خطر بازگشت تجارت کردن و همبستگی: آیا حجم و نوسانات مهم است؟

I investigate a relation between the conditional mean and variance of the aggregate stock return using a model that allows the relevance of the risk-return trade-off and autocorrelation to change over time. The model detects a positive risk-return relation, but the importance of the risk-return relation fluctuates with the level of information flow, measured by volatility. During low-volatility periods, market-wide persistence in returns increases, leading to a failure of the pure risk-return explanation for expected returns. This offers an explanation as to why detection of a positive risk-return trade-off has been challenging, while autocorrelation has been a robust finding.

The intertemporal capital asset pricing model (ICAPM) of Merton (1973) implies a positive relation between the expected market return and its conditional variance, yet the empirical evidence on the sign of the risk-return trade-off is conflicting. These mixed results can have several explanations, but the role of autocorrelation has received less attention than others. In the following, I estimate an empirical model in which the relevance of the risk-return trade-off and autocorrelation can change over time. The model allows controlling for one of the most robust findings in empirical finance: stock returns exhibit serial dependence. I find a positive risk-return relation, but the importance of the risk-return explanation fluctuates with the level of information flow, measured by volatility. Researchers have had difficulties documenting a positive risk-return relation. Often they detect a negative or insignificant relation between the conditional mean and variance of the aggregate return [for an overview, see Brandt and Wang (2010) and Nyberg (2012)]. These mixed results are related to an omitted-variable problem or differences in how the conditional mean and variance are modeled. The former may result if the hedging component of the ICAPM is omitted from an empirical specification (Scruggs, 1998 and Guo and Whitelaw, 2006). The latter arises from the fact that neither of the conditional moments is directly observable, so modeling assumptions shape the results (Brandt and Wang, 2010). The simultaneous role of autocorrelation has attracted less interest. In empirical work, a risk-return specification is often augmented by a first-order autoregressive term that is included to account for nonsynchronous trading (Nelson, 1991 and De Santis and Imrohoroglu, 1997) or test whether the lagged return helps explain the expected return (Bollerslev et al., 1988 and Ghysels et al., 2005). Although the autoregressive component is usually found to be significant, its effect on the mixed risk-return results remains unexplored. If the degree of autocorrelation is constant over time, the standard approach (a conditional risk-return trade-off augmented by a time-invariant first-order autoregressive term) controls for autocorrelation in returns. However, no previous study considers whether the relative contribution of the risk-return trade-off and autocorrelation in explaining the aggregate return changes over time. I investigate the risk-return trade-off using an empirical model that builds on the ICAPM, while inspired by a view that the relevance of the risk-return explanation and autocorrelation may fluctuate with the level of information flow, approximated in empirical work by volatility and volume (e.g., Andersen, 1996). The changing relevance of the risk-return explanation and autocorrelation is economically motivated by the adaptive markets hypothesis (AMH) of Lo (2004). The AMH builds on the concept of bounded rationality (Simon, 1955) and evolutionary principles. Lo (2004) argues that market participants adapt to a constantly changing market environment with satisfactory (as opposed to optimal) behavior attained via heuristics and an evolutionary process. Natural selection ultimately determines the number and composition of the market participants and trading strategies. Under the AMH, prices reflect both information and the prevailing market ecology. The AMH implies that the degree of market efficiency is dynamic and context dependent; it can change in cyclical fashion with market conditions. The AMH treats market conditions as a multidimensional and complex construct, leaving it to the researcher to determine which features should be the focus of empirical modeling. Here, I assume the key market condition is the level of new information. This interpretation agrees with the AMH motivation: changing market conditions are closely linked to the type and amount of available pricing information and how market participants process and use this information. It seems natural, for example, to assume that the survival of market participants and trading strategies that rely on past prices depends on the level of new information needed to be subsumed in prices. The same is particularly true for investors incapable of processing new information. While I do not try to specify an exact formal mechanism behind the changing relevance of the risk-return trade-off, the economic intuition behind the tested model is appealing: the contribution of the risk-return trade-off (efficient pricing) and autocorrelation (inefficient pricing) can depend on the level of new information (market condition). While Kim, Shamsuddin, and Kian-Ping (2011) find support for the AMH and a number of studies indicate that market efficiency varies over time [see survey of Lim and Brooks (2011)], autocorrelation may partly reflect time-varying risk premia (Anderson, 2011) or nonsynchronous trading (Lo and MacKinlay, 1990).1 In other words, even if the financial market is efficient, we may obtain significant autocorrelation if our pricing model is incorrect or infrequent trading is a significant source of autocorrelation. Therefore, I concentrate on the empirically testable implication of the proposed model: the relevance of the risk-return relation should change with the level of information flow. I study daily aggregate stock returns from 1988 to 2011. Daily frequency is chosen because price adjustment to new information unlikely takes longer than a few days in the U.S. stock market. Second, the ICAPM is a continuous-time model. Most authors test its discrete-time approximation using long-term returns [with the notable exception of Bali and Peng (2006)]. My aim is to provide new insight on short-term returns that form longer-term returns. Third, evaluation at a daily frequency allows a natural comparison of the tested model against the models of Sentana and Wadhwani (1992) and Campbell, Grossman, and Wang (1993) that were originally tested on daily data. These heterogeneous agent models serve as natural benchmarks models to the proposed model. I present several new findings concerning the risk-return trade-off and return autocorrelation. First, the model I employ consistently detects a positive risk-return relation. This finding is in line with Ghysels, Santa-Clara, and Valkanov (2005), Bali and Peng (2006), Pastor, Meenakshi, and Swaminathan (2008), and Nyberg (2012), among others. However, the relevance of the risk-return relation and autocorrelation changes with the level of new pricing information, measured by volatility. During low-volatility periods, market-wide persistence in returns increases, leading to a failure of the pure risk-return explanation for expected returns. Consistent with this finding, traditional risk-return specifications (with or without a constant autoregressive term) yield conflicting evidence concerning the risk-return relation. The empirical model takes into account the low-volatility shortcoming of the risk-return explanation. The model is easy to use and intuitively appealing as it summarizes the effect of autocorrelation in one coefficient and shows the contribution of the risk-return relation and autocorrelation in explaining the aggregate return. The model fits the data better than its traditional alternatives or the feedback-trading model of Sentana and Wadhwani (1992) or an empirical version of the volume-autocorrelation model of Campbell, Grossman, and Wang (1993). The results of this study are found to be robust against various sources of potential model misspecifications. The time-varying relevance of the autoregressive term is in line with Kim, Shamsuddin, and Kian-Ping (2011), who find support for the AMH by testing a relation between time-varying return predictability and changing market conditions. I find that the conditional risk-return trade-off is also important in the U.S. stock market, especially during volatile market conditions. It is important to control for the risk-return trade-off in market efficiency studies as a relation between the conditional mean and variance process may cause autocorrelation in returns [for more details, see Hong (1991)]. The results of this study also shed light on the return reversal and momentum literature, where the role of trading volume is found to be significant by Connolly and Stivers (2003) and Wang and Yu (2004). In contrast, I find that volatility is the variable causing market-wide persistence in short-horizon returns. The rest of the paper is structured as follows. In Section 2, I discuss the economic pricing models, reasons for dynamic autocorrelation, and the empirical framework. Section 3 contains a description of the data. In Section 4, I present the results. Concluding remarks are presented in the last section.

In this paper, I investigated the time-varying relative contribution of the risk-return trade-off and autocorrelation in driving expected returns on the U.S. aggregate stock market. This is accomplished by estimating a model in which the level of information flow (measured by volatility and volume) can induce fluctuations in the relevance of the risk-return trade-off and autocorrelation. I use daily data from January 1988 to June 2011. There are three key findings. First, there is a positive relation between the conditional mean and variance of the aggregate stock return. The relevance of the risk-return relation and autocorrelation, however, fluctuates with volatility. Second, trading volume does not affect the autocorrelation structure of the aggregate return. Third, while traditional models (with or without a time-invariant autoregressive term) show inconclusive results, the proposed model consistently detects a positive risk-return trade-off. Since volatility serves as a proxy for the level of information flow, these findings support a view that during low information periods, market-wide persistence in returns increases, facilitating a failure of the pure risk-return explanation for the expected aggregate return. During volatile periods, expected returns can be described using rational (intertemporal) investors acting to maximize their expected utility. This offers a plausible explanation as to why detection of a positive risk-return trade-off has been so challenging, while autocorrelation in stock returns has been a robust finding. The tested model identifies the low-volatility shortcoming of the risk-return explanation and fits the data better than traditional models or two alternative dynamic autocorrelation models. The findings are insensitive to the use of three alternative variance parameterizations, including a parameterization with the incremental information of the VIX. The results are robust against potential time variations in the price of market risk and additional information variables do not help explain the aggregate return. The out-of-sample results strengthen the view that the relevance of the autoregressive term varies over time. The tested model is economically motivated by the adaptive market hypothesis and the ICAPM. While the economic intuition behind the model is based on time-varying market efficiency, it would be unwise to attribute the documented autocorrelation solely to the degree of market efficiency. Market efficiency is always tested in conjunction with an equilibrium model. The significant risk-return trade-off, on the other hand, implies that autocorrelation in unadjusted returns is not evidence against market efficiency. The choice between neoclassical and behavioral finance analysis is often treated as an either-or proposition, but the results clearly demonstrate that behavioral explanations can help explain the mixed risk-return trade-off results and the appearance of autocorrelation in stock returns.