The Effect of Volatility on the Predictability of Returns in Stock Markets: Implications for Risk Management and Investment Strategies

The thesis investigates the relationship between volatility and stock returns, focusing on whether conditional volatility—estimated through GARCH family models—has predictive power on stock market returns. While existing literature predominantly examines the contemporaneous links between returns and volatility - such as the leverage effect and the volatility feedback hypothesis – the thesis emphasizes the potential predictive power of volatility on stock market returns. The thesis is divided into two parts: a theoretical framework and an empirical analysis. The first chapter presents various volatility measures—historical, realized, implied, and conditional—and explores ARCH, GARCH, and their extensions for modeling conditional volatility. The importance of volatility as a risk metric across different regimes is highlighted. Key theories that examine the relationship between volatility and returns are discussed, followed by an overview of investment strategies that rely on volatility measures - volatility targeting, risk parity, and volatility timing. In the empirical section, conditional volatility derived from the GARCH model optimized by information criteria is employed. Daily data from the S&P 500, Nasdaq 100, Euro Stoxx 50, and MSCI Emerging Markets indices are analyzed. The predictive power of volatility is assessed through: (1) linear regressions of lagged volatility on stock market returns at time t, revealing statistically significant but weak predictive power with low R²; (2) nonlinear models—including quadratic specifications, splines, and Generalized Additive Models (GAM)—which provide improved fit over linear models; (3) Granger causality tests that confirm the directional predictive influence of lagged volatility on returns. Findings suggest that volatility-based strategies, such as volatility targeting, may improve risk-adjusted returns. This is supported by the statistically significant coefficients of lagged volatility in the regression models and the Granger causality tests, which indicate a predictive influence of volatility on returns. Nevertheless, the modest explanatory power indicates that volatility signals should be complemented by additional macroeconomic or behavioral factors.