Multiperiod stochastic programming portfolio optimization for diversified funds

• Author: Lawrence V. Fulton,Nathaniel D. Bastian
• Published date: 01 January 2019
• DOI: http://doi.org/10.1002/ijfe.1664
• Date: 01 January 2019

RESEARCH ARTICLE

Multiperiod stochastic programming portfolio optimization

for diversified funds

Lawrence V. Fulton

1

| Nathaniel D. Bastian

2

1

Department of Health Administration,

Texas State University, San Marcos, Texas

2

Army Cyber Institute, United States

Military Academy, West Point, New York

Correspondence

Lawrence V. Fulton, Department of

Health Administration, Texas State

University, San Marcos, TX 78666.

Email: lf25@txstate.edu

Abstract

We investigate a multiperiod, stochastic portfolio optimization model for diver-

sified funds choices associated with traditional 401K or 403B plans. This opti-

mization model minimizes the L

1

‐norm for negative return rate risk (the

downside mean absolute deviation) while examining parameters that maintain

model feasibility. Important components of the model are the incorporation of

appropriate time‐series components and evaluation of scenarios based on

investor outlook. A case study experimentation of the model on five potential

investment funds using historical data from 2003 to 2013 was conducted, and

parameter constraints for diversification and minimum acceptable return rates

were manipulated to produce contour plots. The maximum geometric rate of

return investment strategy provided by the optimization would have resulted

in a 9.7% geometric return rate in 2014 as compared with a 5.0% for a uniform

distribution of investment funds across choices.

KEYWORDS

diversification,financial engineering, portfolio optimization, stochastic programming, time series

1|INTRODUCTION

In 1952, Harry Markowitz proposed a bi‐criteria optimi-

zation (mean–variance [MV]) model for portfolio selec-

tion by considering expected return and variance of

return (Markowitz, 1952); this pivotal paper created the

field of modern portfolio theory (MPT). The basic concept

of MPT states that investors by nature want to select a

portfolio that generates the greatest discounted return at

a given amount of risk. MPT defines risk as variance or

volatility of stock prices as a factor of time. Therefore,

Markowitz proposed that the portfolio with the least var-

iance inherently carries the least risk, and as one takes on

more variance (or risk, in this case, as these terms are

assumed to be synonymous), one wants to earn the

greatest return on that incremental risk. If returns and

risk aversion are normally distributed, then the MV

model is optimal in the expected utility framework

(Hanoch & Levy, 1969; Tobin, 1958).

Criticisms of this approach and its related descen-

dants are that they require investors to have exact knowl-

edge of means, variances, and covariances, which are

difficult to estimate accurately. Markowitz's portfolio

optimization is particularly sensitive to the sample

means (Best & Grauer, 1991). It also allows for often

unsupportable investment strategies in the canonical

model (e.g., shorting positions when shorting is not

allowed; Frost & Savarino, 1988), a problem that is readily

handled with proper formulation. Because of the sensitiv-

ity to means, variances, and covariances, some researchers

------------------------------------------------------- -- --- -- -- --- -- --- -- -- --- -- --- -- -- --- -- --- -- -- --- -- --- -- --- -- -- --- -- --- -- -

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the

original work is properly cited.

© 2018 The Authors International Journal of Finance & Economics Published by John Wiley & Sons Ltd

Received: 9 March 2018 Revised: 11 August 2018 Accepted: 9 September 2018

DOI: 10.1002/ijfe.1664

Int J Fin Econ. 2019;24:313–327. wileyonlinelibrary.com/journal/ijfe 313