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Several empirical studies in finance have examined whether or not the risk associated with any stock market responds differently in two different states of the stock market, especially in bull and bear markets. This paper studies this problem in the modelling framework, where (i) the conditional mean specification considers threshold autoregressive model for two market situations characterized as up and down markets, (ii) the conditional variance (as a measure of time-varying risk) specification is asymmetric in the sense of capturing leverage effect, and (iii) the conditional variance directly affects the conditional mean through the risk premium term in the risk-return relationship. Using daily returns on stock indices of eight countries, comprising four developed countries - the USA, the UK, Hong Kong, Japan - and four important emerging economies, called the BRIC group of countries viz., Brazil, Russia, India and China, we have found that the nature of risk-return relationship is different in up and down markets. Furthermore, the risk aversion parameter, which is significant in most of the countries, is positive in the down markets and negative in the up markets. This finding supports the hypothesis of Fabozzi and Francis (1977) and Kim and Zumwalt (1979), namely, that investors require a premium for taking downside risk and pay a premium for upside variation; moreover, the findings confirm that the nature of risk-return relationship is same for the two groups of countries.

Is the Effect of Risk on Stock Returns Different in Up and Down Markets? A Multi-Country Study