Rank-based adaptive method of estimating beta

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Traditional methods of estimation and testing, such as the Ordinary Least Squares (OLS) method, are efficient if the normality assumption of the error distribution and other assumptions about a liner model are not violated. Adaptive tests are found to be efficient and increases the power irrespective of the condition of the observed data. In particular, stock market data comes along with some skewness, tail weights, outliers and unknown distributions that violates some underlying assumptions for which the estimates from OLS is efficient. The degree to which a security is affected by a systematic risk as compared to the effect on the market as a whole is measured by the security’s beta. Beta estimates of a security on the stock market are obtained from the OLS estimates of the parameters of a linear model. In practice, however, the error distribution of the market model is not known and conclusions made solely using traditional methods may lead to invalid conclusions. Consequently, fund managers, actuaries and investment risk managers may mislead their clients based on financial decisions made based on these beta measures. This study sought to extend robust adaptive methods that considered tail weight, skewness and selector statistics, in estimating security beta with some specified lags. Further comparisons were made between the adaptive procedure and the OLS method. In line with these objectives, monthly data of three companies listed on the Ghana Stock Exchange (GSE), from January 2000 to June 2014, were used. Market models were formulated with some specific lags and estimation of model were done for both traditional and adaptive methods. The study showed that rank-based methods (Wilcoxon and Adaptive) were more robust in estimation when the distribution of the error term of the dataset was non-normal and also in the presence of outlying observations,whiles the LS method was very non-robust. Results indicated that 5% outlier-contamination was enough to cause some instability in the estimates.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the Degree of M.Phil in Acturial Science.