Minimum variance portfolio mathematics


 Pierce Barnett
 1 years ago
 Views:
Transcription
1 Spring 6 Minimum variance portfolio mathematics Consider a portfolio of mutual funds: long term debt securities (D) and sotck fund in equity (E). Debt Equity E(r) 8% 3% % % Cov(r D ; r E ) 7 D;E.3 weights w D w E = w D We can compute the expected return on the portfolio P E(r P ) = w D E(r D ) + w E E(r E ); in our example we have given that w D = w E ; E(r P ) = :8w D + :3w E E(r P ) = :8( w E ) + :3w E = :8 + :5w E ; if we plot it we get E[r_P] The variance of the portfolio w_e P = wd D + we E + w D w E Cov(r D; r E ); in our example we have P = wd + we + w D w E 7 P = ( w E ) + we + ( w E )w E 7 P = 4wE 44w E + 44: This variance as a function of w E is
2 Spring 6 var(r_p) w_e Variance of a portfolio of two risky assets Assume a portfolio composed of two risky assets The expected return is then, the variance of this portfolio will be r P = w D r D + w E r E E(r P ) = w D E(r D ) + w E E(r E ); P = E [r P E[r P ]] = E rp ] [E[r P ] h = E (w D r D + w E r E ) i [w D E(r D ) + w E E(r E )] = = E n(w D r D ) + (w E r E ) + w D r D w E r E h io (w D E(r D )) + (w E E(r E )) + w D w E E(r D )E(r E ) = = w DE(r D) + w EE(r E) + w D w E E(r D r E ) w DE(r D ) w EE(r E ) w D w E E(r D )E(r E ) = rearranging we have = wde(r D) wde(r D ) + wee(r E) wee(r E ) + w D w E E(r D r E ) w D w E E(r D )E(r E ) = = wd E(r D ) E(r D ) + w E E(r {z } E ) E(r E ) + w D w E [E(r D r E ) E(r D )E(r E )] = {z } {z } D Cov(r D ;r E ) E Recall that the correlation coe cient is = w D D + w E E + w D w E Cov(r D ; r E ): D;E = Cov(r D; r E ) D E : then, we can express the portfolio variance as follows: P = w D D + w E E + w D w E Cov(r D ; r E ) = w D D + w E E + w D w E DE D E :
3 Spring 6 Relationship between correlation coe cients and portfolio variance Let s analyze the variance of the portfolio depending on the correlation coe cient of the assets. If D;E =! Cov(r D ; r E ) = D E ; then the portfolio variance becomes and P = w D D + w E E : P = w D D + w E E + w D w E Cov(r D; r E ) = = w D D + w E E + w D w E D E = = (w D D + w E E ) If D;E =! Cov(r D ; r E ) = ; then the portfolio variance becomes that is, P = wd D + w E E P = w D D + w E E + w D w E Cov(r D; r E ) = = w D D + w E E + = = w D D + w E E If D;E =! Cov(r D ; r E ) = D E ; then the portfolio variance becomes and P = abs(w D D by setting that is, we are left with and P = w D D + w E E + w D w E Cov(r D; r E ) = = w D D + w E E w D w E D E = = (w D D w E E ) w E E ): In this case, a perfectly hedging portfolio can be obtained P = abs(w D D w E E ); P = w D D w E E ; P = w E E w D D : In general, the variance of the portfolio expressed as P = w D D + w E E + w D w E Cov(r D; r E ); if we replace w D = w E ; can be rewritten as follows: P = D + w E D w E D + w E E + w E Cov(r D; r E ) w ECov(r D; r E ): If we plot the relationship between standard deviation of the portfolio ( P ) and the proportion of wealth allocated to equity for alternative correlation coe cients, D;E, we obtain 3
4 Spring 6 sigma_p Solid line: DE = Dots line: DE = Circle line: DE = w_e Notice that if all income is allocated to Debt (w E = ) the volatility of the portfolio is that of Debt, whereas if all income is allocated to Equity (w E = ); then the volatility of the portfolio is that of Equity. Then, depending on the correlation coe cient between these two assets we get di erent combinations between w E and P : When DE = (solid line), there is no room for reducing risk by diversi cation. When DE = (dotted line) some risk reduction is possible and this is shown in the shape of the curve. The highest risk reduction is achieved when DE = (circle line) in fact, portfolio volatility can be completely reduced. In our example, this would happen when w E is roughly around :4; and therefore w D is approximately :6: We will compute this optimal allocation later. Computing the minimum variance portfolio Taking the formula of the variance of the portfolio P = D + w E D w E D + w E E + w E Cov(r D; r E ) w ECov(r D; r E ): Which proportion of assets should we choose in order to minimize this variance? Derive P with respect to w E d P dw E = w E D D + w E E + Cov(r D; r E ) 4w E Cov(r D; r E ) = ; that is, w E = D Cov(r D; r E ) D + E Cov(r D; r E ) : 4
5 Spring 6 Notice that when D;E =! Cov(r D ; r E ) = D E ; this equation collapses to In general, w E = D + D E D + E + D E = D( D + E ) ( D + E ) = w E = D D;E D E D + E Cov(r D; r E ) : D D + E : If we apply this to the numbers in our example we obtain P = D + we D + E Cov(r D; r E ) D Cov(r D; r E ) w E ; the minimum variance is attained at that is, d P dw E = w E D + E D;E D E D D;E D E = ; we D D;E D E = D + = 44 4 D;E = 9 5 D;E ; E D;E D E D;E 34 3 D;E then depending on D;E we obtain di erent optimal allocations The riskreturn tradeo D;E =! w E = :5! w E = D;E =! w E = 6:47% D;E =! w E = 37:5% D;E = :9! w E = 64:8! w E = D;E = :3! w E = 8%; then w D = 8% Now, we can put together all the relationships between risk and return, since and given the standard deviation in general E(r P ) = :8 + :5w E ; P = D + w E D + E Cov(r D; r E ) D Cov(r D; r E ) w E ; we could solve for the relationship between expected return and risk, the result is 5
6 Spring 6 E[r_P] sigma_p In the gure, the gross solid line refers to the case D;E = ; the circle line is for D;E = ; the dotted line is for the case D;E = ; and nally, the thin solid line refers to the numerical example D;E = :3: 6
Lesson 5. Risky assets
Lesson 5. Risky assets Prof. Beatriz de Blas May 2006 5. Risky assets 2 Introduction How stock markets serve to allocate risk. Plan of the lesson: 8 >< >: 1. Risk and risk aversion 2. Portfolio risk 3.
More information1 Capital Allocation Between a Risky Portfolio and a RiskFree Asset
Department of Economics Financial Economics University of California, Berkeley Economics 136 November 9, 2003 Fall 2006 Economics 136: Financial Economics Section Notes for Week 11 1 Capital Allocation
More informationCAPM, Arbitrage, and Linear Factor Models
CAPM, Arbitrage, and Linear Factor Models CAPM, Arbitrage, Linear Factor Models 1/ 41 Introduction We now assume all investors actually choose meanvariance e cient portfolios. By equating these investors
More informationDiversification and the RiskReturn TradeOff
Diversification and the RiskReturn TradeOff Dr. Patrick Toche References : Zvi Bodie, Alex Kane, Alan Marcus, Investments, McGrawHill/Irwin. The relevant chapters of this textbook will be followed closely
More informationCapital Asset Pricing Model Homework Problems
Capital Asset Pricing Model Homework Problems Portfolio weights and expected return 1. Consider a portfolio of 300 shares of firm A worth $10/share and 50 shares of firm B worth $40/share. You expect a
More informationCapital Allocation Between The Risky And The Risk Free Asset. Chapter 7
Capital Allocation Between The Risky And The Risk Free Asset Chapter 7 Investment Decisions capital allocation decision = choice of proportion to be invested in riskfree versus risky assets asset allocation
More informationExercise Sheet 4. X r p
Exercise Sheet 4 Exercise The table rovides data on the return and standard deviation for di erent comositions of a twoasset ortfolio. Plot the data to obtain the ortfolio frontier. Where is the minimum
More informationAnswers to Concepts in Review
Answers to Concepts in Review 1. A portfolio is simply a collection of investments assembled to meet a common investment goal. An efficient portfolio is a portfolio offering the highest expected return
More informationFour Derivations of the Black Scholes PDE by Fabrice Douglas Rouah www.frouah.com www.volopta.com
Four Derivations of the Black Scholes PDE by Fabrice Douglas Rouah www.frouah.com www.volopta.com In this Note we derive the Black Scholes PDE for an option V, given by @t + 1 + rs @S2 @S We derive the
More informationLecture 1: Asset Allocation
Lecture 1: Asset Allocation Investments FIN460Papanikolaou Asset Allocation I 1/ 62 Overview 1. Introduction 2. Investor s Risk Tolerance 3. Allocating Capital Between a Risky and riskless asset 4. Allocating
More informationCHAPTER 7: OPTIMAL RISKY PORTFOLIOS
CHAPTER 7: OPTIMAL RIKY PORTFOLIO PROLEM ET 1. (a) and (e).. (a) and (c). After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash and real estate.
More information1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises.
1. Solutions to PS 1: 1. a. (iv) b. (ii) [6.75/(1.34) = 10.2] c. (i) Writing a call entails unlimited potential losses as the stock price rises. 7. The bill has a maturity of onehalf year, and an annualized
More informationCHAPTER 6 RISK AND RISK AVERSION
CHAPTER 6 RISK AND RISK AVERSION RISK AND RISK AVERSION Risk with Simple Prospects Risk, Speculation, and Gambling Risk Aversion and Utility Values Risk with Simple Prospects The presence of risk means
More informationPortfolio Performance Measures
Portfolio Performance Measures Objective: Evaluation of active portfolio management. A performance measure is useful, for example, in ranking the performance of mutual funds. Active portfolio managers
More informationCHAPTER 6: RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS
CHAPTER 6: RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS PROBLEM SETS 1. (e). (b) A higher borrowing is a consequence of the risk of the borrowers default. In perfect markets with no additional
More informationInvestment Analysis (FIN 670) Fall 2009. Homework 5
Investment Analysis (FIN 670) Fall 009 Homework 5 Instructions: please read careully You should show your work how to get the answer or each calculation question to get ull credit The due date is Tuesday,
More informationLecture 2: Delineating efficient portfolios, the shape of the meanvariance frontier, techniques for calculating the efficient frontier
Lecture 2: Delineating efficient portfolios, the shape of the meanvariance frontier, techniques for calculating the efficient frontier Prof. Massimo Guidolin Portfolio Management Spring 2016 Overview The
More informationSolution: The optimal position for an investor with a coefficient of risk aversion A = 5 in the risky asset is y*:
Problem 1. Consider a risky asset. Suppose the expected rate of return on the risky asset is 15%, the standard deviation of the asset return is 22%, and the riskfree rate is 6%. What is your optimal position
More informationWel Dlp Portfolio And Risk Management
1. In case of perfect diversification, the systematic risk is nil. Wel Dlp Portfolio And Risk Management 2. The objectives of investors while putting money in various avenues are: (a) Safety (b) Capital
More informationLecture 2: Equilibrium
Lecture 2: Equilibrium Investments FIN460Papanikolaou Equilibrium 1/ 33 Overview 1. Introduction 2. Assumptions 3. The Market Portfolio 4. The Capital Market Line 5. The Security Market Line 6. Conclusions
More informationChapter 10. Chapter 10 Topics. Recent Rates
Chapter 10 Introduction to Risk, Return, and the Opportunity Cost of Capital Chapter 10 Topics Rates of Return Risk Premiums Expected Return Portfolio Return and Risk Risk Diversification Unique & Market
More informationFinal Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator
University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights
More informationLecture 9: Violation of the classical assumptions
Lecture 9: Violation of the classical assumptions Overview Last week we looked at the output from Excel s regression package. how to test the hypothesis that b = 0 in the equation We learned under the
More informationRISKS IN MUTUAL FUND INVESTMENTS
RISKS IN MUTUAL FUND INVESTMENTS Classification of Investors Investors can be classified based on their Risk Tolerance Levels : Low Risk Tolerance Moderate Risk Tolerance High Risk Tolerance Fund Classification
More informationThe Capital Asset Pricing Model
Finance 400 A. Penati  G. Pennacchi The Capital Asset Pricing Model Let us revisit the problem of an investor who maximizes expected utility that depends only on the expected return and variance (or standard
More informationFin 3710 Investment Analysis Professor Rui Yao CHAPTER 6: EFFICIENT DIVERSIFICATION
HW 4 Fin 3710 Investment Analysis Professor Rui Yao CHAPTER 6: EFFICIENT DIVERIFICATION 1. E(r P ) = (0.5 15) + (0.4 10) + (0.10 6) = 1.1% 3. a. The mean return should be equal to the value comuted in
More informationFund Manager s Portfolio Choice
Fund Manager s Portfolio Choice Zhiqing Zhang Advised by: Gu Wang September 5, 2014 Abstract Fund manager is allowed to invest the fund s assets and his personal wealth in two separate risky assets, modeled
More informationCapital Asset Pricing Model. Joel Barber. Department of Finance. Florida International University. Miami, FL 33199
Capital Asset Pricing Model Joel Barber Department of Finance Florida International University Miami, FL 33199 Capital Asset Pricing Model Meanvariance efficient risky portfolio For each asset j =1, 2,...,
More informationDistinction Between Interest Rates and Returns
Distinction Between Interest Rates and Returns Rate of Return RET = C + P t+1 P t =i c + g P t C where: i c = = current yield P t g = P t+1 P t P t = capital gain Key Facts about Relationship Between Interest
More informationOptimal Risky Portfolios Chapter 7 Investments Bodie, Kane and Marcus
Optimal Risky ortfolios Section escription 7.0 Introduction 7.1 iversification and ortfolio Risk 7. ortfolios of Two Risky Assets 7.3 Asset Allocation with Stocks, Bonds and Bills 7.4 The Markowitz ortfolio
More informationMidterm Exam:Answer Sheet
Econ 497 Barry W. Ickes Spring 2007 Midterm Exam:Answer Sheet 1. (25%) Consider a portfolio, c, comprised of a riskfree and risky asset, with returns given by r f and E(r p ), respectively. Let y be the
More informationCHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM)
CHAPTER 10 RISK AND RETURN: THE CAPITAL ASSET PRICING MODEL (CAPM) Answers to Concepts Review and Critical Thinking Questions 1. Some of the risk in holding any asset is unique to the asset in question.
More informationMeanVariance Portfolio Analysis and the Capital Asset Pricing Model
MeanVariance Portfolio Analysis and the Capital Asset Pricing Model 1 Introduction In this handout we develop a model that can be used to determine how a riskaverse investor can choose an optimal asset
More informationAFM 472. Midterm Examination. Monday Oct. 24, 2011. A. Huang
AFM 472 Midterm Examination Monday Oct. 24, 2011 A. Huang Name: Answer Key Student Number: Section (circle one): 10:00am 1:00pm 2:30pm Instructions: 1. Answer all questions in the space provided. If space
More informationINVESTING IN HIGH RISKRETURN MUTUAL FUNDS: IS IT WORTH THE RISK?
INVESTING IN HIGH RISKRETURN MUTUAL FUNDS: IS IT WORTH THE RISK? Dr. Jeffrey Manzi The University of North Texas at Dallas dr.jamanzi@gmail.com Dr. David Rayome Northern Michigan University drayome@nmu.edu
More informationThe Cyclical Behavior of Debt and Equity Finance Web Appendix
The Cyclical Behavior of Debt and Equity Finance Web ppendix Francisco B. Covas and Wouter J. Den Haan December 15, 2009 bstract This appendix gives details regarding the construction of the data set and
More informationCIGX, LLC WHITE PAPER
CIGX, LLC WHITE PAPER WHAT IS CIGX AND WHAT DOES IT MEAN TO YOU? CIGX IS THE FORMULA FOR WEALTH In economic terms, CIGX is the mathematical formula for wealth or economic output (E), also known as gross
More informationModeling Portfolios that Contain Risky Assets Portfolio Models I: Portfolios with RiskFree Assets
Modeling Portfolios that Contain Risky Assets Portfolio Models I: Portfolios with RiskFree Assets C. David Levermore University of Maryland, College Park Math 420: Mathematical Modeling January 9, 2013
More informationUNDERSTANDING THE CHARACTERISTICS OF YOUR PORTFOLIO
UNDERSTANDING THE CHARACTERISTICS OF YOUR PORTFOLIO Although I normally use this space to ruminate about various economic indicators and their implications, smartly advancing asset prices have encouraged
More information1 Portfolio mean and variance
Copyright c 2005 by Karl Sigman Portfolio mean and variance Here we study the performance of a oneperiod investment X 0 > 0 (dollars) shared among several different assets. Our criterion for measuring
More informationEcon 422 Summer 2006 Final Exam Solutions
Econ 422 Summer 2006 Final Exam Solutions This is a closed book exam. However, you are allowed one page of notes (doublesided). Answer all questions. For the numerical problems, if you make a computational
More informationChapter 7 Portfolio Theory and Other Asset Pricing Models
Chapter 7 Portfolio Theory and Other sset Pricing Models NSWERS TO ENDOFCHPTER QUESTIONS 71 a. portfolio is made up of a group of individual assets held in combination. n asset that would be relatively
More informationChapter 7 Risk and Return: Portfolio Theory and Asset Pricing Models ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 7 Risk and Return: Portfolio Theory and Asset Pricing odels ANSWERS TO ENDOFCHAPTER QUESTIONS 71 a. A portfolio is made up of a group of individual assets held in combination. An asset that
More informationSample Problems. Lecture Notes Equations with Parameters page 1
Lecture Notes Equations with Parameters page Sample Problems. In each of the parametric equations given, nd the value of the parameter m so that the equation has exactly one real solution. a) x + mx m
More information2. Meanvariance portfolio theory
2. Meanvariance portfolio theory (2.1) Markowitz s meanvariance formulation (2.2) Twofund theorem (2.3) Inclusion of the riskfree asset 1 2.1 Markowitz meanvariance formulation Suppose there are N
More informationLongTerm Debt Pricing and Monetary Policy Transmission under Imperfect Knowledge
LongTerm Debt Pricing and Monetary Policy Transmission under Imperfect Knowledge Stefano Eusepi, Marc Giannoni and Bruce Preston The views expressed are those of the authors and are not necessarily re
More informationMean Variance Analysis
Mean Variance Analysis Karl B. Diether Fisher College of Business Karl B. Diether (Fisher College of Business) Mean Variance Analysis 1 / 36 A Portfolio of Three Risky Assets Not a two risky asset world
More informationCFA Examination PORTFOLIO MANAGEMENT Page 1 of 6
PORTFOLIO MANAGEMENT A. INTRODUCTION RETURN AS A RANDOM VARIABLE E(R) = the return around which the probability distribution is centered: the expected value or mean of the probability distribution of possible
More informationEnhancing the Teaching of Statistics: Portfolio Theory, an Application of Statistics in Finance
Page 1 of 11 Enhancing the Teaching of Statistics: Portfolio Theory, an Application of Statistics in Finance Nicolas Christou University of California, Los Angeles Journal of Statistics Education Volume
More informationThe Capital Asset Pricing Model. Capital Budgeting and Corporate Objectives
The Capital Asset Pricing odel Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Overview Utility and risk aversion» Choosing efficient
More informationHomogeneity Learners grouped in one kind of educational institution are perceived to be similar and therefore get the same treatment. Heterogeneity Learners are perceived to be di erent. Adjustments are
More informationThis paper is not to be removed from the Examination Halls
~~FN3023 ZA d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON FN3023 ZA BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences,
More informationReview for Exam 2. Instructions: Please read carefully
Review for Exam 2 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems You are not responsible for any topics that are not covered in the lecture note
More informationGESTÃO FINANCEIRA II PROBLEM SET 3  SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE
GESTÃO FINANCEIRA II PROBLEM SET 3  SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 010011 Chapter 10 Capital Markets and the Pricing of Risk 101.
More informationLife Cycle Asset Allocation A Suitable Approach for Defined Contribution Pension Plans
Life Cycle Asset Allocation A Suitable Approach for Defined Contribution Pension Plans Challenges for defined contribution plans While Eastern Europe is a prominent example of the importance of defined
More informationC C D E C C D E C C D E C C D E C C C Figure 1: Distribution of of s Density 0 1 2 2 4 3 6 4 5 8 4 2 0 0 2 4.5 Fraction of Applications Approved 0.2.4.6.8 1 Figure 2: The CreditScore Regression
More informationThe Term Structure of the Risk Return Tradeoff
The Term Structure of the Risk Return Tradeoff Luis M. Viceira Harvard Business School Netspar Opening Conference Tilburg University Tilburg, March 2005 New Research on Asset Allocation Portfolio choice
More informationCHAPTER 9: THE CAPITAL ASSET PRICING MODEL
CHAPTER 9: THE CAPITAL ASSET PRICING MODEL PROBLEM SETS 1. E(r P ) = r f + β P [E(r M ) r f ] 18 = 6 + β P(14 6) β P = 12/8 = 1.5 2. If the security s correlation coefficient with the market portfolio
More informationMidTerm Spring 2003
MidTerm Spring 2003 1. (1 point) You want to purchase XYZ stock at $60 from your broker using as little of your own money as possible. If initial margin is 50% and you have $3000 to invest, how many shares
More information1. Portfolio Returns and Portfolio Risk
Chapter 8 Risk and Return: Capital Market Theory Chapter 8 Contents Learning Objectives 1. Portfolio Returns and Portfolio Risk 1. Calculate the expected rate of return and volatility for a portfolio of
More informationPutCall Parity. chris bemis
PutCall Parity chris bemis May 22, 2006 Recall that a replicating portfolio of a contingent claim determines the claim s price. This was justified by the no arbitrage principle. Using this idea, we obtain
More informationOptimal portfolio selection in a ValueatRisk framework
Journal of Banking & Finance 25 2001) 1789±1804 www.elsevier.com/locate/econbase Optimal portfolio selection in a ValueatRisk framework Rachel Campbell, Ronald Huisman, Kees Koedijk * Department of Business
More information1 Pricing options using the Black Scholes formula
Lecture 9 Pricing options using the Black Scholes formula Exercise. Consider month options with exercise prices of K = 45. The variance of the underlying security is σ 2 = 0.20. The risk free interest
More informationCHAPTER 2 POPULATION FORECASTING
CHAPTER 2 POPULATION FORECASTING Since the water supply systems are designed for a certain design period, instead of present population, population expected in the design period must be considered in the
More informationEconomics 140A Identification in Simultaneous Equation Models Simultaneous Equation Models
Economics 140A Identification in Simultaneous Equation Models Simultaneous Equation Models Our second extension of the classic regression model, to which we devote two lectures, is to a system (or model)
More informationHolding Period Return. Return, Risk, and Risk Aversion. Percentage Return or Dollar Return? An Example. Percentage Return or Dollar Return? 10% or 10?
Return, Risk, and Risk Aversion Holding Period Return Ending Price  Beginning Price + Intermediate Income Return = Beginning Price R P t+ t+ = Pt + Dt P t An Example You bought IBM stock at $40 last month.
More informationPortfolio Analysis. M. Kateregga
Portfolio Analysis M. Kateregga November 21, 2014 @ AIMS South Africa Outline Introduction The Optimization Problem Return of a Portfolio Variance of a Portfolio Portfolio Optimization in nstocks case
More informationBS2551 Money Banking and Finance. Institutional Investors
BS2551 Money Banking and Finance Institutional Investors Institutional investors pension funds, mutual funds and life insurance companies are the main players in securities markets in both the USA and
More informationThe CAPM (Capital Asset Pricing Model) NPV Dependent on Discount Rate Schedule
The CAPM (Capital Asset Pricing Model) Massachusetts Institute of Technology CAPM Slide 1 of NPV Dependent on Discount Rate Schedule Discussed NPV and time value of money Choice of discount rate influences
More informationChapter 2 Portfolio Management and the Capital Asset Pricing Model
Chapter 2 Portfolio Management and the Capital Asset Pricing Model In this chapter, we explore the issue of risk management in a portfolio of assets. The main issue is how to balance a portfolio, that
More informationThese charts identify short term trends in benchmark relative performance and risk.
The Government Pension Global The Government Pension was established on 1 st January 6. The Government Pension comprises: The Government Pension Global (previously the Government Petroleum, established
More information1 Capital Asset Pricing Model (CAPM)
Copyright c 2005 by Karl Sigman 1 Capital Asset Pricing Model (CAPM) We now assume an idealized framework for an open market place, where all the risky assets refer to (say) all the tradeable stocks available
More informationHow Many Days Equal A Year? Nontrivial on the MeanVariance Model
How Many Days Equal A Year? Nontrivial on the MeanVariance Model George L. Ye, Dr. Sobey School of Business Saint Mary s University Halifax, Nova Scotia, Canada Christine Panasian, Dr. Sobey School of
More informationExecutive Summary of Finance 430 Professor VissingJørgensen Finance 43062/63/64, Winter 2011
Executive Summary of Finance 430 Professor VissingJørgensen Finance 43062/63/64, Winter 2011 Weekly Topics: 1. Present and Future Values, Annuities and Perpetuities 2. More on NPV 3. Capital Budgeting
More informationINTERNATIONAL COMPARISON OF INTEREST RATE GUARANTEES IN LIFE INSURANCE
INTERNATIONAL COMPARISON OF INTEREST RATE GUARANTEES IN LIFE INSURANCE J. DAVID CUMMINS, KRISTIAN R. MILTERSEN, AND SVEINARNE PERSSON Abstract. Interest rate guarantees seem to be included in life insurance
More informationModels of Risk and Return
Models of Risk and Return Aswath Damodaran Aswath Damodaran 1 First Principles Invest in projects that yield a return greater than the minimum acceptable hurdle rate. The hurdle rate should be higher for
More informationMulti Asset Portfolio: Backtesting Report
Multi Asset Portfolio: Backtesting Report Report Prepared for the Hamilton Investment Fund This analysis has been undertaken by Dr Paul Docherty to verify the performance and risk of the Multi Asset Portfolio
More informationEconS 330, Fall 2013 Homework #1: Due September 13th ANSWER KEY
EconS 330, Fall 013 Homework #1: Due September 13th ANSWER KEY Instructor: Ana Espinola, anaespinola@wsu.edu O ce hours: Tuesdays 3.004.00pm, or by appointment 1 Question #115 Points Serious problems
More informationFinancialInstitutions Management
Solutions 3 Chapter 11: Credit Risk Loan Pricing and Terms 9. County Bank offers oneyear loans with a stated rate of 9 percent but requires a compensating balance of 10 percent. What is the true cost
More informationAuke Plantinga and Sebastiaan de Groot 1. November 2001. SOMtheme E: Financial markets and institutions
5,6.$'867('3(5)250$1&(0($685(6 $1',03/,('5,6.$77,78'(6 Auke Plantinga and Sebastiaan de Groot 1 November 2001 SOMtheme E: Financial markets and institutions $EVWUDFW In this article we study the relation
More informationThis is the tradeoff between the incremental change in the risk premium and the incremental change in risk.
I. The Capital Asset Pricing Model A. Assumptions and implications 1. Security markets are perfectly competitive. a) Many small investors b) Investors are price takers. Markets are frictionless a) There
More informationFinancial Econometrics Jeffrey R. Russell Final Exam
Name Financial Econometrics Jeffrey R. Russell Final Exam You have 3 hours to complete the exam. Use can use a calculator. Try to fit all your work in the space provided. If you find you need more space
More informationChapter 7 Risk, Return, and the Capital Asset Pricing Model
Chapter 7 Risk, Return, and the Capital Asset Pricing Model MULTIPLE CHOICE 1. Suppose Sarah can borrow and lend at the risk freerate of 3%. Which of the following four risky portfolios should she hold
More informationREAL ESTATE PORTFOLIO MANAGEMENT & ASSET ALLOCATION
REAL ESTATE PORTFOLIO MANAGEMENT & ASSET ALLOCATION BIBF plays a vital role in the training and development of human capital in the Middle East and North Africa. Our commitment to excellence has strengthened
More informationThe CAPM & Multifactor Models
The CAPM & Multifactor Models Business Finance 722 Investment Management Professor Karl B. Diether The Ohio State University Fisher College of Business Review and Clarification In the last few lectures
More information1. The Classical Linear Regression Model: The Bivariate Case
Business School, Brunel University MSc. EC5501/5509 Modelling Financial Decisions and Markets/Introduction to Quantitative Methods Prof. Menelaos Karanasos (Room SS69, Tel. 018956584) Lecture Notes 3 1.
More informationPositive Weights on the Efficient Frontier
Positive Weights on the Efficient Frontier Phelim Boyle Wilfrid Laurier University August 2012 Acknowledgments This paper is dedicated to Boyle s Winter 2012 graduate finance class at Wilfrid Laurier University
More informationDebt Finance Requests
Chapter 4 Debt Finance Requests A full set of tables is available in the Statistical Tables section. Please view Tables 1 to 8 in conjunction with this chapter. 4.1 Requests for debt finance Thirtyfour
More informationTax Management REPORT
Tax Management Transfer Pricing Report REPORT Reproduced with permission from Tax Management Transfer Pricing Report, 13 TMTR 878, 12/22/2004. Copyright 2004 by The Bureau of National Affairs, Inc. (8003721033)
More informationFTS Real Time System Project: Portfolio Diversification Note: this project requires use of Excel s Solver
FTS Real Time System Project: Portfolio Diversification Note: this project requires use of Excel s Solver Question: How do you create a diversified stock portfolio? Advice given by most financial advisors
More informationThe Behavior of Bonds and Interest Rates. An Impossible Bond Pricing Model. 780 w Interest Rate Models
780 w Interest Rate Models The Behavior of Bonds and Interest Rates Before discussing how a bond marketmaker would deltahedge, we first need to specify how bonds behave. Suppose we try to model a zerocoupon
More informationLESSON 29: MARKOWITZ MODEL
LESSON 29: MARKOWITZ MODEL Harry M. Morkowitz is credited with introducing new concepts of risk measurement and their application to the selection of portfolios. He started with the idea of risk aversion
More informationEquity Risk Premiums: Looking backwards and forwards
Equity Risk Premiums: Looking backwards and forwards Aswath Damodaran Aswath Damodaran 1 What is the Equity Risk Premium? Intuitively, the equity risk premium measures what investors demand over and above
More informationInstructor s Manual Chapter 12 Page 144
Chapter 12 1. Suppose that your 58yearold father works for the Ruffy Stuffed Toy Company and has contributed regularly to his companymatched savings plan for the past 15 years. Ruffy contributes $0.50
More informationRisk Budgeting: Concept, Interpretation and Applications
Risk Budgeting: Concept, Interpretation and Applications Northfield Research Conference 005 Eddie Qian, PhD, CFA Senior Portfolio Manager 60 Franklin Street Boston, MA 00 (67) 439637 7538 8//005 The Concept
More informationskiena
Lecture 19: The Capital Assets Pricing Model Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena The Capital Asset Pricing
More informationThe Cost of Equity in Latin America
Working Paper Nº 12 The Cost of Equity in Latin America Martin Grandes, Demian Panigo and Ricardo Pasquini December 2005 The Cost of Equity in Latin America Martin Grandes The American University of Paris
More informationChapter 9 Interest Rates
Chapter 9 Interest Rates Concept Questions 1. Shortterm rates have ranged between zero and 14 percent. Longterm rates have fluctuated between about two and 13 percent. Longterm rates, which are less
More informationThis paper is not to be removed from the Examination Halls
~~FN3023 ZB d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON FN3023 ZB BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences,
More information