An Introduction to Optimal Portfolio Models from Markowitz to Robust Estimation.

Speaker:  Prof. Stefano Benati - Università di Trento
  Tuesday, May 8, 2018 - to be fixed with the interested students
Title: An Introduction to Optimal Portfolio Models from Markowitz to Robust Estimation.

Organization: the course comprises three lessons of two houers each. The lessons will be delivered in May. The precise dates and time-slots for the three meetings can only be fixed with the help and feedback of the interested students.
Right now I have booked:
Tuesday 8,22 May 14:30-17:30 room M.
Tuesday 15 May 14:30-17:30 meeting room at second floor.
Wensday 9,16,23 May 10:30-13:30 meeting room at second floor.

Students interested into the course are requested to write a mail to:
and to express their suggestions, contraints, and preferences on the dates and time-slots.
Abstract: The short course covers the basic tools to model and solve an optimal portfolio problems, that is, the problem of selecting the best stocks of a financial market. Special emphasis is posed on the links between the three operational problems: model formulation, parameters estimation, computational solution. 


Lesson 1: The Roots of Optimal Portfolio Models.

The Markowitz Optimal Portfolio Problem. Mathematical properties, parameters estimation, experimental results.
The Von Neumann-Morgenstern Utility Theory. Risk adverse and risk taker investor’s behavior. Optimal portfolios of utility maximizer investors. 

Lesson 2: Portfolio models with non-invertible covariance matrices. 

The difficulty of estimating the covariance matrix and three solutions: The Mean/Absolute-Deviation portfolio model, the Markowitz model with cardinality constraints, Shrinkage estimators of the Covariance matrix.

Lesson 3: Portfolio models with robust estimators.

Variance estimators that are robust. The Optimal Median portfolio model. The Median/Risk portfolio models, integer linear programming formulation, experimental results.
Benati, S. “Using medians in portfolio optimization”. Journal of the Operational Research Society 66, n. 5 (2015): 720–31.
Cornuejols, G., Tutuncu, R., “Optimization Methods in Finance”, Cambridge University Press, 2007.
Konno, H, Yamazaki, H. “Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market” Management Science 37, n. 5 (1991): 519–31.
Kwan, Clarence C. Y. “An Introduction to Shrinkage Estimation of the Covariance Matrix: A Pedagogic Illustration”. Spreadsheets in Education 4, n. 3 (2011).
Markowitz, H. “Portfolio Selection». The journal of finance 7, n. 1 (1952): 77–91.
Rockafellar, R.T., S. Uryasev “Conditional value-at-risk for general loss distributions”. Journal of Banking and Finance 26, n. 7 (2002): 1443–71.

Title Format  (Language, Size, Publication date)
CourseProgram plain plain (en, 2 KB, 09/03/18)

Contact person
Romeo Rizzi

Publication date
February 26, 2018