This paper studies the error pattern in case of asset pricing models, using the multivariate nonparametric regression technique to extrapolate possible improvement of fit for the nonparametric model over the usual parametric one. The authors have attempted to compare the parametric and the nonparametric regressions in terms of fit. The study concludes that the nonparametric regression is better than its parametric counterpart and the Epanechnikov Kernel gives better estimate than the Gaussian Kernel.
The objective of this article is to find out a nonparametric regression model capable of
describing the effect of various market indices (stock market index, sector-specific index,
volume of trade, Index of Industrial Production, etc.) on returns of different securities.
This article tries to find out the behavior of error terms in case of Capital Asset Pricing
Model (CAPM) using the nonparametric regression techniques.
Parametric models are fully determined up to a parameter (vector). The fitted models
can easily be interpreted and estimated accurately if the underlying assumptions are
correct. If, however, they are violated then parametric estimates may become inconsistent
and give a misleading picture of the regression relationship. In reality these assumptions
are not followed i.e., errors may not follow a normal distribution and the distribution of
errors may not be symmetric at all.On the other hand, nonparametric models of the risk-return trade-off in capital asset
pricing situations avoid restrictive assumptions on the functional form of the regression
function m (to be discussed in detail below). However, these models may be difficult to
be interpreted and yield inaccurate estimates if the number of regression is large. In the
nonparametric analysis nothing is assumed about the shape of the distribution prior to
analysis. The given data is fitted according to a chosen model and it is tried to find out
the distribution from it.
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