An Examination of Idiosyncratic Volatility-Related Relations

Abstract

This thesis aims to explore the relationship between stock returns and idiosyncratic volatility. It contains an introduction (Chapter 1), three self-independent chapters (Chapters 2 4), and a conclusion (Chapter 5). Chapter 1 includes a description of the development of research in the area of idiosyncratic volatility, an elaboration on our motivations, and the layout for the whole thesis. For Chapter 2, we examine how stock return performance is a joint function of arbitrage risk and investor sentiment. We posit that arbitrage risk and investor sentiment have a complementary effect on the cross-section of stock returns. This is because the former, proxied by idiosyncratic volatility, relates a firm’s stock variation to its specific firm characteristics while the latter links to individual beliefs on a firm’s future cash flows and risks. Our results indicate that the joint effect on the cross-section of stock returns changes from negative to positive as it grows. The joint effect performs better for smaller stocks but not for those with higher book-to-market ratios. The significantly negative (positive) pricing power of the joint effect is crowded into the lowest (highest) sentiment portfolio. These results highlight the importance of measuring and controlling for the effects of arbitrage risk and investor attention when analyzing the performance of the cross-section of stock returns. The impact of the interaction is not susceptible to the replacement of the sentiment index, different exclusion schemes, and business cycles.

For Chapter 3, we investigate the performances of the ARFIMA, HAR, and EGARCH models in capturing the time-varying property of idiosyncratic volatility (IVOL). We find that the expected IVOL predictions by HAR are superior. In diverse portfolio scenarios, a greater degree of judgment is required to assess the pricing ability of expected IVOLs. For the lowest value-weighted quintiles and the expected IVOL estimated by the HAR model, the IVOLreturn relationship is negative. Conversely, the IVOL-return relationship is positive for the expected IVOL estimated by the EGARCH model. Further evidence suggests a complicated and mixed relationship between the expected IVOL estimated by the ARFIMA model and stock returns.

In Chapter 4, we argue that the inconsistency in the relationship between idiosyncratic volatility (IVOL) and stock returns may be due to the mixture of variables employed on both sides. To disentangle this muddled relationship, we decompose the expected and unexpected components of IVOL and stock returns. We use novel models such as ARFIMA and HAR models to estimate expected IVOLs, and we compare our findings to those estimated from the EGARCH model. Our results show that the relationship between unexpected IVOL and unexpected stock returns is consistently negative, whether at the stock or portfolio level. However, the relationship between expected IVOL and expected stock returns is not clear-out. When the expected and unexpected IVOLs are considered simultaneously, the positive relationship maintains in all significant cases.

Chapter 5 concludes with an overall summary of the main findings as well as contributions from the above three essays. We also look forward to the possibilities of future work.

Date of Award	15 Nov 2023
Original language	English
Awarding Institution	University of Bath
Supervisor	David Newton (Supervisor) & Winifred Huang (Supervisor)