Abstract
ABSTRACT The purpose of this work is to present the Weighted Forward Search (FSW) method for the detection of outliers in asset pricing data. This new estimator, which is based on an algorithm that downweights the most anomalous observations of the dataset, is tested using both simulated and empirical asset pricing data. The impact of outliers on the estimation of asset pricing models is assessed under different scenarios, and the results are evaluated with associated statistical tests based on this new approach. Our proposal generates an alternative procedure for robust estimation of portfolio betas, allowing for the comparison between concurrent asset pricing models. The algorithm, which is both efficient and robust to outliers, is used to provide robust estimates of the models’ parameters in a comparison with traditional econometric estimation methods usually used in the literature. In particular, the precision of the alphas is highly increased when the Forward Search (FS) method is used. We use Monte Carlo simulations, and also the well-known dataset of equity factor returns provided by Prof. Kenneth French, consisting of the 25 Fama-French portfolios on the United States of America equity market using single and three-factor models, on monthly and annual basis. Our results indicate that the marginal rejection of the Fama-French three-factor model is influenced by the presence of outliers in the portfolios, when using monthly returns. In annual data, the use of robust methods increases the rejection level of null alphas in the Capital Asset Pricing Model (CAPM) and the Fama-French three-factor model, with more efficient estimates in the absence of outliers and consistent alphas when outliers are present.
Highlights
In spite of the empirical evidence provided by Fama and MacBeth (1973) of the linear risk-return relationship posited by the theory, the literature of asset pricing shortly turned towards the development of multifactor models, which are discussed
Their results, based on jackknife measures of efficiency, indicate that robust methods are less sensitive than ordinary least squares (OLS) to model misspecification – such as extreme excess market returns, and that the superior efficiency of the robust estimators was caused by non-normality in the distribution of residuals
The Forward Search (FS) described by Atkinson and Riani (2000) is a robust method that provides useful plots, which allows one to understand the real structure of the data being analyzed and assess the agreement between the data and the model
Summary
The Capital Asset Pricing Model (CAPM) introduced by Sharpe (1964) and Lintner (1965) represents a pathbreaking milestone in the history of financial theory The publication of these seminal papers led to the development of a large body of research in various areas of finance, both from normative and positive points of view. We apply the FSW estimator on time series regressions of the 25 Fama and French (1993) portfolios It is, to our knowledge, the first application of estimators with high efficiency and high-breakdown point in this context, as previous research, such as Knez and Ready (1997) and Bailer (2005), has focused on the impact of outliers in cross-section regressions using methods which are either efficient or robust.
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