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.
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