Risk Management and Price Pressure

Transcription

1 Risk Management and Price Pressure Huaizhi Chen October 16, 2017 Abstract Many asset managers limit the weights of their asset positions in order to ensure diversification of active bets. Consequently, an individual manager will react to positive returns in his biggest positions by rebalancing into other assets. I document the pervasiveness of this practice in individual funds, and how trading to rebalance high exposure positions collectively leads to price pressure. A value-weighted strategy exploiting this predictability earns 2.83% (2.60% 4-factors adjusted) per quarter on the largest assets in the cross section of equities; contrasting priors that the demand channel for assets only circumstantially affect stock prices. These results are consistent with trading pressure originating from risk management by individual asset managers. I would like to thank my advisors, Dong Lou, and Christopher Polk, for their invaluable guidance, encouragement, and assistance on this project. I also thank Lauren Cohen, Daniel Ferreira, Robin Greenwood, Dirk Jenter, Christian Julliard, Marcin Kacperczyk, Ian Martin, Lubomir Petrasek, Tarun Ramadorai, Dimitri Vayanos, Michela Verardo, David Webb, and seminar participants at the London School of Economics, University of Notre Dame, Hong Kong University of Science and Technology, Hong Kong University, the Federal Reserve Board, and Tulane University for their time and helpful comments. Any errors are, of course, mine and mine only. Previous versions of this paper was circulated as Portfolio Management Pressure. Harvard Business School, hchen@hbs.edu 1

2 1 Introduction In this paper, I argue that rebalancing for risk management by individual managers leads to trading coordinated by an asset s past returns, generating significant non-fundamental demand. This demand channel can be dramatic for stocks that are held widely and in large weights across risk-managed portfolios. For example, consider the case of Apple stocks. Between 2011 and 2012, Apple became the highest valued public company in the world. Apple s outperformance significantly increased its weight in existing investor portfolios. Funds that once had a moderate position in Apple, now contain a position larger in weight than any of their other assets. In an interview on Apple s heavyweight status by the New York Times, a portfolio manager commented, we re sensitive to letting a mutual fund get too outsized a position, and when his portfolio s Apple holdings increased to 9 percent of the total assets, the manager decided to trim a little bit. Furthermore, the trimming of their positions led some investors to act against their own expected returns in Apple. The same portfolio manager lamented, every sale has been a bad sale, referencing the continued performance of Apple stocks 1. Consistent with risk management of portfolios, many investment managers decreased their weight in Apple against realized returns, despite losing out on potential future outperformance. I will show that the tendency for mutual funds to manage their exposures to their largest holdings, even at a cost, extends far beyond just Apple stocks. Actions to limit exposures to individual companies pervades across professional investors and aggregates into a price pressure that affects a large and important cross section of equities. Investment managers undoubtedly use a variety of risk management methods and models in shaping their portfolio. However, a simple guideline that captures the heart of many risk management choices is the rule to diversify and limit exposures to single 1 Apple is Heavyweight in Many Fund Portfolios, New York Times, July 8th

3 asset positions. While this heuristic rule may not match the exact risk/return model used by every investor, it is likely that asset allocation based on most risk/return models will exhibit this rule in practice. The goal of this paper is to show that risk management of portfolios as exhibited through this rule explains investors trading behavior significantly, and that the individual manifestation of risk management in institutional investors collectively generate non-fundamental demand for certain assets. Although the portfolios studied in this paper are mutual funds managed by dedicated professional investors, whose trading patterns are less susceptible to behavioral bias, this pattern of portfolio rebalancing can also be consistent with a behavioral combination of a saliency toward large positions and naive propsect theory mental accounting. This paper makes two primary contributions to the empirical literature. First, I show that professional investors generally tend to rebalance away from return induced weight increases, particularly for large initial positions. This rebalancing behavior is consistent with the aforementioned risk management by actively managed funds. Second, summing up this rebalancing effect across investors, I show that collective rebalancing leads to return predictability that is consistent with coordinated demand pressure on the largest stocks in the cross section of equities. The primary variable examined in this paper is an asset s return driven (passive) change in weight in a portfolio. This is the difference between the asset s initial portfolio weight and its predicted weight under the assumption that the portfolio manager did not trade assets between measurement periods. By construction, any change captured by passive is caused by realized returns alone. However, different from realized returns, the passive variable captures the effect of realized returns on the stock weights of the portfolio. For example, an oversized position, after experiencing small but above average returns, will have larger passive increase than a small (or non-existent) position that experienced significant returns. Intuitively, an investor may be as or more interested in how realized returns had changed his holdings than the realized returns themselves. 3

4 For example, a simple portfolio optimization investor with constant beliefs would have a trading pattern that are better predicted by passive than by realized returns alone. I will show empirically that passive strongly forecasts discretionary trading of assets by mutual funds, independent of realized returns and initial weights. However, the finding in this paper is not fully compatible with simple rebalancing to prior weights, as the discretionary decrease of positions that had large passive increases is the main driver of this behavior. Instead, I find that trades correspond to rediversification of exposures in large concentrated positions. The paper then discusses the risk/return consequences of this specific channel of rebalancing by asset managers on the underlying portfolios. I find that realized returns tend to increase common risk related measurements such as portfolio concentration and active shares. Trading by the portfolio manager drives these measurements away from these changes. Such trading is largely consistent with a pattern of risk management behavior. Because realized returns are the same for each asset across different portfolio, rebalancing by individual funds can cause coordinated trading across the asset management industry. I show that the average of passive across funds forecasts stock returns in the cross section of equities: the average return driven change in weight forecasts lower returns in the short horizon and higher returns at medium horizons, especially for the largest and supposedly liquid stocks in the equity universe. This forecastibility is consistent with price pressure arising from the collective risk management of assets by active portfolios. The price pressure from portfolio risk management lowers prices of high returns stocks and runs counter to the direction of momentum predictability. Finally, I show that the echo effect in momentum returns (Novy-Marx 2012) is related to the attenuation caused by demand pressure and that seasonality of momentum returns can be explained by the strategic timing of this price pressure. 4

5 2 Related Literature This paper s primary goal is to demonstrate that individual asset manager s risk management activities collectively affect the cross section of equity returns. However, its findings also clarifies several empirical phenomenons documented in the existing literature. Classic literature in finance points to two types of returns related trading behavior by investors. Grinblatt, Titman, and Wermer (1998) document that mutual funds appear to chase after stocks that had high historical returns. Odean (1998), in turn, documents that retail investors are predisposed to sell assets that appreciated than assets that depreciated, i.e. the disposition effect of Shefrin and Statman (1985). Both strands of works focus on trading behavior as related to returns in isolation. I argue that the return driven deviations from the initial portfolio weights are more naturally predictive of investor behavior. The work in this paper documents a kinked relationship between actual change in weight and the passive implied change, suggesting that self-enforced limits on large asset positions are an important explanation for why professional investors, such as mutual funds, sell winners and keep losers. Other recent works on the disposition effect include underreaction to news in Frazzini (2006) and the V-shape selling probability in Ben-David and Hirshleifer (2012). This paper documents that significant nonfundamental demand comes from individual portfolio s own risk management practices. This empirical fact furthers a literature on downward sloping demand, particularly from mutual funds, for stocks. A starting point is Shleifer (1986), which documents a significant price effect on the inclusion and exclusion of stocks from a stock index. Price pressure literatures that involve mutual funds includes Coval and Stafford (2007) and Lou (2012) who study mutual fund trading in the presence of asset flows, which induces fund buying and selling. The linkage from prices to mutual fund can be seen in further works that include Greenwood and Thesmar (2011) who study fund ownership structure and underlying stock returns and Anton and 5

6 Polk (2014) who study the reversal of correlated positive movement between assets held under the same mutual funds. A classic paper by Gompers and Metrick (2001) documents increase in returns to large capitalization stocks between 1980 and This occurred along side institutional growth and the accompanying institutional demand for large capitalization stocks. My contribution to this literature is the argument that the individual risk management of portfolios in turn generates non-fundamental demand for stocks. The passive variable used to capture rebalancing of stocks follows the construction also used in Calvet, Campbell and Sodini (2009) who study the rebalancing of asset classes by household investors. Other works in rebalancing include Hau and Rey (2010) who track the global mutual fund flows. This current paper joins them in documenting the active rebalancing of portfolios by investors against realized price changes. However, distinct from the previous studies, the current study confirms that this diversification demand aggregates into a coordinated price impact on stocks and that this behavior as exhibited by professional fund managers is consistent with portfolio risk management. Lastly, this paper contributes to the literature by clarifying the empirical behavior of momentum and institutional demand for assets. Jegadeesh and Titman (1993) first described momentum returns, motivated by technical analysis by industry practitioners. Koijen and Yogo (2015) recently found mean-reversion in institutional demands for the characteristics of book equity, equity to asset, and profitability as determinants of portfolio weights. They find that predictability from this reversion in characteristics demand is most pronounced for the smallest stocks, which are a priori most illiquid assets. This paper instead looks directly at the reversion in portfolio weights as determined by passive dispersion of constituent returns, and find that this rebalancing liquidity demand generates significant predictability on the largest and supposedly most liquid assets in the equity market. 6

7 3 Data The standard CDA/Spectrum mutual fund holdings dataset is used for the mutual fund portfolio holdings from 1980 to The holdings data is observed at the quarterly frequency and is compiled from both mandatory SEC filings and voluntary disclosures. Funds that report prior to the end of the quarter are assumed to have held the same portfolio at the quarter end date (adjusting for stock splits). To separate out the index funds, I drop funds that have the words INDX, IDX, or INDEX in their names. Although some funds had reported at semi-annual frequency prior to mandatory changes in 2003, the majority of funds voluntarily report holdings at the quarterly even prior to these changes. The variables are constructed and the tests conducted on quarterly reporting portfolios. CRSP Mutual Fund data are used to provide mutual fund characteristics and is linked using tables from Wharton Research Data Services. Equity funds are singled out by using the objective code reported by CDA/Spectrum to be aggressive growth, growth, growth and income, balanced, unclassified, or missing. In addition, to prevent potential misreporting of the investment objective codes, I require the ratio of equity holdings to total net asset values to be between 0.75 and 1.2. The lower bound is used to exclude mislabeled equity funds, while the upper bound is used to eliminate data errors. Lastly to ensure data quality, I remove funds that have less than one million dollars in total net assets. I supplement the holdings information with the Ancerno/Abel Noser data on institutional trading to investigate the timing of rebalancing trades. Large institutions such as brokerages, insurance companies, and pension funds, submit the stock transactions by their asset managers to the Ancerno/Abel Noser Corporation for trading cost analysis. Each trade is linked to a unique account code (clientmgrcode). Two data filters are used. Since the calculations of passive are based on the trades per stock, I ensure that each trade observation used comes from institutions that were first observed prior 7

8 to the beginning and last observed after the end of that quarter in the whole sample. I also drop funds that have the words INDX, IDX, INDEX, or BANK appearing in the either name of the specific account or that of the specific manager. After applying data filters, the data sums to about 300 billion dollars of trade volume each quarter and spans 376,200 different accounts from January 2000 to December See Puckett and Yan (2011) for a more detailed discussion of the data and its selection issues. To calculate the dollar volumes for various trades, I use the prices from the end of the previous calendar quarter. I link the Ancerno database to the CDA/Spectrum quarter-to-quarter mutual fund holdings to produce a combined dataset of trades and holdings using a simple procedure. An account in the Ancerno database can represent a portfolio, a fund that is part of the portfolio, or most likely, a subportfolio for an individual client. To approximate portfolio level trading, I match portfolios to client accounts by regressing each change in asset positions against the aggregate trades of each fund in Ancerno per the quarter against the change in each quarter/portfolio set in CDA spectrum database. If the coefficient is significantly positive (t > 10) and explains over 90% of the variation in the portfolio data, then I call the match successful. This process implicitly assumes that the matched client account trades approximates the trades of the entire portfolio. At the end, I obtain matching of about 2800 portfolio/quarter sets between the two databases from 2000 to An inspection of the Ancerno fund and CDA/Spectrum portfolio names indicates that the matches are reasonable. Stock returns, prices, and other stock related characteristics come from the CRSP database. Tests forecasting future returns are done with common stocks traded on AMEX, NYSE, and NASDAQ exchanges. The standard Size/Momentum portfolio returns, as well as the usual cross sectional factors, are taken from Ken French s website. Lastly, quarterly earnings announcement dates for the S&P500 constituents are obtained from the Compustat database. Standardized Unexpected Earnings (SU E) is 8

9 calculated using the code provided by Wharton Research Data Services. 4 Portfolio Rebalancing Let portfolio j at t have stocks {1,..., I} with weights {w 1,j,t,..., w I,j,t }. Given returns {r 1,t t+1,...r I,t t+1 } between t to t+1, a stock i in a passively managed portfolio with the same initial weights would have weights ŵ i,j,t+1 = w i,j,t (1 + r i,t t+1 ) In=1 w i,j,t (1 + r i,t t+1 ) at t+1. Stock i s change in weight in the passive portfolio is then ŵ i,j,t+1 w i,j,t. The actual change in the weight of stock i in portfolio j then can be decomposed into two components: a passive return driven component accountable by initial weights and realized returns alone (assuming reinvestment of dividends), and a discretionary component that isn t captured by the passive portfolio: w i,j,t+1 w i,j,t }{{} = w i,j,t+1 ŵ i,j,t+1 }{{} + ŵ i,j,t+1 w i,j,t }{{}. Total Change(total) Discretionary Change (discret) Passive Change (passive) Figure 1 plots bins of grouped of mutual fund positions from 1990 to Part a shows levels of actual end period weights against the counterfactual weights of a passive portfolio. The positions are organized into half percent bins grouping counterfactual weights. The x axis is the midpoint of the bin and the y axis is the equal weighted average of the actual portfolio weight. The circles represent bins of positions that passively decreased, while x s mark bins of positions that passively increased. If the portfolio managers didn t trade, then the observation would be on the 45 degree line. Through the addition of new positions, on average, the weights of existing positions are lower than what would be implied by a passive portfolio. However, for larger positions, the 9

10 actual weight of an asset that increased is significantly lower than what would be implied by weights and returns alone. This pattern is more striking in figure 2, which shows the observations grouped by bins of passive changes. While asset positions that experienced decreases in weights due to underperformance roughly follow the passive mimicking portfolio (on average, they lie near, albeit slightly below, the 45 degree line), asset positions that experienced relative outperformance deviate significantly. In fact, positions with largest passive increases in weight remain very flat, indicating that the portfolio had significantly decreased its relative holdings. Analysis using stock groups binned by returns shows no strongly discernable pattern with returns alone. The actual trades to rebalance are forecastable in higher frequency than in the semi-annual one shown in figure 1. The total and discretionary weight are forecasted using passive, the asset s initial weight, and its return in Table 2a. The forecasting coefficients for each portfolio/quarter set are averaged in a panel). I find that the return driven changes negatively predict discretionary and total weight changes in the subsequent quarter. Quarterly returns predict weight increases while passive i,j,t predicts weight decreases (Table 2a). For a single position, a unit of passive weight change is met with 22.4% (t=15.46) discretionary decrease, and a 25.1% (t=10.32) total decrease. A second set of coefficient averages are reported in columns 5 to 8. The weighted average is based on the quarterly fraction of total mutual fund assets held by each individual portfolio. The magnitudes of the rebalancing coefficients decrease to % (t=8.25) and 17.68% (t=5.61) respectively, indicating that larger funds rebalance less intensely than smaller funds. The three variables used in the regression explain about 8% of the total variation in the quarterly changes in position weights. I include regression with further lags of the passive in the appendix (Table A3). The forecasting power of passive is the strongest at the quarter-to-quarter horizon. To further explore the channels for portfolio rebalancing, I decompose the variable passive i,j,t. Because funds tend to manage their winners, they would react more 10

11 toward weight increases in particular. I separate return driven changes into increases and decreases and carry the same analysis in Table 3. ŵ i,j,t+1 w i,j,t }{{} passive = (ŵ i,j,t+1 w i,j,t ) 1(ŵ i,j,t+1 > w i,j,t ) }{{} passive + + (ŵ i,j,t+1 w i,j,t) 1(ŵ i,j,t+1 w i,j,t) }{{} passive The main drivers of the rebalancing trades are positions that have appreciated. The negative side of the passive weight changes have small to no quantitative significance. This is consistent with risk management and rediversification of large portfolio positions. Figure 3 is the regression counterpart to table 3, and it plots the fund size weighted coefficients for regressions of discretionary change in weights against further decomposition of passive i,j,t. I find that the reversal coefficients are the strongest for large positive return driven weight changes. This is consistent with trimming of large winning positions. Simple beliefs on constant returns and risk, and direct benchmarking to asset weights would not generate this asymmetry. In addition to the previous test, I also separate the return driven changes into a portion that contains the difference between benchmark weights 2 and a residual difference. ŵ i,j,t+1 w i,j,t = }{{} (ŵ i,j,t+1 b i,j,t+1 ) }{{} + (b i,j,t+1 w i,j,t ) }{{} passive Benchmark Deviation (bench dev) Residual Deviation (res dev) Here b i,j,t+1 is a proxy benchmark weight constructed using past 3 year stock level holding. Both Bench Dev and Res Dev have negative predictive power about future weight changes. These results imply that benchmarking can only explain part of the predictable rebalancing trades by investment managers. 2 Since the true tracking benchmark is unobservable for each fund, I construct proxy indices using market cap weighing of the universe of stocks that the fund had invested in the past 3 years. 11

12 The mechanism proposed by this paper is that the management of individual portfolios visible risk affects the portfolio s trading behavior. It is relevant to examine how these trades in turn affect the composition of individual portfolios. Without prior knowledge of the models used by portfolio managers to measure expected portfolio risk, I use two simple but very widely used measurements of portfolio s risk characteristicsthe herfindahl index, and the active share of the portfolios in question. If portfolio managers are rebalancing against the changes in visible risk caused by return changes, then the changes in the these measurements as caused by discretionary trading should be negatively related to those as caused by realized return. The difference between a fund s counterfactual characteristic with return driven weights and the original characteristic with prior weights is indeed negatively related to the difference between the counterfactual characteristic with new weights and that of the return driven weights. Consistent with the hypothesis, discretionary changes in both measurements of portfolio risks are negatively correlated to changes as driven by returns. A single unit of return driven increase in herfindhal index is undone by 17.1% (t=-2.15) through discretionary decreases in the same quarter and by 12.5% (t=-2.11) discretionary decrease in the follow quarter. A single unit of return driven increase in portfolio activity is undone by 8.1% (t=-2.17) discretionary decrease in the same quarter and 9.9% (t=-3.60) in the subsequent quarter. The t-statistics are clustered at the year/quarter level. 5 Coordinated Demand, Predictability, and Echo Selling by parties to limit portfolio exposures requires buyers who are not portfolio constrained. However, if a stock is held largely and widely by many managed portfolios, there may not be enough buyers in the asset management industry alone to satisfy this demand. Table 2b explores potential counterparties to these rebalancing trades. In general, I find that these trades are not absorbed by the mutual fund or the institutional management industry alone. Table 2b regresses the difference of the proportion of stock 12

13 shares held by the sum of all mutual funds (based on N-Q filings) and all institutional investors (based on 13-F filings) each quarter against past 3-month returns, lagged average passive change in weight, and lagged share-weighted average weights in a portfolio. While the overall industry exhibit strong return chasing behavior based on past returns, this behavior severely decreases for high average weight and high return shares. One standard deviation of passive forecasts a 12 basis point decrease in the total proportion of a stock held by all mutual funds and a 20 basis point decrease in the proportion held by all institutions. These results indicate that high average weights and high return driven deviations in weights forecast net decreases in the proportion of shares held by professional asset managers. The largest rebalancing trades are absorbed by retail investors and non-reporting institutions, indicating the potential existence of demand induced price pressure. Consequently, I hypothesize that there will be significant pricing effects originating from this demand channel. Consistent with a pattern of nonfundamental demand induced price pressure, the passive and passive+ 3 variables are able to forecast negative returns at the rebalancing horizon, and positive returns subsequently. Because passive is generated on past 3 month returns and portfolio weights, it is generally correlated to past return characteristics. Description of the variable, and its correlation to past returns is given in the panel b of table 1. The variable passive generally forecasts lower returns in the short horizon, and higher returns at the longer horizons for large cap stocks. The cumulative returns for holding a portfolio that shorts stocks with the highest passive and longs stocks with the lowest passive is given in Figure 4 (with controls) and Figure 5 (without controls). At shorter horizons of the subsequent 1 to 2 months, passive forecasts negative returns in large cap and high past return stocks. This predictability reverts at the longer horizon of 3 to 8 months depending on the inclusion of controls. Since passive is generally 3 passive+ is simply the share weighted average of passive+. 13

14 correlated with 3 month returns due to its construction, it would likely interact with the standard 3-month momentum predictability of Jegadeesh and Titman, assuming they are separate phenomenons. Table 4 shows value-weighted Fama Macbeth regressions of quarterly stock returns with passive and passive+ controlling for various characteristics. The forecasting power of passive is significant once controlling for past 3 month returns, and is greater in magnitude after One standard deviation of passive forecasts 50 basis points returns between 1990 and 2013, and 64 basis point between 2000 and Furthermore, the returns revert at longer horizons (3 to 8 months). This is consistent with non-fundamental demand. One immediate observation from table 4 is that 3-month realized returns positively forecast future returns once I control for the rebalancing related price pressures. Because the observable rebalancing tend to be at the quarterly horizons, it may very well attenuate momentum based predictability using past performances measured at similar horizons. I explore this channel to explain the momentum not momentum effect documented in Novy-Marx (2012). In Table 5, I regress forward quarter returns on passive, passive+, past 1 month returns, past 2 to 6 month returns, past 7 to 12 month returns, and various controls. I find that controlling for the rebalancing variables increases the magnitude and power of 2 to 6 month past stock return in forecasting future quarterly returns. In fact, the main drivers that result in the insignificance of 2 to 6 month returns are rebalancing based price pressure and the momentum crash of Once controlling for the two issues, 2 to 6 month past performance significantly forecast quarterly returns at the quarterly portfolio formation intervals. A predictive strategy based only past performance or passive alone hides their joint predictability. Table A1a (A1b) shows the long-short returns of portfolios sorted on size and 12- month momentum (size and short-term reversal) from January 1990 to December 2013 and January 2000 to December On average, the long-short momentum portfolios 4 The results remain qualitatively the same after kicking out sample periods such as 2009 with the momentum crash. 14

15 have had negative returns during January, April, July, and October; while most of their portfolio returns come at the end of the quarter. The largest size momentum portfolio, in particular, experienced the largest negative returns during this intra-quarter period. This effect is not apparent in the periods from 1970 to 1990 or from 1950 to 1970 (Table A2a). As documented in the literature, for much of its history, momentum effects tend to be more concentrated in smaller and more illiquid stocks. However, as I document in the most recent era, the dispersion of momentum returns became concentrated in the largest and ideally most liquid stocks of the market. Momentum based portfolios, for large cap stocks, perform negatively in the first halve of the quarter and positively in the second halve. I investigate the hypothesize that the timing of rebalancing based trades is the cause of this seasonality in the subsequent section. 6 Rebalancing Seasonality and the Seasonality of Momentum To understand the timing of rebalancing trades in detail, I examine the intraquarter variation in the trading intensity of my sample of asset managers. A guiding hypothesis is that asset managers tend to trade to rebalance more at times when liquidity is the highest in the underlying market. Collin-Dufresne and Fos (2015) document that strategically informed traders tend to aggregate their trades around select times of higher market liquidity. Complementary to their result, I find that the timing of nonfundamentally related trades also aggregate to periods when informational asymmetry is low and public information is high. This is consistent with strategic timing of nonfundamental trading. The Ancerno database is used to explicitly identify trades by professional asset managing institutions. As a first pass, I aggregate the buy and sell orders from all accounts each month using lagged quarter prices from CRSP to generate dollar volume 15

16 for each asset. The fraction of buys and sells in each month relative to that of the entire quarter is then calculated for the data period. The subsample of institutions have different trading schedules than the aggregate market. Figure A1 panels A and B plot the average monthly dollar fraction of quarterly buys and sells. Evidently, more trades come in January, April, July, and October when compared to the rest of the quarter. This effect is very apparent when comparing money managers to the aggregated equity volume in Panel C. On average, institutional managers trade more intensely during these periods than the other market participants. In fact, these trades do not cancel out within the money management sector. More net trades between money managers and other market participants occur during these months, see panel D. Statistical tests of the difference are presented in the appendix Table A4. Since these months tend to accompany earnings releases by firms, I hypothesize that more rebalancing trades follow individual firm s information release. The matched dataset of individual ancerno reported trading managers to CDA/Spectrum mutual fund holdings is used to test this hypothesis. The description of the matching procedure is placed in the data section. I examine the shares bought and sold for each stock as a fraction of existing holdings by the matched managers. Table 6, panel a shows that a majority of selling and buying of this total fraction as driven by passive comes in during the earnings announcement date and the 10 days following. On the returns level, this period also coincide with significant return predictability in the underlying stock, not seen in the days before the earnings (panel b). I examine the cumulative effect of rebalancing trades between the start of the quarter and when a majority of earnings releases end to pin down the exact price effect of rebalancing trades on stock prices. Intra-quarterly cumulative returns, from the first trading day of the quarter to the day before the last 10% of the S&P constituents make their announcements, are regressed cross-sectionally by value-weighted Fama Macbeth on lagged passive. The second stage coefficient averages are reported in Table 7. The 16

17 variable passive subsumes the negative predictability of the past return characteristics. We observe that a majority of the total quarterly returns predictability by passive, from table 3, comes in during this interval. The univariate regression on passive alone, shows that one standard deviation of passive implies about 49 basis points of return on the underlying. This effect is stronger between 2000 and 2013, and robust to the exclusion of the Momentum Crash in I form intra-quarterly long short portfolios based on the ranking sorting of passive to quantify the economic magnitudes of a portfolio strategy based on front running the portfolio management trades. The long short portfolios are created by first sorting on size using NYSE breakpoints, and then for each size quintile, and going long/short the bottom/top quintile of passive sorted stocks. The returns of these long short portfolios are reported in table 8 with various factor adjustments. This table indicates that the firms that tend to drive this predictability are the firms with market caps greater than 80% of the firms in the NYSE. The largest and supposed most liquid firms are the most affected by the portfolio adjustment pressures. As documented in figure 5 and table 8, the highest passive portfolio has had zero to negative returns until the last thirds of the quarter, while the lowest passive portfolio experienced almost 3% returns. This price pressure does not come at an individual quarter, and is spread out across the year; see panel b of table 8. I use the portfolio rebalancing pressure to explain the underperformance of the standard (2-12) momentum factor (UMD) returns during the announcement season. I create a loser minus winner (LMW) factor whose returns are based off of the decile sorted portfolios in the previous section (bottom 10% minus the top 10%). In table 9, I find that the UMD returns each quarter before the last 10% of the S&P500 constituents make their earnings announcements are increased by adjusting for the passive portfolio. The unadjusted intra-quarter return of UMD from Q to Q is -0.34% (t=-0.46). After adjusting for the standard 3 factors, the return is increased to 0.35% (t=0.53). After incorporating the LMW factor, the 4 factors adjusted return of UMD is increased 17

18 to 1.28% (t=2.22). This is expected as most of the underperformance by UMD is caused by the large capitalization portfolios (See Appendix table A1a). 7 Conclusion In this paper, I argue that the risk management practices by individual asset managers leads to systematic coordination of demand for certain assets. The particular practice examined is the rediversification of active bets and the rebalancing of large stock exposures. While this practice individually lead to potential risk reduction as observed through changes in portfolio characteristics, collectively it also generates coordinated demand, which leads to significant nonfundamental price pressure on large capitalization portfolios. The empirical facts presented here contrasts priors that the institutional demand channel only circumstantially affect stock prices. The mechanism of portfolio exposure related rebalancing is then used to explain several puzzling facts about the dynamics of cross sectional momentum. The first is the echo effect in Novy-Marx (2012) and the second is the intra-quarter seasonality of momentum returns. 18

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22 Actual Weight 9 Tables and Figures Figure 1. Weights of Mutual Fund Positions This figure plots bins of actual and predicted weights of assets held in mutual fund portfolios from 1990 to 2013 at semi-annual frequency. The circles mark stocks that had predicted decreases in weight and the cross mark stocks that had predicted increases. The x-axis is the predicted weight as implied by the portfolios initial holdings and subsequent 6 month returns, assuming no trading by the investor. The y-axis is the 6 month end period weights of assets. If investors bought and held assets on average, then actual weight should follow counter factual weight and lie on the 45% line. While all bins are below the 45% line due to the inclusion of new positions in portfolio on average, the gap between actual and counter factual weight is the highest for the largest predicted increasing positions Degree Line Bins of Increases Bins of Decreases Predicted Weight 22

23 Actual Change in Weight Figure 2. Changes in Weight of Mutual Fund Positions This figure plots bins of actual and predicted change in weights of assets held in mutual fund portfolios from 1990 to 2013 at semi-annual frequency. The x-axis is the predicted change in weight as implied by the portfolio s initial holdings and subsequent 6 month returns, assuming no trading by the investor. The y-axis is the actual weight change of the asset at the end of the 6 months. If investors in the sample just bought and held shares on average, then the actual weight change should line up with the predicted weight change and lie on the 45% line. Instead we observe a clear symmetry. When realized returns drive up asset weights, investors act by discretionarily decreasing the position. On average, assets that have large return driven increases in weights are met with discretionary decrease Degree Line Bins Predicted Change in Weight 23

24 Figure 3. Rebalancing Coefficients for Piece-Wise Separation of passive This plot contains the averaged coefficients of piece-wise passive variables as regressed against total change in weight and discretionary change in weight. For each observation in each portfolio quarter set, passive is separated into 6 pieces based on how far the value is away from 0 as measured by its standard deviation in that portfolio quarter set. In the figure, -3 is defined as passive 1(passive <= 2 std(passive)), -2 is defined as passive 1( 2 std(passive) < passive <= std(passive)), and so on. These variables by definition adds up to passive. The y-axis marks the forecasting regression coefficients of these variables against discretionary and total change in weight of positions in the portfolio. We observe a clear non-linear pattern in rebalancing intensity- most of the rebalancing predictability is on the largest winning portfolios while the largest losing portfolios have little quantitative forecasting power Coefficients of Piece-wise Passive Discretionary Change in Weight Total Change in Weight 24

25 Cumulative Return Per 1 Std of Passive Figure 4. Return Predictability of passive Cumulative coefficients from the Fama Macbeth regression of forward returns for one standard deviation of the passive variable. The sample period is from 1990 to The controls for the regression are lagged 3 month returns, book to market ratio, lagged market capitalization, idiosyncratic volatility, percentage institutional ownership, and turnover. Passive forecasts negative returns in the subsequent 1 to two months. The negative returns revert, and passive forecasts positive returns in the subsequent 3 to 6 months. This is consistent with non-fundamental demand induced price pressure Months After Starting Period 25

26 Cumulative Returns Cumulative Returns Figure 5. Return Patterns for the Long Short passive sorted portfolios. This figure records the portfolio returns of the top decile and the bottom decile of passive sorted portfolios for the higest size quintile size portfolios (i.e. stocks whose market caps are greater than 80% of the firms in the NYSE) without controlling for any other variables. The top panel records the returns from 1990 to 2013, whereas the bottom panel records from 2000 to A visible gap starts early in the quarter and closes into the end of the quarter. The gap is the largest around the middle of each quarter. Consistent with short term price pressure, portfolios that exhibit the highest risk management related selling pressure underperforms in the short horizon, and outperforms in the longer horizon Passive Sorted Portfolios from 1990 to 2013 (Top Quintile NYSE) Bottom Decile Top Decile Trading Days Into the Quarter 0.04 Passive Sorted Portfolios from 2000 to 2013 (Top Quintile NYSE) Bottom Decile Top Decile Trading Days Into the Quarter 26

27 Cumulative Return Cumulative Return Figure 6. Return Patterns for Momentum and Size Sorted Portfolios. This figure records the return patterns for the momentum and size sorted portfolios from Q to Q (top) and Q to Q (bottom). Size 1 is the smallest cap, while size 5 is the largest quintile of NYSE breakpoint equities. The LS portfolio for each size quintile is constructed using the edge momentum quintiles. All the data used to construct the figures come from Ken French s website. Intra Quarter LS Momentum Returns Q to Q Size 1 LS Size 3 LS Size 5 LS Trading Days Into the Quarter Intra Quarter LS Momentum Returns Q to Q Size 1 LS Size 3 LS Size 5 LS Trading Days Into the Quarter 27

28 Table 1. Summary Statistics on Ancerno This table records the summary statistics of the Ancerno Database used in this study. Trades from the starting quarter and ending quarter of individual accounts are drop. Furthermore, accounts with words INDEX, INDX, IDX, or BANK in either the account or manager names are dropped. The data cover January 2000 to December Panel A Summary Statistics Mean Std Min 25 P. Median 75 P. Max N N. of Account Per Quarter 8,550 14,069 3,649 6,748 8,550 19,966 53, N. of Trades Per Account/Qtr , Dollar Value of Buy Trade 161,421 1,390, ,632 8,470 50,611 4,000,000, ,210,492 Dollar Value of Sell Trade 168,576 1,357, ,494 8,344 50,560 2,406,170, ,250,017 Total Sum of Quarter's Buys 305 B 71 B 191 B 238 B 311 B 350 B 488 B 44 Total Sum of Quarter's Sells 314 B 78 B 207 B 244 B 305 B 366 B 474 B 44 Qtrs Observed Per Account ,155 Panel B Correlation Statistics Mean Median Std Ret(1,1) Ret(1,3) Ret(2,6) passive Ret(1,1) 1.06% 0.43% 16.5% 1 Ret(1,3) 3.69% 1.66% 31% Ret(2,6) 6.31% 2.50% 46% passive 0.00% 0.00% 1.88%

29 Table 2. Rebalancing on Portfolio and Aggregated Levels Panel a. This panel reports Fama Macbeth regressions of discretionary changes in weight (discret) and total change in weight (total) against lagged return driven passive change in weight (passive), initial weight (wght), and 3 month returns scaled by total holdings return (sret). The first stage coefficients are obtained by regressing for each portfolio/quarter subsample, requiring at least 20 observations per regression. The coefficients are then pooled into a panel and averaged. Columns 1 through 4 compute the equal weight averages, and columns 5 through 8 compute the averages as weighted by the fraction of the fund s total net asset value to the aggregate mutual fund net asset value for that quarter. The standard errors are clustered quarterly. All right hand side regression variables are winsorized at 2.5% to 97.5% level per portfolio/quarter. The sample is from Q to Q Equal Weighted Coefficients Value Weighted Coefficients discret i,j,t+1 total i,j,t+1 discret i,j,t+1 total i,j,t+1 passive i,j,t (-16.82) (-15.55) (-8.77) (-10.39) (-8.25) (-8.52) (-5.83) (-6.61) wght i,j,t (-30.77) (-27.43) (-23.48) (-22.15) sret(1,3) i,j,t (7.19) (6.47) (5.98) (5.82) Avg rsquared Qtr

30 Panel b. This panel reports Fama Macbeth regressions of the change (difference) in proportion of stocks held (Shares in Mutual Funds/Total Shares Outstanding, Shares held by Institutions/Total Shares Outstanding) between quarters. The right hand side regression variables are winsorized at 2.5% to 97.5%. The left hand side variable is winsorized at 1% and 99% level per quarter to level off extreme observations. The first stage coefficients are obtained by weighted least squares based off of the stock s market cap at the end of past June for the top table. The bottom table examines only the stocks with market cap greater than 80% of the NYSE. The sample is from Q to Q

31 Table 3. Rebalancing Channels This table reports Fama Macbeth regressions of discretionary changes in weight (discret) and total change in weight (total) against lagged return driven positive return driven change in weight (passive + ), negative return driven change (passive ), benchmark deviation (bench dev), residual deviation (res dev), initial weight (wght), and 3 month returns scaled by total holdings return (sret). The first stage coefficients are obtained by regressing for each portfolio/quarter subsample, requiring at least 20 observations per regression. The coefficients are then pooled into a panel and averaged. Columns 1 through 4 compute the equal weight averages, and columns 5 through 8 compute the averages as weighted by the fraction of the fund s total net asset value to the aggregate mutual fund net asset value for that quarter. The standard errors are clustered quarterly. All right hand side regression variables are winsorized at 2.5% to 97.5% level per portfolio/quarter. The sample is from Q to Q Equal Weighted Coefficients Value Weighted Coefficients discret i,j,t+1 total i,j,t+1 discret i,j,t+1 total i,j,t+1 passive+ i,j,t (-17.75) (-13.22) (-10.20) (-8.12) passive- i,j,t (-4.33) (-2.59) (-0.78) (-1.02) bench_dev i,j,t (-19.16) (-11.12) (-12.56) (-8.21) res_dev i,j,t (-15.25) (-9.06) (-7.61) (-5.16) wght i,j,t (-30.61) (-26.90) (-24.54) (-22.17) (-21.98) (-20.06) (-18.96) (-18.23) sret(1,3) i,j,t (6.10) (3.05) (6.15) (2.59) (5.36) (1.58) (5.25) (1.22) Avg Adj Rsq Num Qtrs