Comovement

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Abstract

Building on Vijh (Rev. Financial Stud. 7 (1994)), we use additions to the S&P 500 to distinguish two views of return comovement: the traditional view, which attributes it to comovement in news about fundamental value, and an alternative view, in which frictions or sentiment delink it from fundamentals. After inclusion, a stock's beta with the S&P goes up. In bivariate regressions which control for the return of non-S&P stocks, the increase in S&P beta is even larger. These results are generally stronger in more recent data. Our findings cannot easily be explained by the fundamentals-based view and provide new evidence in support of the alternative friction- or sentiment-based view.

Introduction

Researchers have uncovered numerous patterns of comovement in asset returns. There are strong common factors in the returns of small-cap stocks, value stocks, closed-end funds, stocks in the same industry, and bonds of the same rating and maturity. There is common movement of individual stocks within national markets and also among international markets themselves.

A substantial body of work examines whether the sensitivity of asset returns to common factors such as these can help explain average rates of return. Much less work, however, has been done to understand why common factors arise in the first place. Why do certain groups of assets comove while others do not? What determines assets' betas on these common factors? In this paper, we consider two broad theories of comovement—one traditional, the other more novel—and present new evidence to distinguish between them.

The traditional theory, derived from economies without frictions and with rational investors, holds that comovement in prices reflects comovement in fundamental values. In a frictionless economy with rational investors, price equals fundamental value—an asset's rationally forecasted cash flows discounted at a rate appropriate for their risk—and so any comovement in prices must be due to comovement in fundamentals.

In economies with frictions or with irrational investors, and in which there are limits to arbitrage, comovement in prices is delinked from comovement in fundamentals. This suggests a second broad class of “friction-based” and “sentiment-based” theories of comovement. We examine three specific views of comovement that can be described in these terms.

The first is the category view, analyzed by Barberis and Shleifer (2003). They argue that, to simplify portfolio decisions, many investors first group assets into categories such as small-cap stocks, oil industry stocks, or junk bonds, and then allocate funds at the level of these categories rather than at the individual asset level. If some of the investors using categories are noise traders with correlated sentiment, and if their trading affects prices, then as they move funds from one category to another, their coordinated demand induces common factors in the returns of assets that happen to be classified into the same category, even when these assets' cash flows are uncorrelated.1

Another kind of comovement, which we refer to as the habitat view, starts from the observation that many investors choose to trade only a subset of all available securities. Such preferred habitats could arise because of transaction costs, international trading restrictions, or lack of information. As these investors' risk aversion, sentiment, or liquidity needs change, they alter their exposure to the securities in their habitat, thereby inducing a common factor in the returns of these securities. This view of comovement predicts that there will be a common factor in the returns of securities that are held and traded by a specific subset of investors, such as individual investors.

A third view of comovement, the information diffusion view, holds that, due to some market friction, information is incorporated more quickly into the prices of some stocks than others. For example, some stocks may be less costly to trade, or may be held by investors with faster access to breaking news and the resources required to exploit it. In this view, there will be a common factor in the returns of stocks that incorporate information at similar rates: when good news about aggregate earnings is released, some stocks reflect it today and move up together immediately; the remaining stocks also move up together, but only after some delay.2

Early evidence of friction- or sentiment-based comovement can be found in Vijh (1994), who studies changes in the market betas of stocks added to the S&P 500 index. Standard & Poor's emphasizes that in choosing stocks for inclusion in the S&P 500, they are simply trying to make their index as representative as possible of the overall U.S. economy, not signaling an opinion about fundamental value. If so, inclusion should not change investors' perception of the correlation of the included stock's fundamental value with other stocks' fundamental values. Under the traditional view of comovement, then, inclusion should not change the correlation of the included stock's return with the returns of other stocks.

The friction- or sentiment-based views make a different prediction. Consider first the category and habitat views. The vast popularity of S&P-linked investment products, such as S&P mutual funds, futures, and options, suggests that the index is a preferred habitat for some investors and a natural category for many more. When a stock is added to the S&P, it enters a category (habitat) used by many investors and is buffeted by fund flows in and out of that category (habitat). If arbitrage is limited, these fund flows raise the correlation of the included stock's return with the returns of other stocks in the S&P.

The information diffusion view also predicts a rise in the correlation of the added stock's return with the S&P return. Under this view, stocks in the S&P 500 are quick to incorporate news about aggregate cash flows, perhaps because they have particularly low trading costs or are held by investors with better access to news. When a stock enters the S&P, it starts to incorporate market-wide news at the same time as other S&P stocks, rather than, say, a day later. As a result, it comoves more with other S&P stocks after inclusion than before.

In fact, Vijh (1994) finds that at both daily and weekly frequencies, stocks added to the index between 1975 and 1989 experience a significant increase in their betas on the value-weighted return of NYSE and AMEX stocks, a close proxy for the value-weighted S&P return. In contrast to the fundamentals view, but consistent with the three friction- or sentiment-based views, addition to the index leads to a shift in the correlation structure of returns.3

In this paper, we return to additions to the S&P 500 and provide new evidence in support of the friction- or sentiment-based theories of comovement. First, by applying a univariate regression analysis similar to Vijh's to the longer sample of data now available, we uncover considerably larger effects. While stocks added to the S&P during 1976–1987 experience an average increase in daily S&P beta of 0.067 after inclusion, the average increase in the 1988–2000 period is 0.214. In light of the growing importance of the S&P 500 as both a category and a habitat, the fact that the effect is not only present but larger in more recent data is especially supportive of the friction- or sentiment-based views.

Our second and principal contribution is to introduce a bivariate regression test to distinguish between the two broad theories of comovement. The friction- or sentiment-based views imply that, in a bivariate regression of a stock's return on both the S&P and a non-S&P “rest of the market” index, the S&P beta should go up after inclusion while the non-S&P beta should fall; that these patterns should go in the opposite direction for stocks deleted from the index; and that they should be stronger in more recent data. The fundamentals view, in contrast, predicts no shift in S&P and non-S&P betas after inclusion.

The bivariate regressions provide evidence of friction- or sentiment-based comovement altogether stronger than that uncovered by the univariate tests. At daily, weekly, and even monthly frequencies, the bivariate tests show a striking increase in S&P betas and decline in non-S&P betas. At the daily frequency, for example, S&P betas increase by 0.326 on average over the 1976–2000 period, while non-S&P betas fall by an average of 0.319. Significant results in the opposite direction are observed when stocks are deleted from the index, and the effects are quantitatively larger in more recent data.

We examine the robustness of these findings in several ways. We obtain similar results when analyzing the data from a “calendar time” rather than an “event time” perspective. We also find that the results cannot be attributed to thin trading. Finally, we show that the shifts in S&P betas for stocks added to the index are much larger than those for a sample of “matched” stocks, namely stocks similar to the event stocks in a number of characteristics, but which are not included in the index. This last observation rules out certain fundamentals-based explanations of our results under which inclusion in the S&P coincides with a change in the correlations between stocks' fundamental values, even if it does not cause such a change.

While our results are consistent with all three variants of friction- or sentiment-based comovement—category, habitat, and information diffusion—we also attempt to determine how big a role each of them plays. In particular, we decompose the shift in betas around inclusion into a component due to information diffusion and a residual component, more likely due to category and habitat effects. The information diffusion story has the distinguishing feature that it predicts nonzero cross-autocorrelations between S&P and non-S&P returns. We can therefore identify its effect by including lead and lag terms in the regressions. Our analysis suggests that a small fraction of the daily univariate results and a much larger fraction of the daily bivariate results are due to information diffusion effects.

Our paper adds to a growing body of evidence that can be naturally understood as friction- or sentiment-based comovement. Froot and Dabora (1999) show that the returns of Royal Dutch shares are surprisingly delinked from the returns of Shell shares, even though the two stocks are claims to the same cash-flow stream and therefore have the same fundamental value. Hardouvelis et al. (1994) and Bodurtha et al. (1995) show that closed-end country funds comove as much with the stock market in the country where they are traded as with the stock market in the country where their assets are traded. Lee et al. (1991) find that domestic closed-end funds often comove with small-cap stocks even when their asset holdings consist of large-cap stocks. Pindyck and Rotemberg (1990) uncover evidence of excess comovement in the prices of seven major commodities. Fama and French (1995) show that it is hard to connect the strong common factors in the returns of value stocks and small stocks to common factors in news about earnings.4

Greenwood and Sosner (2002) test the friction- or sentiment-based views using data on additions to and deletions from the Nikkei 225 index. They find increases in beta and R2 following addition to the index, and decreases following deletions. Their evidence is therefore also consistent with our predictions; if anything, the results for the Japanese data are even stronger than those for the U.S. data.

A large literature examines whether index inclusion has a contemporaneous effect on price levels. Harris and Gurel (1986), Shleifer (1986), Lynch and Mendenhall (1997), and Wurgler and Zhuravskaya (2002) find strong price effects for S&P 500 inclusions, while Kaul et al. (2000) and Greenwood (2004) find similar effects in the Toronto Stock Exchange TSE 300 and Nikkei 225 indices, respectively. This literature argues that uninformed demand affects price levels; our paper shows that it may also affect patterns of comovement.5

In Section 2, we present the basic predictions of the three friction- or sentiment-based views of comovement. In Section 3, we test these predictions using data on S&P 500 inclusions and deletions. Section 4 concludes.

Section snippets

Theories of comovement

The traditional theory of return comovement is the fundamentals-based view, under which the returns of two assets are correlated because changes in the assets' fundamental values are correlated. In this section, we briefly present reduced-form models of three alternative friction- or sentiment-based theories of comovement: the category, habitat, and information diffusion views. The models yield the predictions that motivate the empirical work in Section 3.

Consider an economy that contains a

Empirical tests

To test Predictions 1 and 2, we need a group of securities with three characteristics. First, the group must be a natural category or preferred habitat for many investors, or else a set of stocks that incorporate information more quickly than do other stocks. Second, since the predictions concern reclassification, there must be clear and identifiable changes in group membership. Finally, to control for fundamentals-based comovement, a security's inclusion or removal from the group should not

Conclusion

We present two broad theories of return comovement and examine them empirically using data on additions to the S&P 500. The traditional theory, fundamentals-based comovement, is derived from frictionless economies with rational investors and attributes comovement in returns to correlation in news about fundamental value. The alternative theory argues that, due to market frictions or noise-trader sentiment, return comovement is delinked from fundamentals. We consider three specific variants of

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    We thank John Campbell, Ned Elton, Kenneth French, Will Goetzmann, Joel Hasbrouck, Steven Kaplan, Anthony Lynch, Mike Ryngaert, Bill Schwert, Robert Shiller, Tuomo Vuolteenaho, two anonymous referees, seminar participants at Columbia University, Harvard University, the London School of Economics, New York University, Rice University, UCLA, the University of Chicago, the University of Florida at Gainesville, the University of Notre Dame, Yale University and the NBER for helpful comments, Huafeng Chen and Bill Zhang for helpful comments and outstanding research assistance, the Q Group for financial support, and Rick Mendenhall and Standard and Poor's for providing data.

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