رابطه مشروط بین بتا و بازده: شواهد اخیر از بازارهای بین المللی سهام

The risk–return relationship is one of the fundamental concepts in finance that is most important to investors and portfolio managers. Finance theory argues that the beta or systematic risk is the only relevant risk measure for investors. However, many studies have showed that betas and returns are not related empirically, no matter in domestic markets or in international stock markets. This paper examines the conditional relationship between beta and returns in international stock markets for the period from January 1991 to December 2000. After recognizing the fact that while expected returns are always positive, realized returns could be positive or negative, we find a significant positive relationship between beta and returns in up market periods (positive market excess returns) but a significant negative relationship in down market periods (negative market excess returns). The results are robust for both monthly and weekly returns and for two different proxies of the world market portfolio. Our findings indicate that beta is still a useful risk measure for portfolio managers in making optimal investment decisions.

The risk–return relationship is one of the fundamental concepts in finance that is most important to investors and portfolio managers. One of their tasks is to estimate the investment risk. The famous Capital Asset Pricing Model, CAPM (Black, 1972, Lintner, 1965 and Sharpe, 1964) argues that beta or systematic risk is the only relevant risk measure for investment and a positive trade-off between beta and expected returns should exist. Because of its importance and relevance to all investors, it is one of the most extensively tested financial models in the literature. The CAPM states that the expected return of an asset is a positive function of three variables: beta (the covariance of asset returns and market returns divided by the variance of the market returns), the risk-free rate and the expected market return. The major focus of the tests on CAPM is to check whether returns are statistically positively related to betas. Since in reality only realized asset/market returns are available, average realized returns are used to proxy the expected returns and returns on security index are used to proxy the market returns. Empirical tests in 1970s (e.g. Fama & MacBeth, 1973) support the validity of the CAPM. However, empirical evidence in 1990s (e.g. Fama and French, 1992, Fama and French, 1996 and Jegadeesh, 1992) indicates that betas are not statistically related to returns, and so some researchers conclude that beta is dead and suspect the validity of beta in measuring risk. Previous empirical tests are mainly based on the Fama and MacBeth (1973) methodology. However Isakov (1999) argued that this methodology does not leave much opportunity for beta to appear as a useful risk measure in the risk–return relationship for two reasons. First, the model is expressed in terms of expected returns; however, tests can only be performed on realized returns. Secondly, the realized market excess return does not behave as expected since it is too volatile and is often negative. Recent studies (e.g. Pettengill, Sundaram, & Mathur, 1995 for the US market; and Isakov, 1999 for the Swiss market) suggested an alternative approach to assess the reliability of beta as a measure of risk. The alternative approach is that when the realized market returns exceed the risk-free rate of interest (i.e. the realized market excess returns are positive), the betas and realized excess returns should have a positive relationship. Similarly, when the realized market excess returns are negative, the betas and realized excess returns should have a negative relationship. This paper extends this approach and applies it to 13 international stock markets. The results show that beta is still a good measure of risk and is significantly related to realized returns in both up and down market situations. Hence, beta is still a useful measure of risk for investors in making optimal investment decisions. The rest of the paper is organized as follows: Section 2 presents the theoretical framework used in this paper. Section 3 provides a literature review of the relationship between beta and returns. Section 4 describes the data and methodologies used. Section 5 reports our empirical results and Section 6 concludes the paper.

Previous studies on testing unconditional relation between beta (systematic risk) and returns found a weak and nsignificant relationship. However, when taking into account of the conditional relationship between beta and returns, a significant relationship is found. Our study examines this conditional relationship in 13 international stock markets for the period 1991–2000. Like the studies of conditional relationship between beta and returns on the US market, there is a significant positive relationship in up markets and a significant negative relationship in down markets. The results are the same no matter the MSCI world index or an equally weighted world index returns are used to proxy world market returns. Also, our results are robust for both monthly and weekly returns. Unlike previous studies, no January seasonal effect is found in the unconditional relationship between beta and returns. However, a significant positive relationship in up markets and a significant negative relationship in down markets are found for all months in a year. Furthermore, this paper finds that both monthly and weekly market excess returns are, on an average, positive but the symmetry of risk–return relationship in up markets and down markets is weak, which is inconsistent with previous studies of conditional relationship of CAPM. The main reason may be due to the different models used. Overall, this paper shows that high-beta countries do capture higher returns in up markets and poorer returns in down markets than low-beta countries. Our results are clearly useful for international investment. Since significant conditional relationship is observed in the model of international CAPM, the paper supports the continuous use of beta as a relevant risk measure. Beta is still a useful tool in explaining the cross-sectional differences in country returns and for portfolio management (e.g. for market-timing strategies). Hence, international investors and portfolio managers should note our findings in making their optimal investment decisions.