Essays on Idiosyncratic Volatility and Asset Pricing

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)

Download

Essays on the Relation between Idiosyncratic Risk and Returns

A dissertation submitted to the

Graduate School

of the University of Cincinnati

in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

in the Department of Finance-Real Estate

of the College of Business

by

Doina Chichernea

B.S., Academy of Economic Studies, 2001

M.B.A., University of Toledo, 2003

May 2009

Abstract

The central theme of this dissertation is the connection between idiosyncratic risk and returns. In the original literature perfect diversification assumptions eliminate the influence that idiosyncratic risk may have on returns; however, current research shows that once these restrictive assumptions are relaxed, a theoretical role for this particular risk reemerges. The current dissertation empirically investigates the role of idiosyncratic risk in explaining returns. Specifically, the work is organized into two main parts: the first investigates the connection between idiosyncratic risk and momentum, and the second examines the cross-sectional relation between returns and idiosyncratic risk.  The core idea of the first part of this dissertation is that, counter to common belief, the link between idiosyncratic risk and momentum should not be regarded as evidence of the irrational nature of the momentum phenomenon. If idiosyncratic risk is priced, time variation in its premia may rationally generate time series phenomena like momentum.

Various studies reject the notion that momentum profits are compensation for risk by showing that momentum profits are mostly comprised of idiosyncratic components. This dissertation starts with a few remarks on the current stage of the literature, which help make the point that simply documenting the existence of this connection can say nothing about the nature of the underlying process generating momentum (especially since recent theoretical papers show that idiosyncratic components of returns – in particular idiosyncratic risk – may affect risk premia). Using EGARCH-M, the first essay estimates idiosyncratic risk and idiosyncratic risk premia at the individual security level and shows that idiosyncratic risk premia are responsible for between 70 and 90 percent of momentum profits. Although securities in the loser portfolio have higher levels of  idiosyncratic risk than those in the winner portfolio, the idiosyncratic risk premia in the loser portfolio are significantly smaller than those in the winner portfolio. Momentum portfolios formed by sorting on past idiosyncratic risk premia (rather than raw returns) generate significantly positive profits. Overall, the results provide strong empirical evidence that idiosyncratic risk premia vary cross-sectionally in a manner that rationally accounts for (at least portion of) momentum profits.

The next part of this dissertation investigates the cross-sectional relation between idiosyncratic risk and returns. Specifically, the second essay examines the validity of the incomplete information equilibrium model advanced by Merton (1987), by investigating one particular implication that has been largely ignored in previous literature: the interaction between the visibility of a stock and the pricing of its idiosyncratic risk. Four different proxies for visibility provide convincing evidence that idiosyncratic risk premia are larger for neglected stocks, and smaller or even economically insignificant for visible stocks. Results also corroborate Merton’s hypothesis that the size effect previously documented in the literature is likely to be the result of an omitted variable (idiosyncratic risk). The evidence provides support to the idea that market segmentation generated by incomplete information is strong enough to be at least partly responsible for the documented role of idiosyncratic risk in the cross-section of returns.

Part I: Momentum and Idiosyncratic Risk

Remarks on the Connection between Momentum and Idiosyncratic Risk

Introduction

It is now widely documented that buying stocks with recent high returns and selling stocks with recent low returns results in profits that are both statistically and economically significant. Persistence in price has been identified over time (Jegadeesh and Titman (1993), (2001)), across countries (Rouwenhorst (1998); Chui, Titman and Wei (2000)) and across industries (Moskowitz and Grinblatt (1999)).

For the longest time, momentum has been regarded as one of the thorniest anomalies in the face of the rational theory of finance. Largely, the basis of this argument lies in the classic interpretation of the efficient market hypothesis, namely that stock returns should not be predictable using available information. However, under the neo- classical paradigm, returns should be predictable, given any persistence in the riskiness of companies. The literature is slowly starting to recognize this fact – counter to the long standing intuition that momentum is an anomaly, Berk (2008) contends that, if anything, “absence of momentum profits is evidence of irrationality” and “it is hard to conceive of a realistic model linking risk and return that does not admit profits based on portfolios formed on past returns”.

However, the reverse of that statement is not true: existence of momentum alone has nothing to say about rationality. One of the central questions of finance – whether the world generating momentum is rational or irrational – thus becomes even more important at this time. The two available alternative hypotheses are either that (1) the world is rational and time varying risk premia generate momentum or (2) the world is irrational, mispricings generate momentum and they are not corrected because of limits to arbitrage.

Overall, the common view in the literature is that risk based explanations should attribute the source of momentum profits to variations in the common factors risk premia, while behavior based explanations are supported by a relation between momentum profits and firm-specific components of returns. Identifying the source of momentum profits has been the universally accepted approach to assess rationality. In this article, we show that we cannot use sources of momentum to draw inferences about rationality, because idiosyncratic sources of momentum are consistent with both a rational and irrational world. Hence, researchers have to be very careful and invoke this argument with caution, as it can produce dangerously misleading results. Focusing on the connection between idiosyncratic risk and momentum, we show that, contrary to common belief, results to date actually point to the opposite conclusion, namely that such a connection should be interpreted as evidence in favor of rationality, and not against it.

Using the sources of momentum profits to differentiate between rational and irrational explanations for momentum has become an almost universally accepted fact in the finance literature, starting with Jegadeesh and Timan’s original paper, where the authors argue that “to assess whether the existence of relative strength profits imply market inefficiency, it is important to identify the sources of the profits”. They continue  by firmly stating that if such profits are due to idiosyncratic components of security returns, then the results would suggest market inefficiency. This statement alone spurred an extensive stream of research with the sole emphasis on identifying sources of momentum profits, and resting on the uncontested statement that if firm-specific components are an important source of such profits, then it must be that the data supports irrational behavior.

Under behavioral explanations, the main source of momentum should be irrational persistence in the firm specific errors. Since this scenario also implies a link between idiosyncratic risk and momentum, existence of such link has often been considered sufficient proof of irrationality. However, most empirical tests of this implication are plagued by the unavoidable fact that idiosyncratic risk is unobservable and has to be estimated starting from an assumed asset pricing model. Thus these tests are inevitably subject to a classic bad model/joint hypothesis problem. We provide at least one theoretical counterexample, where failure to account for time variation in common factors effectively forces the data to document a (meaningless) link between the idiosyncratic risk and momentum. Thus, we show that conclusions drawn in this case would be premature and eventually false. Moreover, while avoiding to estimate idiosyncratic risk altogether (and thus avoiding the joint hypothesis problem), Dittmar et al (2008) are able to show that persistence in firm specific errors is not a source of momentum, thus correctly concluding that momentum is not an anomaly.

Also in the realm of irrationality, if mispricings are the true source of momentum profits, we should observe that the connection between idiosyncratic risk and momentum exists only conditional on arbitrage costs that would prevent these mispricings from being corrected. We argue that empirical results are not consistent with this regardless if the arbitrage costs considered are transaction costs or holding costs (holding costs are a particularly important issue in this context, since idiosyncratic risk is considered one of the main component of such costs).

On the other hand, in a rational world, time variation of risk factor premia should be responsible for momentum profits. If idiosyncratic risk is rationally priced because of barriers to diversification and its premia are time varying, it is possible that this type of risk is a legitimate and rational source of momentum profits. Hence we identify at least one rational theoretical setting where idiosyncratic risk is related to momentum. Given this information, it is only natural to conclude that documenting a link between idiosyncratic risk and momentum is most likely consistent with either model miss-specification or a world where idiosyncratic risk is rationally priced. Of course, it is still important to distinguish between the two possibilities. However, although we provide some guidelines on how this can be done, the main point of this article is to recognize that both possibilities are essentially in sync with a rational explanation for momentum - in both cases, momentum would be the result of time-varying (common or idiosyncratic) risk premia. Hence, our claim that, counter to common belief, a link  between idiosyncratic risk and momentum is actually consistent with (and not proof against) rationality.

 The reminder of the article is organized as follows. Section 1 describes potential sources of momentum and provides a theoretical counter example where the link between idiosyncratic risk and momentum could falsely be interpreted as evidence of irrationality. Section 2 shows that the link between idiosyncratic risk and momentum is not conditional on arbitrage costs, as irrationality would suggest. Section 3 provides an alternative explanation where idiosyncratic risk is connected with momentum in a perfectly rational setting and discusses the implications. The last section concludes.

Conclusion

This essay argues that the link between idiosyncratic risk and momentum documented in asset pricing should not be regarded as evidence of the irrational nature of  the momentum phenomenon. The common view in the literature is that risk based explanations should attribute the source of momentum profits to variations in the common factors risk premia, while behavior based explanations are supported by a relation between momentum profits and firm-specific components of returns. Identifying the source of momentum profits has been the universally accepted approach to assess rationality.

In this article, we show that we cannot use sources of momentum to draw inferences about rationality, because idiosyncratic sources of momentum are consistent with both a rational and irrational world. Hence, researchers have to be very careful and invoke this argument with caution, as it can produce dangerously misleading results. Focusing on the connection between idiosyncratic risk and momentum, we show that, contrary to common belief, results to date actually point to the opposite conclusion, namely that such a connection should be interpreted as evidence in favor of rationality, and not against it.

Read more