Returns and Volatility: A Study of the Irish Equity Market

Abstract

In an important advance, Merton (1980) proposed that the development of reliable variance estimation models would play an important part in the study of price volatility. In practice, this implies that pricing models should take account of heteroscedasticity. The development of ARCH models (Engle, 1982) is important, as they do this by specifically defining the changing conditional variance. They have had a tremendous impact on financial research. This paper examines the relation between stock returns and volatility, using Irish market data. The two basic hypotheses are: (1) that expected returns are positively related to expected volatility, (a higher risk premium would be required in compensation for higher risk exposure). and (2) unexpected returns are purported to be negatively related to unexpected volatility (a higher than average return may cause a decrease in volatility). Market volatility is examined, using ARMA models. They allow the estimation of expected volatility. Conditional variances are also generated, using a number of variants of the ARCH models. The significance of different possible relationships can then be tested.