SCHOOL OF BANKING & FINANCE

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1 COURSE OBJECTIVES SCHOOL OF BANKING & FINANCE FINS3640 INVESTMENT MANAGEMENT MODELLING Course Outline for Session 2, 2005 This course covers the essential analytical and quantitative tools applied in the investment management industry. The course aims to provide students with the knowledge and skills required to construct and manage portfolios of financial securities. The course examines both index funds and actively managed portfolios, the mix of different types of assets in portfolios, and the role of derivative securities in portfolio management. The course covers portfolio theory, investment analysis, quantitative analysis, factor models and portfolio risk management. An essential component of this course involves the use of software programs (MS-Excel and Barra) in applying concepts to the real-world market environment. PREREQUISITES It is the responsibility of students to ensure the prerequisites have been met before commencing this course. The prerequisite is FINS2624 Portfolio Management. While some knowledge of options and futures is assumed, it is not necessary (although recommended) that students have undertaken FINS3635 Options, Futures and Risk Management. LECTURERS Lecturer Consultation Time Office Location Teaching Weeks Dr. Thomas Henker CFA TBA QUAD3023B 1 7 Dr Henry Yip* TBA h.yip@unsw.edu.au QUAD * Lecturer-in-Charge LECTURES AND TUTORIALS The course consists of one (1) two-hour lecture and one (1) one-hour tutorial. Lectures are conducted between 13:00 and 15:00 on Tuesdays during session at CLB 8. Tutorial times and locations are available from the School s web page under timetable. A 1

2 hard copy of the class times and venues is also posted to the noticeboard outside the School s office on the 3 rd floor of the Quadrangle building. Tutorial allocation is done by TAS. Tutorials are an important extension of lectures for FINS3640, and will provide students with practical skills and the ability to apply theory to real-world problems. The structure of tutorials will involve a selection of problems (listed in the Tutorial Program) from the course prescribed and recommended books by Farrell, Benninga, and Hull, as well as a discussion of selected literature from finance journals listed in the course outline. A number of supplementary questions are also provided. Prior to the tutorial class, students are expected to have attempted the problems. Students are also expected to show and/or submit their work to their tutor prior to the tutorial commencing. During the tutorial class, students are expected to participate in tutorial discussions, understand the approach used to solve the problems, and check the suggested solutions against their own work. Students who still have doubts about any problem after a tutorial class should see their tutor during his/her consultation hours for further explanation and clarification. LECTURE OUTLINE* Week Date Topic 1 26 Jul Introduction & Portfolio Theory 2 2 Aug Portfolio Theory & Application 3 9 Aug Financial Models I CAPM & SIM 4 16 Aug Financial Models II CAPM & SIM 5 23 Aug APT, Index Tracking & Investment Performance Evaluation 6 30 Aug Barra Software demonstration 7 6 Sep Mid Session Examination 8 13 Sep Asset Management Strategies (AMS) 9 20 Sep AMS; Futures in Asset Management (FAM) - - Mid Session Recess 10 4 Oct FAM; Protective Put Strategies Oct Black-Scholes Model Oct Portfolio Insurance I Oct Portfolio Insurance II 14 1 Nov Review - - Final Examination TUTORIAL OUTLINE* 2

3 Week Tutorial Topic Covered 1 NO TUTORIALS 2 Introduction & Portfolio Theory 3 Portfolio Theory & Application 4 Financial Models CAPM & SIM 5 Financial Models CAPM & SIM 6 APT, Index Tracking & Investment Performance Evaluation 7 NO TUTORIALS 8 NO TUTORIALS 9 Asset Management Strategies (AMS) 10 AMS; Futures in Asset Management (FAM) 11 FAM; Protective Put Strategies 12 Black-Scholes Model 13 Portfolio Insurance I 14 Portfolio Insurance II * The lecture and tutorial outlines are subject to change without prior notice. Students will be able to download the lecture slides from the course web page prior the relevant lecture, at the discretion of the lecturer. COURSE ASSESSMENT Assessment % Tutorial 5 Assignment Mid-Session Exam 27.5 Assignment 2 10 Final Examination 40 Total Students must form groups of either 2 or 3 people for the assignments. Both assignments are available from WEBCT on FINS3640 web page. The mid-session exam is based on lecture materials taught in weeks 1-6. The final exam is based on lecture materials taught in weeks FAILURE TO ATTEND AN EXAMINATION Students should notify employers of the requirement to attend examinations. If you miss any of the class tests (for any reason - employment, sickness, timetable clashes etc.), then in exceptional circumstances you may be permitted to sit the missed section at a future date when the school offers 3

4 supplementary examinations. You should talk with the lecturer about this beforehand if you are in doubt. If you are enrolled in class, you are expected to take scheduled examinations. Failure to attend does not automatically lead to re-assessment. USE OF ELECTRONIC CALCULATORS DURING CLASS EXAMINATIONS Students may use their own electronic/scientific calculator for examination purposes. It is to have functionality not significantly different in sophistication to a CASIO-FX80, which is the standard adopted by UNSW. Note that financial calculators, hand-held computers, Apple Newtons, personal information managers or devices with a full alpha-numeric keypad or with character recognition are strictly prohibited. Failure to follow this requirement and use of an unprescribed aid during an examination is a serious offence and will be regarded as academic misconduct. If you are unsure about the calculator you use please come and discuss this with the lecturer prior to the day of the examination. CLASS ANNOUNCEMENTS AND LECTURE MATERIALS You will be able to obtain the latest announcements and course materials via the FINS 3640 web page. This includes notification of interim assessment results. The web page can be accessed via WEBCT at the following address: REQUIRED TEXT AND READINGS Benninga, S. (2000), Financial Modeling, MIT Press (2 nd edition) Farrell, J.L.jr (1997), Portfolio Management: Theory & Application, McGraw-Hill. Lecture notes and supplementary materials: These will be made available on the course website REFERENCE BOOKS Bodie, Z., Kane, A., A.J. Marcus, Investments, 5 th edition, Irwin Publishers Grinold, R., Kahn, R., Active Portfolio Management, 2 nd Edition, McGraw-Hill Hull, J., Options, Futures and Other Derivative Securities, 5 th edition, Prentice Hall. Reilly and Brown, Investment Analysis and Portfolio Management, 5 th or 6 th edition, Dryden Press. COURSE FORMAT Lectures will be presented as a mix of theory, computer demonstrations, and practical exercises. The computer demonstrations aim to give students the opportunity to learn how to solve problems in relation to lecture material, as well as the problems encountered in the assignments. Students will benefit from reading lecture materials and prescribed readings before class and coming to class prepared to participate in class discussion. Please note that attendance at lectures, tutorials and examinations is required under the guidelines for the Bachelor of Commerce degree. INFORMATION CONCERNING STUDENT CONDUCT & RESPONSIBILITIES Students should be aware of general University, Faculty of Commerce and Economics, and School of Banking and Finance rules, of which are discussed in detail in the UNSW Undergraduate Handbook and on the Websites of the University, Faculty and School, in particular:

5 SPECIAL CONSIDERATION Students should refer to The University of New South Wales Calendar Procedures as well as policies concerning special consideration on the web. The website information is available as follows: Current Students Special Consideration & Supplementary Examination Policy Students must be familiar with the information outlined from both websites. As a first step, students must make a formal application submitted to NewSouth Q. You must have supporting (original) documentation (e.g. doctor s certificate). You must lodge your application within 3 working days of the event to which you are requesting special consideration. Students should be aware that minor ailments are not eligible grounds for special consideration. Any unsubstantiated request for special consideration will be considered to be minor. Special consideration requests should also not be viewed as an insurance policy by students. It is advised that students always make their best effort to meet the assessment requirements, including attendance of the examinations as best they are able. Students are expected to complete their work in a timely manner so that an illness in the last few days will not jeopardise the submission of an assignment. Such illness will not constitute grounds for special consideration. SUPPLEMENTARY EXAMINATIONS An application for special consideration does not guarantee an offer of supplementary examination and/or a pass in the subject. The Assessment Review Committee will decide on whether a supplementary examination is to be granted. The School s administrative officer will only contact students who are granted a supplementary examination. If a student is granted a supplementary examination but does not attend the supplementary examination, he/she will not be granted further assessment except in exceptional circumstances. Students are advised that if they are intend to travel overseas at the end of this session, they should consider taking out travel insurance which allows supplementary examinations as valid circumstances for cancelling travel. 5

6 Lecture Program Part 1 EQUITY PORTFOLIO MANAGEMENT Weeks 1-2: Portfolio Theory, Application and Quantitative Analysis - Covariance and correlation between stocks - Return and variance of a portfolio - Risk and return measurement - Diversification benefits and limits: unsystematic and systematic (market) risk - Optimal weights for each level of risk: the efficient frontier - Indifference curves of individual investors to choose the optimal portfolio - Matrix manipulation (theory and Excel) - Computing the efficient frontier in Excel Reading: Prescribed - Benninga Chapters 7-9, Farrell Chapters 1 and 2 Recommended - de Vassal (2001) Risk Diversification Benefits of Multiple-Stock Portfolios, Journal of Portfolio Management Recommended - Kritzman (1994), About Time Diversification Financial Analysts Journal Weeks 3-4: Single Index Model and CAPM - Introduction of the risk-free asset, Capital Market Line (CML) - Market portfolio on the efficient frontier - Assumptions underlying the Capital Asset Pricing Model (CAPM) - Valuation of (in)efficient portfolios: Security Market Line (SML) - Total risk (CML) versus systematic risk (SML) - Problems with the CAPM, e.g. what is the market? - Adjustments to CAPM: no risk-free asset, different borrowing/lending - Linear Regression (theory and Excel) - Estimation of beta: time-variation, measurement error, fundamental methods Reading: Prescribed - Benninga Chapters 10-11, Farrell Chapters 3 and 4 Prescribed - Markman, A whole lot of %&)^^% Weeks 5-6: Arbitrage Pricing Theory (APT), Index Tracking, Investment Performance Evaluation - Assumptions underlying the Arbitrage Pricing Theory (APT) - Barra - Multi-factor return generating process - Risk-adjustment of portfolio returns - Attribution of investment performance: Market Timing versus Stock Selection - Index tracking portfolios, tracking error measurement Reading: Prescribed - Rohweder (1998), Implementing Stock Selection Ideas: Does Tracking Error Optimisation Do Any Good?, Journal of Portfolio Management Recommended - Chan, Karceski, Lakonishok (1999), On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model, Review of Financial Studies Recommended - Roll (1992), A Mean/Variance Analysis of Tracking Error, Journal of Portfolio Management 6

7 ASSESSMENT For Part 1: First assignment - DUE week 6, Tuesday, 30 th August, 2005 (Assignment 1 - Questions available from WEBCT on FINS3640 web page) For each group, 1 paper hardcopy assignment to be submitted during lecture. Late submissions incur a 5-mark penalty per calendar day. MID-SESSION EXAMINATION:Week 7 - Tuesday 6 th September 2004 During lecture time (13:00-15:00) (based on lecture material Weeks 1-6) Part 2 ASSET MANAGEMENT Week 8: Asset Management Strategies - Active versus passive strategies - Disciplined stock selection, measuring predictive ability - Translating stock rankings into excess return forecasts The following topics are presented in week 9 - Long/Short strategies - Strategic and tactical asset allocation - Dynamic asset management: theory, practitioners approach, and academic suggestion Prescribed Reading: Farrell Chapters 8-9 Week 9: Futures in Asset Management - Marking-to-market and liquidity reserve - Futures pricing anomalies and tactical asset allocation - The role of futures in tactical asset allocation The following topic is presented in week 10 - The role of futures in active strategies including market timing, group rotation, and alpha capture Prescribed Reading: Farrell Chapter 12; Hull Chapters 2-4 Part 3 DERIVATIVES IN PORTFOLIO MANAGEMENT Week 10: Protective Put Strategies - Evaluating the performance of alternative protective put strategies Prescribed Reading: Figlewski et al. (1993), Evaluating the Performance of the Protective Put Strategy, Financial Analysts Journal, 49, July-August, pp , 69 Yip (2005), A Spreadsheet Application to Evaluate the Performance of Protective Puts, Working Paper, University of New South Wales Week 11: The Black-Scholes Model - Evaluating the performance of alternative protective put strategies - continued - The log-normal distribution - Monte Carlo simulation of stock prices - The Black-Scholes model for dividend paying stocks and index options Prescribed Reading: Benninga Chapters 15-16; Hull Chapters Week 12: Portfolio Insurance I - Portfolio insurance defined - The pros and cons regarding the use of listed put options for portfolio insurance 7

8 - The use of stocks and bonds to create a put option synthetically - The use of index futures to create an index put option synthetically - Ways to finance the put option borrowing money or selling shares on hand - Tracking the life of a listed put and a synthetic put Prescribed Reading: Benninga Chapter 17; Hull Chapters Week 13: Portfolio Insurance II - Dynamic hedging: tracking the life of a protective put that uses (i) a listed option, and (ii) a synthetic option - Insuring total portfolio returns: determining the optimal exercise price and number of puts - Portfolio insurance and share market crash Prescribed Reading: Benninga Chapter 17; Hull Chapters Second assignment DUE week 13 Tuesday, 25 th October 2005 (Assignment 2 Questions available from WEBCT on FINS3640 web page) For each group, 1 paper hardcopy assignment to be submitted during lecture. Late submissions incur a 5-mark penalty per calendar day. Week 14: Revision - Feedback on the 2 nd assignment - An overview and summary of the second part of the course 8

9 Tutorial Program: Week 2 Farrell Chapter 1 Questions 1, 3, 7, 8, 9 Supplementary Questions S1 What is risk? How is it measured? S2 Calculate (a) the expected return for each asset class and (b) the expected rate of return for an equally-weighted portfolio from the information below. Asset Sectors State of Economy Probability Telecommunciations Retail Gold Market Return Recession % 26.0% 13.0% -17.0% Below Average % 21.0% -8.0% -11.0% Average % 2.0% 6.0% 18.0% Above Average % -11.0% 40.0% 29.0% Boom % -10.0% 23.0% 38.0% S3 From the question above, (a) calculate the standard deviation of returns for each asset class and (b) the standard deviation of the portfolio return. S4 What is diversification and why is it important? What does portfolio theory say about diversification? S5 Calculate the covariance and correlations between the 4 asset classes using the information provided in question S2. S6 - Assume you have 2 stocks in a portfolio and are given the following information: Expected Returns: R1 = 0.09, R2 = 0.18 Standard Deviations: s1 = 0.04, s2 = 0.09 Correlation Coefficient r = -0.5 (a) Calculate the expected return, portfolio variance and portfolio standard deviation for 6 individual portfolios based on the portfolio weights of stock 1 varying as follows: 0%, 20%, 40%, 60%, 80%, 100%. (b) Chart the expected return and portfolio standard deviation for the portfolio weight combinations in (1) above. (c) Re-calculate your portfolio variance and portfolio standard deviations for all portfolios where the correlation coefficient varies as follows: +1, +0.5, 0, -0.5, -1. Chart your results. Week 3 Farrell Chapter 2 Questions 1, 3, 17, 20 Supplementary Questions: S1 - Assume all securities have the same standard deviation, s. Assume the covariance between any two stocks is the same, c. (a) Write the formula for the portfolio variance of an equally-weighted portfolio with n securities. (b) What is the risk of a portfolio if n is very large? (c) What is the risk of the portfolio if the correlation between all the assets is zero? 9

10 S2- Consider a three-asset world with the following parameters: r A =10% r B =12% r C =14% σ A 2 =0.3 σ B 2 =0.4 σ C 2 =0.6 σ AB =0.02 σ AC =-0.05 σ BC =0.06 Suppose you also have two portfolios with the following portfolio weights: Portfolio 1: w A =30%, w B =20%, w C =50% Portfolio 2: w A =50%, w B =40%, w C =10% (a) Translate the problem/information into matrix notation. (b) Calculate mean expected return and variance for each portfolio. (c) Calculate the covariance and the correlation coefficient of the portfolio s return. (d) Create a risk - return graph of convex combinations of the portfolios. S3 - Matrix Algebra: For the following matrices (a) Transpose Q and R (b) Calculate X=R T R (c) Calculate F=X+Q and G=X-Q (d) Calculate C=QR, D=RQ, E=R T Q (e) Calculate the inverse of Q 3 Q = 5 2 S4 What is the difference between discrete returns and continuously compounded returns? (Hint: See Benninga). Week 4 Benninga Chapter 7 Questions 1, 2, 3, 4; Benninga Chapter 9 Question 1 Farrell Chapter 3 Questions 1, 2, 5, 7 S1 Outline the most important issues raised by Markman in his article A whole lot of %&)^^%. Week 5 Benninga Chapter 8 1, 2. 3; Benninga Chapter 11 Questions 1, 2 Farrell Chapter 3 Questions 26, 34, 43; 44 Week 6 Farrell Chapter 4 Questions 1, 5, 7, 9, 11, 12, 14 Supplementary Questions: R = S1 What is the difference between market timing and stock selection? What are the measures that can be used to decompose the two components of active returns? 10

11 S2 What is the role of market indices in performance measurement? How might indices be constructed? S3 Why is the risk-adjustment process important in the measurement of performance? S4 Outline the most important points raised in the following articles: Chan, Karceski and Lakonishok (1999) Rohweder (1998) Weeks 7 & 8 NO TUTORIAL Week 9 Farrell Chapter 8 Questions 1, 5, 13, 14, 16. Week 10 Farrell Chapter 8 Questions 20, 21. Farrell Chapter 9 Questions 11, 12, 14. Farrell Chapter 12 Questions 14, 21. Note the following missing information in Farrell Chapter 12: For question 14, the volatility measure is missing. Assume that it is 17.5% p.a. Also assume that the index level is 475, same as the price of the index futures. Week 11 Farrell Chapter 12 Questions 12, Note the following missing information in Farrell Chapter 12: For question 12, the level of the index is needed to compute the value of asset underlying each futures contract. However, the question provides the index futures price. In your calculation, assume that the index value is the same as the price of the index futures. Question 23 does not inform users of the change in portfolio value after one year. Assume that the portfolio rises 4% to $10.4 million after one year. Supplementary questions: S1. Given S 0 = $10, X = $10, r = 5%, σ = 20%, the premium of a one-month put is $ and the cost of a two-month put is $ Suppose money is borrowed to buy puts, calculate the profit/loss of a) buying a two-month put today, and b) buying two consecutive one-month puts with the same exercise price at $10, two months later on the assumption that stock prices at the end of the first and second months are $8 and $9, respectively. Week 12 Benninga Chapter 16 Questions 4 and 7. For Question 4, you may construct a spreadsheet (similar to that used in Yip (2005) p. 201 Discussion Question C part (iii)) to compute a column of intrinsic values and a column of BS values of a put option using a range of exercise prices from 25.5 to 35 at 50-cent intervals, S = 30, t = 0.5, r f = 5% and σ = 20% to 11

12 infer the answer. For Question 7, calculate the price of a put option on the same stock index with the same exercise price and maturity instead. Supplementary questions: S1. Why do index fund managers prefer using put options on an index to insure their portfolios from adverse market movements to a bundle of options on individual stocks? Hull (5 th edition) Chapter 12, p. 258: 12.1 What does the Black-Scholes stock option pricing model assume about the probability distribution of the stock price in one year? What does it assume about the continuously compounded rate of return on the stock during the year? 12.2 The volatility of a stock is 30% per annum. What is the standard deviation of the proportional price change in one trading day (assuming 252 trading days in one year)? Week 13 Benninga Chapter 17 Question 1. Hull (5 th edition) Chapter 14, pp. 326: 14.9 (This question has been modified.) Suppose that a stock is currently $20 and that a put option with strike price $25 is created synthetically using a position in the stock that is changed frequently. Consider the following two scenarios: a) Stock price increases steadily from $20 to $35 during the life of the option. b) Stock price oscillates widely, ending up at $35. Which scenario would make the synthetically created option more expensive? Explain your answer. Supplementary questions: S1. In theory, a synthetic put should behave exactly like a listed put so that the two positions result in the same P/L on option expiration date. However, this is often not the case in practice. Explain. S2. Write down the Black-Scholes equation for a European put option written on an index. Based on this equation, if you would like to create a European put option written on an index synthetically, what is the composition of the portfolio? Alternatively, if you were to replicate the put option by creating a synthetic position that has the same delta as the listed put, what is the composition of the position? Week 14 Hull (5 th edition) Chapter 14, pp : 14.7 Why did portfolio insurance not work well on October 19, 1987? A fund manager has a well diversified portfolio that mirrors the performance of the S&P 500 and is worth $360 million. The value of the S&P 500 is 1200 and the portfolio manager would like to buy insurance against a reduction of more than 5% in the value of the portfolio over the next six months. The risk-free interest rate is 6% per annum. The dividend yield on both the portfolio and the S&P 500 is 3%, and the volatility of the index is 30% per annum. 12

13 a) If the fund manager buys traded European put options, how much would the insurance cost? (Hint: The portfolio value is 300,000 (360m/1,200) times that of the index. Since the portfolio mirrors the performance of the index, if the portfolio falls by 5%, the index will also fall by 5%. This implies an exercise price of 1140 (1200*0.95). As the size of one index put option is 100 times the index portfolio (refer to week 11 lecture on the product and contract specification of an index option), the manager needs to buy 3,000 index put option.) c) If the fund manager decides to provide insurance by keeping part of the portfolio in risk-free securities, what should the initial position be? d) If the fund manager decides to provide insurance by using nine-month index futures, what should the initial position be? Supplementary question: S1 Extending the previous question from Hull, suppose that a week later, the index value drops to How should the manager rebalance the futures position? Is the change in futures position expected? Why yes or why not? 13