The non-linear trade-off between return and risk and its determinants
研究美国股市1963至2017年间收益与总风险的非线性关系，发现该关系随时间变化且依赖于风险水平，正向权衡主要出现在低波动期和中等风险区间，高风险时方向反转，且受情绪、宏观、信用、流动性和公司变量影响。
We estimate a discrete approximation of the risk-return trade-off for the US market by using the whole universe of stocks from July 1963 to September 2017. We find the relationship between return and total risk to be time-varying and also dependent on the level of risk considered. The proposed positive trade-off is mainly observed during low volatility periods and when we move from low risk up to medium-high risk investments. However, the direction of the trade-off is inverted for the highest risk alternatives especially during high volatility periods. The temporal variation of the risk-return trade-off can be explained by a series of sentiment, macro, credit risk, liquidity and corporate variables. All these determinants suggest that the positive relationship between return and risk is more evident during periods where economic, financial and market conditions improve.