Investigating the Relationship between Size Factor, Value Factor and Market Risk Premium (Complementary or Substitution) in Explaining the Portfolios Excess Returns Changes

The impact of risk factors on stock returns is an issue in market- based accounting research. Most of the debate is centered on their incremental ability to predict future earnings. The focus of the recent studies in capital market has also been on the factors effective in the decline of investment risk and their effects on the stock returns. One such study is the three factors model by Fama and French (1993), which shows the effect of risk factors in explaining stock return changes better. The present study aims at examining the relationship between size factor, value factor and market risk premium in order to investigate whether they are complementary or substitution in explaining the time-series variation in portfolio returns. In other words, do these factors proxy for the same risk and contain the same information? Hypotheses: This study examines three factors of Fama & French model, in order to investigate its usefulness in explaining the component of the time-series variation of listed companies in Tehran stock exchange. The primary goal is investigating the relationship between size factor, value factor and market risk premium. Thus research hypotheses are developed as follows: H1. Size factor, value factor and market risk premium explain the changes of portfolios excess returns. H2. Value factor and market risk premium are complementary or substitution in explaining of changes in the excess returns of portfolio. H3. Size factor and market risk premium are complementary or substitution in explaining of changes in the excess returns of portfolio. H4. Size factor and value factor are complementary or substitution in explaining of changes in the excess returns of portfolio. The sample companies in the present study consists of 80 listed companies in Tehran Stock Exchange during the period of 2003-2010. The data required for the research is gathered through Tadbir Pardaz software. Market risk premium factor is the excess return on the market portfolio. Size factor is defined as the monthly difference between average return on small size portfolios and the average return on big size portfolios. Value factors is defined as the monthly difference between average return on the high B/M portfolios and the average return on the low B/M portfolios. We use Wald test to evaluate the joint significance of the intercepts and Seemingly Unrelated Regression method (SUR) for the joint significance of the coefficients. If the coefficients of a tested risk factor are jointly significant, then this variable is a useful factor in explaining portfolio returns and vice versa. The first hypothesis was supported. Size factor, value factor and market risk premium are significant in explaining the variation of size & B/M portfolio returns and incrementally important in explaining the time-series variation of portfolio returns. The second hypothesis shows the sum of the market risk premium and value factor explaining the time-series variation of four (1, 2, 5, 6) individuals portfolios while the value factor explaining the time-series variation of four (1, 2, 5, 6) individual portfolios. The third hypothesis shows the sum of the market premium and size factor explaining the time-series variation of five (2, 3, 4, 5, 6) individual portfolios while the value factor explains the time-series variation of five (2, 3, 4, 5, 6) individual portfolios. The fourth hypothesis shows the size factor and value factor explaining the time-series variation of six (1, 2, 3, 4, 5, 6) individual portfolios while the value factor explaining the time-series variation of four (1, 2, 5, 6) individual portfolios and size factor explaining the time-series variation of five (2, 3, 4, 5, 6) individual portfolios. Asset pricing tests show that size factor, value factor and market risk premium explain the time series variation in the excess returns of similar sets of portfolio. Results indicated that risk factors are incrementally important in explaining the time series variation of portfolio returns. Findings show that market risk premium factor and value factor explain the variation in similar set of portfolios and contain similar information and can be viewed as substitutes for each other. Although in explaining portfolio returns, they are complementary sources of information for investors, market risk premium factor and value factor interpreted as risk factors are substitutes rather than complements. Market risk premium and size factor can be viewed as substitutes for each other. An asset pricing implication of the results is that these factors can be used interchangeably in asset pricing tests, because these two risk factors explain the variation in similar set of portfolios and contain similar information content. The size factor and value factor explain the variation in non-similar set of portfolios and they contain non-similar information, so they can be viewed as complementary for each other. This study indicates that the users in their prediction can only consider the value factor and size factor, while market premium factor does not provide more information for them. This paper employs the Fama & French (1993) model as the benchmark asset pricing model in the Iran stock market. Hence, testing the robustness of our results using alternative model such as the Cahart (1997) model is another possible avenue for future research.