BASIC ROBUST PORTFOLIO
OPTIMIZATION MODELS
Guide: Prof. Dr. Raghu Nandan Sengupta
Co-Guide: Prof. Dr. Joydeep Dutta
Submitted by: Abhishek Dhandharia (Y9026)
Ruchir Golecha (Y9452)
Introduction
Introduction
Portfolio Optimization is the way of selecting various types
of assets such as shares, bonds etc. in some proportions
such as to make the portfolio better according to some
conditions
Conditions will basically combine, directly or indirectly,
considerations of the expected value of the portfolios rate of return as well as the returns dispersion
Robust Counterpart
Model II: Mean Absolute Deviation Model
Robust Counterpart
Model III: Minimax Model
Robust Counterpart
Model IV: C-Var Model
Robust Counterpart
Model V
Robust Counterpart
Model VI
Robust Counterpart
Data Description and Preprocessing
Daily closing prices of companies composing 3 different
stock exchanges indices
Dow Jones Industrial Average (U.S.)
Hang Seng (Hong Kong)
NIFTY 50 (India)
Considered stock values for 2 years period i.e. Feb 1,
2012 to Jan 31, 2014 for stocks of NIFTY and Dow Jones
and for 1 year period of Feb 1, 2012 to Jan 31, 2013 for
stocks of Hang Seng
To overcome the missing data problem we averaged out
the subsequent and preceding price value to obtain the
missing data information
Data Description and Preprocessing
Results and Discussion
Simulations done on Minimax and C-VaR Models
Compared the weight distribution and risk return
graph for deterministic and robust counterpart for
three different levels of probabilities
Minimax Model Dow Jones 2012 Weights Distribution Comparison
Minimax Model Dow Jones 2012 Risk-Return Comparison
Minimax Model NIFTY 2012 Weights Distribution Comparison
Minimax Model NIFTY 2012 Risk Return Comparison
Minimax Model Hang Seng 2012 Weights Distribution Comparison
Minimax Model Hang Seng 2012 Risk Return Comparison
Minimax Model Dow Jones 2013 Weights Distribution Comparison
Minimax Model- Dow Jones 2013 Risk Return Comparision
Minimax Model NIFTY 2013 Weights Distribution Comparison
Minimax Model NIFTY 2013 Risk Return Comparison
C-VaR Model Dow Jones 2012 Weights Distribution
C-VaR Model Dow Jones 2012 Risk Return Comparison
C-VaR Model NIFTY 2012 Weights Distribution
C-VaR Model NIFTY 2012 Risk Return Comparison
C-VaR Model Hang Seng 2012 Weights Distribution
C-VaR Model Hang Seng 2012 Risk Return Comparison
C-VaR Model Dow Jones 2013 Weights Distribution
C-VaR Model Dow Jones 2013 Risk Return Comparison
C-VaR Model NIFTY 2013 Weights Distribution
C-VaR Model NIFTY 2013 Risk Return Comparison
Inference
Bibilography [1] Ida, M. (2001): Mean-variance portfolio optimization model with uncertain coefficients,
Fuzzy Systems, 2001, The 10th IEEE International Conference, 3, 1223-1226
[2] Shiwei Li (2010): A Portfolio Optimization Model on Condition That Short Selling Is Not Permitted, Management and Service Science (MASS), International Conference, 1,3, 24-26
[3] Baumann, P., Trautmann, N. (2013): Portfolio-optimization models for small investors, Mathematical Methods of Operations Research, 77, 3, 345-356
[4] Ben-Tal A., El Ghaoui, L. and Nemirovski, A. (2009): Robust Optimization, Princeton Series in Applied Mathematics, Princeton University Press
[5] Markowitz, Harry (1952): Portfolio selection, The journal of finance 7.1, 77-91
[6] Seth, R., Sengupta, R.N. (2008): Reliability in Portfolio Optimization Using Uncertain Estimates, Unpublished thesis submitted at IIT Kanpur
[7] Kumar, R., Sengupta R.N. (2011): Robust Portfolio Optimization of Chance Constrained Problems Using Exteme Value Distribution, Unpublished thesis submitted at IIT Kanpur
[8] References for data
http://finance.yahoo.com
https://www.leinenbock.com/
http://code.google.com/p/finance-data-to-excel/
http://www.stockhistoricaldata.com