The Conditional Relationship between Beta and Stock Returns: An Empirical Study in the Colombo Stock Market

The objective of this research is to find out the conditional relationship between beta and stock returns for the period 1999 to 2013 in the Sri Lankan market. This study tests whether the beta factor has an ability to influence on the stock returns and attempts to investigate the conditional relationship between beta and stock returns in Sri Lanka. This study reveals that the relationship between beta- return is positive during the up market condition and the relationship is negative during the down market condition in Colombo Stock Exchange during the study period. Therefore, the beta-realized return relationship is hold in the Colombo Stock Exchange with market condition such as up and down markets.


Introduction
Since the mid-nineteenth century, pricing of financial securities have been considering important research theme among the corporate finance. From Markowitz (1952) modern portfolio theory, Sharpe (1964), ), Merton (1976, Fama & MacBeth (1973) and Black & Scholes (1974) are developing financial market and asset pricing models for determining stock prices and the factors influencing their variations of stock return.
The Capital Asset-Pricing Model (CAPM) is widely used to evaluate portfolio performance and estimate cost of capital of firms (Rossi, 2016). According to the Sharpe (1964), Lintner (1965) and Black (1972) version of CAPM, the beta of a stock is considered as the only factor for variations of return on stocks. Fama & MacBeth, 1973;Stambaugh, 1982).
The CAPM assumes that there is a positive linear relationship exist between the risk of stock measured by beta and its expected (or realized) return. The validity of the model is dependent on the following two conditions: first, the market portfolio (often represented by a stock market index) must be efficient, secondly, the existence of a linear relationship between the expected returns and respective beta of stock. These two conditions are inseparable as each necessarily implies the each other. There are numbers of researches have been undertaken in various countries by various researchers but still the results are subjects to debate. The CAPM has been subject to numerous tests especially after Fama & MacBeth (1973) that have led to contradictory conclusions. (Davis, 1994;Fama & French, 1992;He & Ng, 1994;Miles & Timmermann, 1996;Roll, 1977 Fama & MacBeth, 1973;Stambaugh, 1982 (Fama & French, 1992;Lakonishok & Shapiro, 1984 The finding of this study may provides insights for potential investors to make their investment in a profitable manner and that will positively contribute to our economy. The rest of paper is organized as follows: Section 2 summaries the literature review. Section 3 describes the data and methodology. Section 4 presents empirical evidence of the study. Section 5 concludes the research.

Literature Review
In the early 1990s, Fama and French, published contradictory results in 1992 and 1993 on the CAPM. In the both articles, they question the relationship between the beta of a security and its average returns between 1963 and 1990, concluding that the CAPM is weak for the period between 1941 and 1990. Fama and French (1992) propose a multifactor model. In addition to the market betas, they taken into account the price-earnings (P/E) ratio, firm size, book to market ratio and january-effect in explaining the average returns of US exchanges: NYSE, AMEX and NASDAQ. According to Fama and French (1992), if stocks are rationally valued, the risks of equities would be linked to multidimensional factors, such as firm size, book to market ratio. Other empirical contradictions of the CAPM have been documented by Bhandari (1988), he finds that there is a positive relationship exist between leverage and expected return, which is not explained by Beta. The assumptions of the CAPM should be positive and linear. The studies by Black et al. (1972) and Fama and MacBeth (1973) validated the statements of the model for the period prior to 1969. However, subsequent studies indicate that the relationship between beta and the expected return on equities might not be significant (Fama & French, 1992). Pettengill, Sundaram, and Mathur (1995)  They suggest that the given market premium, there is systematic relationship between beta and portfolio realized. Nimal (2006a) investigates the conditional relationship between beta and return on individual stocks in the Tokyo Stock Exchange (TSE) and reveals significant conditional relationship is exist between beta and return even when individual stocks returns are considered.

Methodology
The study includes all common stocks listed

5.Conclusion
The traditional unconditional CAPM of Sharpe (1964), Lintner (1965) and Black (1972) states that the beta-realized return relationship is positive and liner. Many studies after Fama and Macbeth (1972) provides evidences against the unconditional CAPM. The negative market premium is