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

Abstract

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 through a model where (i) the conditional mean specification considers the threshold autoregressive model for two market situations characterized as up and down markets, (ii) the conditional variance 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, and Japan - and four important emerging economies, called the BRIC group, we have found that the nature of risk-return relationship is different in up and down markets. Furthermore, the risk aversion parameter is positive in the down markets and negative in the up markets. This finding supports the hypothesis that investors require a premium for taking downside risk and pay a premium for upside variation. Finally, the findings suggest that the nature of risk-return relationship is same for the two groups of countries.

Keywords

• Asymmetric Risk Aversion
• Leverage Effect
• Up and Down Markets
• Threshold Regression
• Exponential GARCH-M