On successful completion of this course, the student should:

• have a thorough and deep knowledge of some asset pricing and some positive (economics) portfolio selection models. In particular, he/she must be able to provide OLS estimates for both CAPM and APT equations parameters. He/she must be able to construct optimized portfolios according to the closed forms taught at lesson derived from multivariate functions calculus applications. Finally, the student should be able to perform data scraping, getting data needed for the models, and to organize them in a database.
• be able to use her/his programming skills in simple Excel spreadsheets and/or in high programming languages such as Gauss or MatLab, not only for financial models and algorithms dealt with at lesson but also for other similar problems.
• have acquired general skills in the field of algorithms and applied programming for asset pricing and portfolio selection which enable him/her to make educated choices in a problem solving practice framework. To be specific, the student should be able set up Excel spreadsheets and/or high level language, GAUSS or MatLab, codes implementing CAPM and APT and related portfolio selection solutions derived applying multivariate calculus optimization techniques in both original and new kind of problems.
• be capable to give a presentation both in front of a general practitioners' audience and a more academic one about the models dealt within the course
• have acquired a method of study both thanks to a wide knowledge of the main streams in which financial modelling is evolving, theoretical continued learning, and a confident practice with respect to the main high level programming languages, GAUSS and MatLab, which are continually evolving, best practice continued learning.

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%.

• 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    

• 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 successfully.