As per the research study of Bali and Cakici, there is a negative relation presented in between the expected returns and that of the idiosyncratic volatility. However, the relation is not robust enough while calculating the average portfolio returns in terms of diverse weight schemes. The authors found out that no significant difference was there among the quintile portfolio returns by the construction according to idiosyncratic volatility that had equal weight. Merton stated that whenever the investors fail to diversify the portfolios in a complete manner with the consideration of different frictional costs, pricing of idiosyncratic risk is possible. Mixed results in case of examining the relationship presented between the expected stock returns and that of idiosyncratic risk have been found many a time, for example, negative cross-sectional relation present between idiosyncratic volatility that is of one-month lagged and the monthly stock returns. However, many other authors found the contemporaneousness related to risk-return tradeoff, which means there is a positive relation between the expected idiosyncratic volatility and the monthly stock returns.
Therefore, it means the research studies implicitly presuppose the fact that constant idiosyncratic risk premium can be found over the time. Fu stated that substantial variability in case of idiosyncratic risk over time points towards the ineffectiveness of the available literature while identifying the positive relation situated there. It is because the time varying characteristic has not been captured in the earlier studies as per the conditional idiosyncratic volatility. EGARCH model proposed by Nelson was taken into account by Fu by the use of monthly data and the researcher succeeded in providing in-sample estimates related to the conditional idiosyncratic with the variance based on stock returns. During the study, Fu found a major positive relation. Later, Spiegel with Wang developed the out-of-sample estimate while predicting the idiosyncratic volatility along with liquidity. They found that with greater idiosyncratic risk level, the stock returns get increased which results into liquidity decrease of the stock. Their major discovery involves the core role of liquidity as well as idiosyncratic on determining stock returns.