Asset pricing models under parameter nonstationarity
Varma, Jayanth R.
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Asset pricing theory in modern finance deals with the valuation of risky assets, particularly, financial securities. Apart from its application in portfolio management, asset pricing theory is used in corporate finance to determine the cost of capital for the firm and to evaluate projects for capital budgeting purposes. The premier asset pricing theory, today, is the Capital Asset Pricing Model (CAPM) which asserts that the expected rate of return on any security rises linearly with its riskiness where the measure of riskiness is the beta (the covariance between the security return and the market rate of return divided by the variance of the market return). Computationally, the beta is usually obtained by regressing the security returns on the market return. Obviously, this procedure is valid only if the betas are constant over time . This thesis deals with the situation where the betas may change over time. Three alternative methods have been used to estimate these no stationary betas : ‘ 1. Kalman Filtering : In this model we postulate that the betas change gradually from period to period; the changes in each period are independently normally distributed. The estimation of time varying betas can then be formulated as a Kalman Filtering problem. The variance of the random changes in the betas can then be estimated by maximum likelihood. Estimating this model on a sample of 45 securities revealed that in the case of 18 securities the hypothesis of stationary betas could be rejected at the 1% level of significance (in 13 of these cases the significance is 0.12). 2. Bayesian Detection Qi Structural Breaks : In this model we assume that the betas could undergo large changes at some random points of time which may be called break points; between these points the betas do not change. This is known as a structural breaks was extended to estimate this model. Using this model it was found that the breaks in the betas were significant at the 12 level in the case of 30 out of 45 securities (in 27 cases the significance level is 0.1%). 3. Mixed Model : The mixed model attempted to combine the features of both of the above models allowing both gradual continuous changes and some abrupt jumps. This model did not perform better than the structural break model. Computer algorithms for all the above models were implemented on the VAX—11/750 computer system at the Institute; the code written in Fortran with core routines in Assembler. The empirical results discussed above evidence for nonstationarity of betas market; apart from statistical significance, the observed changes in the betas are substantial in magnitude. It is also empirically established that the nonstationarity of betas leads to very high estimation error in the value of the betas at any point of time. These empirical results have serious implications for the use of CAPM in portfolio management and corporate finance: 1. The betas cannot be estimated by ordinary regression; sophisticated econometric methods are mandatory. 2. Betas cannot be estimated once and for all; frequent revision is essential. 3. Since the betas are not known with certainty, the cost of capital obtained from the CAPM is also subject to error. The work also has implications for using the CAPM in empirical research in finance. In discussing these implications of time varying betas, we have implicitly assumed that when the assumption of constant betas is dropped, a multiperiod version of the CAPM would still hold. In other words, at each period the CAPM relationship will obtain if we use the correct betas for that period. The thesis discusses the theoretical justification for such a multiperiod CAPM. The thesis also subjects the multiperiod CAPM itself to an empirical test. In this test we do not assume that the betas are constant over time; instead, we use an instrumental variable approach which does not require the time path of betas to be perfectly known. The methodology involves pooled time series cross—sectional regression using the most efficient Generalized Least Squares and Maximum Likelihood estimation. The test which was carried out on a database of over 30000 prices on 45 securities in the Bombay Stock Exchange does not reject the CAFM. In view of the paucity 0+ empirical work in the Indian context on the validity of the CAPM this finding is important though replication on a larger sample of securities is desirable to provide conclusive evidence in favour of the theory.
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