Developments in Mean-Variance Efficient Portfolio Selection

M. Agarwal

• Publisher: Palgrave Macmillan
• Year: 2015
• Print ISBN: 9781137359919
• eBook ISBN: 9781137359926
• Topic: Business
• Subtopic: Finance
• Index: Business

This book discusses new determinants for optimal portfolio selection. It reviews the existing modelling framework and creates mean-variance efficient portfolios from the securities companies on the National Stock Exchange. Comparisons enable researchers to rank them in terms of their effectiveness in the present day Indian securities market.

1

Introduction

1.1 Introduction

The sacrifice of current money and other resources for future benefits is referred to as an investment. Investing is done with an aim of earning returns, which involves two key aspects: time and risk. The present outflow of funds is certain, but the future gains are uncertain and involve risk. A deliberate and careful investment decision leads to the creation of a portfolio of assets. Investment decisions are to be taken within the framework provided by the complex of financial institutions and intermediaries comprising the capital market. The capital market also provides the mechanism for channelling current savings into investments. Portfolio analysis starts with information concerning individual securities and ends with conclusions concerning portfolios as a whole.

The importance of an investment decision is emphasised more in this phase of recession and recoveries in the global economies, examples of which include the economic crisis in Cyprus, Greece and Iceland, as well as the aftermath of the UK banking crisis. The rapidly increasing growth of voluminous literature on portfolio selection in the recent years indicates the widespread interest of the academic and business communities in this area. It further emphasises the importance of investment decisions in today’s world. This book is written to provide an aid to different types of investors in the selection of securities and the creation of an optimal portfolio of assets.

Mean-variance criterion introduced by famed economist and Nobel Laureate Harry Markowitz (1952) is by far the most widely known efficiency¹ criterion for investment analysis. Efficiency is defined in terms of either lower variance at the same level of mean return or higher mean return at the same level of variance. An optimal portfolio is more than a long list of good stocks and bonds; it is a balanced whole providing an investor with protections and opportunities with respect to a wide range of contingencies (Markowitz, 1959). Markowitz provided the direction to incorporate the multiple objectives of an investor in portfolio construction. The multidimensional nature of this decision is captured through the use of multi-criteria decision making (MCDM) framework, which provides the methodological ground to solve the problem of portfolio construction.

A portfolio optimisation model making use of the potentials of a quadratic programming approach for a real life investor with multiple constraints is developed and tested throughout the course of this book. The preferences of investors and key features of investment opportunities must be clearly understood and linked to each other to ensure optimal investment decisions. Incorporation of fundamental accounting, financial and corporate governance variables in a mean-variance portfolio selection model accounts for the multiple objectives of an investor. The crucial role of portfolio attributes like expected return, dividend returns, variance, the responsiveness of stock’s return to index return (Beta), trade volume, price-to-earnings ratio, market capitalisation, operating profit margin, net profit margin, free float, free cash flows and other such factors are identified for creation of efficient portfolios.

The objective function of an investor is to minimise risk that is variability of returns as defined by Markowitz. The real world financial markets, economic conditions/scandals, and attitude and priorities of an investor impose a number of constraints that need to be incorporated for careful selection of securities. The actual scenario faced by an investor, his/her set of constraints and the objective of risk minimisation is simulated in various model formulations. An attempt has been made to identify and suggest the alternate parameters for practical application of the developed model. Empirical testing of the model has been also undertaken for Nifty 50 securities of the National Stock Exchange of India and FTSE 100 securities of the London Stock Exchange, UK. The performance of resulting portfolios created using alternate portfolio selection model formulations as per investor preferences are compared using the Sharpe and Treynor ratio. A comparison and tests of the performance of proposed portfolio selection model, vis-à-vis Markowitz’s model for portfolio selection and the index portfolios have also been undertaken.

This chapter introduces the concept of portfolio selection and its relevance in today’s world. It discusses the research gaps, significance of portfolio selection decisions, objectives of writing this book, research methodology adopted, research hypothesis, sources of data, chapter scheme and possible limitations.

Background

Introduced more than 60 years ago in the pioneering work by Markowitz, the mean-variance optimisation is one of the most popular approaches to portfolio selection. The basic assumptions of his theory are that a rational investor has either multivariate normally distributed asset returns or, in the case of arbitrary returns, a quadratic utility function. In the validity of these assumptions, Markowitz has shown that the optimal portfolio for the investor rests on the mean-variance efficient frontier. The portfolio of financial assets has been defined as efficient if, and only if, for any given expected return there is no other portfolio with lower variance, and for any given variance there is no other portfolio with higher expected return. The efficient frontier consists of all efficient portfolios. James Tobin (1958), another Nobel Laureate economist, based his theory of investment choice under conditions of uncertainty on the mean and variance of the distribution of returns. The Markowitz-Tobin analysis remains the cornerstone of the work in the field of investment analysis.

The advantage of mean-variance criterion is that the investor can focus on the first two aspects of the distribution of returns: the expected return (E) or mean and the variance (V). The investors tend to diversify risk by building portfolios comprising of a number of common stocks, or stocks and cash, bonds, derivative products, etc. The desire to stabilise the income stream is sine qua non for investment diversification. The greater the number of securities included in a portfolio, the lower its variance. However, institutional restrictions and costs limit the actual size of portfolios.

The concept of diversification and efficient frontier provided logical basis for selecting a portfolio based on individual utility curves. An approximation of a utility function by a quadratic in a certain neighbourhood is central to the Markowitz (1959) rationale for mean and variance. Thereafter, single index model (Sharpe, 1964), multi-index models (Fama and French, 1992), utility-based models, stochastic dominance-based models, correlation-based models, and models based on criteria such as safety first, skewness, geometric mean returns and so on have emerged for portfolio selection.

Building an equity portfolio is considered more varied than building debt portfolios because of the multiplicity of objectives. The primary objective of equity portfolios could be to generate absolute returns with low volatility over a long time period, to generate long-term capital growth from a diversified portfolio investing predominantly in equities or to generate capital appreciation and income distribution from an investment which outperforms the specific indices such as Sensex or Nifty. The objective could also be to generate long-term capital growth from an actively managed portfolio comprising equities, equity-related securities and equity derivatives. Another objective could be to generate higher than benchmark returns and long-term capital appreciation. Not only are the objectives multiple but so are the avenues for investment. While creating an equity portfolio, an investor can focus on benefitting from arbitrage opportunities, equity derivative strategies, pure equity investments and some small balance in debt and money market instruments.

New approaches for portfolio selection have emerged in the recent years with developments of new techniques in the field of operations research and management science, advancements in information technology and better accessibility of market information through databases such as Thompson Reuters Eikon. The MCDM approach has been applied to the problem of portfolio selection by researchers in finance. Hurson and Zopounidis (1995) provided the justification for applying the MCDM framework to the composition of an optimal portfolio. They suggest that because risk originates from various sources, its nature is multidimensional. Also, the preferences and objectives of investors are many. By incorporating a number of other criteria in addition to the traditional mean-variance, MCDM builds realistic models. This approach is advantageous as it can create portfolios specific to the preferences of an investor, while incorporating financial market factors at the same time. The rather restrictive norms imposed on the behaviour of investors by the classical approaches of portfolio selection are lifted by the MCDM framework by including the attitude and preferences of a real life investor.

Portfolio management has been defined as an ongoing process involving setting up of investment objectives and constraints, developing investment strategies, composing portfolio, initiation and implementation by managers and traders, performance evaluation, monitoring market conditions and revision/rebalancing (Maginn et al., 2007). It is an integrated set of planning, execution and feedback functions (Xidonas et al., 2009), the planning of which involves formulation of objectives and expectations. Investors’ return objectives, risk tolerance, liquidity needs, regulatory and taxation requirements, as stated in the investment policy statement, form the basis for this step. Execution may be carried over by portfolio managers by initiating portfolio decisions based on analysis and implementing them. Monitoring, rebalancing and portfolio evaluation are finally carried out in the feedback stage. The focus of this monograph is on the stage of portfolio creation as per the relevant market conditions and investor preferences.

The various portfolio constraints faced by an investor include illiquidity, short-selling, minimum capital requirements, diversification, dividend, volatility, volume, turnover and many more. These constraints have an impact on the portfolio strategy. The Martingale technique, quadratic programming, the Markovian chain process, the Lagrange multiplier, Riccatti equations, mixed integer and heuristic approaches have all been used by researchers worldwide to study such constraints. Limited empirical research work makes it imperative to develop a portfolio selection model which is best suited to current capital markets conditions and accommodates for multiple objectives of the investor.

Substantial improvements in the availability of large data sets, real time information and software capable of performing complex computations is continuously contributing towards improved research work in portfolio selection. Better understanding of the markets and evolving economic models provide the base to add further to the Modern Portfolio Theory. A distinction needs to be made between the real behaviour of an investor vis-à-vis rational behaviour. Investors’ priorities, preferences and the decision rules they follow are instrumental in the selection of securities in the basket of assets.

The traditional approaches of mean-variance portfolio selection, diversification principle, single factor models using beta and multifactor models all have proved to be extremely useful in the past. Although they are necessary for tackling the problem of portfolio selection, they are not sufficient. The incorporation of accounting variables such as operating profit margin, net profit margin, free cash flows; financial market variables such as dividend yield, price-to-earnings ratio, trade volume, etc. and corporate governance variables like promoters’ shareholding, free float, the number of independent directors, etc. would help in improving the existing portfolio selection models. These would represent both the fundamentals of securities in question and the personal preferences of an investor. The MCDM approach can facilitate in synthesising together the theoretical as well as practical aspects of portfolio creation. This approach can ease the complexity of the multi-criteria problem and simplify the use of criteria from different context, resulting in portfolios specific to an investor’s preferences. Understanding of the e...

Table of contents

• Cover
• Title
• 1  Introduction
• 2  Advances in Theories and Empirical Studies on Portfolio Management
• 3  Contributions to the Portfolio Theory
• 4  Mean-Variance Efficient Portfolio Selection: Model Development
• 5  Mean-Variance Quadratic Programming Portfolio Selection Model: An Empirical Investigation of India’s National Stock Exchange
• 6  Mean-Variance Portfolio Analysis Using Accounting, Financial and Corporate Governance Variables-Application on London Stock Exchange’s FTSE 100
• 7  Summary, Conclusions and Suggestions for Future Research
• Annex
• Notes
• References
• Index