Significance of serial cross-correlations after controlling for a specific factor structure in security returns, The

significance of serial cross-correlations after controlling for a specific factor structure in security returns, The

Higgins, Eric James

Two important sources of predictability in security returns are serial cross– correlations and time-varying factors. Hameed (1997) finds that serial crosscorrelation patterns in security returns do not exist after controlling for a general, time-varying factor structure in returns. This paper finds significant serial cross-correlations in daily returns after controlling for autocorrelation and the Fama and French (1993) factors. When returns are conditioned on prior market-wide information, serial cross-correlations in daily returns are found to be significant only after bad news.

Introduction

Two interesting sources of predictability that have been identified in security returns are serial cross-correlations and significant time-varying factor structures. Recent studies by Fargher and Weigand (1998) and Richardson and Peterson (1999) find the existence of significant serial cross-correlations in security returns. Hameed (1997) suggests that serial cross-correlations and time-varying factor structures may be related. He finds that a time-varying factor model can explain the existence of serial cross-correlation patterns in security returns. The purpose of this study is to extend the studies by Hameed ( 1997) and Fargher and Weigand (1998) by examining whether the Fama and French (1993) three-factor model accounts for serial cross-correlation patterns in daily security returns.

Most of the previous research on the existence of serial cross-correlations in security returns has focused on weekly security returns. Lo and MacKinlay (1990) document that the returns of small stocks lag the returns of large stocks. Boudoukh, Richardson, and Whitelaw (1994), however, suggest that serial cross-correlations in security returns are simply a manifestation of return autocorrelation and contemporaneous correlations among assets. Hameed (1997) supports this conclusion by finding that serial cross-correlations are not significant after controlling for portfolio return autocorrelation. Richardson and Peterson (1999) find, however, that significant serial cross-correlations exist in weekly returns after controlling for portfolio return autocorrelation.

Fargher and Weigand ( 1998) extend the literature on serial cross-correlations by examining daily returns. They find that significant serial cross-correlations exist in daily security returns after controlling for the existence of daily autocorrelations. They show, however, that the strength of the serial cross-correlations has decreased over time.

The literature on the existence of time-varying factors is also extensive. Keim and Stambaugh (1986) were among the first to find time-varying risk premiums that are related to a set of predictor variables reflective of levels of asset prices. One of the most studied factor models in recent financial research is that of Fama and French (1993). Fama and French find that a model containing risk premia related to size, book-to-market equity ratio (BE/ME), and the market explains a significant amount of variation in returns. The three factors are shown to account for the predictable variation in other factors such as the dividend yield and the earnings-price ratio.

Given that serial cross-correlations and time-varying factor models both appear to explain predictable variation in returns, it is likely that there is a relationship between these two sources of predictability. Recent studies examine the possible relationships between serial cross-correlations and time-varying factor models. Hameed (1997) shows that a general, time-varying, two-factor model can explain the existence of serial cross-correlation patterns in returns. McQueen, Pinegar, and Thorley (1996), however, show that significant serial cross-correlations occur after good news, even after controlling for a specific factor structure that includes the term spread, the dividend yield, the default spread, and the inflation rate. Thus, there is no clear answer as to whether significant serial cross-correlations exist after controlling for time-varying factors.

The recent studies on serial cross-correlations have left several unanswered questions, especially regarding the nature of serial cross-correlations in daily returns. First, are serial cross-correlations in daily returns significant after controlling for a specific factor structure such as that proposed by Fama and French (1993)? Hameed ( 1997) finds that serial cross-correlations in weekly returns are not robust to a general factor structure, but McQueen, Pinegar, and Thorley (1996) find that serial cross-correlations in monthly returns are significant after controlling for a specific factor structure. Second, is the significance of daily serial cross-correlations unidirectional? That is, do large-firm returns lead small-firm returns without the reverse being true? Brennan, Jegadeesh and Swaminathan (1993) show that it is important to consider bi-directional causality in security returns. Third, do serial cross-correlation patterns in daily returns exhibit the same asymmetric pattern documented by McQueen, Pinegar, and Thorley (1996)?

This study extends the current literature by examining these questions. First, we examine the significance of serial cross-correlations in daily returns after controlling for the specific factor structure in the three-factor model of Fama and French ( 1993). The Fama and French factors are chosen because of their significance in explaining return variation and their wide examination in the literature. Second, this study examines whether daily small-firm returns can be used to predict large-firm returns. Finally, this study examines whether there is a difference in daily serial cross-correlations when there is prior good news or bad news. Thus, this study provides further evidence documenting the predictability of security returns by further examining the significance of serial cross-correlations and the validity of the factors used in the Fama and French model.

The results of this study show that a significant first-order serial cross-correlation exists in security returns, after controlling for the Fama and French (1993) factors. Serial cross-correlations are not shown to be asymmetric. Lagged small-firm returns are found to predict large firm returns. Interestingly, serial cross-correlations between small and large firms are found to be significant only when prior information is bad. We conclude that serial cross-correlations are a significant source of predictability in security returns after controlling for a specific factor structure. Our results are not entirely consistent, however, with existing theories explaining the existence of serial cross-correlations in security returns.

Data Sources and Portfolio Formation Size-Sorted Portfolios

Four size-sorted portfolios of daily security returns taken from the Center for Research in Security Prices (CRSP) database for New York Stock Exchange and American Stock Exchange (NYSE/AMEX) securities, from April 1, 1976 to December 30, 1994, are used to examine serial cross-correlations patterns.1 Return portfolios for each dataset are formed yearly based on prior year values for size, where size is defined as the market value of equity on the last trading day of the prior year. To be included in the portfolio formation process, a firm must not have more than two consecutive non-trading days during the year. This screen eliminates firms with excessive non-trading, which may induce spurious predictability in returns. Also, a firm must have a closing price and number of shares outstanding available on the last trading day of the year. Annually, there are an average of 1383 securities in each portfolio with an average of 518 securities being eliminated by the non-trading screen.

Each security is examined individually for each day to determine if it is included in the return portfolios. Thus, on any given day, the number of securities in each portfolio and the composition of each portfolio are allowed to change. To be included in the daily return portfolios on any given day t + 1, a security must have a transaction price available on day t and on day t – 1.2 This maximizes the number of securities in each portfolio that have returns calculated from transaction prices. This should reduce spurious autocorrelation and potentially serial cross-correlation arising from non-synchronous trading.

Development of the Three-Factor Model

In order to use the three-factor model of Fama and French (1993), two mimicking return portfolios that account for size effects and BE/ME effects need to be developed. Size and BE/ME-sorted portfolios of daily security returns are created from the CRSP database for NYSE/AMEX listed securities from April 1, 1976, to December 30, 1994. Return portfolios are formed yearly based on prior year values for size and BE/ME.

Size is defined as the market value of equity on the last trading day of the prior year. Book equity is defined as a firm’s prior year-end book value of common equity plus any deferred taxes and investment tax credits for the prior year, taken from the Standard & Poor’s COMPUSTAT data base.3 This value for book equity is divided by the firm’s market value of equity from the CRSP database on March 31 in the year that returns are to be calculated.

To be included in the portfolio formation process, a security must be included simultaneously on the CRSP and COMPUSTAT databases. Additionally, a firm must not have more than two consecutive non-trading days during the year.

BE/ME-sorted returns are computed using methodology similar to Jaffe, Keim, and Westerfield (1989). Only firms with a December 31 fiscal year-end and firms that are not subsidiaries are included in the BE/ME sample. A firm must also have a year-end book value of equity available from the COMPUSTAT database and a price and current shares outstanding available from the CRSP database on March 31 to be included in the BE/ME sample.4 Returns for the BE/ME series are calculated from April I to March 31 of the next year. This approach to calculating returns avoids the look-ahead bias associated with using year-end prices to calculate financial ratios.5 To be included in the size-sorted portfolios, a firm must have a closing price and number of shares outstanding available on the last trading day of the year.

After identifying the securities included in the portfolio formation process for a given year, the securities are sorted into four size portfolios, and each size portfolio is sorted into four portfolios based on BE/ME. This creates 16 size and BE/ME– sorted portfolios. Subtracting the average daily return of the largest size-sorted portfolios from the average daily return of the smallest size-sorted across each of the BE/ME categories creates the mimicking return portfolio for size. Subtracting the average daily return of the highest BE/ME-sorted portfolios from the average daily return of the lowest BE/ME-sorted portfolios across each of the size categories creates the mimicking return portfolio for the book-to-market equity ratio. Thus, this procedure creates a size-sorted return portfolio free of BE/ME effects and a BE/ME– sorted return portfolio free of size effects. The portfolio creation procedure is repeated each year and results in two daily return series that should account for size and book-to-market equity ratio effects in returns.

Conclusions

This study compares the predictive ability of serial cross-correlations in security returns with the predictive ability of the Fama and French (1993) factors. Also, this study provides further documentation of the significance of serial cross-correlation patterns in daily security returns. The study examines the significance of serial cross– correlations after controlling for good news and bad news in security returns. Also, the study examines whether there is an asymmetry in daily serial cross-correlations as has been documented in monthly and weekly security returns.

We find evidence of a significant serial cross-correlation pattern between large and small firms, after controlling for the Fama and French (1993) factors. We show that large-firm returns do lead small firm returns. We also find evidence of a significant negative relationship between large-firm returns and lagged small-firm returns, which is inconsistent with previous results using monthly and weekly returns. We document a bad news effect in serial cross-correlations as well. Large-firm returns lead small firm returns only when prior large-firm returns are negative. We also show that there are some differences in the predictability of large and small firm returns through time. While we are not able to show that serial cross-correlations dominate a factor structure in predicting returns, we do document their significance given a specific factor structure.

1 The starting date for the size-sorted return series is chosen to match the sample time period available for the creation of the Fama and French (1993) factors.

2 This screening procedure is similar to that used by Chordia and Swaminathan (2000). They suggest that this procedure minimizes the impact of non-synchronous trading for NYSE/AMEX listed securities.

This definition of book equity is similar to that of Fama and French (1993). 4 Firms with negative BE/ME ratios are excluded.

5 Banz and Breen (1986) discuss the potential look-ahead bias that exists when using accounting data.

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Eric Jame Higgins

Kansas State University

David R. Peterson

Florida State University

Copyright University of Nebraska, Board of Regents Summer 2001

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