REGRESSION EQUATION FITTING AS AN APPROACH TO MODELLING FINANCIAL DATA

Abstract

Many financial models deal with concepts that are linked to regression. The unpopularity of its use in
application is due to the fact that the residuals distribution is not normal. A key example is that of the
study of the risk-adjusted return of the portfolio. The general equation is regarded as
r - Rf = α + β ( Km - Rf ) (1)
Where r is the fund's return rate, Rf is the risk-free return rate, and Km is the return of the index. This
can be regarded as the usual equation for CAPM excepting the existence of α. β is the ´beta´ derived
from the classic Sharpe’s representation of equilibrium prices. When fitting a regression we include an
error term ε and α represents how much better the fund did than the predicted CAPM. We revise this
problem considering that the residuals are distributed according to Stable distributions, not necessarily a
normal. Some related financial problems are considered in a similar fashion. Monte Carlo experiments
are developed for comparing different methods for estimating the so-called beta-coefficients.