Perspective on behavioral finance, we take a new look at the characteristics of investors’ risk preference, building the D-GARCH-M model, DR-GARCH-M model, and GARCHC-M model to investigate their changes with states of gain and loss and values of return together with other time-varying characteristics of investors’ risk preference. Based on a full description of risk preference characteristic, we develop a GARCHCS-M model to study its effect on the return skewness. The top ten market value stock composite indexes from Global Stock Exchange in 2012 are adopted to make the empirical analysis. The results show that investors are risk aversion when they gain and risk seeking when they lose, which effectively explains the inconsistent risk-return relationship. Moreover, the degree of risk aversion rises with the increasing gain and that of risk seeking improves with the increasing losses. Meanwhile, we find that investors’ inherent risk preference in most countries displays risk seeking, and their current risk preference is influenced by last period’s risk preference and disturbances. At last, investors’ risk preferences affect the conditional skewness; specifically, their risk aversion makes return skewness reduce, while risk seeking makes the skewness increase. 1. Introduction Risk preference refers to the attitude people hold towards risks, which is a key factor in studies on investors’ decision-making behavior. Standard financial theory assumes that investors are rational and believes that when making investment decisions they tend to have invariant risk preferences-risk averse. However, as the research goes, people gradually find that the investors’ decision-making behavior in real life does not always comply with the assumption of rationality and their behaviors are usually limited by their own cognitive biases and external environment, leading to their risk preferences varying with different situations. With the development of behavioral finance, a multitude of research indicated that the result of investment in the financial market can affect their decisions, making them exhibit inconsistent risk preference. Prospect Theory proposed by Kahneman and Tversky  had described some prominent psychological traits of investors in their decision-making under uncertainty. Their experiments suggested that individuals tend to be risk averse with gain and risk seeking with loss, which have been confirmed by a variety of subsequent studies. For example, Laughhunn and Payne  found evidence that 20 managers in the process of their multiple risk choice
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