Risk-Return Analysis of Sectorial Portfolios of Stocks

ABSTRACT.The efficient frontier (risk-return profile) signifies the minimum risk achieved through diversification, i.e., the systematic risk, which has to be taken for any value of the expected returns. Using the Modern Portfolio Theory (MPT) of mean variance optimization, we estimate and compare of different long-only sectorial portfolios. Based on a longitudinal monthly data of average stock returns, efficient frontiers are obtained solving multiple optimizations through quadratic programming in R-statistical computing tool. We find that all the sectorial portfolios of stocks follow MPT in general as the risk associated with it increases on increasing the expected rate of the return but the slope of the efficient frontier decreases. Different sectors behave differently when it comes to the risk-return relationship. On a broad basis, the efficient frontiers of each sector can be classified into three bands: Band 1 always lies on the left side of Band-2, and Band 2 in turn always lies on the left side of Band 3. Since, ideally all the sectors should have exhibited similar behavior, i.e., same expected returns for any given level of risk undertaken, therefore, either there is a persistence of information asymmetry or there exists investor's bias towards certain sectors.JEL Classification: G11Keywords: risk-return, diversification and portfolio choice(ProQuest: . denotes formulae omitted.)1. The Modern Portfolio TheoryThe modern portfolio theory (MPT) of "portfolio selection" (Markowitz 1952) is based on the diversification of risk principle. It proposes optimization of risk, measured in terms of volatility, for an expected return. By maintaining a portfolio containing multiple securities, one can achieve the benefits of diversification and reap an expected level of return for minimum risk. The risk-return profile or as MPT would coin it as "efficient frontier", can be obtained, after solving a mean variance optimization problem, for a given portfolio. Further, different portfolios on the efficient frontier can be combined in long/short combinations to generate new portfolios lying on the efficient frontier. For a given portfolio, one cannot do better than the estimates given by the efficient frontier, unless the portfolio is modified.The inclusion of risk- free security1 (short term government securities) in a portfolio opens for better risk-return opportunities as compared to the efficient frontier. The new portfolio is composed of the risk-free security and the sub-portfolio as per the maximum Sharpe Ratio2 on the efficient frontier. The new portfolio has a linear risk-return profile or, the Capital Allocation Line - running between the risk-free security and the subportfolio on the efficient frontier, and provides better returns for a given risk as compared to the efficient frontier. The risk-free security and the subportfolio may be combined in different long/short combinations to generate different risk-return profiles within and beyond the Capital Allocation Line.A combination of stocks (assets) beat the risk-return profile of a single stock (asset) for that the diversification of the portfolio results in a higher correlation between various stocks (assets). The security risk that is diversifiable by holding a diversified portfolio is known as specific/unsystematic risk. On the other hand, the risk that is not diversifiable and is dependent on the market is known as systematic/portfolio/market risk. Thus the efficient frontier is the minimum risk, i.e., the systematic risk, which has to be taken for any value of the expected returns. The MPT is based on number of assumptions: (i) asset returns are normally distributed variables, (ii) cross asset correlations are constant forever,3 (ii) efficient market hypothesis holds true, (iii) investors are rational and risk averse, (iv) information symmetry holds true, (v) all securities can be divided into any size, (vi) investor actions do not influence prices as they are price takers, and (vii) investors have the ability to borrow an unlimited amount of money at the risk-free rate. …