Construction of market index, efficient portfolios and a test for capital market efficiency

Abstract

Individual investors in the capital market often wish to hold portfolios that "follow the market" but consist of only a small number of scrips. This study addresses the problem of designing a compact portfolio of scrips that closely mimics a specified market index. It attempts to construct a few indices based on a sample of scrips and relate them to the RBI share price index. The use of indices in portfolio selection is explored under the two-parameter model of risk and return developed by Markowitz. The rationale behind holding a market portfolio is that such a portfolio is considered well-diversified and "efficient"-meaning the non-market risk component is virtually zero. In this thesis, Stepwise Multiple Regression Analysis is used to identify a few scrips that closely approximate the behavior of the market index. Since various stocks traded in the market may be correlated with one another, the existence of multicollinearity can affect parameter estimates. To address this, Principal Component Analysis is employed. Based on these analyses, three indices are developed from a small set of stocks. These indices were found to be highly correlated with the RBI share price index. It was discovered that market behavior can be approximated by tracking the performance of only three scrips, which explain about 90% of the variation in the market index. Portfolio theory centers around the existence of an opportunity set for investments and an associated efficient frontier, which is the locus of all portfolios offering the maximum expected return for a given level of risk, or the minimum risk for a given expected return. It is argued that the market portfolio-the portfolio of all securities in the market-is a point on this efficient frontier. To verify this premise, several portfolios were constructed to minimize risk for pre-specified levels of return. The efficient portfolio frontier formed by a sample of 15 scrips was found to be a hyperbola, as postulated by portfolio theory. The relative position of the market indices in terms of the risk-return trade-off was then examined. The RBI index and its proxy indices were found to be relatively inefficient in terms of their return-generating capacity when compared with the optimal portfolios constructed, indicating market inefficiency.