Course Details for A.Y. 2018/2019

Course Objectives

The students quantitative and programming capabilities are applied to asset pricing and positive (economics) portfolio selection corporate finance modelling.

Course Content

• assets returns and risk; (a) how to compute an asset return, pages 9-13 (Lo and MacKinlay, 1999): i. discrete vs continuously compounded asset returns: ii. overlapping and non overlapping returns; iii. capital gains, dividend yields and return indexes; (b) expected returns and risk gauges, e.g. standard deviation, interquartile differences; (c) which distribution represents best stock returns, pages 13-20 (Lo and MacKinlay, 1999); (d) Market efficiency and returns predictability, chapter 2 (Lo and MacKinlay, 1999): i. testing the Random Walk Hypothesis: ii. returns prediction and trading rules; A. technical analysis; B. statistical learning and pattern recognition; (e) variability of pairs of stocks, covariance and Bravais Pearson correlation index; (f) linear relation between two stock returns and its estimation through ordinary least squares: regression line;
• diversication effects when only risky assets are available, (Markowitz, 1959) Portfolio Selection: (a) n = 2 risky stocks portfolio: i. minimum variance opportunity set; ii. efficient portfolios frontier; iii. global minimum risk portfolio; (b) n > 2 risky stocks portfolio: i. efficient portfolio for a given expected return; ii. how to choose among portfolios represented on the minimum variance opportunity set: A. (Markowitz, 1959) mean variance criteria; B. stochastic dominance criteria;  first order stochastic dominance;  second order stochastic dominance; C. indifference curves in the risk return space, marginal rate of transformation (supply), marginal rate of substitution (demand); for a  quadratic utility function;  logarithmic utility function; iii. Two Fund Separation Theorem, (Tobin, 1958) with risky assets only;
• some empirical guesses about Data Generating Processes of joint stock returns; (a) equally weighted portfolio experiment; (b) systematic vs idiosyncratic risk:  single index model;  market model; (c)  properties i.  additivity principle; ii. covariance and total risk, variance, of a portfolio; iii. covariance of two stocks expressed as a function of their j ; iv. partitioning of total risk, standard deviation of a stock in systematic and idiosyncratic risk, R2 and regression line;
• CAPM of Sharpe-Lintner-Mossin, (Sharpe, 1963), (Lintner, 1956), (Mossin, 1966); (a) assumptions; (b) a simple derivation of the Security Market Line; (c) about CAPM and market eciency: Jensen's ; (d) how to discount risky cash ows: i. risk adjusted rate of return; ii. certainty equivalent; (e) ex post CAPM; i. derivation; ii. the characteristic line of a stock;
• CAPM without riskless asset, two factor model of (Black, 1972); (a) orthogonal portfolio derivation; (b) a simple derivation of the Security Market line without riskless asset; (c) (Roll, 1977) critique about the efficiency of the market portfolio, numerical example;
• Ross (1976) APT. a) a new Data Generating Process: multi index model vs multi factor model, orthogonalizing factors; b) a proof of how arbitrage portfolios which endure no risk, neither idiosyncratic nor systematic, must have nil returns on average; c) risk premia and risk sensitivities; d) APT parameters estimation approaches overview; e) Using APT in Asset management e.1) Passive investment strategies; e.2) Active investment strategies;

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

Prerequisites and Learning Activities

The students quantitative and programming capabilities are applied to corporate finance modelling. To be specific, the course will focus on capital budgeting models, i.e. the choice of industrial investment projects, in both a deterministic and a stochastic framework.

Assessment Methods and Criteria

**Pre Assessment** A preliminary assessment of prerequisite skills is not performed in this course. **Formative Assessment** The formative assessment of this course teaching and learning process is performed through  class participation during lessons: A) students may be asked to answer questions about topics dealt with at lesson; students may ask instructor questions during lessons both about the very topic dealt with at lesson and about correlated topics they are particularly interested in. B) summary of previous week lessons: a student is randomly selected to sum up topics dealt with in the previous sessions, actually introducing extant session; C) short seminars: students are required to apply their skills in Calculus, Stochastic Calculus, Numerical Analysis and Mathematical Statistics to specific problems in finance, proposing their own solutions previously prepared as homeworks. **Summative Assessment** The summative assessment of this course is performed through A) Written tests: i) during the semester module a mid term and a final test at the end of the semester are given for students attending lessons; ii) a comprehensive test is given in ordinary exam sessions for students not attending lessons and for attending students that do not pass mid term and final semester tests; B) Homeworks and take home projects: some compulsory homeworks are given on specific topics to let students delve into the subject at her/his own pace; some optional take home projects are suggested to students particularly interested in applying quantitative methods of their choice to finance problems. C) Oral exams: after achieving at least an average pass grade in written tests during the semester or, as an alternative, an equivalent valuation on a comprehensive written test in an ordinary exam session, students are required to take an oral exam made up of: 1) questions about mistakes in written tests; 2) one's choice topic question. **aims and formative purposes** students are evaluated with respect to three different dimensions of learning:  A) Baseline theoretical knowledge provided through lessons and suggested reading list: tested through open questions to be answered through short essays; B) Problem solving involving symbolic calculus and stochastic calculus capabilities: tested through questions about model building and algorithms tuning for specific formal problems; C) Programming capabilities: tested through small (large) problems in class (at home) assignments to be programmed in a high level language, e.g. MatLab, Gauss, Ox, Scilab. **Evaluation criteria** 1) final numerical results achievement; 2) style:  2.1) in modelling – possibly new –  solutions in a symbolic layout;  2.2) in writing codes for extant models; 2.3) in prose for short essays questions. **Assessment breakdown** Formative and Summative Assessment towards the definition of a final grade weights on the final grade: In class participation 5%; Summary of previous week lessons 10%; Short seminars (if given, else the weight is given to class participation) 5%; In Class written tests 50%; Home assignments (homeworks and take home projects) 25%; Oral Exam 5%.

Textbooks

• Thomas E. Copeland, J. Fred Weston, and Kuldeep Shastri,, Financial Theory and Corporate Policy , Addison-Wesley. 2005. Fourth Edition    
• Luenberger, D, Investment Science , Oxford University Press. 1998.    
• Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N. Goetzmann, Modern Portfolio Theory and Investment Analysis , Wiley. 2014. Ninth Edition    

Notes

• prerequisite exams listed are only suggestive of the kind of topics and skills the prospective student has to master in view of attending the course. Therefore, students that have attended courses with different names but with similar topics can attend the course with profit.

Course page updates

• A.Y. 2017/2018
• A.Y. 2018/2019
• A.Y. 2019/2020
• A.Y. 2020/2021