Capital asset pricing model (CAPM) and Indian stock market with autoregressive integrated moving average model
THE objective of this study is to empirically investigate the applicability of CAPM for some selected stocks listed in the Bombay Stock Exchange (BSE) over the period January, 2014-August, 2015. More specifically, the study is directed to examine (i) the individual risk premia were directly related to market premia, (ii) the risk-return relation for these stocks were positive as dictated by the CAPM, (Hi) the stocks were ‘underpriced ’or ‘overpriced ’and (iv) the risk adjusted relative performance of these selected stock with respect to the market, (v) the role of CAPM in the choice of stocks by a rational investor.
The Market Model, developed by Sharpe (1964), holds that most shares maintain some degree of positive correlation with market portfolio. When market rises, most shares tend to rise. Sharpe postulated a linear link between a security return and the market return as a whole such that the excess return on a security is linearly and proportionately related to the excess return on the market portfolio. Let us consider a security i with expected return E(R.). Then for any risk free return (R*), CAPM definition is that
|( 1 )|
Where E(Ri) =expected rate of return on security i
Rt* =risk free rate of return
E(Rm) =expected rate of return on the market portfolio
E(Rit)-Rt* =the excess of rate of return on security i over the risk free rate of return
= the risk premium for the security i
E(Rmt)-Rt* =the expected rate of market return over the risk free rate
= the market premium
βi-=the sensitivity of the risk premium of the security i to the market premium
Therefore, the equation (1) states that the risk premium for any individual security (i) equals the market premium times the corresponding β1.
Thus, according to Sharp's model, the only common factor affecting all securities is the market rate of return. All other factors, like dividend yields, price-earning ratios, quality of management and industrial features bear no separate influence on E(Rit).
The study shows that (a) CAPM held good completely for 13 stocks. So CAPM was not found to be applicable to all the stocks under study. (b) 19 stocks display white noise. For 12 of these stocks CAPM held completely (i.e., α=0, β≠0) and for 5 of these stocks CAPM held partially (i.e., α≠0, β≠0). (c) 11 stocks display ARIMA (p, o, q) structures of stochastic process. For 10 of these stocks CAPM holds partially (i.e., α≠0, β≠0). However, one of these stocks is found to be supportive of CAPM. (d) 10 stocks with white noise or ARIMA (p, o, q) structures, displaying support for CAPM completely (i.e., α=0, β≠0) or partially (i.e., α≠0, β≠0) and which excelled both by the Trenor and Sharpe measures, were, ‘undervalued’ by nature. These are Bharat Petrolium, Cipla Ltd, HDFC, Kotac Mahendra, Larsen, Lupin, Maruti Suzuki Ltd., Punjab National Bank, Asian Paints, Hindustan Unilever. (e) For 5 of the stocks having white noise structures, which excelled both by the Trenor and Sharpe measures, CAPM held completely. Evidently, all these stocks are ‘undervalued’. These are Bharat Petrolium, Kotac Mahendra, Punjab National Bank and Asian Paints and Hindustan Unilever. All these stocks are defensive.
It considers a time period January, 2014—August, 2015 for some selected stocks listed in the Bombay Stock Exchange (BSE).
A rational investor may decide to choose a stock with the potentiality of (i) attaining superior risk-adjusted performance in the market (ii) stabilizing the volatility of portfolio which he already possesses and (iii) reaping higher actual rate of returns than expected. In such case, he would choose a ‘defensive’, ‘undervalued’ stock. In this case, his choice gets limited to 3 stocks (Cipla, Asian Paints and Hindustan Unilever) with white noise structure for returns.
This study empirically investigates the applicability of CAPM for 30 selected stocks listed in the Bombay Stock Exchange (BSE) over the period January, 2014—August, 2015. More specifically, the study is directed to examine if individual risk premia were directly related to market premia, if the risk-return relation for these stocks were positive as dictated by the CAPM, if the stocks were ‘underpriced’ or ‘overpriced’ and the role of CAPM in the choice of stocks by a rational investor.
CAPM, Systematic Risk, Skewness, Jarque-Bera Test, Jensen Statistics, Cointegration, Stationarity, Adaptive Expectation, ARIMA (p, d, q) forecasts.