FINANCE ASSIGNMENT

Finance Assignment

Mean-Variance Portfolio Optimization

Introduction

Investors are anxious about their investment due to the world recession. However, investors are more concern with the future condition of their recession whether it going to be worst or better as it will have direct impact of their investment. Investor must know that recession is the part of natural phenomenon in economy. The stock market in recession hit hard as people go for safer and diversified investment so they won't make so much of lose. Before investing their money people look for investment which comprises of minimum risk and maximum profit, hence, an optimal portfolio.

However, statistical procedure applied to demonstrate the diversified portfolio of an assts like stocks and bonds which can minimize the risk and improve the performance of the portfolio. This theory is termed as Markowitz portfolio theory that undertakes to maximize expected return for a given amount of portfolio risk or equally minimize risk for a given level of expected return through the proper selection of the different assets. Moreover, the theory proposed that the individual risk of an asset or stock should not be measured on the root of their variation or volatility from their expected return.

In this paper we will discuss the Markowitz mean-variance portfolio optimization problem which aims to find the optimal portfolio that maximizes utility function on the portfolio risk and return.

Discussion

The selection process of the portfolio divided in to 2 stages. The first stage consists of the observation and experience which cease with impression regarding the future performance of securities. As far as second stage is concern, the applicable notions concerning future performances that cease with the choice of portfolio. The aim of the theory is to allocate the investor fund in most favorable assets i.e. between different nature of the assets. A quantitative tool, Mean variance optimization (MVO) facilitates the investors for the allotment of the funds through considering the tradeoff between risk and return (Lucas, 1978, pp. 1429).

This theory was developed by Henry Markowitz which was based on the assumption that capital markets are efficient. Establishment of efficient markets in practice boils down to the treatment of capital markets as perfectly competitive, in which the same effect may operate institutional investors and individuals, and the information reaches on equal terms and at the same time. Researchers describe each investment in the capital market is the rate of return (Er) and a risk rate of return measured by the variance (s2). The investment portfolio consists of many financial assets described by the expected rate of return on the portfolio (Erp) and the variance of the portfolio (s2p). These models describe a portfolio consisting of two risky assets:

s2p = x2A * * S2A + S2B 2 x2B xAxBsAsBrAB

Erp = xAErA + xBErB

Where xA and xB are participating (in the range from 0 to 1) the individual shares in the portfolio. Hence, the selection of an optimum assets portfolio has a major interest in the field of finance. The basic idea is to maximize a utility ...