High-Frequency Return-Implied Volatility Relationship: Empirical Evidence from Nifty and India VIX

The risk-return trade-off is a fundamental query in financial literature. Theories envisage the relationship to be positive in long run. However, empirical evidence suggests that the relationship is negative in short-run. This paper investigates the shortterm relationship of risk-return using model-free implied-volatility as a proxy for risk. The relationship is tested by employing high-frequency five-minute interval data of return and model-free implied volatility. Previous studies argue three competing hypotheses to elucidate the short-term relationship. Leverage hypothesis and volatilityfeedback hypothesis are founded on the causality of the relationship between return and volatility. Recent developments of the behavioural finance offer explanations based on existing biases of the market participants. This study examines the short-run relationship considering these three competing hypotheses. The Vector Auto regression (VAR) is employed to test the traditional leverage and volatility-feedback hypotheses. The VAR predicts unidirectional relationship in favour of leverage hypothesis, albeit inconclusive in case of extreme distributions of these two timeseries. The exploratory analysis of intra-day behaviour of return and implied-volatility in a short interval of reveal that VAR methodology is inadequate to elicit the extreme behaviour of the relationship. The quantile regression framework captures the relationship in the extreme movements of return and model-free implied-volatility. The relationship elicits that traditional hypotheses namely leverage and volatility-feedback are inadequate to capture the complete spectrum of the dynamic relationship between these two time-series. Rather, results from quantile regressions reveal that the explanation of the relationship is improved considering recently developed behavioural hypotheses. The study gathers support for the affect’s heuristics of behavioural theory in which traders react differently to positive and negative returns. The negative innovation in returns are the most significant factors for the sharp rise of India VIX, indicating the consistency of the behavioural explanation. The study reveals that the short-term relationship between risk-return is not only negative but also asymmetric. Among the three competitive hypotheses, the behavioural hypothesis best explicates the negative and asymmetric relationship between risk and return.