The students quantitative and programming capabilities are applied to normative asset pricing and portfolio selection modelling.

Course Prerequisites

To successfully attend the course students must have been previously exposed to topics dealt with in the following courses:

Financial Data Analytics and Investment Data Driven Decisions I

• Asset pricing, portfolio selection and data analytics: from positive economics modelling to normative approaches. asset management issues and algorithmic solutions.
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• portfolio selection in practice. the closed forms positive economics portfolio selection cases derived using unconstrained and Lagrangean constrained optimization are used as benchmarks for constrained numerical optimization:
  • a) constraints used in practice:
    • a.1) no short selling positions;
    • a.2) holding positions;
    • a.2) turnover;
    • a.3) factor sensitivity;
    • a.4) cardinality;
    • a.5) minimum holding and transaction size;
    • a.5) round lot;
    • a.6) tracking error;
    • a.7) other soft constraints;
  • b) tail risk measure constraints:
    • b.1) VaR optimized portfolios;
    • b.2) CVaR optimized portfolios.
  • c) incorporating transation costs in portfolio optimization:
    • c.1) linear;
    • c.2) piecewise linear;
    • c.4) quadratic;
    • c.5) fixed;
  • d) incorporating taxes in portfolio optimization.

• robust equity portfolio construction:
  • a) box uncertainty
  • b) ellipsoidal uncertainty

• shrinkage methods and the Black Litterman model for equity portfolio construction: in this framework the same constraints listed above are conveniently introduced.

• VaR and CVaR constrained equity portfolio construction: 
  • VaR analytics recap;
  • closed forms for VaR optimized portfolios
  • numerical optimiziation for Var optimized porfolios

• Performance testing. main performance ratios:
  • 1) Sharpe Ratio;
  • 2) Jensen's alpha;
  • 3) Tracking Error;
  • 4) Information Ratio;
  • 5) Sortino Ratio;
  • 6) Maximum Draw-down;
  • 7) VaR;
  • 8) CVaR; Stress testing of portfolio strategies.

On successful completion of this course, the student should

• have a thorough and deep knowledge of some asset pricing and some normative portfolio selection models. In particular, he/she must be able to estimate using also Bayesian statistical methods the main inputs for portfolio modelling. He/she must be able to construct optimized portfolios using Monte Carlo and bootstrapping methods and numerical optimization approaches as well, having laid out the mathematical setting to be simulated and/or optimized. 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 level 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 numerical optimization and Monte Carlo or bootstrapping simulation in view of achieving portfolio selection solutions 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.

Programming skills in Excel and in a matrix oriented language such as MatLab, Gauss, Ox, Scilab, Octave. The student should be confident in calculus in both univariate and multivariate functions studies, in the basics of probability calculus, namely main continuos and discrete density functions. In order to attend the course it is highly advisable to have passed the following exams or equivalent: Probability And Mathematical Statistics, Foundations Of Programming And Laboratory, Operation Research And Optimization in addition to Financial Data Analytics and Inverstment Data Driven Decisions I.