And Liquidity-Related Variation in the Correlations and Mean Returns Across Stocks and T-Bonds

Flight-to-Quality- and Liquidity-Related Variation in the Correlations and Mean Returns across Stocks and T-Bonds1 Naresh Bansal,a Robert Connolly,b and Chris Stiversc a John Cook School of Business Saint Louis University b Kenan-Flagler Business School University of North Carolina at Chapel Hill c Terry College of Business University of Georgia This version: December 19, 2007 1We thank Tyler Henry, Lubos Pastor, Robert Savickas, Cheick Samake, John Scruggs, Jahangir Sultan, and seminar participants at the University of Georgia, the 2007 Financial Management Association meeting, the 2007 Washington Area Finance Conference, and the 2007 Southern Finance Association meeting for helpful comments. Please address comments to Naresh Bansal (e-mail: [email protected]; phone: (314) 977-7204; Robert Connolly (email: Robert [email protected]; phone: (919) 962-0053); or to Chris Stivers (e-mail: [email protected]; phone: (706) 542-3648). Flight-to-Quality- and Liquidity-Related Variation in the Correlations and Mean Returns across Stocks and T-Bonds Abstract Over the crisis-rich 1997 to 2005 period, we document new time-series and cross-sectional evidence which suggests a sizable flight-to-quality- and liquidity-related variation in the correlations and mean returns across stocks and T-Bonds. Our collective results support the premise of a \searching" in the relative valuation of stocks and bonds during times of market stress. First, higher levels of stock implied volatility (IV) and stock illiquidity and higher time-series variability in stock IV are associated with both: (1) a much lower correlation in the subsequent returns of stock and T-bond returns, and (2) much greater time-series variability in the subsequent stock IV and illiquidity values. Second, daily stock returns are negatively and appreciably related to the contemporaneous stock IV change, and more-liquid stocks exhibit both: (1) greater respon- siveness to the IV change, and (2) a more negative stock-bond correlation in stressful times. Third, stock IV changes are positively related to the T-bond returns. Finally, when stock IV is relatively high, the subsequent mean returns and turnover are relatively greater for portfolios of more-liquid stocks, as compared to portfolios of less-liquid stocks. JEL Classi¯cation: G12, G14 Keywords: Stock and Bond Correlations, Flight-to-Quality, Liquidity 1. Introduction For decades, researchers have recognized the central role of the joint distribution of equity and bond returns in asset pricing, portfolio allocation, and risk management problems. Recent work has examined time-variation in the comovement of stock and bond returns (see, e.g., Flem- ing, Kirby, and Ostdiek (1998), (2001), and (2003), Scruggs and Glabadanis (2003), Hartmann, Straetmans, and Devries (2001), Connolly, Stivers, and Sun (2005), (2007), Gulko (2002), Li (2002), and Baele, Bekaert, and Inghelbrecht (2007)). These papers document substantial time- variation in stock-bond return comovements with sustained periods of a negative correlation that seem unable to be explained by traditional long-term fundamentals in the sense of Campbell and Ammer (1993) or Fama and French (1989). Economic and political crises can temporarily shock ¯nancial markets in the sense of Kodres and Pritsker (2002). Recent examples of such crisis include the 1997 East Asian ¯nancial crisis, the 1998 Russian foreign debt default, the 1999 Brazilian currency crisis, the 2001 terrorism crisis, and the 2003 Iraqi war. During such crises, flight-to-quality and liquidity may be particularly important in understanding the joint stock-bond return distribution. In this paper, we present new time-series and cross-sectional evidence on this issue by examining the crisis-rich 1997 to 2005 period. We begin by examining whether the correlation between daily 10-year T-bond futures and equity index futures can be linked to variation in stock implied volatility, stock liquidity, and futures volume. Next, to probe deeper, we evaluate conditional stock-bond correlations, mean returns, and turnover for disaggregate stock portfolios that are comprised of individual stocks with di®erent levels of volatility, liquidity, and market capitalization. By conditional, we mean that we evaluate these portfolio-level parameters under various market conditions. We appeal to the following premise to motivate our empirical investigation. When expected stock volatility and illiquidity increase substantially, then riskier stocks are likely to be revalued lower relative to safer T-bonds with flight-to-quality and/or liquidity pricing influences. Times of market stress are likely to be associated not only with higher levels of stock volatility and illiquidity, but also with higher time-series variability in these `market conditions' variables. The high variability may induce \searching" in the relative valuation of stocks and bonds during times 1 of market stress, with a resulting negative (or, at least, lower) correlation in returns. Such market dynamics may also be associated with prominent di®erences in the conditional mean returns and turnover across stocks with di®erent levels of return volatility and liquidity. We examine the 1997 to 2005 period, with separate evaluations for the 1997 to 2000 and 2001 to 2005 subperiods, for several reasons. First, Chordia, Sarkar, and Subrahmanyam (2005) and Connolly, Stivers, and Sun (2005) ¯nd that the 1997 to 2000 period is a particularly rich period, with multiple ¯nancial crises such as those listed in our second paragraph. Second, the 2001 to 2005 subperiod is entirely out-of-sample, relative to these prior papers. Our work features the implied volatility from equity index options, stock illiquidity derived from joint return-volume behavior, and the trading volume from stock and T-bond futures markets. These variables do not directly relate to stock-bond correlations or cross-sectional di®erences in realized stock means. Rather, we use these variables to describe market conditions, where relatively higher levels and/or higher time-series variability of these `market conditions' variables are one way to qualify times of market stress. Presumably, flight-to-quality and liquidity pricing influences should be relatively more important during such times of market stress. We use the CBOE's VIX as a measure of the stock market's implied volatility (IV). For stock illiquidity, we evaluate both a return-reversal measure (RRV) that follows from Pastor and Stambaugh (2003), and a price-impact measure (PIM) that follows from Amihud (2002). To measure the relative degree of futures trading, we construct a standardized measure of volume for the S&P 500 index and 10-year T-bond futures. Our standardization procedure controls for both the long-term growth in futures volume and the quarterly cycle in futures volume. Our empirical investigation has four major components. Each is intended to address di®erent aspects of the general hypothesis that flight-to-quality (FTQ hereafter) and liquidity di®erences may be important in understanding variations in conditional correlations and mean returns across stocks and T-bonds. The ¯rst two major components of our work investigate the time-series behavior of market-level returns and other market-level variables. Our last two major components focus on cross-sectional di®erences across stocks, so they feature spot return data. Motivated by the episodic nature of stock market crises, the ¯rst major component of our empirical investigation features a regime-switching model. We extend prior work by estimating a bivariate regime-switching model on daily stock and T-bond futures returns in a speci¯cation 2 that allows the stock and bond volatilities, means, and their return correlations to vary across regimes. We use the estimated regime episodes to examine how stock liquidity, implied volatility, and futures volume di®er across the two regimes. The intent is to use the regime-switching estimation to provide a broad description of market di®erences in stressful times, which should provide intuition and perspective for our subsequent analysis. We are interested in whether the regime-switching estimation will depict a plausible `bad regime,' where FTQ and liquidity pricing influences seem likely to be important in understanding joint stock-bond price formation. If so, we hypothesize that the bad-regime days will be associated with appreciably higher stock volatility, a lower stock-bond correlation, higher mean bond returns, and greater time-series variability in stock IV and stock liquidity. We also hypothesize that bad-regime day t will be preceded by higher levels of stock IV, stock illiquidity, and futures trading volume as measured through day t ¡ 1; which would, presumably, reflect day t expectations.1 Our ¯ndings are in line with all our hypothesized empirical characteristics, with a stock-bond correlation of +0.14 in the good regime and -0.43 in the bad regime. The second major component of our empirical investigation has a forward-looking focus. We hypothesize that high values of stock IV, stock illiquidity, and futures volume will be associated with a lower subsequent correlation between stock and T-bond returns. This aspect of our work builds on Connolly, Stivers, and Sun (2005), (2007), who ¯nd that the stock IV level is negatively related to the correlation of subsequent stock and T-bond returns. In addition to adding the stock illiquidity and futures volume to the analysis, we also extend prior work by examining whether the recent time-series variability of stock IV is informative about the subsequent stock- bond correlation. With persistence in the volatility of stock IV, we hypothesize that a high IV variability should be associated with a lower subsequent correlation, which would support the notion of a \searching" in the relative valuation of stocks and bonds as uncertainty fluctuates. In a univariate setting, we ¯nd a sizable and reliable negative relation between the stock-bond correlation and lagged measures of either stock IV, stock illiquidity, the stock futures volume, and the recent variability in the stock IV.

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