positively to indicators of recession and negatively to indicators of expansion.

Transcription

1 EQUITY MARKET ORDER FLOW, MACROECONOMIC FUNDAMENTALS, AND EXPECTED STOCK RETURNS Abstract This paper examines the forecast power of stock market order flows for future economic fundamentals and expected market returns. We find that aggregate market order flow and the order flow differential between big and small stocks contain valuable information about future output growth rates and the excess market returns, information that is not captured by prominent business cycle indicators or marketwide liquidity. Our results are consistent with a model in the spirit of Evans and Lyons (2007) where marketwide order flow aggregates fundamental information that exists within the market in a dispersed microeconomic form and with the notion in Chan (1993) that market makers, who receive noisy signals about the value of their stocks, overlook this fundamental information conveyed collectively by the sum of other stocks signals. Our work extends empirical analysis from the foreign exchange and bond markets.

2 1. Introduction In a setting where information is distributed heterogeneously across agents, marketwide order flow aggregates information that exists within the market in dispersed microeconomic form and conveys a valuable signal about how investors bet on their expectations about fundamentals with their wallets (Evans and Lyons, 2007). The information content of marketwide order flow has been studied in a variety of settings. Green (2004), for instance, finds that the government bond order flow reveals fundamental information about riskless rates. Evans and Lyons (2007) show that foreign exchange (FX) order flows forecast macro fundamentals and FX market returns. Albuquerque, Francisco, and Marques (2008) document that a marketwide private information measure obtained from stock market order flows predicts FX market and industry stock returns. This paper adds to this literature by investigating the forecast power of two distinct marketwide order flow measures for output growth rates and expected stock returns. The first of these measures is marketwide order flow (OFM). OFM in bond and FX markets is shown to have forecast power for economic fundamentals. The second measure is novel and specific to the stock market. We define OFD as the order flow differential between big and small stocks and argue that this measure correlates with the time-variation in marketwide risk aversion. We present evidence consistent with this argument. To the best of our knowledge, this paper is the first to analyze the relation among aggregate stock market order flows, macroeconomic fundamentals, and expected stock market returns. Our main results are as follows. OFM and OFD have strikingly strong forecast power for output growth rates over the subsequent monthly, quarterly, and annual periods. This forecast power is robust to controls for contemporaneous return factors (the excess market return, SMB, HML, and WML), business-cycle indicators (the default spread and term spread), and measures of liquidity (the marketwide averages of Amihud (2002) price impact measure and percentage bid-ask spread). Keeping all else constant, a one standard deviation increase in OFM predicts a statistically and economically significant 0.63 percent increase in the production growth rate over the subsequent year. This finding is in line with the notion that the sum of all trades by investors conveys otherwise unavailable information about future macro fundamentals. Similarly, a one standard deviation increase in OFD forecasts the production growth rate to be 0.36 percent lower over the subsequent year. This indicates that a higher than average demand for big stocks relative to small stocks signals a slow down in the real economy and is consistent with the countercyclical nature of risk aversion. 1 1 Rosenberg and Engle (2002) provide evidence that an empirical measure of risk aversion is related positively to indicators of recession and negatively to indicators of expansion. 2

3 Linking our marketwide order flow measures to future stock market returns, we find that aboveaverage values of OFM predicts higher-than-average equally-weighted market returns over subsequent periods. Specifically, a one standard deviation increase in OFM forecasts an increase of 2.51 percent in the equally-weighted market return over the following quarter. The finding of a positive relation between OFM and future market returns is broadly consistent with a model in which market makers, in face of a noisy signal about their stock, cannot condition on the signals for other stocks, the sum of which conveys a signal about the macroeconomy (Chan, 1993). The forecast power of OFM disappears at horizons longer than a quarter, suggesting the information in order flows is fully incorporated in prices by then, or when returns are value-weighted, suggesting that market makers for stocks that have greater investor bases capture a greater fraction of the fundamental information dispersed across the market. Our analysis also reveals that an above-average OFD forecasts a higher-than-average equallyweighted market return over prediction horizons ranging from monthly to annual, with a one standard deviation increase in OFD predicting the equally-weighted market return to be 4.91 percent higher over the subsequent quarter. The positive association between OFD and the expected market return is consistent with our hypothesis that this variable captures changes in risk aversion, widening when risk aversion increases and narrowing when risk aversion declines. In the case of value-weighted returns, the forecast power of OFD disappears over prediction horizons longer than a quarter, reinforcing our above argument that market makers for big stocks are better informed about the macro signal in the aggregate order flow. Nonetheless, it is striking that the signal contained in OFD is not incorporated into prices for extended periods. It is also noteworthy that neither the excess market return nor SMB return factors closely related to OFM and OFD contains as much information about future production growth rates as the order flow variables. One possible reason why returns may not forecast future fundamentals better than order flows is that market makers may not be able to condition, in a timely fashion, on the signals for other stocks, which collectively convey information about the macroeconomy (Chan, 1993). The noise thus induced in individual stock returns will not wash away in aggregation since it is correlated across market makers and future corrections that occur as market makers eventually learn about the macro signal would be captured by the aggregate order flow measures. The rest of the paper is organized as follows. Section 2 summarizes the relevant literature and develops our main hypotheses. Section 3 presents our data and variables. Section 4 and Section 5 discuss our results on the forecast power of order flows for output growth rates. Section 6 investigates the relation between order flows and expected returns. Section 7 concludes. 3

4 2. Relevant Literature and Hypothesis Development The extant literature suggests that marketwide order flows contain valuable information about macroeconomic fundamentals. Studying the government bond market, Green (2004) finds that order flow reveals fundamental information about riskless rates. The author shows that the informational role of order flow increases after public information releases, consistent with the notion that some investors are better than others in converting public information into private forecasts. Similarly, Brandt and Kavajecz (2004) study the process of price discovery for U.S. Treasury securities and find that about a quarter of the daily variation in yields on nonannouncement days is explained by order flow, with the effect being permanent and strongest when liquidity is low. Pasquariello and Vega (2006) find that the unanticipated U.S. Treasury bond market order flow has a significant and permanent impact on daily bond yield changes during both announcement and non-announcement days, with the effect being stronger when the dispersion of beliefs among investors is high and the announcements are noisy. In a study that draws a close parallel with our work, Evans and Lyons (2007) introduce a general equilibrium model in which fundamental information that is first manifested at the firm-level and is not symmetrically observed by all agents imbues foreign exchange market order flows with an important role in aggregating information. Based on this model, the authors conjecture that FX market order flows (i) should forecast future macro fundamentals, (ii) do so significantly better than FX market returns, and (iii) should forecast FX market returns. Their empirical tests provide support for these conjectures. Evidence from the stock market is scarce. Albuquerque, Francisco, and Marques (2008) develop a model of equity trading where private information can be firm-specific or marketwide and use intraday trade and quote data to construct a measure of the industry-level daily order flow driven by marketwide private information (MPI). Testing the model, the authors show that the industry MPI forecasts returns of the affiliated firms in most of the industries examined and that MPI for certain industries forecasts foreign exchange returns. Our paper contributes to this literature by investigating the forecast power of two distinct aggregate stock market order flow measures for future output growth rates and expected market returns. The first of these measures is aggregate market order flow (OFM). We motivate our first hypothesis by extending the insights in Evans and Lyons (2007) to the stock market. The authors develop a general equilibrium model based on the intuition that a significant part of the information relevant to current FX spot prices is not known publicly at any point in time but instead exists within the market in a dispersed form. This information is not reflected in prices 4

5 until it is assimilated by market makers and, hence, cannot be captured by variables based on contemporaneous security prices. Based on this intuition: Hypothesis 1: A higher-than-average OFM should forecast a higher-than-average future output growth rate and this forecast power should be robust to the inclusion of variables such as the default spread, term spread, and marketwide liquidity. Our second measure is novel. We define OFD as the difference between the order flows for big and small stocks and argue that, to the extent that investors regard big stocks as safer investments than small stocks, this measure should capture time variation in marketwide risk aversion. In order to convince the reader that this argument is a plausible one, we motivate the measure using evidence from Campbell, Chan, and Viceira (2003). The authors develop an approximate solution method for the optimal consumption and portfolio choice problem of an infinitely longlived Epstein-Zin utility maximizer choosing between multiple risky assets. In their empirical test, the authors analyze how investors allocate their wealth to stocks, bonds, and Treasury bills subject to an investment opportunity set described by a VAR system that includes short-term ex post real and nominal interest rates, excess stock and bond returns, the dividend-price ratio, and the term spread. The fractions of wealth invested in bonds and stocks by an investor with the knowledge of the full VAR model are presented in Table 1. The positive linear relationship between the relative risk aversion and the difference between bond and stock allocations is evident in Figure 1. The intuition here is that the hedging demand for bonds increases disproportionately to the hedging demand for stocks when risk aversion is higher. A similar intuition may be applied, within the stock market, to big stocks and small stocks 2. According to habit persistence models of investor utility (e.g. Campbell, 1996; Campbell and Cochrane, 1999) as well as the empirical evidence reported in Rosenberg and Engle (2002), risk aversion is countercyclical, high prior to/during recessions and low prior to/during expansions. Consequently: Hypothesis 2: The order flow differential between big and small stocks should be positively related to marketwide risk aversion and higher-than-average values of this measure should forecast a deterioration of macroeconomic fundamentals. This hypothesis may also be pitched in terms of hedging demands. Spiegel and Subrahmanyam (1992) provide uninformed traders with a new role by replacing the common price inelastic noise trader with a strategic utility-maximizing rational hedger. This is an important notion 2 Yogo (2006) shows that the returns for small stocks are more procyclical than the returns for big stocks, which suggests that big stocks are better hedges against adverse wealth shocks. 5

6 since rational hedgers, unlike liquidity traders, trade for strategic reasons and the sum of their trades thus contains macroeconomic information. In support of the importance of hedging trades, Campbell and Viceira (1993) show that a significant part (between 20 and 50 percent) of the demand for stocks by long-lived risk-averse investors is due to intertemporal hedging motives. The demand for big stocks should increase disproportionately more than the demand for small stocks prior to economic downturns, since big stocks deliver more wealth during recessions than do small stocks. This shows up in the order flow differential between big and small stocks and OFD therefore forecasts future macroeconomic conditions. There is evidence that common factors in stock market returns forecast economic fundamentals. Using data from ten countries, Liew and Vassalou (2000) investigate the link between the returns on the market, SMB (small-minus-big), HML (high-minus-low book-to-market), and WML (winners minus losers) portfolios and future GDP growth. The authors document a positive relation between the excess market return, SMB, and HML and the GDP growth rate over the subsequent year for five of the ten countries studied. For the U.S. market, they find that the excess market return and SMB contain information about future GDP growth over and above the Treasury bill yield, dividend yield, term spread, and lagged industrial production growth. Evans and Lyons (2007) assert that the information that exists within the market in a dispersed form is not reflected in prices until it is assimilated by market makers. Chan (1993) develops a model of imperfect information in which market makers, presented with a noisy signal about the value of their stocks, cannot condition on the macro information contained in other stocks signals. Based on the arguments in these two models, our third hypothesis is that: Hypothesis 3: The macroeconomic signal conveyed by aggregate order flow measures should be superior to the information contained in return-based factors. We extend the intuition in Chan (1993) further and argue that the two aggregate order flow measures should capture the corrections that occur as market makers learn about the macro signal and will thereby forecast the market returns over subsequent periods. Hence: Hypothesis 4: Marketwide order flow and the order flow differential between big and small stocks should forecast future stock market returns. We examine the first two hypotheses in Section 4 by linking future production growth rates to OFM and OFD. Hypotheses 3 and 4 are tested in Sections 5 and 6, respectively. The next section describes our data and variables. 6

7 3. Data and Variables Our data comprises all common shares at the intersection of the Center for Research in Security Prices (CRSP) monthly return files, COMPUSTAT Industrial Annual files, and the New York Stock Exchange (NYSE) Trades and Quotes (TAQ) or Institute for the Study of Security Markets (ISSM) databases. We restrict our sample to common stocks trading on the NYSE in order to ensure that our results are not influenced by differences in trading protocols across venues or in trading characteristics across asset classes. In order to be included in the sample in a given measurement period (from July of year t to June of year t+1), a stock should have return and shares outstanding data from CRSP for at least one month in the measurement period, accounting data from the previous fiscal year-end financial statement, and intraday trade and quote data from TAQ. Intraday trade and quote data come from the ISSM for the period 1988 through 1992 and from NYSE TAQ for the period 1993 through Trades for all NYSE common shares are signed using the Lee and Ready (1991) algorithm and, for each stock, monthly (quarterly) order flows are computed as the volume generated in buyer-initiated trades less the volume generated in seller-initiated trades over the month (quarter). 3 This order flow is scaled by the total share volume generated over the period to obtain a standardized measure for stocks with varying degrees of trading activity. The marketwide order flow (OFM) in each period (month or quarter) is the equally-weighted average of the individual stock order flows in that period. In order to compute the order flow differential between big and small stocks (OFD), we divide the sample into six size and book-to-market sorted portfolios as in Fama and French (1993, 1996). Our measurement periods begin at the end of June of year t and at the end of June of year t+1. At the beginning of each measurement period, stocks are sorted on size (MVE market value of common equity at the beginning of the measurement period) and book-to-market equity (BM the ratio of book value of common equity as of the previous fiscal year end to the market value of equity as of the beginning of the measurement period). Then, stocks are assigned to two size (small and big: S and B) and three book-to-market categories (low, medium, and high: L, M, and H) using the size and BM breakpoints provided at Kenneth French s personal website. Based on this categorization, the six size and BM portfolios are formed (S/L, S/M, S/H, B/L, B/M, and B/H) and equally-weighted order flows are computed for each of these portfolios (OF p, ). t 3 Each trade is matched with the first quote occurring at least five seconds prior to the trade. The trade is classified as a buy if it occurs above the prevailing quote midpoint, and vice versa. If the trade has occurred exactly at the quote midpoint, the tick-test is applied a trade is classified as a buy if it results in an upward price tick and a sell if it results in a downward price tick. 7

8 OFD is then defined as the difference between the arithmetic averages of the small and big stock portfolio order flows in each period. OFD (t) = 1 / 3 [OF BL (t) + OF BM (t) + OF BH (t)] 1 / 3 [OF SL (t) + OF SM (t) + OF SH (t)] Monthly data for the returns for the six size-bm sorted portfolios, equally-weighted and valueweighted market portfolios (EWRET and VWRET), and small-minus-big (SMB), high-minus-low (HML), and momentum (WML) factors are from Kenneth French s personal website. We use the monthly size-bm portfolio returns to compute quarterly returns where required. In order to avoid the effect of compounding on long horizon returns, the quarterly return for any quarter is defined as the sum of the monthly returns in that quarter. The marketwide illiquidity measure (ILLIQ) is computed as the equally-weighted cross-sectional average of the individual stock illiquidity measures estimated monthly using daily return and volume data from CRSP following Amihud (2002). Specifically, illiquidity for a stock is estimated in each month as the slope coefficient from a regression of the absolute daily stock return on the daily transaction volume. We use two sets of output growth rates: monthly and quarterly. The data for both of these sets come from St. Louis Fed FRED. The seasonally-adjusted industrial production index is available at a monthly frequency. We use this index to compute industrial production growth rates for monthly (PG (t, t+1)), quarterly (PG (t, t+3)), semiannual (PG (t, t+6)), and annual (PG (t, t+12)) prediction horizons that start immediately after the explanatory variables and controls are measured. The quarterly dataset includes the real GDP growth rate (YG) in addition to PG and is mainly used to demonstrate that our results are robust to using non-overlapping prediction intervals, different proxies for economic growth, and data measured at different frequencies. The left panel of Table 2 reports the means, medians, and standard deviations of the explanatory variables and controls for the monthly series. A mean (median) of 3.64 (3.99) percent and a standard deviation of 4.60 percent for OFM indicates net aggregate buying pressure over the sample period. The positive and significant mean for OFM is also documented in past studies (e.g. Chordia, Roll and Subrahmanyam, 2002). Potential explanations include the absence of limit order trades in the estimation of order flows and the fact that our sample period largely coincides with the extended bull market of the 1990s. OFD has a positive and significant mean (median) of 5.63 (5.46) percent and a standard deviation of 2.81 percent, suggesting that buying pressure for big stocks is consistently greater than for small stocks over this sample period. 8

9 The mean (median) spread between the yield on Moody s Baa grade seasoned bond portfolio and the 20-year Treasury constant maturity rate, DEF, is 1.62 (1.54) percent over the sample period. The mean (median) spread between the yields on 10-year Treasury constant maturities and the three-month Treasury bill rate, TERM, is 3.00 (2.81) percent. The average price impact of buying one round lot of shares is 79 (75) basis points, with a standard deviation of 21 basis points. Finally, the U.S. industrial production grows at a mean (median) monthly rate of 0.23 (0.25) percent over the sample period, which translates to an annual growth rate of about 2.73%, experiencing monthly contractions as large as percent and expansions as large as 2.17 percent. Looking at the four return factors, we see that the mean (median) monthly excess return on the market portfolio is 0.68 (1.19) percent, which corresponds to an annual equity premium of about 8.15 percent. The mean (median) excess return for small stocks over big stocks, SMB, over the sample period is 17 (11) basis points, with a standard deviation of 3.7 percent. The value premium, HML, has a mean (median) of 34 (33) basis points and a standard deviation of 3.38 percent. Lastly, the mean (median) return on a portfolio that is long in past winners and short in past losers, WML, is 0.88 (1.10) percent, with a standard deviation of 4.76 percent. The right-hand panel of Table 2 presents the contemporaneous correlations between these variables. The correlation between OFM and OFD is OFM correlates closely with TERM, with a coefficient of This is consistent with marketwide order flows containing information about future macroeconomic fundamentals, given interpretation of TERM as a prominent indicator of future output growth (Chen, 1991). OFD correlated with TERM, ILLIQ, and PG, with coefficients of -0.44, 0.43, and Given the research evidence that risk aversion exhibits countercyclical behavior (Rosenberg and Engle, 2002), these correlations lend indirect support to our thesis that OFD captures time-variation in risk aversion. The contemporaneous correlations between OFM and MKT (0.24) and OFD and SMB (-0.34) are indicative of price pressure effects. Other interesting associations to note are the correlations between DEF and marketwide illiquidity (0.60), DEF and MKT (-0.17), DEF and PG (-0.30), and ILLIQ and PG (-0.30). We show later in the paper that these effects persist over several future periods. The preliminary analysis reported in this section indicates a reasonable degree of variability in the variables under study and yields encouraging results regarding the information content of the two order flow variables. The following section investigates whether OFM and OFD contain information about future economic fundamentals incremental to that in returns and proxies for liquidity and business conditions. 9

10 4. The Forecast Power of Marketwide Order Flow Measures for Economic Fundamentals We start by examining the forecast power of the monthly aggregate market order flow (OFM) and average order flow differential between big and small stocks (OFD) for the seasonallyadjusted industrial production growth rates, PG (t, t + k), over subsequent twelve-months. We present regression results for monthly (PG (t, t+1)), quarterly (PG (t, t+3)), semiannual (PG (t, t+6)), and annual (PG (t, t+12)) prediction horizons. Prediction horizons longer than a month involve overlapping intervals and the induced bias in the estimated standard errors is corrected through the Hansen-Hodrick (1980) adjustment. It is important to show that order flow provides information beyond well-established business-cycle indicators and marketwide liquidity, so we incorporate controls for the contemporaneous default spread (DEF), term spread (TERM), and aggregate price impact (ILLIQ). These variables are described in the previous section. The ordinary least squares slope estimates and Hansen-Hodrick (1980) adjusted t-statistics from these regressions are reported in Table 3. The link between OFM and future production growth rates is negative but insignificant for monthly and quarterly prediction horizons. For quarterly and annual prediction horizons, the relation becomes positive and significant. A one standard deviation increase in OFM predicts a statistically and economically significant 0.20 standard deviation increase (corresponding to 0.63 percent) in the production growth rate over the subsequent year. OFD is related negatively to future production growth rates over monthly, quarterly, and annual prediction horizons that start immediately after the order flow observation. A one standard deviation increase in OFD forecasts a 0.25 standard deviation decline in the monthly and quarterly production growth rates (0.13 and 0.27 percent) and a 0.12 standard deviation (0.36 percent) decline in the annual growth rate. The coefficient estimates for the control variables are also of interest. Consistent with the extant research exemplified by Fama and French (1989) and Chen (1991), we find that DEF and TERM forecast future output growth rates. There is a statistically significant negative relation between DEF and future PG over horizons of one quarter or longer. A one standard deviation increase in DEF forecasts a production growth rate decline of 0.25 standard deviations over the subsequent quarter, 0.38 standard deviations (0.71 percent) over the subsequent six months, and 0.43 standard deviations (1.32 percent) over the subsequent year. TERM is related positively and significantly to PG over semiannual and annual prediction horizons. A one standard deviation increase in TERM forecasts an increase of 0.23 standard deviations (0.25 percent) over a semiannual prediction horizon and 0.15 standard deviations (0.47 percent) over an annual prediction horizon. Finally, a higher than average level of marketwide illiquidity predicts a slow down in output growth. 10

11 In order to check that the results obtained in the previous table are not specific to industrial production or driven by overlapping prediction horizons, we repeat this test using nonoverlapping monthly periods for production growth rates and non-overlapping quarterly periods for real GDP growth. In the first test, future monthly production growth rates up to a year ahead are regressed on the current month s OFM and OFD. In the second test, future quarterly real GDP growth rates up to four quarters ahead are regressed on the current quarter s OFM and OFD. The coefficient estimates, Newey-West adjusted t-statistics, and the R-square values from these regressions are presented in Table 4. Panel A reports the results for monthly production growth. A one standard deviation increase in OFM predicts a statistically significant increase between 0.15 and 0.20 standard deviations (8 to 11 basis points) in the production growth rates 10 through 12 months after OFM is measured, with R-squares ranging from 0.02 to A one standard deviation increase in OFD, on the other hand, predicts a statistically significant decline of 0.15 to 0.27 standard deviations (8 to 14 basis points) in eleven of the twelve subsequent months, with R-squares ranging between 0.02 and The results for quarterly real GDP growth reported in Panel B yields identical conclusions. An increase in OFM predicts an increase in the real GDP growth in the last quarter of the twelve-month prediction horizon, while OFD is negatively and significantly related to the growth rates in each of the four subsequent quarters. Where does this evidence lead us? First, the finding that OFM and OFD have forecast powers for future production growth rates extends the evidence from bond and foreign exchange markets (Brandt and Kavajecz, 2004; Green, 2004; and Evans and Lyons, 2007) that the sum of all trades contains information about macroeconomic fundamentals. The fact that this forecast power is robust to controls for business cycle indicators and marketwide liquidity suggests that the information conveyed by order flow is unique. Given the evidence in Rosenberg and Engle (2002) that risk aversion is countercyclical, the strong negative relation between OFD and future production growth rates is also in line with our argument that the spread between the big and small stock order flows contains information about changes in marketwide risk aversion. There is strong empirical evidence that order flows are contemporaneously associated with price changes (e.g. Chordia, Roll, and Subrahmanyam, 2002). In the next section, we ask whether the information in OFM and OFD is subsumed by the return factors from a four-factor empirical asset pricing model in the spirit of Fama and French (1993, 1996) and Carhart (1997) including the excess market return (MKT) and stylized empirical premiums including small-minus-big (SMB), high-minus-low (HML) (Fama and French, 1993, 1996), and winners-minus-losers (WML) (Carhart, 1997). 11

12 5. Comparing the Information Contents of Order Flow-Based Variables and Return-Based Factors In this section, we investigate whether the information that we have shown to be present in the order flow variables OFM and OFD is superior to that contained in returns. To accomplish this, we add to our set of control variables the three common factors reported in Fama and French (1993, 1996) to explain well the time-series of stock returns and the momentum factor a la Carhart (1997). The four factors, then, are the return on a broad market portfolio in excess of the risk-free rate (MKT), the return on a portfolio that is long in small stocks and short in big stocks (SMB), the return on a portfolio that is long in value stocks and short in growth stocks (HML), and the return on a portfolio that is long in past winners and short in past losers (WML). While the asset pricing theory holds that all the relevant information about future economic fundamentals should be captured by MKT, there is strong empirical evidence in the research cited above that SMB, HML, and WML play an important role in explaining expected stock returns. Thus, without taking a stand on whether these factors have rational or behavioral origins, we incorporate them as controls in our benchmark model along with the excess market return. 4 Table 5 reports the adjusted R-square statistics and model p-values from the regressions of future monthly, quarterly, semiannual, and annual production growth rates on (i) the order flow variables: OFM and OFD, (ii) the four-factor model constituents: MKT, SMB, HML, and WML, and (iii) the business cycle variables and illiquidity: DEF, TERM, and ILLIQ. The order flow factors explain 8.54, 14.58, and17.54 percent of the variation in the production growth rate over the subsequent month, quarter, and year, with the bulk of the forecast power for prediction horizons shorter than a year coming from OFD. The total amount of variation explained by the four-factor model constituents is 0.00, 0.04, and 0.03 for monthly, quarterly, and annual prediction horizons, and almost all of this explanatory power is due to MKT and HML. Thus, the forecast power of the order flow variables is clearly superior to that of the return factors at all prediction horizons. This indicates that OFM and OFD, despite being related to MKT and SMB, contain more accurate information about future output growth rates. Finally, DEF, TERM, and ILLIQ explain 5.95/18.05/26.86 percent, 0.00/1.53/2.60 percent, and 4.58/14.77/30.90 percent of the variation in future monthly/quarterly/annual production growth rates when used as the only variable in the model. These R-squares, however, are not additive. The R-square of a 4 The relation between order flow variables and return factors is clearly of relevance. A downward-sloping demand curve for stocks (Kaul, Mehrotra, and Morck, 2000) or price pressure effects will create a mechanical positive relation between OFM and MKT and a mechanical negative relation between OFD and SMB. Linking SMB to time-varying risk aversion through OFD is an interesting twist that we do not explore in the current paper. 12

13 model including all three variables is 6.57/22.22/42.78 percent, suggesting these variables, particularly DEF and ILLIQ, capture similar macroeconomic effects. Table 6 presents the coefficient estimates and t-statistics from regressions that replicate the test for the forecast power of OFM and OFD for production growth rates (see Section 4) after including the four return factors as additional controls. Our results from the previous section on the relation between OFM and OFD and future production growth rates remain the same or get stronger, while the four return factors are, by and large, devoid of significant predictive content in the presence of the order flow variables. The only exception is that of HML subsuming the forecast power of TERM for production growth rates over semiannual and annual prediction horizons. Our finding that variables constructed from monthly order flows contain more information for future production growth rates than factors constructed from monthly returns is a challenge to conventional asset pricing models. One possible reason why return-based variables may not forecast future fundamentals better than order flow-based variables is that market-makers are not always able to use the correct pricing function to update prices in the face of aggregate order flow. This story is consistent with the notion in Chan (1993) that, when presented with a noisy signal about the value of their stock, market makers cannot instantaneously condition the stock price on the signals of other stocks (in our case, embedded in order flows), the sum of which reveals fundamental information. Alternatively, risk-averse market makers, when exposed to inventory considerations, may deliberately set biased prices even though they know the correct pricing rule. This is likely to be manifested in a larger (smaller) than optimal sensitivity of stock prices to order flow in periods of inventory shortage (surplus), which will cause prices to overreact (underreact) to order flow. In either case, realized returns will be noisy if the above noted biases are not completely independent across market makers so that the noise gets washed away in aggregation. An implication of this noisy-return story is that, if the information in the order flow variables is more accurate than that in the return factors, OFD and OFM should forecast marketwide returns in the subsequent periods as individual security prices are corrected to incorporate the fundamental information contained in the sum of all trades. Specifically, expected stock returns should be related negatively to OFD given our thesis that this variable captures signals about changes in marketwide risk aversion and positively to OFM given the view that the information in aggregate order flow is incorporated into the prices with a lag. In the next section, we address this research question and investigate the predictive power of OFM and OFD for aggregate market returns over subsequent periods. 13

14 6. Linking Marketwide Order Flow to Expected Returns We argued in the previous section that market makers may not be able to instantaneously incorporate the macroeconomic signal in aggregate marketwide order flow into prices. This would induce noise into returns and cause (i) stock returns to be cross-autocorrelated and (ii) marketwide order flows to predict stock returns. Chan (1993) studies the first of these hypotheses and finds supportive evidence. This section studies the second. We start by regressing the equally-weighted market returns over monthly (RET (t, t+1)), quarterly (RET (t, t+3)), semiannual (RET (t, t+6)), and annual (RET (t, t+12)) prediction horizons on OFM (t) and OFD (t), controlling for DEF (t), TERM (t), and ILLIQ (t). The results are presented in Panel A of Table 7. The relation between OFM and the subsequent equally-weighted market return is positive and is statistically significant over monthly and quarterly horizons. A one standard deviation increase in OFM forecasts the market return to be 0.21 standard deviation (corresponding to 1.11 percent) higher over the subsequent month and 0.24 standard deviation (2.51 percent) higher over the subsequent quarter. The positive association between OFM and future market returns is consistent with the noisy return story. The intuition here is that market makers focus predominantly on deciphering the noisy signals about the value of their own stock and fail to incorporate the fundamental information collectively conveyed by the signals of other stocks in a timely manner. OFM, therefore, forecasts the adjustment in stock prices that occurs as this fundamental information is assimilated by market makers. OFD is positively and significantly related to the expected market returns over all prediction horizons examined. A one standard deviation increase in OFD predicts the equally-weighted market returns to be 0.31 standard deviations (1.65 percent) higher over the subsequent month, 0.47 standard deviations (4.91 percent) higher over the subsequent quarter, and 0.20 standard deviations (3.71 percent) higher over the subsequent year. This positive link between OFD and expected returns reinforces our thesis that OFD captures information about changes in marketwide risk aversion, with a disproportionate increase in the big stock order flows over small stock order flows forecasting higher expected returns. Note that this argument is also in line with the wide-spread belief among practitioners that blue-chip stocks are safe havens when things go awry in the economy. 5 5 We do not take a stand on whether this belief is rational or irrational. OFD should capture changes in risk aversion regardless of whether the demand for big stocks increases due to rational hedging concerns or behavioral biases of investors as long as the changes in the demand for big stocks over the demand for small stocks reflects investors attitude against risk at that point. 14

15 The results for value-weighted market returns are reported in Panel B of Table 4. Value-weighted averaging sees the forecast powers of the two order flow variables decline, with OFM becoming completely insignificant and OFD losing its forecast power for prediction horizons longer than a quarter. A one standard deviation increase in OFD leads to an increase of 0.19 standard deviations (0.79 percent) in the value-weighted market return over the subsequent month and 0.29 standard deviations (2.16 percent) over the subsequent quarter. The insignificance of OFM in forecasting value weighted returns tells us that market makers in stocks with greater market capitalizations may be less prone to the biases induced by the lack of knowledge about aggregate order flow. This is conceivable since these market makers can capitalize on the knowledge of the trades of a larger investor base and thus gather a larger fraction of the macro information dispersed across the market. The weakening of the predictive power of OFD suggests the risk aversion effect is more pronounced for small capitalization stocks than large capitalization stocks, which is a consistent with the safe haven story discussed before. Finally, looking at the control variables, we observe a positive and significant relation between TERM and the expected equally-weighted market return over all prediction horizons, consistent with the evidence reported in Fama and French (1989). A one standard deviation increase in TERM forecasts increases in the equally-weighted market return of 0.16 standard deviations (0.84 percent) over the subsequent month, 0.28 standard deviations (2.86 percent) over the subsequent quarter, and 0.39 standard deviations (7.33 percent) over the subsequent year. The negative and significant relation between DEF and value-weighted market returns seems counterintuitive and stands at odds with the positive and significant relation reported in Fama and French (1989) for the period This is a puzzle beyond the scope of the current inquiry. 6 Collectively, the evidence presented in this section is consistent with the view that marketwide order flows aggregate information about macro-fundamentals that is dispersed across agents. As Evans and Lyons (2007), we find that this information is private in the sense that it is not incorporated into returns instantaneously. It takes the price-setters some time to understand the macro signal that is embedded in the sum of all trades. This gives rise to the predictive power of OFM and OFD for future market returns. 6 A possible explanation may be based on our sample being comprised exclusively of relatively more liquid NYSE stocks whose valuations may benefit from a flight to liquidity among investors. An analysis of the predictive power of DEF for returns at the size-bm portfolio level (results not tabulated) reveals that the negative relation is only significant for the big stocks and small growth stocks within our sample. 15

16 7. Conclusion In a setting where information exists within the market in a dispersed form, marketwide order flow conveys a valuable signal about future macroeconomic fundamentals. In this paper, we show that aggregate market order flow (OFM) and the average order flow differential between big and small stocks (OFD) contain valuable information about future macroeconomic fundamentals that is not captured by established business-cycle indicators, return-based factors, and marketwide liquidity. It is shown elsewhere in the foreign exchange market (Evans and Lyons, 2007) and the government bond market (Green, 2004) that marketwide order flow conveys information about future macro fundamentals. Our evidence that above average values of aggregate stock market order flow predicts higher-than-average output growth and stock market returns in the subsequent quarters is in line with this evidence. The second measure that we employ is the order flow differential between big and small stocks, OFD. Our motivation in using this novel measure is as follows. There is considerable anecdotal evidence that big stocks are perceived as safe havens that investors flock into when marketwide risk aversion augments in face of increased scrutiny about the economic outlook. This sort of behavior is not completely unfounded given the returns for small stocks are much more procyclical than the returns on big stocks (Yogo, 2006). We argue that a widening in OFD signals an increase in the marketwide risk aversion and predicts (a) a slow down in the output growth rate consistent with the countercyclical nature of risk aversion (Rosenberg and Engle, 2002) and (b) an increase expected returns. We find evidence supporting these two hypotheses. The information in marketwide order flows does not seem to be incorporated into prices contemporaneously. The forecast power of the two marketwide order flow measures for output growth rates clearly surpasses those of the contemporaneous excess market return and stylized empirical return premiums associated with size, book-to-market, and momentum. This gives rise to a role for OFM and OFD in predicting future marketwide returns over horizons ranging from a month to a year. Specifically, one standard deviation increases in OFM and OFD forecast the equally-weighted market return to be 2.51 and 4.91 percent (0.24 and 0.47 standard deviations) higher over the subsequent quarter. These results can be reconciled with a model in which market makers who receive a noisy signal about their stock cannot instantaneously condition on the signals for other stocks, the sum of which reveals valuable information about the macroeconomy (Chan, 1993). The two order flow variables seem to capture the corrections in prices that come about as the market makers learn about the aggregate macro signal. 16

17 Where do we go from here? A possible way that our study can be extended is through the categorization of order flows by trade size. Barclay and Warner (1993) find that most of the price change for a sample of NYSE firms is due to medium-sized trades, consistent with the notion that informed investors strategically spread trades over time in order to conceal their private information in uninformed trading volume. We might thus expect that measures of aggregate market order flow obtained exclusively from medium-sized trades to contain more accurate information about future fundamentals and returns. Another possibility is to redefine the OFD measure as the average differential between the order flows for bonds and stocks. Such an approach has the advantage of using two asset classes whose returns differ much more significantly than those for big stocks and small stocks in how they correlate with wealth shocks. Finally, the fact that OFD relates to future macroeconomic fundamentals and expected returns in a manner consistent with our risk aversion story is suggestive about the origins of the size premium, SMB, which would be related intimately to OFD in the presence of a downward sloping demand curve. 17

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