide by the societal rules by trying to get Desdemona from her father, Barbantio. He sees her father as having the power to tell her, Desdemona, who to marry because that was the custom of the society. A womans father was the lord of [her] duty until he gives over that lordship to his daughters husband (I,iii,212). This means that it was her duty to do whatever she told him to do (including to marry a particular person). Roderigo appeals to the power of Barbantio rather than going directly to Desdemona which is what Othello does. But, Othello undermines the lordship of Barbantio by doing that. Iago reveals this when he tells Barbantio that [his] daughter [Desdemona] and the moor are making the beast with two backs (I,i,130). The fact that Desdemona is having sex with someone before getting her fathers permission goes against the rules of the seduction-hunt to which Roderigo is adhering. Barbantio does finally give this power over to Othello saying I have done (I,iii,219). Othello and Desdemonas relationship started out not following the rules, but eventually fell back under their cover. While Cassios relationship with his mistress Bianca is one that does not follow these type of mainstream societal rules, it has rules nonetheless. Cassio successfully seduces Bianca by means of sexual contact. He has sex with her and attaches a minimal importance to that and she in turn clings onto that importance. She shows her dependence on him during the encounter they have. What, keep a week away? Seven days and nights, Eightscore eight hours, and lovers absent hours complains Bianca to Cassio, describing how she missed him (III,iv,196-7). She is only his mistress and yet by performing in bed he gave her the impression that he was in a sort of relationship with her whereby he was impl icitly required to visit her on a regular basis.The scene in which Othello murders Desdemona, he acts entirely as a predatory animal, lacking human characteristics. Othello kills her using no manmade instrument. He simply smothers her. This is the same up-close, intimate, primitive way that an animal is required to kill. Ironically, Othello justifies the action as a man would. His justification relies on the higher duties he has to other men, saying she must die, else shell betray more men (V,ii,7). He is attempting to humanize himself while dehumanizing her through tricking himself into thinking he is a rational being. This murder scene also reveals itself to be ironic when looked at with regard to the passage in which it is said that Desdemona will tame Othello (III,iii,25). During the murder scene it is her existence which brings out the most primal of his actions (the urge, and ability, to kill). She does not tame his animalistic side but rather aggravates it. Moments b efore Othello commits suicide, directly after he kills Desdemona (his wife), Othello says he is a circumcised dog (V,ii,416). At this moment he at last sees plainly, the deception has cleared away from his mind, and he understands himself to be an animal, not a human, as he had thought before. The fact that he is not human reveals to him that he did not hunt (as a controlled sport) Desdemona, as he thought he had. But that instead he was only participating in a very base, animalistic action lacking in rules, control or humanity.Through evaluating Othello in reference to hunting, it becomes apparent that as the men in the play are hunting the women, Iago is hunting the men (and by consequence, also the women). He is the key designer of the play, and essentially wrote the play by planning out its action. He says he will ensnare as great a fly as Cassio (II,i,183). Similarly, Iago says he intends to lead Othello by the nose, like an ass (I,iii,445), and then, later, in the second act, Iago again says he will make Othello an ass (II,ii,331). These phrases show that Iago sees himself as the human hunter. He verbally changes people who are thought of as humans into animals over whom he has control and dominance. Iago will control how they perceive the world and eventually trap them by means of these fabricated perceptions.When Iago kills his wife, Emilia, he follows through with the above explored male-hunts-female relationship. He kills her at the point that she is no longer running from him, at the point that she is no longer obeying the turns he says he makes unquestioningly. But, although she thinks that she is defying him by stopping her running, in reality he has cornered her, he has hunted her down. Emilia says tis proper I obey him [Iago], but not now (V,ii,233). She believes that she is going against him, standing up to him, but in truth Iago wants her to tell Othello that Desdemona was not actually committing adultery because he wants Othello to commit suicide. Iago then kills her, which is the completion of a hunt, and this action is understood because she was perceived to be disobeying her lord. Unlike Othello, Iago maintains his human status in murdering because he remains entirely in control of the events occurring at the point that he murders. This human control is shown physically in that Iago uses his manmade sword to kill Emilia, he does not revert to the animalistic smothering Othello uses to kill Desdemona.The hunter/hunted relationships which are explored throughout Othello draw a parallel between the supposedly refined court life, and the life in the wild.

Geography of the United States of America

The United States of America is the third-largest country in the world based on population and land area. The United States also has the worlds largest economy and is one of the most influential nations in the world. Fast Facts: United States Official Name: United States of AmericaCapital: Washington, D.C.Population: 329,256,465 (2018)Official Language: None, but most of the country is English-speaking  Currency: US dollar (USD)Form of Government: Constitutional federal republicClimate: Mostly temperate, but tropical in Hawaii and Florida, arctic in Alaska, semiarid in the great plains west of the Mississippi River, and arid in the Great Basin of the southwest; low winter temperatures in the northwest are ameliorated occasionally in January and February by warm chinook winds from the eastern slopes of the Rocky MountainsTotal Area: 3,796,725 square miles (9,833,517 square kilometers)Highest Point: Denali at 20,308 feet (6,190 meters)  Lowest Point: Death Valley at -282 feet (-86 meters) Independence and Modern History The original 13 colonies of the United States were formed in 1732. Each of these had local governments and their populations grew quickly throughout the mid-1700s. During this time, tensions between the American colonies and the British government began to rise, as the American colonists were subject to British taxation without representation in the British Parliament. These tensions eventually led to the American Revolution, which was fought from 1775-1781. On July 4, 1776, the colonies adopted the Declaration of Independence. Following the American victory over the British in the war, the U.S. was recognized as independent of England. In 1788, the U.S. Constitution was adopted and in 1789, the first president George Washington took office. Following its independence, the U.S. grew rapidly. The Louisiana Purchase in 1803 nearly doubled the nations size. The early to mid-1800s also saw growth on the west coast, as the California Gold Rush of 1848-1849 spurred western migration and the Oregon Treaty of 1846 gave the U.S. control of the Pacific Northwest. Despite its growth, the U.S. also had severe racial tensions in the mid-1800s as African slaves were used as laborers in some states. Tensions between the slave states and non-slave states led to the Civil War, and 11 states declared their secession from the union and formed the Confederate States of America in 1860. The Civil War lasted from 1861-1865. Ultimately, the Confederate States were defeated. Following the Civil War, racial tensions remained throughout the 20th century. Throughout the late 19th and early 20th centuries, the U.S. continued to grow and remained neutral at the beginning of World War I in 1914. It later joined the Allies in 1917. The 1920s were a time of economic growth in the U.S. and the country began to grow into a world power. In 1929, however, the Great Depression began and the economy suffered until World War II. The U.S. also remained neutral during this war, until Japan attacked Pearl Harbor in 1941, at which time the U.S. joined the Allies. Following WWII, the U.S. economy again began to improve. The Cold War followed shortly thereafter, as did the Korean War from 1950-1953 and the Vietnam War from 1964-1975. Following these wars, the U.S. economy, for the most part, grew industrially and the nation became a world superpower concerned with its domestic affairs because public support had wavered during previous wars. On September 11, 2001, the U.S. was subject to terrorist attacks on the World Trade Center in New York City and the Pentagon in Washington, D.C., which led to the government pursuing a policy of reworking world governments, particularly those in the Middle East. Government The U.S. government is a representative democracy with two legislative bodies, the Senate and the House of Representatives. The Senate consists of 100 seats, with two representatives from each of the 50 states. The House of Representatives consists of 435 seats, the occupants of which are elected by the people from each of the 50 states. The executive branch consists of the president, who is also the head of government and chief of state. The U.S. also has a judicial branch of government that is made up of the Supreme Court, the U.S. Court of Appeals, U.S. District Courts, and State and County Courts. The U.S. is comprised of 50 states and one district (Washington, D.C.). Economics and Land Use The U.S. has the largest and most technologically advanced economy in the world. It mainly consists of the industrial and service sectors. The main industries include petroleum, steel, motor vehicles, aerospace, telecommunications, chemicals, electronics, food processing, consumer goods, lumber, and mining. Agricultural production, though only a small part of the economy, includes wheat, corn, other grains, fruits, vegetables, cotton, beef, pork, poultry, dairy products, fish, and forest products. Geography and Climate The U.S. borders both the North Atlantic and North Pacific Oceans and is bordered by Canada and Mexico. It is the third-largest country in the world by area and has a varied topography. The eastern regions consist of hills and low mountains, while the central interior is a vast plain (called the Great Plains region). The west has high rugged mountain ranges (some of which are volcanic in the Pacific Northwest). Alaska also features rugged mountains as well as river valleys. Hawaiis landscape varies but is dominated by volcanic topography. Like its topography, the climate of the U.S. also varies depending on location. It is considered mostly temperate but is tropical in Hawaii and Florida, arctic in Alaska, semiarid in the plains west of the Mississippi River and arid in the Great Basin of the southwest. Sources United States. The World Factbook, Central Intelligence Agency. United States Profile. Countries of the World, Infoplease.

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Economics And Its Interaction With Politics - 949 Words

I went in my masters program interested in economics and its interaction with politics, but once I took my first course in international affairs I knew the direction I wanted my studies and subsequent career to take. I was so invigorated by these classes that I not only took many of them, but also some multiple times including National Security Policy and Crisis Management. All of these classes reinforced the importance of international relations in my mind, particularly regarding interactions with non-state actors. I want to further strengthen my knowledge and capabilities in global policy research through a PhD in government with my focus being on international relations, specifically conflict. In addition to the aforementioned courses I took a number of classes that helped me to hone in on my underlying interest in many facets of international relations. In Political Sociology and the Global Economy I examined the rise of the global economy and its basis in earlier more localized efforts. I took part in fascinating discussions on what being a nation means in Social Movements, Protest and Change during the early days of the Arab Spring. I further developed these early interests at the Humphrey School of Public Affairs. Through Global Economic Policy I led a working group in our presentation of India/Brazil supposed intellectual property violations as if we were the WHO writing to the WTO. This experience examining from another’s perspective was compounded when I workedShow MoreRelatedAsfasf754 Words   |  4 Pagesgovernments have responded to economic issues. b. Analyze how technological innovation has affected economic development and society. c. Explain how interpretations of the Constitution and debates over rights, liberties, and definitions of citizenship have affected American values, politics, and society. d. 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Capital Asset Prices a Theory of Market Equilibrium Under Conditions of Risk free essay sample

American Finance Association Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk Author(s): William F. Sharpe Source: The Journal of Finance, Vol. 19, No. 3 (Sep. , 1964), pp. 425-442 Published by: Blackwell Publishing for the American Finance Association Stable URL: http://www. jstor. org/stable/2977928 . Accessed: 23/08/2011 00:15 Your use of the JSTOR archive indicates your acceptance of the Terms Conditions of Use, available at . http://www. jstor. org/page/info/about/policies/terms. sp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [emailprotected] org. Blackwell Publishing and American Finance Association are collaborating with JSTOR to digitize, preserve and extend access to The Jou rnal of Finance. http://www. jstor. org The VOL. XIX journal of FINANCE No. 3 SEPTEMBER 1964 CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* WILLIAM F. SHARPEt I. INTRODUCTION ONE OF THE PROBLEMSwhich has plagued those attempting to predict the behavior of capital markets is the absence of a body of positive microeconomic theory dealing with conditions of risk. Although many useful insights can be obtained from the traditional models of investment under conditions of certainty, the pervasive influence of risk in financial transactions has forced those working in this area to adopt models of price behavior which are little more than assertions. A typical classroom explanation of the determination of capital asset prices, for example, usually begins with a careful and relatively rigorous description of the process through which individual preferences and physical relationships interact to determine an equilibriumpure interest rate. This is generally followed by the assertion that somehow a market risk-premium is also determined,with the prices of assets adjusting accordingly to account for differencesin their risk. A useful representation of the view of the capital market implied in such discussions is illustrated in Figure 1. In equilibrium, capital asset prices have adjusted so that the investor, if he follows rational procedures (primarily diversification), is able to attain any desired point along a capital market line. He may obtain a higher expected rate of return on his holdings only by incurring additional risk. In effect, the market presents him with two prices: the price of time, or the pure interest rate (shown by the intersection of the line with the horizontal axis) and the price of risk, the additional expected return per unit of risk borne (the reciprocal of the slope of the line). A great many people provided comments on early versions of this paper which led to major improvementsin the exposition. In addition to the referees, who were most helpful, the author wishes to express his appreciation to Dr. Harry Markowitz of the RAND Corporation,Professor Jack Hirshleifer of the University of California at Los Angeles, and to Professors Yoram Barzel, George Brabb, Bruce Johnson, Walter Oi and R . Haney Scott of the University of Washington. AssociateProfessorof Operations Research,Universityof Washington. 1. Althoughsome discussionsare also consistentwith a non-linear (but monotonic) curve. 425 426 The Journalof Finance At present there is no theory describing the manner in which the price of risk results from the basic influences of investor preferences, the physical attributes of capital assets, etc. Moreover, lacking such a theory, it is difficult to give any real meaning to the relationship between the price of a single asset and its risk. Through diversification, some of the risk inherent in an asset can be avoided so that its total risk is obviously not the relevant influence on its price; unfortunately little has been said concerning the particular risk component which is relevant. Risk Capital Market Line 0 Expected Rate of Return Pure InterestRate FIGURE 1 In the last ten years a number of economists have developed normative models dealing with asset choice under conditions of risk. Markowitz,2 following Von Neumann and Morgenstern, developed an analysis based on the expected utility maxim and proposed a general solution for the portfolio selection problem. Tobin showed that under certain conditions Markowitzs model implies that the process of investment choice can be broken down into two phases: first, the choice of a unique optimum combinationof risky assets; and second, a separate choice concerningthe allocation of funds between such a combination and a single riskless 2. Harry M. Markowitz, Portfolio Selection, Efficient Diversification of Investments (New York: John Wiley and Sons, Inc. , 1959). The major elements of the theory first appearedin his article Portfolio Selection,The Journal of Finance, XII (March 1952), 77-91. 3. James Tobin, Liquidity Preference as Behavior Towards Risk, The Review of Economic Studies, XXV (February, 1958), 65-86. CapitalAssetPrices 427 asset. Recently, Hicks4 has used a model similar to that proposed by Tobin to derive corresponding conclusions about individual investor behavior, dealing somewhat more explicitly with the nature of the conditions under which the process of investment choice can be dichotomized. An even more detailed discussion of this process, including a rigorous proof in the context of a choice among lotteries has been presented by Gordonand Gangolli. Although all the authors cited use virtually the same model of investor behavior,6 none has yet attempted to extend it to construct a market equilibriumtheory of asset prices under conditions of risk. We will show that such an extension provides a theory with implications consistent with the assertions of traditional financial theory described above. Moreover, it sheds considerable light on the relationship b etween the price of an asset and the various components of its overall risk. For these reasons it warrants considerationas a model of the determinationof capital asset prices. Part II provides the model of individual investor behavior under conditions of risk. In Part III the equilibrium conditions for the capital market are considered and the capital market line derived. The implications for the relationship between the prices of individual capital assets and the various components of risk are described in Part IV. II. OPTIMAL INVESTMENT POLICY FOR THE INDIVIDUAL The Investors Preference Function Assume that an individual views the outcome of any investment in probabilistic terms; that is, he thinks of the possible results in terms of some probability distribution. In assessing the desirability of a particular investment, however, he is willing to act on the basis of only two para4. John R. Hicks, Liquidity,The Economic Journal, LXXII (December, 1962), 787802. 5. M. J. Gordon and Ramesh Gangolli, Choice Among and Scale of Play on Lottery Type Alternatives, College of Business Administration,University of Rochester, 1962. For another discussion of this relationship see W. F. Sharpe, A Simplified Model for Portfolio Analysis, Management Science, Vol. 9, No. 2 (January 1963), 277-293. A related discussioncan be found in F. Modiglianiand M. H. Miller, The Cost of Capital, CorporationFinance, and the Theory of Investment, The AmericanEconomic Review, XLVIII (June 1958), 261-297. 6. Recently Hirshleifer has suggested that the mean-variance approach used in the articles cited is best regarded as a special case of a more general formulation due to -Arrow. See Hirshleifers InvestmentDecision Under Uncertainty,Papers and Proceedings of the Seventy-Sixth Annual Meeting of the AmericanEconomic Association, Dec. 963, or ArrowsLe Role des ValeursBoursierespour la Repartitionla Meilleuredes Risques, InternationalColloquiumon Econometrics,1952. 7. After preparingthis paper the author learned that Mr. Jack L. Treynor, of Arthur D. Little, Inc. , had independentlydeveloped a model similar in many respects to the one describedhere. UnfortunatelyMr. Treynors excellent work on this subject is, at present, unpublished. 428 The Journal of Finance meters of this distribution-its expec ted value and standard deviation. This can be representedby a total utility function of the form: U = f(E,, a,) where Ew indicates expected future wealth and cw the predicted standard deviation of the possible divergence of actual future wealth from Ew. Investors are assumed to prefer a higher expected future wealth to a lower value, ceteris paribus (dU/dEw 0). Moreover, they exhibit risk-aversion, choosing an investment offering a lower value of aw to one with a greater level, given the level of Ew (dU/dow 0). These assumptions imply that indifference curves relating Ew and co will be upward-sloping. To simplify the analysis, we assume that an investor has decided to commit a given amount (WI) of his present wealth to investment. Letting Wt be his terminal wealth and R the rate of return on his investment: R we have Wt R WI + Wi. This relationship makes it possible to express the investors utility in terms of R, since terminal wealth is directly related to the rate of return: U = g(ER, OR) . Figure 2 summarizes the model of investor preferences in a family of indifference curves; successive curves indicate higher levels of utility as one moves down and/or to the right. 10 8. Under certain conditions the mean-variance approach can be shown to lead to unsatisfactory predictions of behavior. Markowitz suggests that a model based on the semi-variance(the averageof the squareddeviationsbelow the mean) would be preferable; in light of the formidablecomputationalproblems,however, he bases his analysis on the variance and standard deviation. are 9. While only these characteristics requiredfor the analysis, it is generally assumed that the curves have the property of diminishingmarginal rates of substitution between EW and aw, as do those in our diagrams. 10. Such indifferencecurves can also be derived by assuming that the investor wishes to maximize expected utility and that his total utility can be representedby a quadratic function of R with decreasingmarginal utility. Both Markowitz and Tobin present such a derivation. A similar approachis used by Donald E. Farrar in The Investment Decision Under Uncertainty (Prentice-Hall, 1962). Unfortunately Farrar makes an error in his cardinal utility axioms to transderivation; he appeals to the Von-Neumann-Morgenstern form a function of the form: E(U) = a+ bER cER2 -CR2 into one of the form: E (U) = k1 E -k2aR2. Wt WI Wi is That such a transformation not consistent with the axioms can readily be seen in this form, since the first equation implies non-linear indifferencecurves in the ER aR2 plane while the second implies a linear relationship. Obviously no three (different) points can lie on both a line and a non-linear curve (with a monotonic derivative). Thus the two functions must imply different orderings among alternative choices in at least some instance. Capital Asset Prices 429 CYR // -7.. /he or .. Ineten poruiy The~. uv Thsetofinvestmentopportuniti ureshtoewihmsm shsuiiy Every investment plan available to him may be representedby a point in the ER, OR plane. If all such plans involve some risk, the area composed of such points will have an appearance similar to that shown in Figure 2. The investor will choose from among all possible plans the one placing him on the indifference curve representing the highest level of utility (point F). The decision can be made in two stages: first, find the set of efficient investment plans and, second choose one from among this set. A plan is said to be efficient if (and only if) there is no alternative with either (1) the same ER and a lower CR, (2) the same OR and a higher EB Thus investment Z is inefficientsince or (3) a higher ER and a lower CR. investments B, C, and D (among others) dominate it. The only plans which would be chosen must lie along the lower right-hand boundary (AFBDCX)- the investment opportunity curve. To understand the nature of this curve, consider two investment plans -A and B, each including one or more assets. Their predicted expected values and standard deviations of rate of return are shown in Figure 3. 430 The Journal of Finance If the proportion a of the individuals wealth is placed in plan A and the remainder (1-a) in B, the expected rate of return of the combinationwill lie between the expected returns of the two plans: ER= aERa + (1 a) ERb The predicted standard deviation of return of the combination is: RC Va2Ra 2 + (1 a)2 Rb2 + 2rab a(1 a) CRaORb Note that this relationshipincludes rab, the correlation coefficientbetween the predicted rates of return of the two investment plans. A value of +1 would indicate an investors belief that there is a precise positive relationship between the outcomes of the two investments. A zero value would indicate a belief that the outcomes of the two investments are completely independent and -1 that the investor feels that there is a precise inverse relationship between them. In the usual case rab will have a value between o and +1. Figure 3 shows the possible values of ERc and ORCobtainable with differentcombinations of A and B under two different assumptions about OR aRb -B CRa- I l I ERa FIGURE 3 I I I ERb ER CapitalAssetPrices 431 the value of rab. If the two investments are perfectly correlated, the combinations will lie along a straight line between the two points, since in this case both ERC and oRc will be linearly related to the proportions invested in the two plans. 11If they are less than perfectly positively correlated, the standard deviation of any combination must be less than that obtained with perfect correlation (since rabwill be less); thus the combinations must lie along a curve below the line AB. 2AZB shows such a curve for the case of complete independence (rab 0); with negative correlation the locus is even more U-shaped. 13 The manner in which the investment opportunity curve is formed is relatively simple conceptually, although exact solutions are usually quite difficult. 14 One first traces curves indicating ER, ORvalues available with simple combinations of individual assets, then considers combinations of combinations of assets. The lower right-hand boundary must be either linear or increasing at an increasing rate (d2 CR/dE2R; 0). As suggested earlier, the complexity of the relationship between the characteristics of individual assets and the location of the investment opportunity curve makes it difficult to provide a simple rule for assessing the desirability of individual assets, since the effect of an asset on an investors over-all investment opportunity curve depends not only on its expected rate of return (ERI) and risk (CR1), but also on its correlations with the other available opportunities (rii, rI2 . , rin). However, such a rule is implied by the equilibrium conditions for the model, as we will show in part IV. The Pure Rate of Interest We have not yet dealt with riskless assets. Let P be such an asset; its risk is zero (oRp = 0) and its expected rate of return, ERR, is equal (by definition) to the pure interest rate. If an investor places a of his wealth 11. ERC = aERa + (1 -a) ERb = ERb + (ERa ERb) butab a)2 cvRb2 + 2rab a(1 a) rRa aRb ORC= V/a2Ra2 + (1thereforethe expression underthe squareroot sign can be factored: 1, YRc = /[aaRa + (1 GO)cRb]2 a YRa + (1 (OYRa a) aRb 0Rb + YRb) a 12. This curvature is, in essence, the rationale for diversification. 13. When rab YRb ERbERa = 0, the slope of the curve at point A is ERb , at point B it is ERa . When rab =-1, the curve degeneratesto two straight lines to a point on the horizontal axis. 14. Markowitz has shown that this is a problem in parametricquadraticprogramming. An efficientsolution techniqueis describedin his article, The Optimizationof a Quadratic Function Subject to Linear Constraints,Naval Research Logistics Quarterly, Vol. 3 (March and June, 1956), 111-133. A solution method for a special case is given in the authorsA SimplifiedModel for Portfolio Analysis,op. cit. 432 The Journal of Finance in P and the remainderin some risky asset A, he would obtain an expected rate of return: ERC= aERP+ (1 a) ER1a The standard deviation of such a combination would be: 0Rc Va202Rp + ( -a)2aua2 + 2rpa a(1-a) (}RplRa but since ORp = 0, this reduces to: CrR = (1 a) (Ra. This implies that all combinations involving any risky asset or combination of assets plus the riskless asset must have values of ERC and OCR which lie along a straight line between the points representing the two components. Thus in Figure 4 all combinations of ER and OR lying along OaR P FIGURiE 4 v the line PA are attainable if some money is loaned at the pure rate and in some pBlaced A. Similarly, by lending at the pure rate and investing in combinations along PB can be attained. Of all such possibilities, howB, ever, one will dominate: that investment plan lying at the point of the curve where a ray from point P is tangent original investment opprortunity to the curve. In Figure 4 all investments lying along the original curve Capital Asset Prices 433 from X to cPare dominated by some combination of investment in 4 and lending at the pure interest rate. Consider next the possibility of borrowing. If the investor can borrow at the pure rate of interest, this is equivalent to disinvesting in P. The effect of borrowing to purchase more of any given investment than is possible with the given amount of wealth can be found simply by letting a take on negative values in the equations derived for the case of lending. This will obviously give points lying along the extension of line PA if borrowingis used to purchase more of A; points lying along the extension of PB if the funds are used to purchase B, etc. As in the case of lending, however, one investment plan will dominate all others when borrowing is possible. When the rate at which funds can be borrowedequals the lending rate, this plan will be the same one which is dominantif lending is to take place. Under these conditions, the investment opportunity curve becomes a line (POZ in Figure 4). Moreover, if the original investment opportunity curve is not linear at point c, the process of investment choice can be dichotomized as follows: first select the (unique) optimum combination of risky assets (point c), and second borrow or lend to obtain he particular point on PZ at which an indifference curve is tangent to the line. 5 Before proceeding with the analysis, it may be useful to consider alternative assumptions under which only a combination of assets lying at the point of tangency between the original investment opportunity curve and a ray from P can be efficient. Even if borrowingis impossible, the investor will choose 4 (and len ding) if his risk-aversion leads him to a point below 4)on the line Pq). Since a large number of investors choose to place some of their funds in relatively risk-free investments, this is not an unlikely possibility. Alternatively, if borrowing is possible but only up to some limit, the choice of 4) would be made by all but those investors willing to undertake considerablerisk. These alternative paths lead to the main conclusion, thus making the assumption of borrowing or lending at the pure interest rate less onerous than it might initially appear to be. III. IN EQUILIBRIUM THE CAPITAL MARKET In order to derive conditions for equilibrium in the capital market we invoke two assumptions. First, we assume a common pure rate of interest, with all investors able to borrow or lend funds on equal terms. Second, we assume homogeneity of investor expectations:16 investors are assumed 15. This proof was first presented by Tobin for the case in which the pure rate of interest is zero (cash). Hicks considersthe lending situation under comparableconditions but does not allow borrowing. Both authors present their analysis using maximization subject to constraints expressed as equalities. Hicks analysis assumes independenceand thus insures that the solution will include no negative holdings of risky assets; Tobins covers the general case, thus his solution would generally include negative holdings of some assets. The discussion in this paper is based on Markowitz formulation, which on includesnon-negativityconstraints the holdingsof all assets. 16. A term suggested by one of the referees. 434 The Journal of Finance to agree on the prospects of various investments-the expected values, standard deviations and correlation coefficients described in Part II. Needless to say, these are highly restrictive and undoubtedly unrealistic assumptions. However, since the proper test of a theory is not the realism of its assumptionsbut the acceptability of its implications,and since these assumptions imply equilibrium conditions which form a major part of classical financial doctrine, it is far from clear that this formulation should be rejected-especially in view of the dearth of alternative models leading to similar results. Under these assumptions, given some set of capital asset prices, each investor will view his alternatives in the same manner. For one set of prices the alternatives might appear as shown in Figure 5. In this situaaR Cl C2 -C3 C1/ / ~~ B B~2 1/ A3/ P FIGURE 5 ER tion an investor with the preferences indicated by indifferencecurves A1 throughA4 would seek to lend some of his funds at the pure interest rate and to invest the remainderin the combination of assets shown by point since this would give him the preferredover-all position A*. An investor 4,0 with the preferencesindicated by curves B1 through B4 would seek to invest all his funds in combination 4, while an investor with indifference curvesC1throughC4 would invest all his funds plus additional (borrowed) Capital Asset Prices 435 funds in combination 4 in order to reach his preferred position (C*). In any event, all would attempt to purchase only those risky assets which enter combination b. The attempts by investors to purchase the assets in combination 4 and their lack of interest in holding assets not in combination would, of course, lead to a revision of prices. The prices of assets in 4 will rise and, since an assets expected return relates future income to present price, their expected returns will fall. This will reduce the attractiveness of combinations which include such assets; thus point (among others) will move to the left of its initial position. 7 On the other hand, the prices of assets not in will fall, causing an increase in their expected returns and a rightwardmovement of points representingcombinationswhich include them. Such price changes will lead to a revision of investors actions; some new combination or combinations will become attractive, leading to different demandsand thus to further revisions in prices. As the process continues, the investment opp ortunity curve will tend to become more linear, with points such as moving to the left and formerly inefficient points (such as F and G) moving to the right. Capital asset prices must, of course, continue to change until a set of prices is attained for which every asset enters at least one combination lying on the capital market line. Figure 6 illustrates such an equilibrium condition. 8All possibilities in the shaded area can be attained with combinations of risky assets, while points lying along the line PZ can be attained by borrowing or lending at the pure rate plus an investment in some combination of risky assets. Certain possibilities (those lying along PZ from point A to point B) can be obtained in either manner. For example, the ER, aR values shown by point A can be obtained solely by some combination of risky assets; alternatively, the point can be reached by a combination of lending and investing in combination C of risky assets. It is important to recognize that in the situation shown in Figure 6 many alternative combinations of risky assets are efficient (i. e. , lie along line PZ), and thus the theory does not imply that all investors will hold On the same combination. 9 the other hand, all such combinations must be perfectly (positively) correlated,since they lie along a linear border of 17. If investors consider the variability of future dollar returns unrelated to present price, both ER and cR will fall; under these conditions the point representingan asset would move along a ray through the origin as its price changes. 18. The area in Figure 6 representingER aR values attained with only risky assets has been drawn at some distance from the horizontal axis for emphasis. It is likely that would place it very close to the axis. a more accurate representation 19. This statement contradicts Tobins conclusion that there will be a unique optimal combination of risky assets. Tobins proof of a unique optimum can be shown to be incorrect for the case of perfect correlation of efficient risky investment plans if the line connectingtheir ER, aR points would pass through point P. In the graph on page 83 of this article (op. cit. ) the constant-risklocus would, in this case, degenerate from a loci, thus giving family of ellipses into one of straight lines parallel to the constant-return multiple optima. 436 The Journalof Finance the ER, oR region. 20This provides a key to the relationship between the prices of capital assets and different types of risk. aRl B p FIGURE 6 ER IV. THE PRICES OF CAPITAL ASSETS We have argued that in equilibrium there will be a simple linear relationship between the expected return and standard deviation of return for efficient combinations of risky assets. Thus far nothing has been said about such a relationshipfor individualassets. Typically the ER,ORvalues associated with single assets will lie above the capital market line, reflecting the inefficiencyof undiversifiedholdings. Moreover, such points may be scattered throughout the feasible region, with no consistent relationship between their expected return and total risk (OR). However, there will be a consistent relationshipbetween their expected returns and what might best be called systematic risk, as we will now show. Figure 7 illustrates the typical relationship between a single capital 20. ER, 0R values given by combinations of any two combinationsmust lie within the region and cannot plot above a straightline joining the points. In this case they cannot plot below such a straight line. But since only in the case of perfect correlationwill they plot along a straight line, the two combinationsmust be perfectly correlated. As shown in Part IV, this does not necessarily imply that the individual securities they contain are perfectly correlated. Capital Asset Prices 437 asset (point i) and an efficient combination of assets (point g) of which oR it is a part. The curve igg indicates all ERJ, values which can be obtained with feasible combinations of asset i and combination g. As before, we denote such a combination in terms of a proportion a. of asset i and 1 would indicate pure investa) of combination g. A value of a (1 ?R _ P FiGuRE 7 ER ent in asset i while a = 0 would imply investment in combination g. Note, however, that a = . 5 implies a total investment of more than half the funds in asset i, since half would be invested in i itself and the other half used to purchase combination g, which also includes some of asset i. This means that a combinationin which asset i does not appear at all must be represented by some negative value of a. Point g indicates such a combination. In Figure 7 the curve igg has been drawn tangent to the capital market line (PZ) at point g. This is no accident. All such curves must be tangent to the capital market line in equilibrium,since (1) they must touch it at the point representing the efficient combination and (2) they are continuous at that point. 2 Under these conditions a lack of tangency would 21. Only if rig = -1 will the curve be discontinuousover the range in question. 438 The Journal of Finance imply that the curve intersects PZ. But then some feasible combinationof assets would lie to the right of the capital market line, an obvious impossibility since the capital market line represents the efficient boundary of feasible values of ER and OR. The requirement that curves such as igg be tangent to the capital market line can be shown to lead to a relatively simple formula which relates the expected rate of return to various elements of risk for all assets which are included in combinationg. 22Its economic meaning can best be seen if the relationship between the return of asset i and that of combination g is viewed in a manner similar to that used in regression analysis. 28Imagine that we were given a number of (ex post) observations of the return of the two investments. The points might plot as shown in Fig. . The scatter of the R, observations around their mean (which will approximate ERi) is, of course, evidence of the total risk of the asset CRi. But part of the scatter is due to an underlyingrelationshipwith the return on combination g, shown by Big, the slope of the regression line. The response of R, to changes in Rg (and variations in Rg itself) account for 22. The standard deviation of a combinationof g and i will be: or = V/a2aRi2 + (1 a)2 ORg2 + 2rig a(l a) cRiaRg at a = 0: do but or = 1 rjgcvRjaTgl daL = d[0Rg2 Rg at a = 0. Thus: da a [cvRg- rigaRil will be: The expectedreturnof a combination E = aERi + (1 ca) ERg Thus, at all values of a: dE dL = _ [ERg ERJ] and, at a = 0: dcv cvRg- rigcfRi dE ERg-ERi Let the equationof the capitalmarketline be: CvR = S(ER P) = where P is the pure interest rate. Since igg is tangent to the line when c lies on the line: (ERg, CvRg) qp,Rg~- jgj dR rigq. ,i Rg ERgERi ERg P 0, and since or: E rgRE l+ LERg ERi. -P] [ERg-P 23. This model has been called the diagonal model since its portfolio analysis solution can be facilitated by re-arranging data so that the variance-covariance the matrix becomes diagonal. The method is described in the authors article, cited earlier. CapitalAssetPrices Return on Asset i (Ri) 439 . , ~~~ig -4.. ERi Return FIGuRE8 on Combination g (Rg) much of the variation in Ri. It is this component of the assets total risk which we term the systematic risk. The remainder,24 being uncorrelated with Rg, is the unsystematic component. This formulation of the relationship between R, and Rg can be employed ex ante as a predictive model. Big becomes the predicted response of Ri to changes in Rg. Then, given ORg (the predicted risk of Rg), the systematic portion of the predicted risk of each asset can be determined. This interpretation allows us to state the relationship derived from the tangency of curves such as igg with the capital market line in the form shown in Figure 9. All assets entering efficient combination g must have (predicted) Big and ER, values lying on the line PQ. 25Prices will 24. ex post, the standarderror. 25. /Big20 Rg2 g BigcRg ORi aRi2 and: Big =- -rigcvRi 4 oRg The expressionon the right is the expressionon the left-hand side of the last equation in footnote 22. Thus: Big = E- Rg P + [EgiP] ERI. 440 The Journal of Finance djust so that assets which are more responsive to changes in Rg will have higher expected returns than those which are less responsive. This accords with common sense. Obviously the part of an assets risk which is due to its correlationwith the return on a combinationcannot be diversifiedaway when the asset is added to the combination. Since Bigindicates the magnitude of this type of risk it should be directly related to expected return. The relationsh ipillustrated in Figure 9 provides a partial answer to the question posed earlier concerning the relationship between an assets risk Q Big 0 J______________ t -f Pure Rate of Interest -P ~~~~~~~~~~E FIGURE 9 and its expected return. But thus far we have argued only that the relationship holds for the assets which enter some particular efficient combination (g). Had another combination been selected, a different linear relationshipwould have been derived. Fortunately this limitation is easily overcome. As shown in the footnote,26 we may arbitrarily select any one 26. Consider the two assets i and i*, the former included in efficient combination g and the latter in combinationg*. As shown above: Big = -[E1,gP] and: + [E P] ERI Capital Asset Prices 441 of the efficient combinations, then measure the predicted responsiveness of every assets rate of return to that of the combination selected; and these coefficients will be related to the expected rates of return of the assets in exactly the mannerpictured in Figure 9. The fact that rates of return from all efficient combinations will be perfectly correlatedprovides the justification for arbitrarily selecting any one of them. Alternatively we may choose instead any variable perfectly correlated with the rate of return of such combinations. The vertical axis in Figure 9 would then indicate alternative levels of a coefficient measuring the sensitivity of the rate of return of a capital asset to changes in the variable chosen. This possibility suggests both a plausible explanation for the implication that all efficient combinations will be perfectly correlated and a useful interpretation of the relationship between an individual assets expected return and its risk. Although the theory itself implies only that rates of return from efficient combinations will be perfectly correlated, we might expect that this would be due to their common dependence on the over-all level of economic activity. If so, diversification enables the investor to escape all but the risk resulting from swings in economic activity-this type of risk remains even in efficient combinations. And, since all other types can be avoided by diversification, only the responsiveness of an assets rate of return to the level of economic activity is relevant in BJ*g* = rj*g* = rj*g Thus: Bi*g*oRg* Bi*gcrRg [ERg* P + [E *-P] ER11* Since Rg and Rg* are perfectly correlated: and: B. = Bi*g[ [ ORg Crjg Since both g and g* lie on a line which intercepts the E-axis at P: YRg ERg-P ERg* P and: (yRg* Bj*g* = Bi*g P Thus: [E g p] ERi* = Bi*g from which we have the desired relationship between R,* and g: [ ]ER:P + [ E Pz] Bj*g[] ErP+ [El IP] Bi*g must therefore plot on the same line as does Big. 442 The Journal of Finance assessing its risk. Prices will adjust until there is a linear relationship between the magnitude of such responsiveness and expected return. Assets which are unaffected by changes in economic activity will return the pure interest rate; those which move with economic activity will promise appropriatelyhigher expected rates of return. This discussion provides an answer to the second of the two questions posed in this paper. In Part III it was shown that with respect to equilibrium conditions in the capital market as a whole, the theory leads to results consistent with classical doctrine (i. e. , the capital market line). We have now shown that with regard to capital assets considered individually, it also yields implications consistent with traditional concepts: it is commonpractice for investment counselorsto accept a lower expected return from defensive securities (those which respond little to changes in the economy) than they require from aggressive securities (which exhibit significant response). As suggested earlier, the familiarity of the implications need not be considereda drawback. The provision of a logical framework for producing some of the major elements of traditional financial theory should be a useful contributionin its own right.