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The capital asset pricing model and the probability of bankruptcy: theory and empirical tests. Turnbull, Stuart McLean,


Empirical evidence shows that the Capital Asset Pricing Model (CAPM) is misspecified. Securities of low systematic risk consistently earn more than predicted by the model, the reverse being true for securities of high systematic risk. Whilst the relationship between ex-post returns and systematic risk appears to be linear, the estimated regression coefficients are significantly different from their theoretic values. Various attempts to explain theoretically the causes of the misspecification have been explored, but fail to provide an adequate explanation of all the observed deficiencies. The dissertation examines how the mechanism of bankruptcy affects the structure of returns for corporate financial assets. The hypothesis of the thesis is that the probability of bankruptcy across securities and across time is reflected in the residual return after abstracting from the market. Using stochastic control theory, a two variable extended form of the continuous time analogue of the CAPM is derived. The second variable is associated with the probability of bankruptcy. The model provides a natural explanation of the deficiencies of the CAPM. A discrete time ex-post formulation of the model is used to test empirically the hypothesis. This necessitates being able to measure the probability of bankruptcy. A model formulated in terms of a firm's ability to raise funds, either internally or externally, to cover fixed charges is developed, and the probability of bankruptcy estimated using the maximum likelihood methodologies of logit analysis and probit analysis. The ability of the model to predict bankruptcy is tented on a secondary sample of bankrupt firms. Excellent results are obtained with the model predicting bankruptcy, for some firms, four or five years before the actual occurrence. Using a pooling of time series and cross section data to estimate the coefficients of the regression equation representing the hypothesis, evidence is found indicating that bankruptcy is an explanatory factor of common stock returns.

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