OPTIMAL PORTFOLIO SELECTION

Abstract

In this project, the modern portfolio theory (MPT) is written with a primary objective of showing how it aids an investor to classify, estimate, and control both the kind and the amount of expected risk and return in an attempt to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return. A methodology section is included which examined applicability of the theory to real time investment decisions relative to assumptions of the MPT and have plotted the graph . The theories that are used to analyse the problem and the empirical findings provide the essential concepts such as standard deviation, risk and return of the portfolio. Further, diversification, correlation and covariance are used to achieve the optimal risky portfolio. There will be a walk-through of the MPT, with the efficient frontier as the graphical guide to express the optimal risky portfolio. This paper studies the 25 NIFTY stocks with large market capitalisation and small midcap over a period of 2 years. This study also includes the analysis of long term government bonds with maturity of 10-20 years. We develop a portfolio which allocates financial assets by maximising expected return subject to the constraint that the expected maximum loss should meet the risk limits set by the risk manager. The techniques used take into consideration the return and the risk of each asset in order to build the best portfolio. Three sets of portfolios are considered for investors with different investing styles i.e. which includes only stock, a mix of stocks and bonds in order to diversify the risk and the final one considers only government bonds which is suitable for those investors who would like to take a break from the fixed deposits but would still want a set certain amount of return on investments. The set of all efficient portfolios is called the efficient frontier. All risk-averse investors who act to maximize expected utility have an optimal portfolio on this frontier. Based on the risk-aversion factor and the investment time horizon of each investor, portfolio optimization is carried for to maximize utility as well as return and minimize risk for all kinds of investors. Thereafter, we would need to plot and analyse these portfolios for three different sets and perform cluster mapping for the same for the same set of stocks and bonds. The findings of the study bring out the importance of the investor’s investing pattern and style keeping in mind the utility and the risk aversion factor