Robust estimation of factor models in finance
Bailer, Heiko Manfred
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Standard asset-pricing models entail expressions for expected returns in terms of coefficients relative to risk factors. Methods to estimate premiums of risk factors have, at its core, a single or multiple linear regression models. Ordinary least squares (OLS) estimation is the common choice. However, it is well established that financial returns are heavy-tailed, skewed, and vary over time. This dissertation shows that small fractions of outlying observations bias OLS estimates and inflate its variability. Outlying observations include months, firms, time periods, and gross errors. Some subset of outlying firms may have some economic value, which leads to a great fear of simply rejecting them. This dissertation uses exploratory data analysis and the robust MM-estimator to separate influential observations from the bulk of the data and to estimate risk premiums on both groups. The key results are: OLS alphas from the single-factor market model are often over-estimated due to outliers and positive asymmetry of the returns distribution. OLS betas are highly sensitive to outliers. Robust alphas and betas are superior in predicting future returns and risk, and are insensitive to the choice of returns type and returns that are dirty, e.g. not split or dividend adjusted.The risk premium as found by Fama & French (1992) to be flat for beta and negative for size is a small size firm and seasonality effect. The risk premiums for beta (size) are positive (negative) only in January and for a tiny number of influential small size firms. Once adjusted the beta (size) risk premiums become negative (positive), confirming partial results of Knez & Ready (1997). The seasonality effect appears to be small compared to influential firm effect, only since seasonal effects average out. The January effect is significant and spills over into February and March; in addition, size shows seasonal and book-to-market quarterly variability. Overall the MM-estimator is shown to be not only an easy-to-use alternative to the OLS estimator, unbiased towards small fractions of unusual observations, but also a tool that can be used to identify and analyze influential observations and to find trading strategies.
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