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