An empirical investigation of the long memory effect on the relationship between downside risk and stock returns: Evidence from international stock markets

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Long memory suggests that past returns can influence future returns over extended periods, indicating potential predictability. The aim of this study was to empirically examines the interplay between long memory effects, downside risk, and stock returns across five major international equity markets (S&P 500, FTSE 100, Nikkei 225, DAX, and ASX) from 2000 to 2022. An ARFIMA model which quantify fractional differencing was used in conjunction with a correlation matrix, regression and Granger causality test to investigate the interplay. The findings revealed a significant long memory across all markets, with Nikkei 225 exhibiting the strongest persistence, attributed to Japan’s prolonged economic stagnation. Counterintuitively, lagged downside risk positively predicts returns, aligning with behavioural theories of investor overreaction to tail events. Bidirectional causality between risk and returns underscores reflexive market dynamics. The study bridges a critical gap by integrating long memory into downside risk models, demonstrating that persistent volatility amplifies tail risk premiums. The findings of this study suggest that financial market regulators need to seriously considers adaptive regulatory tools due to the dual long memory in returns and downside risk necessitates. To the author´s knowledge, this study is the first to bridge a critical gap in the literature by systematically integrating long memory effects with downside risk metrics so as to provide a more robust framework for understanding risk-return dynamics, as it accounts for the persistent nature of volatility and tail risk, which traditional short-memory models often overlook.

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