# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

11 Pages

### fin7

Course: ECON 3330, Spring 2008
School: Cornell
Rating:

Word Count: 1391

#### Document Preview

Tools Portfolio 4 Econ 333 Spring 08 1 Portfolio Tools 4 Our goals: Understand the importance of mean-standard deviation diagram and know how to locate within the diagram the efficient frontier of risky assets, the capital market line, the minimum variance portfolio, and the tangency portfolio. Compute and use both the tangency portfolio and the efficient frontier of risky assets. Understand the linkage...

Register Now

#### Unformatted Document Excerpt

Coursehero >> New York >> Cornell >> ECON 3330

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Tools Portfolio 4 Econ 333 Spring 08 1 Portfolio Tools 4 Our goals: Understand the importance of mean-standard deviation diagram and know how to locate within the diagram the efficient frontier of risky assets, the capital market line, the minimum variance portfolio, and the tangency portfolio. Compute and use both the tangency portfolio and the efficient frontier of risky assets. Understand the linkage between mean-variance efficiency and risk-expected return equations. Describe how to compute the beat of a portfolio given the betas of individual assets in the portfolio and their respective weights. Understand what the market portfolio is, what assumptions are needed for the market portfolio to be the tangency portfolio, i.e. for the Capital Asset pricing Model (CAPM) to hold. Econ 333 Spring 08 2 Portfolio Tools 4 The issue is that of analyzing the portfolio selection of an investor seeking to maximize the expected return given the variance of its future returns. As tools for illustrating how to achieve higher average returns with lower risk, mean-variance analysis and the CAPM are routinely applied by brokers, pension fund managers, and consultants when formulating investment strategies and giving financial advices. A firm grasp of mean-variance analysis and the CAPM also is becoming increasingly important for corporate managers. The need to understand the determinants of share value, and what actions to take to increase this value in response to the pressures of stockholders and directors is higher than ever before. They can apply these tools to hedge their risks optimally and diversify their portfolio. One of the lessons of the CAPM is that while diversifying investments can reduce the variance of a firm's stock price, it does not reduce the firm's cost of capital (weighted average of the expected rates of return required by the financial markets for a firm's debt and equity financing). As a result, diversification can create value only if it increases the expected returns of real assets. Corporate also use these tools to evaluate their capital expenditure decisions. Econ 333 Spring 08 3 Portfolio Tools 4 The assumptions of mean-variance analysis: When making investment decisions today, investors care only about the means and the variances of the returns of their portfolios over a particular period: They are risk-averse and have preference for higher means and lower variances. Higher mean return because on average they'll be wealthier. Lower variance because it implies less dispersion in the possible wealth outcomes. Notice that when using the variance as a measure of risk / dispersion it is assumed that returns are normally distributed. Financial markets are frictionless: This assumption simplifies the computation of the feasible set. It implies that all investments are tradable at any price and in any quantity, both positive or negative , there is no transaction costs, regulations, or taxes. Although these assumptions may not hold in some cases, the general results are perceived to remain: portfolio dominates individual assets; covariances are more important than variances for risk-return equations; and optimal portfolios (in the meanvariance sense) can generally be found if one knows the inputs. Econ 333 Spring 08 4 Portfolio Tools 4 Given the previous assumptions, an investor would always like to be on the efficient frontier. This frontier contains many portfolios and which of these investors select depends on their personal trade-off between mean and variance. Because investors who treat variance as the sole measure of risk want to select meanvariance efficient portfolio, it is important to know how to construct them. Result (two-fund separation): All portfolios on the mean-average efficient frontier can be formed as a weighted average of any two portfolios on the efficient frontier. Illustration and example: (In class) Econ 333 Spring 08 5 Portfolio Tools 4 So far (portfolio tools 4) we have only consider optimal portfolios selection when there is no risk-free asset. Accounting for a risk-free asset sharply simplifies the analysis. Because of the two-fund separation principle, when there is a risk-free asset only "one key" portfolio need to be found. If there is a risk-free asset, it is necessarily the minimum variance one and thus must be on the efficient frontier. As a result, we need to be concerned with only one efficient risky portfolio (once combined with the efficient risky portfolio, the risk-free generate asset the entire boundary of the feasible set). This optimal risky portfolio will be called the tangency portfolio: it is the unique optimal portfolio that contains no investment in the risk-free asset. The line from rf and tangent to the efficiency frontier is called the capital market line CML. Result: Under the assumptions of mean-variance analysis, and assuming the existence of a risk-free asset, all investors will select portfolios on the CML. Econ 333 Spring 08 6 Portfolio Tools 4 The result above suggests that the CML is the key to optimal investment for every investor interested in maximizing expected return for a given amount of variance risk. Investors who are extremely risk-averse will select a portfolio close to the risk-free asset, achieving a low expected return but also a low variance for their future wealth. Investors who are only slightly risk averse will select a portfolio high up on the CML, possibly above T if they choose to sell short the risk-free asset. They would achieve a higher expected return than more risk-averse investors, but the larger variance also makes the possibility of realizing large losses quite high. CML line equation: Mean return CML T R p = rf + RT - r f T p rf Trade-off between risk and return: larger implies the financial markets offer greater expected return improvements for given increases in risk. Standard Econ 333 Spring 08 deviation 7 Portfolio Tools 4 General lesson from the mean-standard deviation diagram: there is no necessary relation between mean and standard deviation (portfolios with the same standard deviation can have different means) Implication: it pays to identify efficient portfolios which maximize mean return for a given standard deviation. The tangency portfolio serves double duty: useful for identifying proper investment weights, but also useful for addressing what determines mean returns. But, how to identify the tangency portfolio? Result: The ratio of the risk premium of every stock and the portfolio to its covariance with the tangency portfolio is constant. In clear, is constant. ri - r f Illustration: (In class) ~ cov( ~i , R T ) r The result holds for the tangent portfolio as well (of course!) Econ 333 Spring 08 8 Portfolio Tools 4 Finding the efficient frontier of risky assets: Because of two-fund separation, the identification of any two portfolios on the boundary is enough to construct the entire set of risky portfolios that minimize variance for a given mean return. One can use the minimum variance portfolio of the risky assets as of the two portfolios since computing its weights is so easy. For the other portfolio, it is also possible to draw a tangent line from every point on the vertical axis of the mean-standard deviation diagram to the hyperbolic boundary (except for minimum variance point V). (i) Select any return that is less than the expected return of the minimum-variance portfolio. (ii) Compute the hypothetical tangency portfolio by pretending that the return in step i is the risk-free asset, even if a risk-free asset does not exist. (iii) Take the weighted averages of the minimum variance portfolio and the hypothetical tangency portfolio found in step ii to generate the entire set of mean-variance efficient portfolios. The weights on the minimum variance portfolio must be less than 1 to be the top half of the hyperbolic boundary. Illustration: (in class) Econ 333 Spring 08 9 Portfolio Tools 4 The relation between risk and expected return: A secondary benefit of identifying a mean-variance efficient portfolio is that it generates an equation that relates the risk of an asset to its expected return. If historical data provide unreliable estimates of the true expected rates of return of the stocks of individual corporations, how to obtain such estimates? Solution: When a risk-free asset exists, the relation between the relevant risk of an investment and its expected return is given by: ~ cov(~, RT ) ri ri - rf = ~ ( RT - rf ) var(RT ) Beta Illustration: (In class) Econ 333 Spring 08 10 Portfolio Tools 4 Betas In a regression, give the slope of the coefficient ri - rf = ( RT - rf ) Betas and covariances are essentially the same measure of marginal variance Securities market line versus mean-standard deviation diagram The securities market line is the graphical representation of mean versus beta. The tangency portfolio has a beta of 1 The risk free asset has a beta of 0 Illustration: In class Econ 333 Spring 08 11
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Cornell - INFO - 2300
Cornell - INFO - 2300
ReminderProject 3, part I due tonight at midnightUploading files and PHP graphicsINFO/COM S 230: Intermediate Web Design and ProgrammingMidterm infoTime: 7:30-9PM, Tuesday 3/11 Place: Olin 155 Format: On paper Closed book, closed notes However
Cornell - ILROB - 4710
GROUND RULES FOR COLLABORATIVE LAW PROCESS 1. 2. 3. 4. Attack the problems and concerns at hand, not each other. Avoid positions; rather, express yourself in terms of needs and interests and the outcomes you would like to achieve. Work for what you b
Cornell - ILROB - 4710
COLLABORATIVE LAW PARTICIPATION AGREEMENTI. PURPOSE_ and his/her attorney, _, and_ and his/her attorney, _, have chosen to use the principles of Collaborative Law to settle the issues arising from the dissolution of their marriage or domestic part
Cornell - ILROB - 4710
Cornell - ILROB - 4710
Warning Concerning Copyright Restrictions The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries
Cornell - ILROB - 4710
Cornell - ILROB - 4710
Warning Concerning Copyright Restrictions The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries
Cornell - ILROB - 4710
ILROB 471 Organizations and NegotiationProfessor Michele WilliamsAgenda Turn in Post-Negotiation Paper (upload a copy onto Blackboard!) In the News Integrative Bargaining (reviewed) Exercise Video Case and Debrief Wrap-up 2008 Michele Willi
Cornell - ILROB - 4710
ILROB 471 Organizations and NegotiationProfessor Michele WilliamsAgenda Getting to Yes Conflict Exercise El-Tek Discussion and Wrap-up 2007 Michele Williams. All Rights Reserved.Pilots Thwart Merger Plans 2007 Michele Williams. All Right
Cornell - ILROB - 4710
ILROB 471 Organizations and NegotiationProfessor Michele WilliamsAgenda Emotion, Power and Negotiation Style (The Coleman account ) Reflective Paper Assignment Amanda Dispute Discussion and Wrap-up Gender (next week) 2007 Michele Williams.
Cornell - ILROB - 4710
ILROB 471 Organizations and NegotiationProfessor WilliamsAgenda Distributive Tactics Negotiation Exercise (Used Car) Fishbowl Negotiation Break Auction Netscape Case Discussion Wrap-upFocusStrategy Distributive (fixed-pie) Integrative (
Cornell - ILROB - 4710
ILROB 471 Organizations and NegotiationProfessor Michele WilliamsAnnouncement: Sign out an IClickerAgenda In the News Negotiation Paradigms Psychological Biases Personal Experience Coffee Contract Double Negotiation Discussion Video and W
Cornell - ILROB - 4710
ILROB 471 Organizations and NegotiationProfessor WilliamsAgenda Ethics In the News Negotiation Preparation Break Negotiation Discussion and Wrap-up Post Negotiation Analytic PaperA Question of Ethics You see a sign on a vacation home,
Cornell - ILROB - 4710
ILROB 471 Organizations and NegotiationProfessor WilliamsProfessor Michele WilliamsTeaching Assistant:Chia-Ming Chan, cc489@cornell.eduAgenda Introduction and Overview Syllabus Break Negotiation Exercise Discussion Wrap-upWe negotiate
Cornell - ILROB - 4710
ILROB 471 Organizations and NegotiationProfessor Michele Williams 2008 Michele Williams. All Rights Reserved.Agenda Gender Dispute Resolution Frameworks Emotion Management Tool Kit Telepro Negotiation Discussion and Wrap-up Mediation in Ac
Cornell - ILROB - 4710
Berkeley - MATH - 16A
016A S2 Homework 1 SolutionJae-young Park September 2, 2007 0.1 *10 Use intervals to describe the real numbers satisfying the inequality x -1 and x &lt; 8. Solution You may change the expression little bit: -1 x &lt; 8, which is equivalent. Using inte
E. Michigan - PHYS - 221
E. Michigan - CHEM - 371
CHEM 371 Fall 2007 Professor Wilmes Exam 4 50 minutesName_ EMU ID#_ By signing below, I state that I agree to and will follow all aspects of the Student Conduct Code with regard to academic honesty: Signature__Instructions: This is a closed book
E. Michigan - CHEM - 372
E. Michigan - CHEM - 372
E. Michigan - CHEM - 372
E. Michigan - CHEM - 372
Penn State - ENGL - 015
LJ Palombo 10/15/07 Ms. Spanier To Party or Not to Party To live a healthy life, you must find a balance your free time. You should use some of your time for work and some for play. My preferred form of play would be to party. By party, I mean to go
Penn State - KINES - 061
LJ Palombo Target Heart Rate Training Zone : 121 181 bpmWorkout 1 20 minutes of cardio work (aerobics) Lower Body: (1 set, 10-12 reps) Leg Press - machine Leg Extension - machine Leg Curl - machine Lunge - dumbbell Upper Body: (1 sets, 8-10 reps)
Michigan - ENG - 125
Curtice 1 (I am sorry that I sent you the incorrect version, I saved these paper versions as Escuerdo4 and Escudero4 on my laptop and I think that this was an accident.) Mark Curtice English 125 section 56 Instructor Escudero This is a much better pa
E. Michigan - PHY - 221
Penn State - COMM - 150
1 Comm. 150 SoundIn this scholarly article I will be analyzing the use of sound in Superbad. I this film I chose one scene in particular and it's the one where the two cops pick up McLovin and take him to an abandoned parking lot. When the three ar
Penn State - HIST - 011
1 As a young adult Adolf Hitler was failing high school and wanted to pursue a career in art, but was not accepted into the art schools. Spending most of his adolescent years poor and jobless, he would beg for money and food. Later he volunteered to
Penn State - COMM - 150
1Comm. 150 CinematographyThe film images create a depth of field, which is the distance before and behind the main focus. In the film Billy Madison, you can clearly see the attribute of depth of field when Billy goes back to school and is sitting
Penn State - HIST - 011
Chp 24: The New Imperialism, 1869-1914 The New Imperialism: Motives and Methods -Explosion of territorial conquests in 16th century -10 million sq. miles and 150 million people were ruled by Europe and the United States during this time Political Mot
Penn State - COMM - 150
1Comm. 150 EditingEditing is the only form which is unique to cinema. In the film Longest Yard, the newer version with Adam Sandler is what I saw as a good film to analyze for its editing techniques. I realized that there are no limits in editing
Michigan - ANTHRO - 101
ANTHRO Lecture 9-18-07 Culture &quot;Codebook&quot; of reality; transforms physical reality Into experienced reality Systems of proof vary in different cultures Reality is subjective Picasso what criticized for distorting human features We learn what standard
Michigan - ANTHRO - 101
Lecture 9-20 Holism: define (look in textbook) Earth is 15 billion years old Carl sagan: &quot;Cosmic Calendar&quot; Every billion years = 24 days Every 475 = 1 second Jan 1: origin of the universe May 1: origin of the milky way humans: have only been here for
Michigan - ANTHRO - 101
October 9, 2007 Lecture Tectonic and Landforms Below, crust, Below lithosphere, is the liquid asthenosphere Earth works much like a convection over, the core is hot enough for convection through the mantel Patterns of landscape on earth are a result
Michigan - ANTHRO - 101
Fluvial systems: where do rivers come from? Hydrologic cycle Evapotranspiration Precipitation Infiltration Runoff Ground water: water table rises after rain, lowers during drought Carbonic acid action dissolves limestone, producing caverns Cavern col
Michigan - GEOSCI - 201
Nate Strick GEOSCI 201 Lab: due September 19, 2007Question 1) The earth's atmosphere is thickening, which will have dramatic and rapid effects of the Earth's climate. Carbon Dioxide levels in the atmosphere have gone up since Roger Kevelle first st
Michigan - SAC - 236
John Sharp SAC 236 Section 006Hustle &amp; FlowChris Brewer, independent film director and writer of Hustle &amp; Flow, along with lead actor Terrence Howard's truly riveting performance transformed the genre and made it present. Hustle &amp; Flow picked up w
Michigan - SAC - 236
John J Sharp October 9, 2007 SAC 236 / RC 236Alfred Hitchcock's NotoriousThe shot I chose for part A of the exercise starts at 3:26 after the camera pans right across Cary Grant's back and comes to rest behind his right shoulder. The camera is pl
Michigan - SAC - 236
John Sharp SAC 236 Section 006Alfred Hitchcock's North by NorthwestThe scene I chose for part A of the exercise begins at 00:08:38 of part one and ends at 00:03:45 of part two after Cary Grant is taken to Lester Townsend's house. This scene begins
Michigan - SAC - 236
John Sharp October 18, 2007 SAC 236 Section 006Alfred Hitchcock's Rear WindowThe shot I chose for part A of the exercise starts at 00:39:32 as the subjective camera tilts down facing out of James Stewart's apartment rear window. The window and sil
Michigan - SAC - 236
The sound I chose for part A of the exercise starts at 00:32:30 as James Stewart, Doris Day, and Bernard Miles enter the Marakesh Police Station. This scene takes place immediately following the murder of Louis Bernard at the Marakesh Police Station
E. Michigan - MATH - 107
Michigan - ENG - 125
Mark Curtice Instructor Escuerdo English 125 section 56 Cum Hoc Fallacy The Cum Hoc Ergo Propter Hoc is an Informal fallacy of the sub family of the Non Causa Pro Causa (Curtis). The fallacy type involves a premise that does not carry the burden of p
UGA - RELI - 1001
RELI 1001 Rothacker MWF Judaism Unit Review Religion-is seeking and responding to that which humans experience as ultimate or holy (Dr. Roger Schmidt) o Ultimate-most important; defines one's existence o Holy-sacred; set apart o Religion comes from r
Michigan - ENG - 125
Mark Curtice Instructor Escudero English 125 section 56 March 11, 2008 Common Place Book and Writing Journal 3 Common Place Book1 A &quot;Imagine waking up in the morning, looking out your window and seeing this view. Breathtaking,isn't it? What would
Michigan - ENG - 125
Mark Curtice English 125 sec. 026 Professor Escuerdo January 16, 2008 Essay- How does the style match the purpose? The style of &quot;Acquiring a Japanese Family&quot;, &quot;Palestinian Like Me&quot;, and &quot;37 Just Walk By: Black Men and Public Space&quot; matches the author
E. Michigan - MATH - 107
E. Michigan - MATH - 107
Michigan - ENG - 125
Mark Curtice English 125 section 56 Instructor Escuerdo Common Place book and writing journal I. 1. Expect money market mutual fund yields to fall three-quarters of a percentage point, to about 3.25%, within the next 30 days, says Peter Crane, presid
UGA - RELI - 1001
RELI 1001 ROTHACKER MWF CHRISTIANITY MAIN POINTS Christianity-trinitarian monotheism Jesus of Nazareth 4 bce- 30 ce o Didn't call him Jesus he was called Yesuwah, relating to Joshua Christ of Faith = central doctrine o Devotional approach; church/Sun
E. Michigan - ACC - 241
Johana Castillo E00035787 ACC 241 Computer Project One TR 1:00pm-2:15pm Prepared for Dr. Okopny Double Diamond Skis Shaping and Milling Department Production Report (Weighted Average Method) Quantity Schedule and Equivalent UnitsQuantity Schedule U
E. Michigan - ACC - 241
Johana Castillo E00035787 ACC 241 Computer Project Three TR 1:00pm -2:15pm Prepared for Dr. Okopny Down Under Products, Ltd. Second Quarter Production Budget Total for Quarter 195,000 27,540 222,540 16,050 206,490Budgeted sales Add desired ending i
E. Michigan - ACC - 241
Johana Castillo E00035787 ACC 241 Computer Project Two TR 1:00pm - 2:15pm Prepared for Dr. OkopnyACOUSTIC CONCEPTS, INC. Contribution Income Statement For the Month of JuneSales Less: Variable expenses Contribution margin Less: Fixed expenses Net
Michigan - ENG - 125
Mark Curtice English 125 section 56 Instructor EscuerdoResubmissionCommon Place book and writing journal I. 1. Expect money market mutual fund yields to fall three-quarters of a percentage point, to about 3.25%, within the next 30 days, says Peter
UGA - GEOL - 1121
Chapter 1 History of Universe: Earth-only planet w/ liquid water on surface Started w/ Big Bang 15 billion yrs ago Composition today: 75% H, 23% He, 2% other Expansion: galaxies are separating Matter distributed in clouds &amp; within smaller clouds
N.C. State - BIO - 181/183
Karmen Best BIO 181L sec 240 11/26/07Protein Isolation by Means of ElectrophoresisIntroduction The purpose of the protein isolation lab is to gain more knowledge about molecules and how they are isolated and separated by electrophoresis. Understa
N.C. State - BIO - 181/183