UBC Theses and Dissertations
An investigation of the market model when prices are observed with error Gendron, Michel
The market model, which relates securities returns to their systematic risk (β), plays a major role in finance. The estimation of β , in particular, is fundamental to many empirical studies and investment decisions. This dissertation develops a model which explains the observed serial correlations in returns and the intervaling effects which are inconsistent with the market model assumptions. The model accounts for thin trading and different frictions in the trading process and has as special cases other models of thin trading and frictions presented in the finance literature. The main assumption of the model is that the prices observed in the market and used to compute returns differ by an error from the true prices generated by a Geometric Brownian Motion model, hence its name, the error in prices (EIP) model. Three estimation methods for β are examined for the EIP model: the Maximum Likelihood (ML) method, the Least Squares (LS) method and a method of moments. It is suggested to view the EIP model as a missing information model and use the EM algorithm to find the ML estimates of the parameters of the model. The approximate small sample and asymptotic properties of the LS estimate of β are derived. It is shown that replacing the true covariances by their sample moments estimates leads to a convenient and familiar form for a consistent estimate of β. Finally, some illustrations of six different estimation methods for β are presented using simulated and real securities returns.
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