The Dynamic Relationship Between Stock Returns And Volatility Analysis

In the modern investment theory and practice, there are two fundamental variables, stock returns (R) and its volatility (σ2). The relationship between them was widely studied in many classic assets pricing models, including the Capital Assets Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). However, all these model or theory discussed their relationship under the static and equilibrium assumption or environments. But real investment is dynamic and non-equilibrium, which needs the dynamic analysis of the relationship between return and its volatility. Many researches, including theoretic and empirical ones, have discovered two dynamic effect, that is "leverage effect" and "volatility feedback effect", which can be used to explain the inter-temporal negative correlation between return and volatility.In theory, starting from the definition of volatility, I deduced the impact of the current stock price unexpected change on the future volatility:In the risk-neutral market, the impact of unexpected changes on yield volatility is symmetric; however this symmetry will be broken under the assumption that investors have risk preferences."Leverage effect" is one theoretical explanation of the inter-temporal negative correlation from the perspective of the company’s financial leverage changes (Christie,1982), this paper has verified the effect from another perspective;"volatility feedback effect" is another theoretical explanation from the perspective of risk premium (Goyal and Clara,2003), this paper has reviewed this literature and verified the effect using dividend discount model (DDM).Using the daily weekly and monthly return data of A-share stocks, this paper examines the "leverage effect" and "volatility feedback effect" in a firm-level. This is a main difference with other domestic researches whose focus was on the market-level and their data were market index. In the firm-level, the two effects can be studied under the market factor and firm-own factor. In the stock exchange market, stock price is affected not only by itself but also by the whole market. The change of the whole market can significantly affect investors’ sentiment and the following behaviors, and then stock price is changed. What’s more, considering the time-serial characteristic of return and volatility variables, this paper examines the contemporaneous effect and lagged effect, respectively. It’s necessary to do this because researches (Duffee,1995) say the contemporaneous effect and lagged effect are opposite.The empirical results are as follows:1) there is no "leverage effect" in daily and weekly data using GARCH family models, but the "volatility feedback effect" can be supported.2) Both "leverage effect" and "volatility feedback effect" can be supported by monthly data using panel regression. The contemporaneous effect of market return on stock volatility is negative while stock return on stock volatility is positive. The contemporaneous effect of market return on stock volatility is negative while stock return on stock volatility is positive. The contemporaneous market factor tends to diminish the "leverage effect" and "volatility feedback effect", while the lagged market factor tends to reinforce both effects.3) The "leverage effect" is stronger for the stock with higher market capitalization and lower debt ratio, while the "volatility feedback effect" is stronger for the stock with lower market capitalization and higher debt ratio.According to different data frequency, this paper select different models, including GARCH family models and panel analysis models. The method of mean group estimator developed by Person and Smith (1995) is employed.