Target prices, relative valuations and the compensation for liquidity provision

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1 REVISED USC FBE FINANCE SEMINAR presented by Ernst Schaumburg FRIDAY, October 27, :30 am 12:00 pm, Room: JKP-202 Target prices, relative valuations and the compensation for liquidity provision Zhi Da and Ernst Schaumburg, October 25, 2006 Abstract We document that S&P500 stocks experience intermittent large liquidity shocks which are mainly idiosyncratic in nature. The liquidity events can be identified using equity analyst target prices as instruments for changes in fundamental values. The associated short-run reversals are economically and statistically significant and of a magnitude not easily explained by transaction costs alone. Our findings point to a significant premium required by investors for providing immediacy even in the market for the most liquid stocks. JEL Classification: G12 We would like to thank Paul Gao, Kathleen Hagerty, Robert Korajczyk, Robert McDonald, Amiyatosh Purnanandam, Avanidhar Subrahmanyam, seminar participants at Goldman Sachs Asset Management, HEC Montreal, the July 2006 NBER Asset Pricing Workshop, University of Notre Dame, Northwestern University, Vanguard and especially Ravi Jagannathan for his numerous suggestions and insights. We gratefully acknowledge financial support from the Financial Institutions and Markets Research Center at the Kellogg School of Management. zda@nd.edu, Mendoza College of Business, University of Notre Dame. e-schaumburg@northwestern.edu, Kellogg School of Management, Northwestern University. 1

2 1 Introduction The significant price concessions associated with with trading large blocks of small cap stocks has been well documented in the literature going back to Kraus and Stoll (1972) and Loeb (1983). In most market microstructure models, the price impact can be interpreted as a direct result of inventory costs and/or asymmetric information, both of which presumably play a larger role for small stocks. The size and duration of the price impact associated with uninformed trading is then a natural measure of the liquidity of an asset. Since the average price impact is at least an order of magnitude larger for small stocks than large stocks (c.f. Loeb (1983)), it is natural to think of large stocks as being uniformly liquid. In reality, however, large stocks, although generally liquid, may experience episodes of illiquidity. In this paper we ask whether it is possible to identify such episodes of illiquidity for individual stocks and, if so, identify the reward for liquidity provision. In particular, we focus on the S&P500 universe which on average is highly liquid although at any given point in time a handful of stocks may experience periods of low liquidity. We propose a novel empirical strategy for identifying such periods of low liquidity by using information contained in equity analysts target prices. Target prices can help in discerning whether recently observed returns, at least in part, were driven by uninformed trading and therefore did not reflect changes in underlying fundamentals. A price concession leads to a short-run discrepancy between fundamental value and price. Since the fundamental value itself is unobservable, the discrepancy is instead proxied for by the spread between target price and price. We measure this spread by the target price implied expected return (T P ER), defined as the ratio of consensus 12 month ahead target price to current market price: T P ER t = T P t /P t 1. While conventional liquidity measures must disentangle information and liquidity-based trades ex-post, the T P ER instrument has the potential to directly control for changes in fundamental values in real time. This allows the ex-ante identification of the subset of stocks for which the cost of immediacy currently is the highest. For the identification to work, an unusually large large (or small) TPER should indicate a large price concession and hence a higher degree of illiquidity. Unfortunately, the signalto-noise ratio of the TPER is likely to be poor for a number of reasons. First, the consensus analyst target price is known to be noisy due to disagreement among analysts, the lack of a commonly agreed upon absolute valuation model and the presence of analyst biases. 1 Second, the target price itself is not a direct measure of fundamental value since it contains a substantial forward-looking systematic risk component. To illustrate this, consider the 1 See e.g. Michaely and Womack (2002). 2

3 analyst s target price forecast within an n-factor framework. The TPER can be decomposed into three components: n 1 T P ER = E A [α] + β M E A [Mkt] + β ie A [λ i ] i=1 Only the first component, the analyst s estimated alpha, contains any signal about the current deviation between price and fundamentals as perceived by the analysts. The second and third terms reflects the familiar forward-looking systematic risk components consisting of market risk and other risk factors. E A [ ] denotes analyst s expectations which could be contaminated by noise due to difference of opinion, modeling error and behavioral biases. In many cases the first term will be swamped by the other two components, which contain no information about fundamental value. Moreover, they will contain considerable noise when analysts have limited ability to forecast factor loadings and/or factor risk premia as documented in Figure 1 and Figure 2. In this case, a naive sort on TPER could implicitly be a sort on beta. The solution we propose is to sort on TPER within groups of similar stocks, i.e. stocks with similar risk characteristics. This will serve to eliminate much of the noise from the systematic risk component and isolate the relative value identified by the analyst. 2 within-group sort on TPER is therefore more likely to produce a spread in alpha which contains the signal about deviations from fundamental values. similar stocks we in this paper consider industry sectors. A As a proxy for groups of Based on these observations, we implement a sector-neutral long-short strategy designed to capture liquidity effects identified by the TPER instrument. The portfolio is constructed in the following manner: at the end of every month, we consider the set of S&P500 stocks for which at least one analyst has announced a target price during the first 25 calendar days of the month. 3 Within each sector we sort the stocks according to their T P ER and construct an equally weighted portfolio which is long the highest T P ER stocks from each sector and short the lowest T P ER stocks from each sector. Since the portfolio is equally weighted, it is by construction sector neutral. Over the period , this strategy has yielded a substantial abnormal return of 203bps per month. 4 We interpret this alpha as a measure of 2 The latter is likely more precisely estimated given the prevalence of industry specialization among analysts and the widespread reliance on relative valuation models, as discussed further below. 3 The average 5-day lag between the portfolio formation and the beginning of the one month holding period eliminates announcement effects as discussed below. Without this gap our results are strengthened. 4 As discussed in detail below, the choice of sampling period is dictated by the ex-ante availability of the detailed Standard & Poors sector classification used. The abnormal return is robust to various models used for risk adjustment. 3

4 the cost of immediacy. 5 While the average cost of immediacy is clearly related to the notion of aggregate liquidity, there is likely a very large idiosyncratic component to the cost of immediacy for individual high/low TPER stocks. In fact, at the monthly frequency, we do not find any relationship between the Pastor and Stambaugh (2003) aggregate liquidity factor and the profits of our benchmark strategy. Instead we find a very strong relationship between the abnormal return and individual stock liquidity characteristics. In particular, we document that stocks entering our long-short portfolio in a given month experience a significant increase in their bid-ask spreads, price impact measures (Breen, Hodrick, and Korajczyk (2002)) and Amihud illiquidity measures (Amihud (2002)). Moreover, the abnormal return is highly correlated with these liquidity measures across time. In line with Campbell, Grossman, and Wang (1993) and Conrad, Hameed, and Niden (1994), we also document an increase in turnover for stocks entering our portfolio as well as a significant change in the order imbalance between seller and buyer initiated trades. By analyzing mutual fund holdings for a large subset of US equity mutual funds, we also find evidence of significant imbalances in institutional buying/selling pressures for stocks with subsequent extreme TPERs. In addition, we observe a substantial increase in the dispersion of analysts target price forecasts for stocks entering our portfolio, consistent with market makers decreasing liquidity of individual stocks in response to an increased degree of information asymmetry as in Sadka and Scherbina (2004). Our results also indicate that, even in the case of the most liquid stocks, the price corrections which generate the abnormal profits accrue over a period of several weeks on average. This finding is at odds with the common presumption is that the price effects of liquidity motivated trades tend to dissipate more quickly. Pastor and Stambaugh (2003), for instance, in their construction of an aggregate liquidity factor, focus on liquidity effects that play out within one day. 6 should be attributed to liquidity induced price movements. It is far from clear, however, what duration in general As has been argued in the limits-to-arbitrage literature, liquidity effects, albeit temporary, could be of a considerably longer duration as in Shleifer and Vishny (1997) and recent empirical papers by Gabaix, Krishnamurthy, and Vigneron (2005) and Sadka and Scherbina (2004). Even in markets 5 The magnitude of the compensation for providing immediacy (134 bps for the long portfolio and 69 bps for the short portfolio per month) documented in this paper is comparable to those documented by Keim and Madhavan (1996) (50 to 100 bps as in Figure 1 of their paper) and by Coval and Stafford (2005) (79 bps as in Table 5 of their paper). 6 In their study of block trades Keim and Madhavan (1996) find that the price impact of a sell order on lasts on average one day. Buy orders on the other hand tend to have a more permanent effect, much of which accrues during the first day. 4

5 for liquid assets (e.g. S&P500 stocks), informational asymmetries may exist which lead to specialization by market makers with limited capital. The resulting capital immobility can significantly extend the duration of deviations from fundamentals, as has been argued in Berndt, Douglas, Duffie, Ferguson, and Schranzk (2005). We investigate a number of alternative sources of the abnormal returns on the T P ER sorted portfolios. We conclude that the profit is not likely driven by: (1) delayed reaction to stock recommendation (c.f. Womack (1996)); (2) reaction to target price revisions (c.f. Brav and Lehavy (2003) and Asquith, Mikhail, and Au (2005)); (3) post-earning-announcement drift (PEAD); or (4) pure short-term return reversal (c.f. Jegadeesh (1990) and Lehman (1990)). Although behavioral explanations cannot be completely ruled out, we believe that the empirical evidence in favor of liquidity events is far more compelling. By reinterpreting the within-sector TPER sort as a relative value sort, our findings contribute to the recent research on equity analyst s target prices: Although analysts fail to assess fundamental values themselves with any degree of precision, they on average get relative valuations right. As in Boni and Womack (2006), this finding can be motivated by the fact that most analysts specialize in a sector (rather than being generalists) and typically cover about half a dozen stocks within the same industry. By analyzing the specifics of a handful of similar firms, the analyst is well situated to rank the relative strength of each stock going forward, although he may have significantly less insight into the forecasting of macro factors which affect the performance of the sector as a whole. Focusing on relative price forecasts within the same sector eliminates much of the effect of systematic risk factors while preserving the relative strength information contained in analysts price targets. 7 The success of our benchmark portfolio clearly demonstrates that information embedded in the level of target prices, if properly exploited, can lead to superior investment results. Several previous studies have examined investment strategies based on information provided by analysts mainly stock recommendations. 8 Most of these investment strategies, however, have produced risk-adjusted paper profits which disappear after accounting for transaction 7 Boni and Womack (2006) show that an investment strategy based on stock recommendation revisions within the same industry improves the return significantly compared to a similar strategy without industry control. The current paper takes a similar approach by explicitly canceling out industry effects, thereby isolating the relative value identified by analysts. However, this paper uses target prices rather than recommendations which allows for a more direct interpretation of rankings as relative valuations. The portfolios resulting from our relative value sort in fact look quite different. They resemble short-run reversal rather than momentum as in Boni and Womack (2006). Finally, the focus here is on S&P500 stocks with the aim of explicitly accounting for transaction costs. 8 Two examples are Dimson and Marsh (1984) and Barber, Lehavy, McNichols, and Trueman (2001). Michaely and Womack (2002) provides and excellent survey of related papers. 5

6 costs incurred from high portfolio turnover. By contrast, our benchmark portfolio involves only S&P 500 stocks and produces a risk-adjusted return of around 100bp per month after accounting for direct transaction costs and a measure of price impact. 9 Our main results extend beyond the S&P500 universe to the set of all stocks in the First Call database with regular analyst coverage over the extended sample period from 1997 to In this larger sample we show that the strategy works best for small stocks and especially value stocks. We attribute the effect of the book-to-market ratio to the fact that analysts estimates for value firms (with a higher fraction of tangible assets) may be less noisy than for growth firms, thus providing a more precise control for fundamental value. Small stocks, on the other hand, tend to be more illiquid due to informational asymmetries. One would therefore expect the cost of immediacy to be higher, which may explain the better performance of our long-short strategy for small stocks. Interestingly, we also find that the strategy performs significantly better in certain industries such as consumer discretionary and industrials. The remainder of the paper is structured as follows: Section 2 provides a description of data sources. The portfolio construction and the main results for the S&P500 sample are given in section 3. Section 4 describes the full sample results and Section 5 concludes. 2 Full Sample Data Description The target price data for this study is provided by First Call and has the important advantage over other data sources that it contains accurate dating of analysts reports. 10 At the end of each month from Dec 1996 to Dec 2004, we include only stocks for which there is at least one (12 month ahead) target price announcement during the first 25 calendar days of the month. It is important to note that, as a result, even our full sample includes almost no extremely small stocks since these do not receive regular analyst coverage. We do not fill in the blanks using older target prices in order to avoid introducing an upward bias in the target prices. The bias arises because analysts are more likely to issue a target price when they are in favor of a stock, as documented in Brav and Lehavy (2003). 11 In addition, 9 The abnormal returns derive equally from the long and short side of the portfolio and it is possible to implement a version of the strategy where the shorting of individual stocks is replaced by shorting S&P index futures or sector ETFs. 10 See footnote 3 of Brav and Lehavy (2003) for a detailed discussion. 11 Specifically, Brav and Lehavy (2003) show that about 90% of buy / strong buy recommendations are issued with target prices while only 61% of sell / strong sell recommendations are issued with target prices. Furthermore, sell / strong sell recommendations only account for less than 5% of all recommendations as documented in Jegadeesh et. al (2004). 6

7 we only keep target price announcements during the first 25 calendar days of the month for two reasons. First, we want to make sure that our results are not purely driven by an immediate market reaction to target price announcements, a phenomenon considered in Brav and Lehavy (2003) and Asquith, Mikhail, and Au (2005). 12 Second, a lag of at least 5 days makes our portfolio trading strategies easier to implement since investors are given ample time to collect and digest target price information. Table 1 presents a summary of the resulting full sample containing approximately 1700 stocks each month, increasing from 1095 in 1996 to 1796 in For each stock, we have on average 2.5 target prices per month. The sample on average covers 76% of the CRSP stock universe in terms of market capitalization, increasing from 55.5% in 1996 to 83% in Our sample also covers most of the representative stocks, which are constituents of the major equity indices. For instance, in 2004, our sample covers 496 of the S&P 500 stocks, 980 of the Russell 1000 stocks and 2780 of the Russell 3000 stocks. On average, 54% of the stocks in our sample are listed on the NYSE, 43% are listed on NASDAQ and the remaining 3% are listed on the AMEX. The median market capitalization of stocks in our sample, averaging over the sampling period, is 919M much larger than that of all NASDAQ stocks (85M), but slightly smaller than that of all NYSE stocks (963M). A key variable of interest in this paper is the target price implied expected return oneyear-ahead (T P ER). T P ER is defined as the consensus target price (split adjusted) divided by the end of month stock price minus one, or T P ER t = T P t /P t 1, where the consensus target price T P t is the simple average of all target prices received during the first 25 calendar days of month t. 13,14 The mean T P ER during this sampling period is 40% (the median is 24%), substantially higher than one would expect for the market as a whole. This is partly due to the fact that analysts are far more likely to issue target prices when they favor a stock. In addition, the target price may reflect deliberate optimism on the part of the analyst as proposed in Bradshaw and Brown (2005): The mean T P ER was as high as 64% (median 36%) in 2000 during the final stages of the NASDAQ bubble. We break down our sample into sectors according to the first two digits of Standard 12 The fact that there is a significant market reaction to target price revisions controlling for the arrival of other information provides evidence that investors on average consider target prices to be informative. 13 Defining the consensus target price using median does not alter the results in any significant way. 14 Bradshaw and Brown (2005) show that analysts do not appear to exhibit persistent differential abilities in forecasting target prices. We therefore use simple averages of target prices without exploiting knowledge of individual analyst identities. 7

8 and Poor s GICS (Global Industry Classification Standard). 15,16 Using IBES data, Boni and Womack (2006) show that the GICS sector and industry definitions match well with the areas of expertise of most analysts as defined by the set of stocks covered by each analyst. The GICS is therefore a natural choice of sector definition although we also consider 1-digit SIC codes and the Fama-French industry definitions below. The GICS used in this paper are obtained from various sources: Standard and Poor s publishes the GICS classification of S&P500 stocks on its website. Historical GICS for some companies are available in COM- PUSTAT starting in Dec 1994, however, all GICS classifications prior to 1999 are backfilled. For stocks in our sample whose GICS are not available from the above two sources, we assign the GICS according to the first three digits of its Industry Classification Code (the dnum variable in COMPUSTAT). 17 Since there are too few stocks in the Telecommunications Services sector, we group them with the Information Technology sector to form a combined Technology sector. The resulting 9 sectors are: Energy, Materials, Industrials, Consumer Discretionary, Consumer Staples, Health Care, Financials, Technology and Utilities. This classification is also consistent with the way sector ETFs are formed. Panel C of Table 1 shows the sector break down of our sample both in terms of number of stocks and in terms of market capitalization. The three largest sectors are Consumer Discretionary, Financials and Technology, which together account for almost 60% of the entire sample. The sector break down of our sample is in line with that of the broad market as proxied by the S&P500 index. Across time, we observe the dominance of the Technology sector in 2000 due to the NASDAQ bubble and the recent increase of the Energy sector due to the surge in oil prices. The S&P500 universe which is the main focus of this paper distinguishes itself in several respects: First, S&P500 stocks receive the most attention and coverage by analysts. On average, analysts issue target prices for around 350 of the S&P500 stocks each month and the average number of target prices per stock each month is 4 significantly higher than that of the average stock in the First Call database (2.5). Therefore, the consensus target price 15 The GICS was introduced in 1999 by Standard & Poor s and Morgan Stanley Capital International (MSCI) with the goal of providing a set of global sector and industry definitions more useful for investment purposes. 16 The 4 or 6-digit GICS would, in principle, yield better sector control, but the number of stocks in each sector would drop dramatically, making the results too noisy. For example, using the 4-digit GICS would leave us with, on average, less than 15 stocks in each industry group per month for our benchmark S&P 500 stock sample and making it nonsensical to sort within each industry group. 17 Specifically, for stocks whose GICS are available from the first two sources, we can observe their dnums and can infer the mapping from dnum to sector for these stocks. Making use of this mapping, we can assign a large portion of our sample stocks into sectors. We establish the remaining 150 dnum-to-sector mappings manually based on a detailed sector description provided by Standard and Poor s. 8

9 used to compute T P ER for S&P500 stocks is less prone to outliers and presumably more accurate. Second, S&P500 stocks are on average more liquid and cheaper to trade, which makes it easier to bound the potential impact of transaction costs. Finally, the GICS sector assignment of S&P500 stocks is done directly by Standard & Poor s and does not rely on a sometimes arbitrary mapping from SIC codes. As mentioned, the GICS sector classification is of particular importance because it closely mirrors the way analysts are specialized. The relative TPER within GICS sectors therefore conceptually provides a more precise signal of deviations from fundamentals. Since the GICS (Global Industry Classification Standard) was officially launched by Standard & Poor s and Morgan Stanley Capital International (MSCI) in 1999, we focus on the sample period starting in January 1999 to avoid issues with backfilling. Throughout the study, we obtain prices and returns from CRSP. In computing various portfolio characteristics, we make use of data from COMPUSTAT and TAQ. Finally, we also use stock recommendation and earning announcement data obtained from First Call. 3 The profitability of sector-neutral long-short strategies using S&P500 stocks This section describes the construction of a sector neutral long-short portfolio of S&P500 stocks which exploits temporary deviations between the prevailing market prices and fundamentals as measured using information contained in analyst target prices. 3.1 Excess returns and alphas At the end of each month from December 1998 to December 2004 and within each sector, we rank the S&P500 stocks into 9 groups according to their current month T P ERs. 18 We form 9 equal weighted portfolios: Portfolio 1 consisting of the highest TPER stocks from each sector, portfolio 2 consisting of the second highest,..., and finally portfolio 9 consisting of the lowest TPER stocks from each sector. For each of the resulting 9 portfolios, we compute the first month post-formation excess returns (in excess of the risk-free rate). The results are summarized in Panel A of Table 2. The excess returns are in general increasing in T P ER: Portfolio 1, where analysts predict the highest 12 month return (for each stock relative to all S&P 500 stocks within the same sector), earns the highest first month excess return (158bp) 18 In line with common practice in the empirical asset pricing literature, we exclude stocks with share prices below five dollars in order to ensure that the results are not unduly influenced by the bid-ask bounce. This price filter has little impact on the S&P 500 sample, eliminating less than 1% of the stocks. 9

10 while portfolio 9 earns the lowest first month excess return ( 19bp). The return on the spread portfolio (1 minus 9) can be regarded as the return to a portfolio of long-short sector strategies (long stocks with the highest TPERs and short stocks with the lowest TPERs within each sector). Forming long-short strategies within sectors has two advantages: if analysts in fact are capable of forecasting the relative performance of stocks within the same sector, then a sector neutral long-short strategy should directly pick up this skill. Second, to the extent that stocks in the same sector have similar systematic risk exposures (factor risk), sector neutrality serves to reduce the exposure to systematic risks which the analysts have no comparative advantage in forecasting. The first month return to the spread portfolio 1-9 is as high as 177 bps with a t-value of Panel A also shows that the excess returns to portfolios 1 and 9 and the spread portfolio are not significantly different from zero beyond the first month after portfolio formation. Figure 3 illustrates this point for the spread portfolio. In fact, most of the first month return (110 bp out of 177bp) accrues during the first two weeks post portfolio formation. The significant first month excess returns on the spread portfolio 1-9 might of course simply be the result of systematic risk exposures. For instance, Jegadeesh, Kim, Krische, and Lee (2004) find some evidence that analysts chase glamor (i.e. growth) stocks and stocks with recent strong performance. On the other hand, TPER has market price in the denominator, so the TPER sort may capture the effect of a sort on short-run or intermediate-term reversal. To account for these effects, we regress the monthly excess returns on the Fama-French (1993) three factors, the Carhart (1997) momentum factor and the Fama-French short-run reversal factor. 20 The results in Panel A of Table 2 show that the risk-adjusted returns are even higher and more significant than the average excess returns themselves: our sector neutral long-short strategy (the spread portfolio 1-9) yields a highly significant three-factor alpha of 203 bps (t-value of 5.06). In addition, the sector neutrality of the long-short strategy helps in reducing (but not eliminating) the systematic risk exposures. The spread portfolio 19 About 87% of the S&P 500 stocks are listed in NYSE (NASDAQ accounts for 12% and AMEX accounts for less than 1%). We verify that our results are not driven by the NASDAQ stocks in our S&P 500 stock sample. Excluding NASDAQ stocks leads only to negligible changes in the results. For example, the profit in portfolio 1-9 is 174 bp (t-value of 3.50) and the three-factor alpha is 188 bp (t-value of 3.94). 20 The three factors are: MKT, SMB and HML. MKT is the market return minus risk free rate. SMB is the return to a zero-investment portfolio of longing small stocks and shorting big stocks. HML is the return to a zero-investment portfolio of longing high book-to-market stocks and shorting low book-to-market stocks. The momentum factor, UMD, is the return to a zero-investment portfolio of longing past winners and shorting past losers. The short-term reversal factor, DMU, is constructed as the return on a zero investment portfolio which is long last months losers and short last months winners. The time series of factor realizations as well as detailed descriptions can be found on Ken French s website: 10

11 only loads significantly on the Market and the momentum factor. The positive loading on the MKT factor is intuitive since, ceteris paribus, high beta stocks will receive higher target prices relative to their current market price. Interestingly, the highly significant negative loading on the momentum factor indicates that the spread portfolio tends to load up on intermediate-term losers and short intermediate-term winners, as we shall see. However, relative winners and losers within S&P500 sectors do not map into the overall winners and losers as defined in a standard short-run reversal strategy (involving a broad universe of traded stocks). This explains why the loading on the reversal factor is insignificant. 21 In the remainder of the paper we use the five factor model as our benchmark for computing risk adjusted returns. If the cross sectional dispersion of TPER reflects differences in liquidity, then the profitability of the spread portfolio could be due to exposure to an aggregate liquidity risk factor. To investigate this, we add the Pastor and Stambaugh (2003) value weighted liquidity factor as a sixth pricing factor in Panel B of Table 2. The alpha of the spread portfolio is virtually unchanged (201bp, t-value of 4.95) and the market and momentum factors remain the only factors with significant loadings. The implication is that, to the extent the spread portfolio return is (partly) driven by liquidity, it is not systematic liquidity as captured by the Pastor and Stambaugh (2003) factor. Figure 4 summarizes our results so far. It shows the monthly time series of five-factor riskadjusted return to our trading strategy and the market excess return. During our sampling period from Jan 1999 to Dec 2004, it is clear that the sector-neutral long-short strategy has a much better risk-return trade-off than the overall market portfolio. The monthly Sharpe ratio of the spread return and the five factor alpha are 0.41 and 0.67, respectively, and are all clearly better than that of the market (SR Mkt = 0.01) during the same period. 22,23 The time series before 1999 is shaded to highlight the fact that the GICS is backfilled and the long-short strategy was infeasible ex-ante prior to The performance of our long-short 21 Part of the large alpha is due to the negative momentum exposure. Risk adjusting using a standard 3-factor Fama-French model yields an alpha of 196bp with a t-stat of If we alternatively risk adjust the spread portfolio excess return using the returns on Size and B/M sorted portfolios with similar characteristics (along the lines of to Daniel and Titman (1997)) the alpha increases to 210 bp with a t-value of 2.72, as shown in the last columns of Table 2B 22 The five factor-model-alpha can be thought of as the excess return of a trading strategy since factors are also excess returns. 23 From Figure 4, it can also be seen that the average annualized alpha increases from 1999 to 2000 and then drops off over the subsequent years until This pattern is similar to the investor sentiment factor derived in Baker and Wurgler (2005) and may indicate that investor sentiment as partly driving the liquidity events that we identify. 11

12 strategy (portfolio 1-9) is slightly reduced when including the period (the average alpha drops to 162 bps, t-stat 4.21), likely in part because of the noise introduced by the inaccurate backfilling of the GICS in Compustat. It is important to note the crucial role played by sector control. If we instead form portfolios based on ranking the T P ER across all stocks rather than within each sector, and compute the first month post-formation portfolio excess returns, they lose their significance, as shown in Table 3. The long-short portfolio 1-9 (long stocks with the highest T P ER and short stocks with the lowest T P ER) produce a spread of only 79bp (t-value of 0.86), much smaller than the spread of 177 bp when the long-short position is constructed within sector. In addition, without sector control, the profit becomes more volatile due to its higher exposure to systematic risk factors, resulting in a less significant five factor alpha (t-value of 2.44 versus 5.06 with sector control). This is broadly consistent with the findings in Boni and Womack (2006) in the context of analyst recommendations and provides further evidence that it is the relative target prices and not the level of target prices which convey the most information about fundamentals Robustness of the benchmark portfolio specification In order to investigate the robustness of our findings, we in Table 4 consider the effect of various alternative portfolio formation strategies. Comparing the results in Panel A and B it is clear that the equal weighted strategies on average do better than value weighted strategies. 25 It also emerges that dispensing with the 5 day gap, i.e. allowing target price collection during the last 5 days of the portfolio formation month, strengthens the profitability of the spread portfolio. This is to be expected given the well documented announcement effect, see e.g. Brav and Lehavy (2003). We also investigate the effect of using alternative sector specifications. The naive 1-digit SIC sector definition does poorly (except in the no gap equal weighted scenario) while the Fama-French 10-sector specification does much better than the 1-digit SIC but is still strictly dominated by the 9 sector GICS. This is consistent with the relative value interpretation since the 9 sector GICS agruably provides the better proxy for the areas of specialization of analysts (see e.g. Boni and Womack (2006)). Since we focus our attention to the S&P500 sample with an average of 350 observations in the cross-section each month, we do not explore the potential beneficial effects of more precise sector control by moving to the more detailed 24 The significance of the abnormal returns stem from the significant negative loading on UMD. The Fama- French 3-factor alpha is 127bp with a t-value of Value weighting is done separately within each sector long and short so that each sector position remain equal weighted. 12

13 23 GICS industry groupings or 59 GICS industries. Our benchmark definition of TPER is only one of many possible. In table 4 we consider the alternative specification ATPER = average(t P t /P t ), i.e. the average of each analyst s target price divided by the market price on the announcement date, rather than the average target price divided by the market price on the portfolio formation date. Table 4 shows that the alternative TPER specification does significantly worse than our benchmark specification, indicating that the price at the end of the month is more informative than a weighted average of prices collected during the month. Finally we check the effect of imposing a stricter requirement on the minimum number of target prices required in a given month for a stock to be included. Requiring at least 3 target prices does not in general reduce the alpha, but the t-stat (while still significant) does deteriorate due to the reduction in sample size. Overall, we conclude that our qualitative results are robust to changes in the specifics of the portfolio formation strategy. A close inspection of Figure 4 shows that a few particularly large risk adjusted returns fall during January months, especially in 2000 and To ensure that our results are not driven by the January effect, we also report the excess returns and five-factor-alpha of the spread portfolio excluding the month of January in Table 4. After excluding January, the return and alpha of our long-short strategy (portfolio 1-9) in the benchmark scenario drop in magnitude to 155 bps and 183 bps, respectively with modest reductions in the levels of significance (given a loss of 8.3% of the data). We therefore conclude that the January effect is not a main driver of our results. 3.3 Portfolio characteristics and profit after transaction costs Table 5 reports various portfolio characteristics. The first 12 characteristics are those studied in Jegadeesh, Kim, Krische, and Lee (2004), which have been identified in the previous literature as having predictive power for future stock returns. These 12 characteristics are categorized into 5 groups. The first group contains momentum and trading volume variables including RETP (cumulative market-adjusted return in months -6 through -1 preceding the month of portfolio formation), RET2P (cumulative market-adjusted return in months -12 through -7 preceding the month of portfolio formation), FREV (analysts earnings forecast revisions), SUE (the most recent quarter s unexpected earnings) and TURN (average daily volume turnover in the six months preceding the month of portfolio formation). The second group contains valuation multiples such as EP (the earnings-to-price ratio) and BP (the book-to-price ratio). The third group contains growth indicators such as LTG (mean analyst forecast of expected long-term growth in earnings) and SG (the rate of growth in sales over the 13

14 past year). The fourth group contains a firm-size variable SIZE defined as the natural log of a firm s market capitalization. The fifth group contains fundamental indicators such as TA (total accruals divided by total assets) and CAPEX (capital expenditures divided by total assets). 26 Apart from these 12 characteristics, we also report Price (the closing price at the end of the month of portfolio formation), RET1M (the return during the month of portfolio formation) and T P ER. Finally, we also compute various liquidity-related variables. The first variable is a price impact measure Pimpact which measures the average percentage change in price caused by round-trip-trade of $1 million worth of the stock within an hour. Pimpact is constructed following the technique described in Breen, Hodrick, and Korajczyk (2002). The second variable is a bid-ask spread measure Pspread defined as the average difference between current ask and bid divided by the midpoint. The next two measures are first estimated by Madhavan, Richardson, and Roomans (1997). Espread measures the effective bid-ask spread which accounts for the possibility of a cross where trade can occur within the bid-ask spread. Phi measures the non-information component of the bid-ask spread and can be thought of as the reward to market maker for providing immediacy. 27 The first four liquidity measures are computed using intraday data from TAQ during the month of portfolio formation (i.e. the month immediately prior to the holding period). The fifth variable is liquidity measure Amihud discussed in Amihud (2002). 28 All the liquidity measures are reported on a normalized basis (normalized by the cross-sectional means in each month) to account for a level shift as a result of the decimalization in early Table 5 shows that T P ER in general increases with growth indicators. If a firm has experienced high sales growth (SG) over the past year or if its long term growth rate is expected to be high (as captured by LTG), its stock is more likely to be associated with a higher T P ER. This is consistent with Jegadeesh et. al. (2004) s finding that analysts generally prefer glamour stocks with higher growth potential. In addition, T P ER is generally decreasing in past returns (RETP, RET2P and RET1M). This is not surprising 26 Detailed descriptions of each of the 12 characteristics and their construction can be found in Jegadeesh, Kim, Krische, and Lee (2004). 27 To a large extent, Phi is similar to another measure for the temporary or non-informational part of the trading cost the Realized Spread, developed by Huang and Stoll (1996). In fact, the correlation between Phi and Realized Spread is close to 0.5 in our sampling period. We decide to use Phi as the Realized Spread measures became considerably noisy after the decimalization in early To compute the Amihud measure, on each trading day, we first compute the ratio between absolute daily return and the daily dollar trading volume. This ratio is then averaged during the month to get the Amihud liquidity measure. 14

15 since recent losers (winners) are likely to trade at lower (higher) prices and price enters denominator when computing T P ER. Consistent with this explanation, the average trading price for stocks in portfolio 1 is about $32 much lower than that of stocks in portfolio 9 which is $45. Finally, the SIZE and BP of portfolio 1 and 9 are similar, which explains why our long-short strategy (portfolio 1-9) has small factor loadings on SMB and HML. In general, the two extreme portfolios have higher than average liquidity measures, which means they are more illiquid than the average stock. The liquidity variables in Table 5 also allow us to answer a more interesting question: Can the profit of our long-short strategy overcome the transaction costs? On one hand, we expect lower than average transaction costs since we are trading stocks in the S&P 500 index and have excluded penny stocks. On the other hand, our long-short strategies involve monthly portfolio rebalancing, which potentially could amplify the transaction costs and wipe out any paper profits. To gauge the magnitude of the transaction costs, we focus our attention on portfolio 1 and 9. On average, there are 33 stocks in each of the two portfolios each month and the monthly portfolio turnover ratio is 73.7% and 80.4% for portfolio 1 and 9 respectively. Therefore, an estimate of transaction cost (bid-ask spread + price impact) for portfolio1 is: 73.7% ( ) = 28.4 bps. For portfolio 9, it is 80.4% ( ) = 26.6 bps. 29 The transaction costs are considerably smaller than the three-factor alphas of 134 bps and 69 bps. Altogether, the sector neutral long-short strategy (portfolio 1-9) yields a risk-adjusted profit net of transaction costs of 148 bps ( ) per month, or 17.8% per year, which is both statistically and economically significant. In addition, the transaction cost can be further reduced by over-weighing more liquid stocks and under-weighing less liquid stocks as in Korajczyk and Sadka (2004). 3.4 Are the profits driven by past returns or past target price changes alone? The definition of TPER involves dividing by the current stock price and the question arises whether our results are simply driven by a sort on price. To investigate this possibility, we sort stocks into 9 portfolios according to the inverse of the stock price (1/P) at the end of the month within each sector. This strategy produces an insignificant risk-adjusted return of only 76bps (118bps before risk adjustment) as shown in Table 7 column This is not surprising because low-priced stocks tend to be small stocks so a sort on 1/P is in part a sort 29 The implicit assumption behind this calculation is that we trade 1 million dollar worth of each stock within an hour. 30 If we exlude the momentum factor UMD, the alpha becomes only 38bps (t-value of 0.66). 15

16 on size. Controlling for the Size factor therefore eliminates much of the profit. Qualitatively similar results hold when sorting on other price ratios, such as earnings price or sales price ratios. Since T P ER is defined as a ratio between target price and market price; therefore, its current level is influenced jointly by its past return and past revisions in the target price. Previous studies have shown that a change in market price (past return) or change in target price alone is associated with future return. For example, Jegadeesh (1990) and Lehman (1990) have documented significant short-run stock return reversal at horizons of 1 month or less. This is consistent with our finding as our benchmark long-short portfolio 1-9 involves long position in past losers and short position in past winners. However, short-term return reversal alone does not drive our results. Table 7 reports the profits and alphas to alternative sector-neutral long-short trading strategies based on the S&P500 stock sample. For the purpose of comparison, the results of our long-short strategy based on T P ER are reproduced in the first row of table 7. The third column shows the results to a long-short strategy based on the short-term return reversal. Specifically, we form portfolios by sorting the S&P 500 stocks within sectors based on the past 1 month return alone, and then long the past losers and short the past winners. The loser-minus-winner return spread is 122 bps and significant with a t-value of However, once adjusted for risk using the five factors, the significance disappears. The five-factor-alpha is only 62 bps with a t-value of This result differs from the previous literature on reversal effects mainly because of the more recent sample period and restricting attention to the set of S&P500 stocks receiving analyst coverage so that no small stocks are in our sample. Changes in target prices are known to be positively related to future returns (Brav and Lehavy 2003, Asquith, Mikhail and Au 2005). This relationship is also evident in our S&P 500 stock sample. We examine the most recent target price change in the past-three-month period for each stock in our 9 within-sector T P ER-sorted portfolios. If the current target price exceeds 1.05 last target price, we classify the change as an upgrade; if the current target price is smaller than 0.95 last target price, we classify the change as a downgrade; otherwise, we classify it as a reiteration. If there is no target price announcement in the 3rd and 2nd month preceding the current month, we classify it as missing. We then report the percentage of upgrade, downgrade, reiteration and missing for each portfolio in Table 8. As one would expect, S&P 500 stocks receive frequent target price coverage: less than 1.5% of these stocks have a target price during the current month but none during the previous two months. The percentage of target price upgrades increases monotonically with T P ER. 31 We get comparable but weaker results by sorting on the past 3 month return. In addition, the profit and alpha are even smaller (108 bps and 4 bps per month) if there is no sector control. 16

17 In portfolio 1, which has the highest T P ER and first one month return, the recent target price changes are dominated by upgrades (percentage of upgrade and downgrade are 55.4% and 22.0% respectively). The reverse is true for portfolio 9 where the majority of the stocks suffered recent downgrades (percentage of upgrade and downgrade are 19.7% and 56.7%, respectively). However, analysts revision in target price alone does not drive the future return. Defining the change in the target price DT P t as T P t /T P t 1 and sorting stocks into 9 portfolios based on DT P within sectors does not yield any significant portfolio return spread for our S&P 500 stock sample. The results are provided in column 4 of Table Finally, we examine a strategy based on both past return and target price revision. Within each sector, we conduct a 3 by 3 independent sort based on DT P and the past one month return. We then go long past losers with high DT P and short past winners with low DT P. This long-short strategy now generates a significant profit of 156 bps per month (t-value of 3.00) and a significant alpha of 126 bps per month (t-value of 2.36), (See column 5 of Table 7). 3.5 Are the profits driven by earning announcements or stock recommendations? Analysts provide investors with information in addition to target prices such as earning forecast and stock recommendations, which are known to affect future returns. To ensure that our results are not driven by pure Post-Earning Announcement Drift (PEAD), we examine stocks in each of the within-sector T P ER-sorted portfolios of S&P 500 stocks for which there was no earnings announcement during the portfolio formation period. The exact time for each earning announcement is obtained from the First Call Historical Database (FCHD). We report the excess return and the three-factor-alpha for the sub-sample with no earnings announcements in Table 9. On average, 58% of the target price coverage occurs during a month with no earning announcement. This percentage is quite stable across all T P ERsorted portfolios for our S&P 500 stock sample (although it is slightly higher for the extreme portfolio 1 and 9). Our results do not seem to be driven by delayed reaction to earning announcement (or post-earning announcement drift). If we focus on the subsample with no earning-announcement during the month of portfolio formation, the profit and five-factor alpha not only do not disappear, but become even higher (207 bps and 222 bps respectively). To show that our results are not driven by stock recommendation alone, we construct 32 The computation of DT P restricts us to a subsample of our S&P500 stocks where there are target price announcements during the preceding month. We verify that the profit to our benchmark T P ER-based strategy hardly changes when we move to this subsample. 17