Financial Portfolio Optimization - arXiv

[Pages:60]arXiv:1301.4194v1 [q-fin.PM] 17 Jan 2013

A thesis submitted for the degree of

Master of Technology In

Modeling and Simulation

entitled

Financial Portfolio Optimization:

Computationally guided agents to investigate, analyse and invest!? By

Ankit Dangi CENTRE FOR MODELING AND SIMULATION

UNIVERSITY OF PUNE

June, 2012

CERTIFICATE

This is to certify that the work incorporated in this thesis entitled "Financial Portfolio Optimization: Computationally guided agents to investigate, analyse and invest!?" is a bonafide work carried out by Ankit Dangi in partial fulfillment of the award of the degree of Master of Technology in Modeling and Simulation of University of Pune, during the second half of Academic year 2011-12 under our supervision. Material as has been obtained from other sources has been duly acknowledged in the thesis and that this work has not been submitted elsewhere for a degree.

Dr. Abhijit Kulkarni SAS Solutions OnDemand (SSO) Advanced Analytics Laboratory SAS Research and Development India

Date: June 15, 2012 Place: Pune, India

Dr. Sukratu Barve Assistant Professor Centre for Modeling and Simulation University of Pune

Prof. Anjali Kshirsagar Director

Centre for Modeling and Simulation University of Pune

DECLARATION

I hereby declare that the thesis "Financial Portfolio Optimization: Computationally guided agents to investigate, analyse and invest!?" submitted for the degree of Master of Technology in Modeling and Simulation to the University of Pune has not been submitted by me for a degree to any other University.

Date: June 15, 2012 Place: Pune, India

Ankit Dangi M. Tech. (M&S), Batch 2010-12

Acknowledgements

Words wouldn't suffice for the deep sense of gratitude with which I would like to sincerely thank my guide Dr. Abhijit Kulkarni for his guidance throughout the course of this work.

I would like to whole-heartedly acknowledge Prof. Uttara V. Naik-Nimbalkar and Dr. T. V. Ramanathan from Department of Statistics, University of Pune.

I am grateful to Dr. Mihir Arjunwadkar, Dr. Sukratu Barve and Prof. Anjali Kshirsagar from Centre for Modeling and Simulation, University of Pune.

I am thankful to Dr. Lokesh Nagar, Mr. Viswanath Pothinindi, Dr. Sourish Das, Mr. Prasad Paranjpe, Mr. Gaurav Singh, Dr. Swarup De, Mr. Mousum Dutta and Mr. Ashwin Deokar from SAS Solutions OnDemand, SAS Research and Development India.

I am thankful to my parents, family and friends for their support and encouragement.

v

Contents

1 Portfolio Optimization

2

1.1 Introduction, Background & Motivation . . . . . . . . . . . . . . . . . . 2

1.2 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Problem Formulations

10

2.1 Markowitz Modern Portfolio Theory (MMPT) . . . . . . . . . . . . . . . 10

2.2 Robust Formulation addressing Parameter Uncertainty . . . . . . . . . . 11

2.3 Risk-based Asset Allocation Strategies . . . . . . . . . . . . . . . . . . . 13

3 Computationally Guided Agents Approach

17

3.1 Conceptual Representation . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Classes of Solver Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Super-agent Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Empirical Validation and Results

25

4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Nature of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.3 Scenario 1: Bearish Market . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.4 Scenario 2: Bullish Market . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Conclusion and Future Work

35

A Return and Risk Measures

37

A.1 Return Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

A.1.1 Absolute Return Measures . . . . . . . . . . . . . . . . . . . . . . 37

A.1.2 Relative Return Measures . . . . . . . . . . . . . . . . . . . . . . 37

A.1.3 Absolute Risk-Adjusted Return Measures . . . . . . . . . . . . . 38

A.1.4 Relative Risk-Adjusted Return Measures . . . . . . . . . . . . . 38

A.2 Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

A.2.1 Absolute Risk Measures . . . . . . . . . . . . . . . . . . . . . . . 39

A.2.2 Relative Risk Measures . . . . . . . . . . . . . . . . . . . . . . . 39

A.2.3 Tail Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . . 39

B Business & Technical Constraints

40

C Characteristics of Solver Agents

42

vi

Abstract

Financial portfolio optimization is a widely studied problem in mathematics, statistics, financial and computational literature. It adheres to determining an optimal combination of weights that are associated with financial assets held in a portfolio. In practice, portfolio optimization faces challenges by virtue of varying mathematical formulations, parameters, business constraints and complex financial instruments. Empirical nature of data is no longer one-sided; thereby reflecting upside and downside trends with repeated yet unidentifiable cyclic behaviours potentially caused due to high frequency volatile movements in asset trades. Portfolio optimization under such circumstances is theoretically and computationally challenging. This work presents a novel mechanism to reach to an optimal solution by encoding a variety of optimal solutions in a solution bank to guide the search process with regard to the global investment objective formulation. It conceptualizes the role of individual solver agents that contribute optimal solutions to a bank of solutions, and a super-agent solver that learns from the solution bank, and, thus reflects a knowledge-based computationally guided agents approach to investigate, analyse and reach to optimal solution for informed investment decisions.

Conceptual understanding of classes of solver agents that represent varying problem formulations and, mathematically oriented deterministic solvers along with stochasticsearch driven evolutionary and swarm-intelligence based techniques for optimal weights are discussed in this work. Algorithmic implementation of the computational guidance approach from a bank of optimal solutions is presented by an enhanced neighbourhood generation mechanism in the Simulated Annealing algorithm. A framework for inclusion of heuristic knowledge and human expertise from financial literature related to investment decision making process is reflected via the introduction of controlled perturbation strategies using a decision matrix for neighbourhood generation. Empirical validation of the proposed methodology has been carried out for Bearish and Bullish market scenarios.

vii

Contributions

Academic/Computational Contributions

? Computationally guided agents approach to financial portfolio optimization that incorporates varying problem formulations, variety of parameters, and complex business constraints.

? Conceptualization of a computational model comprising of various classes of solver agents that contribute optimal solutions to a bank of solutions that guides a superagent solver towards obtaining optimal solutions for a global investment objective.

? Development of a novel mechanism in Simulated Annealing algorithm for neighbourhood generation using solution bank approach.

? Conceptualization of a perturbation strategy using decision matrix for controlled disturbances to decisions variables during neighbourhood generation.

Contributions to SAS Research and Development

? Portfolio Optimization Component of Asset Performance Management Solution - Development of Robust Portfolio Optimization Formulation - Development of Risk-based Asset Allocation Strategies

? Platform for Innovation (SASFoundry) and Knowledge Management (SAS ToolPool) - Simulated Annealing for Global Optimization (Algorithm Development) - Ant Colony Optimization for Continuous Domains (Algorithm Development) - A Suite of Benchmark Functions for Global Optimization

viii

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download