Mathematical Models In Portfolio Selection: The case Of The Emerging Nairobi Stock Exchange

Abstract

A GREAT deal of theoretical and empirical work has been carried out in recent years, on the use of mathematical models as an aid to the selection of investment portfolios containing equities. Some of the models have been advanced include Harry Markowitz (1952) portfolio theory: capital asset pricing model (CAPM) whose critics have argued its limitation in application though thought to be the best model available and Stephen Ross (1976) Arbitrage pricing theory (APT) . The arbitrage pricing model attempts to capture the limitations of CAPM and recognizes the sensitivities to a number of factors that influences their return. After a discussion of the background to portfolio selection models, the paper discusses work done on the manner in which share returns move over time. Next the paper examines the principles behind various portfolio selection models, discussing in some detail the work of Markowitz, Sharpe and developments by Stephen Ross. Employing the data from the Nairobi Stock Exchange between Jan 2004 and Dee 2008 under the light of the methodology proposed, the research investigates the relationship between the stock returns and measured risk for each model. This study therefore attempts to engage elements of~f!1 Portfolio Theory, Capital Asset Pricing Model and Arbitrage Pricing Theory to disco~er how each can be used in the process of portfolio selection.