The intertemporal relationship between downside risks and expected stock returns: Evidence from time-varying transition probability models

The increasing inter relationship between financial markets have led to the discovery of new risk dynamics particularly when considering downside risk. Recent advances in econometric modelling have prompted the search for new insights into the intertemporal dynamics between downside risks and expected stock returns. Therefore, the aim of this study was to investigate this relationship in the S&P 500, the FTSE 100, the DAX, the Nikkei 225, and the TSX Composite, covering the period from January 2000 to December 2023. Using a time-varying transition probability model, the findings revealed consistent negative correlations between downside risk measures and expected returns across all markets, with CVaR exhibiting stronger inverse relationships compared to VaR. These findings challenge the classical risk-return trade-off but align with behavioural explanations where heightened risk aversion during downturns suppresses returns. The regime-switching analysis further uncovers asymmetry in transition probabilities where high-risk regimes persist with a 74% probability, while low-risk regimes show greater stability. By implication, this study provides empirical support for regulatory frameworks prioritizing tail risk mitigation, particularly in volatile markets. Key Words:Downside Risk; Expected Return; Scaling Behaviour; Time-Varying Transition Probability Models; Value-at-Risk; Conditional Value-at-Risk