The Use Of Quadratic Filter For The Estimation Of
Time-varying β
Author(s)
M. Gastaldi, A. Germani & A. Nardecchia
Abstract
The beta parameter is used in finance to estimate systematic risk and usually it is
assumed to be time invariant. The literature shows that there is now considerable
evidence that beta risk is not constant over time. The aim of this paper is the
estimation of time-varying Italian industry parameter betas using a new approach
based on the Kalman filter technique and on polynomial estimates. This
approach is applied to returns of the Italian market over the period 1991-2001.
Keywords: time-varying beta, additive non-Gaussian noise, Kalman filter.
1 Introduction
The market effect on the returns of single assets is one of the most investigated
arguments in finance. The Capital Asset Pricing Model (CAPM) suggests that
the market effect is due to the relationship between the asset returns and the
market portfolio returns. Moreover, the asset sensibility to the variations of the
market portfolio returns produces the single asset expected returns. Parameter β
measures the asset sensibility to the variations on the market returns [1].
In the classical financial analysis, parameter β is assumed to be time invariant
and returns have a Gaussian distribution [2], but there is considerable general
evidence that these assumptions are invalid in several financial markets as
US markets [3] and Australia [4].
During the first 1970’s researchers saw the first applications of the Kalman
filter to the estimation of the systematic risk [5,6]. The proposed model for β
was the Random Walk Model [7] requiring the estimation of the unknown
variances. Many researchers investigated the validity of the CAPM in presence of
Keywords
time-varying beta, additive non-Gaussian noise, Kalman filter.
Related Book
Other papers in this volume
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