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«MULTIFREQUENCY NEWS AND STOCK RETURNS Laurent E. Calvet Adlai J. Fisher Working Paper 11441 NATIONAL BUREAU OF ...»

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Laurent E. Calvet

Adlai J. Fisher

Working Paper 11441



1050 Massachusetts Avenue

Cambridge, MA 02138

June 2005

Calvet: Department of Finance and Economics, HEC School of Managament, 78351 Jouy-en-Josas Cedex, France, and NBER, calvet@hec.fr. Fisher: Sauder School of Business, University of British Columbia, 2053 Main Hall, Vancouver, BC V6T 1Z2, adlaifisher@sauder.ubc.ca. We received helpful comments from Andrew Abel, John Campbell, John Geanakoplos, Bruno Solnik, Robert Stambaugh, Amir Yaron, Jessica Wachter, and seminar participants at CREST, Paris I Panthéon-Sorbonne, and the Wharton School. We are very appreciative of financial support provided for this project by the HEC Foundation, the UBC Bureau of Asset Management, and the Social Sciences and Humanities Research Council of Canada. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.

©2005 by Laurent E. Calvet and Adlai J. Fisher. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.

Multifrequency News and Stock Returns Laurent E. Calvet and Adlai J. Fisher NBER Working Paper No. 11441 June 2005 JEL No. G12, C22


Recent research documents that aggregate stock prices are driven by shocks with persistence levels ranging from daily intervals to several decades. Building on these insights, we introduce a parsimonious equilibrium model in which regime-shifts of heterogeneous durations affect the volatility of dividend news. We estimate tightly parameterized specifications with up to 256 discrete states on daily U.S. equity returns. The multifrequency equilibrium has significantly higher likelihood than the classic Campbell and Hentschel (1992) specification, while generating volatility feedback effects 6 to 12 times larger. We show in an extension that Bayesian learning about stochastic volatility is faster for bad states than good states, providing a novel source of endogenous skewness that complements the "uncertainty" channel considered in previous literature (e.g., Veronesi, 1999). Furthermore, signal precision induces a tradeoff between skewness and kurtosis, and economies with intermediate investor information best match the data.

Laurent E. Calvet Department of Finance and Economics HEC School of Management 78351 Jouy-en-Josas Cedex France and NBER calvet@hec.fr Adlai J. Fisher Sauder School of Business University of British Columbia 2053 Main Mall Vancouver, BC V6T 1Z2 Canada adlai.fisher@sauder.ubc.ca

1. Introduction The recent asset pricing literature suggests that stock prices are driven by shocks with very heterogeneous degrees of persistence. For example, market returns are predictable at a range of business-cycle horizons; some variables provide best forecasts over intervals of twelve months or less while others increase in power out to five years and more. 1 Complementary studies emphasize even more persistent sources of variations in returns, including technological innovation (e.g., Greenwood and Jovanovic, 1999), exogenous demographic changes (e.g., Abel, 2003), and low frequency movements in consumption or dividend growth (Bansal and Yaron, 2004). 2 At the other end of the spectrum, high-frequency returns permit a large number of observations and thus potentially more precise econometric inference. Researchers have correspondingly related daily and intraday price movements to weather news (Roll, 1984), macroeconomic announcements (Andersen, Bollerslev, Diebold, and Vega, 2004), internet bulletin boards (Antweiler and Frank, 2004), analyst reports 3 and corporate announcements.4 The existing literature thus documents persistence levels in stock market news ranging from daily intervals to several decades.

Our research builds on this evidence by developing an equilibrium framework with news shocks at many different frequencies. Why has the existing literature not addressed this agenda? We offer two explanations.

First, it might seem plausible that some financial questions are best addressed in isolation at a single horizon. Following this logic, equity premium studies largely focus on annual data, while market efficiency research mainly uses higher frequencies. Recent evidence suggests, however, that fluctuations at different frequencies can interact.

Lochstoer (2004) thus shows that a slowly-evolving generational state variable controls business-cycle variation in risk premia. Similarly, Andersen, Bollerslev, Diebold, and Vega (2004) provide evidence that the high-frequency impact of macroeconomic news depends on the state of the business cycle.

A second, and more pragmatic, impediment to multifrequency research is that complexity grows quickly with the number of components. Recent contributions (e.g., Bansal and Yaron, 2004; Lochstoer, 2004) demonstrate not only the empirical advantage of using two persistence levels, but also that formal estimation becomes more difficult and high-dimensional calibration more necessary with a more complex setup.

1 See, for example, Lettau and Ludvigson (2001).

2 Endogenous mechanisms for extremely persistent fluctuations include habit formation (Campbell and Cochrane, 1999), durable consumption goods (Yogo, 2004a), and the dynamics of capital accumulation with adjustment costs (Jermann, 1998).

3 See, e.g., Womack (1996).

4 An extensive literature studies stock price reactions to corporate announcements including quarterly earnings, dividend policy, securities issuances and changes of control. See, e.g., MacKinlay (1997).

1 Our paper proposes a new direction to address these problems by developing a parsimonious equilibrium framework based on recent advances in multifrequency econometrics. An Epstein-Zin consumer receives an exogenous consumption stream, and prices a flow of correlated dividends with regime-switching in the mean and volatility of their growth rates.5 The model thus follows the recent trend to model dividends and consumption as correlated but not identical processes (e.g., Campbell and Cochrane, 1999).

Exact solutions for equilibrium prices, return dynamics, and filtered beliefs are available. Unlike previous Lucas tree economies considered in the literature (e.g., Bansal and Yaron, 2004; Lettau, Ludvigson, and Wachter, 2004), our setup implies that higher volatility reduces prices for any level of the elasticity of intertemporal substitution.

We specify news arrivals with a Markov-switching multifractal (MSM), a stochastic volatility model characterized by a small number of parameters but an arbitrarily large number of frequencies (Calvet and Fisher, 2001, 2002, 2004; Calvet, Fisher, and Thompson, 2004). Under this specification, news volatility is hit by exogenous shocks with highly heterogeneous durations, which range from one day to more than a decade in empirical applications. Earlier work shows that MSM captures the outliers, volatility persistence and power variation6 of financial series, while permitting maximum likelihood estimation and analytical multi-step forecasting. MSM compares favorably with standard volatility models such as GARCH(1, 1) both in- and out-of-sample (Calvet and Fisher, 2004). It is now natural to embed it into an equilibrium framework.

The multifrequency equilibrium model inherits the appealing properties of MSM.

It is tightly parameterized and permits structural estimation by maximum likelihood.

We estimate our specification on an index 7 of US equities over the period 1926-2004.

Versions of the model with six to eight volatility frequencies provide significant improvements in likelihood relative to lower dimensional specifications. The model also improves on earlier specifications of single frequency news arrivals (Campbell and Hentschel, 1992, hereafter “CH”), even though our approach uses fewer parameters.

Our model generates volatility feedback, the property that upward revisions to anticipated future volatility tend to decrease current returns. Consistent with a multifrequency perspective, previous researchers have studied this topic at a range of different 5 Following Hamilton (1989, 1990), researchers have used regime-switching to help explain financial phenomena including stock market volatility, return predictability, the relation between conditional risk and return, the term structure of interest rates, and the recent growth of the stock market. Contributions include Abel (1994, 1999), Bansal and Zhou (2002), Cecchetti, Lam and Mark (1990), David (1997), Kandel and Stambaugh (1990), Lettau, Ludvigson and Wachter (2004), Turner, Startz and Nelson (1989), Veronesi (1999, 2000, 2004), Wachter (2004), and Whitelaw (2000).

6 Power variation relates to the behavior at small time scales of sums of powers of absolute values of returns. See Calvet and Fisher (2002), Barndorff-Nielsen and Shephard (2003) and Andersen, Bollerslev, and Diebold (2003).

7 We splice the Schwert (1990a) and value-weighted CRSP indices, as in CH.

2 horizons. For example, French, Schwert, and Stambaugh (1987, hereafter “FSS”), CH, and Wu (2001) assess feedback effects in daily, weekly, and monthly data, while Pindyck (1984), Poterba and Summers (1985), Bansal and Yaron (2004), and Lettau, Ludvigson and Wachter (2004) emphasize volatility movements at the business cycle range and beyond.8 A multifrequency approach might therefore prove useful in this context.

Intuition suggests that high-frequency volatility shocks help to capture the dynamics of typical day-to-day variations, while lower-frequency movements generate the strong feedback required to fit the most extreme daily returns. Volatility feedback models are thus a natural setting where the interaction of various frequencies seems intuitively important. The paper can be viewed in this sense as a first step towards bringing together branches of the lower-frequency macro-finance and higher-frequency financial econometrics literature.

The multifrequency equilibrium generates substantially larger feedback effects than previous research. For instance, CH find that feedback amplifies the volatility of dividend news by only about 2%; they attribute this result to the property of GARCH-type specifications that the volatility of volatility can only be large if volatility itself is high.

In our stochastic volatility MSM specification for dividend news, feedback rises with the number of components and the likelihood function, increasing to between 12% and 24% for the preferred specifications with six to eight components. The multifrequency equilibrium model thus generates an unconditional feedback that is 6 to 12 times larger than in previous literature.9 A substantial level of endogenous skewness is difficult to obtain in our full-information equilibrium with symmetric dividends. Earlier volatility feedback studies attempt to address this by introducing predictive asymmetry (CH) or skewness (Wu, 2001) directly into the econometric specification of dividends. Our work instead investigates whether higher return moments can be modeled through the endogenous equilibrium implications of imperfect investor information and learning. We thus generalize our setup to allow that the investor observes noisy signals of the volatility components and then makes Bayesian inferences about the latent volatility state. The separation of dividends from consumption implies that the price:dividend ratio is linear in investor beliefs, making the model tractable.

Our learning model generates two main sets of results. First, signal precision has little effect on the unconditional mean and variance of stock returns. To explain this, 8 Investigation of volatility feedback in a general equilibrium setting was pioneered by Barsky (1989) in a two-period setting and Abel (1988) in the dynamic case. French, Schwert and Stambaugh (1987) and Campbell and Hentschel (1992) use GARCH-type processes to show that ex-post returns are negatively affected by positive innovations in volatility. Bekaert and Wu (2000) provide further support for this hypothesis.

9 Based on the paramater estimates presented in Wu (2001), unconditional volatility feedback is 3.5% for his model estimated on monthly data, and is negative for his model estimated on weekly data.

3 we show that the price:dividend ratio (P:D) in the learning model is the conditional expectation of its full-information counterpart. This implies the same mean and lower variance, which is the analogue in our setup of the variance bounds discussed by LeRoy and Porter (1981) and Shiller (1981). In our model, however, the reduction in variance is negligible because large movements of the P:D ratio are induced by shifts in the most persistent volatility components. Learning about these rare changes is therefore a transitory phenomenon that has limited impact on stock return variance, and we verify this logic numerically. The sizeable volatility feedback implied by our full-information specification is thus robust to changes in information quality.

Our second learning result is that changes in the most persistent components have strong effects on the higher moments of returns. In particular, varying the precision of the volatility signal generates a sizeable tradeoff between endogenous skewness and kurtosis. When investors have perfect information, volatility shocks are incorporated fully and immediately into price, regardless of the direction of change. By contrast, when the volatility component signals are poor, investors rely on dividend news to make inferences about the volatility state. They still learn quickly about volatility increases, because a single extreme fluctuation is highly improbable with low volatility. Learning about reduced volatility must be slow, however, because dividend news observations near the mean are a relatively likely outcome regardless of the true volatility state. Thus, bad news about volatility incorporates quickly into price, while good news trickles out slowly.10 This asymmetry creates the observed tradeoff between endogenous skewness and kurtosis as information quality changes.

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