Selection criteria for regression models and their application to abnormal event studies in finance

This paper, which is concerned with the development of model selection criteria in the context of regression analysis, was motivated by the following application. The assessment of the impact of abnormal events, such as the announcement of a merger or financial restructuring, on share price performance presupposes the specification of a model that appropriately describes ‘normal’ share price behaviour. Traditionally, in the Finance literature, this model is taken to be a simple linear regression of excess share price returns on the excess return on the market index. In addition, two constrained forms of this simple model, viz. a model with a zero intercept term and unconstrained market index coefficient (Capital Asset Pricing Model), and a model with a zero intercept term and coefficient of the market index that is put equal to 1 (Market adjusted model) have been considered as alternatives. An appropriate set of model selection criteria for evaluation of these models based on the MSEP (mean square error of prediction) and the MSE (mean square error) principles are developed. The selection criteria are then applied to a large number of share prices on the New York and Johannesburg Stock Exchanges. In the case of the New York Stock Exchange, no particular model tended to be the dominant selection but in the case of the Johannesburg Stock Exchange the procedure was more unequivocal and in a very high percentage of cases a simple Market Adjusted Model rather than an unconstrained model was selected. This selection pattern is clearly related to the fact that, on average, share returns on the JSE exhibit lower fits against market returns than do share returns on the NYSE. This is related to the higher volatility of the JSE and the persistent problems of thin trading on this market. The analysis represents an interesting example of how unstable relationships are often more effectively described by fitting a model of lower complexity.