An Autoregressive Approach of the Arbitrage Pricing Model to the Portuguese Stock Market

ABSTRACT We use an autoregressive methodology in relation to the Arbitrage Pricing Model (APT) developed by Mei (1994), applying it, for the first time, to the Portuguese stock market. The results suggest that the number of risk factors explaining stock returns varies with time and that these were not the same, which seems to be strong evidence against the APT. Also, after testing the statistical significance of the factor risk premiums, it seems that we can conclude that the stock returns could be explained by more than one factor and that those factors are priced. JEL: G12 Key words: APT; Capital asset pricing models; Arbitrage; Risk factors; Autoregressive models. I. INTRODUCTION By emphasising the possibility of existing several risk factors, the APT, at least intuitively, seems to be superior to the CAPM. Although there are different approaches for testing the APT, we can identify two major ones: one that uses factor analysis for identifying the factors and the other that defines a priori the risk factors using variables with economic meaning. The recent methodology developed by Mei (1994), does not follow any of those methodologies in order to identify the risk factors, in the context of the APT. The intuition behind this approach is that today's returns can, partially, be explained by yesterday's returns. This paper is divided into five sections. After this introduction, in a second section, we briefly present the APT. A synthesis of the methodology developed by Mei (1994), our sample and the tests are presented in the third one. The results are presented in the fourth section and the conclusions in the fifth. II. THE APT MODEL According to the APT, in equilibrium, the stock returns, or the returns of a group of stocks, in a period t, can be explained by: [R.sub.i,t] = R([E.sub.0,t]) + ([[lambda].sub.k,t] + [f.sub.k,t])[B.sub.i,k] + [[epsilon]. sub.i,t] (1) where: [R.sub.i,t] is the return on a stock or group of stocks; R([E.sub.0,t]) is the expected return on a risk free asset; [[lambda]. sub.k,t] are the risk premium factors; [[beta]. sub.i,k] represents the sensitivity of stock i (or group of stocks) to the movements of K factors; [f.sub.k,t] is a group of random factors with mean equal to zero; [[epsilon]. sub.i,t] is the specific random variable, also with zero mean, usually known as noise variable. Some major assumptions are that, at the beginning of the period, the factors are independent; also that the factors and the noise variable are not correlated, as well as the different stocks (i's) (or groups of stocks). III. METHODOLOGY 3.1 The model It is assumed that the APT model explains the returns of a stock or groups of stocks. If we can obtain information about [[beta]. sub.i] (stock sensitivities to the k factors changes), it is possible to estimate (1) using a cross sectional regression. Mei's (1994) contribution is a new methodology for obtaining [[beta]. sub.i]. So, assuming that the historical returns contain information about [[beta]. sub.i] and that some parameters are constant across firms, we can use (1) and apply an autoregressive approach. If: [S'. sub.t] = ([S.sub.1,t], ., [S.sub.k,t]) = ([f.sub.1,t], ., [f.sub.k,t]) + ([[lambda].sub.1,t], ., [[lambda].sub.k,t]) and [B'. sub.i] = ([B.sub.i,1], ., [B.sub.i,k]) then [R.sub.i,t] = [[lambda]. sub.0,t] + [S.sub. 't][B.sub. 't] + [[epsilon]. sub.i,t], i = 1, . N t = 1, . T (2) In order to obtain information about [[beta]. sub.i], we use historical data and equation (1) for each stock i, from t-1 until t-k, and being: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Assuming S as non-singular: [B. …