by
Fatma Sonmez Saryal
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of the Joseph L. Rotman School of Management
University of Toronto
Abstract
In this thesis, I study three aspects of idiosyncratic volatility. First, I examine the relation between idiosyncratic volatility and future stock returns. Next, I examine the share price effect and its interaction with the idiosyncratic volatility on stock returns. Finally, I examine the time series pattern of monthly aggregate monthly idiosyncratic volatility. In the first chapter, I examine the relation between idiosyncratic volatility and future stock returns. In their paper, Ang, Hodrick, Xing, and Zhang [AHXZ (2006)] show that idiosyncratic volatility is inversely related to future stock returns: low idiosyncratic volatility stocks earn higher returns than do high idiosyncratic volatility stocks. The main contribution of this paper is to provide evidence that it is the month to month changes in idiosyncratic volatility that produce AHXZ’s results. More specifically, a portfolio of stocks that move from Quintile 1 (low idiosyncratic volatility) to Quintile 5 (high idiosyncratic volatility) earns an average risk-adjusted return of 5.64% per month in the month of the change. Whereas, a portfolio of stocks that move from the highest to the lowest idiosyncratic volatility quintiles earns -0.94% per month in the month of the change. Eliminating all firm- month observations with idiosyncratic volatility quintile changes, I find the opposite results to AHXZ: it is persistently low idiosyncratic volatility stocks that earn lower returns than do persistently high idiosyncratic volatility stocks. I find that many of the extreme changes in idiosyncratic volatility are related to business events. In general, the pattern usually observed is that an announcement or an event increases uncertainty about a stock and hence, its idiosyncratic volatility increases. After the event, uncertainty is resolved and the stock returns to a lower idiosyncratic volatility quintile.
In the second chapter, I examine how the level of the share price interacts with idiosyncratic volatility to affect future stock returns. Ignoring transaction costs, a trading strategy that is long high-priced and short low-priced stocks earns positive abnormal returns with respect to the Fama-French (1992) three factor model. However, the observed positive abnormal returns are less significant if momentum is taken into account via the Carhart (1997) four factor model. Also the relation between idiosyncratic volatility and future stock returns differs for price sorted portfolios: it is negative for low and mid-priced stocks but positive for high-priced ones. These results are robust for low and-mid-priced stocks evenafter momentum is included. However, the positive relation for high-priced stocks disappears due to relatively large loadings on momentum for high idiosyncratic volatility stocks. I also show that skewness and momentum are significant determinants of idiosyncratic volatility for low-priced stocks and high-priced stocks respectively. One implication is that the importance of idiosyncratic volatility for future stock returns may in part be due its role as a disguised risk factor: either for momentum for high-priced stocks and skewness for low and mid-priced stocks.
In the third chapter, I investigate the time series pattern of aggregate monthly idiosyncratic volatility. It has been shown that new riskier listings in the US stock markets are a reason for the increase in idiosyncratic volatility during the period 1963-2004. First, I show that this is more pronounced for Nasdaq new listings. Second, I show that for Nasdaq, prior to 1994 low-priced new listings became riskier, whereas during the internet bubble period it is the higher-priced listings that became riskier. Third, I show that institutional holdings have increased over time and have had a different impact on each new listing group: a negative for pre-1994 listings and a positive impact for post-1994 listings. Hence, I conclude that the observed time-series pattern of idiosyncratic volatility is a result of the changing nature of Nasdaq’s investor clientele.
Introduction
There is a fast-growing and controversial literature dealing with the impact of idiosyncratic volatility (Ivol) on stock returns. Standard asset pricing models, such as the Capital Asset Pricing and Fama-French (1992) models conclude that only systematic risk factors should be related to future returns. This is because firm specific (idiosyncratic) risk can be eliminated by diversification, and therefore investors do not require a risk premium for bearing that risk. However many investors hold undiversified portfolios for a variety of reasons. In these situations, firm specific risk may play a role in affecting future returns.
The pricing of idiosyncratic risk in the cross-section of security returns has been the subject of research for almost 40 years. In early work, Douglas (1969) and Lintner (1965) found that the variance of the residuals from the market model was highly significant in explaining the cross-section of stock returns. More recently the debate on the relevance of Ivol has been revived with conflicting results. Lehmann (1990), Goyal and Santa-Clara (2003), Malkiel and Xu (2003), Spiegel and Wang (2005), and Fu (2008) present evidence of a positive relationship between Ivol and future returns. Bali, Cakici, Yan and Zhang (2005) and Bali and Cakici (2008) find that there is no significant relation between firm specific risk and future returns. Finally, Ang, Hodrick, Xing, and Zhang [AHXZ (2006)] find a strongly significant negative relationship between Ivol and security returns. In a follow-up paper [AHXZ (2008)], they show that this pattern is also visible internationally. After controlling for almost all related firm characteristics, AHXZ call their result a “puzzle”: why do low Ivol firms earn higher future returns than ones with higher Ivol? This “puzzle” has attracted recent attention and there has been increasing interest in explaining AHXZ’s controversial result.
In this paper, I replicate AHXZ’s results for the period from July 1963 to December 2000 and confirm the “puzzle”1. On average the value-weighted low Ivol portfolio earns approximately 1% per month more than that of the value-weighted high Ivol portfolio. These results are even more pronounced when equally-weighted portfolio returns are used. I then investigate the effect of changes in a firm’s Ivol on its future return. The AHXZ results are generated by relating returns earned in month t with the stock’s Ivol in month t–1. I relate the returns earned in month t with the stock’s Ivol in month t–1 and month t. I consider three cases: the Ivol is similar in both months, the Ivol in month t–1 is significantly less than that in month t, and the Ivol in month t–1 is significantly greater than that in month t. The behavior of these three groups is markedly different. For those stocks that experience a significant change in Ivol, the return earned in month t is consistent with the contemporaneous Ivol and is inconsistent with the Ivol in month t−1.
I find that it is the change in Ivol from month to month that produces AHXZ’s results. Stocks that move from the lower to the higher Ivol quintiles earn significantly high contemporaneous positive returns. For example, if a firm moves from Quintile 1 (low Ivol) to Quintile 5 (high Ivol) it earns an average risk adjusted return of 5.64%per month in the month of the change. Similarly stocks that move from the highest to the lowest Ivol quintiles earn lower returns in the month of the change. The set of stocks that experiences moves from the lowest to the highest or highest to the lowest quintile is about one quarter of the total sample. If I eliminate all firm months in which Ivol changes, I find that low Ivol stocks earn consistently lower returns than these of high Ivol stocks, which is opposite to the results of AHXZ and in line with the theory.
The change in idiosyncratic risk ranking from one month to the next has an asymmetric impact on future returns. If the change is from low to high Ivol, then it has a higher impact (5.64% per month) than when the change is from high to low (−0.94% per month). This is similar to the differential stock market reaction to good versus bad news.
The changes in Ivol that drive AHXZ’s apparent anomaly appear to be related to identifiable business events. Many of the extreme changes in Ivol from the lowest to the highest quintile are related to merger and acquisition activity (M&A), earnings announcements, CEO changes, law suits and so on. While not all events lead to extreme changes in Ivol, many extreme changes in Ivol are related to some identifiable event. The pattern usually observed is that an announcement or an event increases uncertainty about a stock and hence its Ivol increases. After the event, uncertainty is resolved and the security returns to a lower Ivol. For example, about 10% of all migrations from the lowest to the highest Ivol quintile are firms that have an acquisition announcement around the time of the change in Ivol. More than 50% of all stocks that migrate from the lowest to the highest Ivol quintile and then return to the lowest quintile within two months have M&A related news during that period. Another source of increased uncertainty that leads to an increase in Ivol is earnings announcements. About 6% of all migrations from the lowest Ivol quintile to the highest quintile are firms that have an earnings announcement month around the time of the change in Ivol.
The rest of this paper is organized as follows. In Section 2, I confirm AHXZ’s results using their sample period.2 In Section 3, I investigate the effect of changes in Ivol ranking on future realized stock returns. The asymmetric impact of changes in a security’s ranking on future returns is examined. In Section 4, I consider robustness checks. In Section 5, I provide a discussion of the possible explanations for the empirical results in the paper. In Section 6, I discuss the related issues in the Ivol literature while extending the sample period to 2008. Conclusions are in Section 7.
©Copyright by Fatma Sonmez Saryal (2010)
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