A Framework for Robust Estimation of Beta Using Information Fusion Approach

Abstract

In terms of financial management, the precise estimation of the beta of a financial asset is of vital importance. Beta is the measure of the relationship between the return of an asset or a portfolio and the market return and means the systematic risk within the scope of the Capital Asset Pricing Model. In general, it is known that the distribution of returns is significantly non-normal with thick-tail and skewness features. The ordinary least square (OLS) estimator that focuses on the centre of a distribution loses its effectiveness in such cases as the divergence of the distribution from normality, the presence of outliers, and heteroscedasticity. Quantile regression (QR), which is regarded as a non-parametric method, shows robustness against the specified phenomena. QR reveals the information carried by the distribution in tails as the returns focus on the whole of distribution. This means different beta for each percentile requiring investigation, and causes the problem of fusion of this information. Ordered Weighted Averaging (OWA) operators can merge the information coming from different percentiles at a required orness level depending on the attitude of the investor towards the risk. This study also suggests the use of OWA operators in addition to different quantile combination techniques used in the literature. As a result of the analysis performed based on Borsa Istanbul (Istanbul Stock Exchange) data, it was shown that OWA operators have a performance that is comparable to OLS and quantile combination techniques.