Rank-based adaptive method of estimating beta
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Date
NOVEMBER, 2015
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Abstract
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.
Description
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.