Developments in Mean-Variance Efficient Portfolio Selection

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.

Portfolio selection modelling dates back to the development of mean-variance¹ model of Markowitz. The concept of diversification and an efficient frontier provided the logical basis for selecting a portfolio based on individual utility curves. Roy (1952) provided a specific point on the efficient frontier whereby he attempted to minimise the upper bound of the chance of a dread event. Roy’s principle of safety first, further supported the concept of diversification of resources among a wide variety of assets. Utility was defined in terms of minimisation of a chance of a catastrophe. Markowitz used statistical analysis and Roy used econometric analysis for the purpose of their studies. Tobin (1958) provided the basis for two fund separation theorem in the context of portfolio selection whereby an investor allocates his resources among risky and riskless assets. The theory propounded by Tobin was based on the risk avoiding behaviour of investors and was conceptually shown to be superior to the Keynesian theory of liquidity preference.

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). The important criterion identified by the investors are high returns which are rather consistent that is, have less variability. Efficient portfolios are the ones yielding the highest returns for a given degree of risk or providing least risk for a given level of return. Mean-variance criterion provides an intuitive explanation for diversification. Investors would most often choose the portfolios which maximises their expected utility while taking into consideration any other constraints they might be facing.

The limited literature available in India in the area of portfolio selection compared to the efficient markets of the developed économies, such as the United States (US) and the United Kingdom (UK) prompted us to conduct an in-depth study in this field. Although the effect of various financial and accounting factors on security returns has been studied separately, no efforts have been made to integrate these factors for the benefit of an investor. The present quest tries to fills these voids. On the basis of knowledge gained from reviewing the research efforts of the past and the emerging issues in the Indian capital markets, portfolio modelling has been attempted using the quadratic programming approach.

Application of theoretical portfolio selection models to the real life capital markets in order to facilitate the investor in making the optimal decisions requires serious research. The entire purpose of portfolio modelling is defeated if the model created cannot be put to practical use. A portfolio selection model should not be so complex as to discourage the investors from using it. A large number of investors exist in the equity markets at any point of time. All investors in the market may not be identical. They may differ with respect to their risk bearing capacity, preference for quick gains versus regular income or other priorities. Thus, the same model may not be applicable to all of them. The practical application of portfolio selection models assumes significant importance.

The issue of portfolio construction involving analysis of various aspects by an investor — fundamental accounting, financial as well as governance — has been dealt with here through the application of MCDM approach from the field of operations research. A multi-objective quadratic programming model with the objective function of minimising variance (volatility) and constraints relating to multiple decision criteria such as return (capital and dividend), systematic risk (beta), marketability (trade volume and price-to-earnings ratio), management efficiency (operating profit margin), profitability (net profit margin), governance (free float) and future investment opportunities (free cash flows) has been obtained. The portfolio selection model has been applied to London Stock Exchange’s FTSE 100 to generate Pareto optimal portfolios.

This chapter showcases a reflection of the research work presented. The use of complex programming techniques, the latest research software and the integration of multiple factors describing investor’s preferences are able to tap the requirements of an investor from a portfolio beyond just mean and variance. While attempting to minimise risk, an investor is faced with a variety of constraints including earning good returns, dividends, marketability of securities and promising future opportunities. Investors also desire liquidity, management efficiency, profitability, adequate market capitalisation, free float per cent and free cash flows from their portfolio. Substantial interest of promoters and other institutions in the script, free float factor, industrial and company diversification are a few other aspects that an investor seeks from his/her portfolio. An attempt has been made to incorporate all these considerations of an investor for developing and testing of a multi-criteria optimisation model for portfolio selection.