Risk-Return Analysis of Sectorial Portfolios of Stocks

ABSTRACT.The 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, 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 frontier decreases. Different sectors behave differently when it comes to the risk-return relationship. On a broad basis, the 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 choice(ProQuest: ... denotes formulae omitted.)1. The Modern Portfolio TheoryThe modern 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 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 can be obtained, after solving a mean variance optimization problem, for a given portfolio. Further, different portfolios on the frontier can be combined in long/short combinations to generate new portfolios lying on the frontier. For a given portfolio, one cannot do better than the estimates given by the frontier, unless the is modified.The inclusion of risk- free security1 (short term government securities) in a opens for better risk-return opportunities as compared to the frontier. The new is composed of the risk-free security and the sub-portfolio as per the maximum Sharpe Ratio2 on the frontier. The new has a linear risk-return profile or, the Capital Allocation Line - running between the risk-free security and the subportfolio on the frontier, and provides better returns for a given risk as compared to the 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 results in a higher correlation between various stocks (assets). The security risk that is diversifiable by holding a diversified 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 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) 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. …