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Faculty Working Paper 92-0176 1 992:1 76 copy
Institutional Trades and
Intra-Day Stock Price Behavior
THE
THE
2 8 18
Louis K. C Chan Josef Lakonishok
Department of Finance Department of Finance
University of Illinois University of Illinois
Bureau of Economic and Business Research
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
BEBR
FACULTY WORKING PAPER NO. 92-0176
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
November 1992
Institutional Trades and
Intra-Day Stock Price Behavior
Louis K. C. Chan
Josef Lakonishok
Department of Finance
Forthcoming, Journal of Financial Economics
Institutional Trades and Intra-Day Stock Price Behavior
Louis K. C. Chan
Josef Lakonishok
August 1992
Both authors are from the College of Commerce, University of Illinois at
Urbana-Champaign, Champaign, IL 61820. We thank Gil Beebower and Vasant
Kamath from SEI for providing us with the data and for sharing their insights
on various aspects of trading. We also thank Bill Bryan, Eugene Fama, Ken
French, Charles Lee, Richard Leftwich, Harold Mulherin, Mitchell Petersen,
Mark Ready, Jay Ritter, Andrei Shleifer and an anonymous referee for helpful
suggestions, and Rohit Gupta and Peng Tu for research assistance. This paper
has been presented at the Amsterdam Institute of Finance, the Conference on
Security Markets Transaction Costs at Vanderbilt University, the CRSP seminar
at the University of Chicago, INSEAD, the Institute of Quantitative Investment
Research (Europe), the NBER Summer Conference on Behavioral Finance, Ohio
State University, Tel Aviv University, the University of Illinois and the
University of Wisconsin-Madison. Computing support was provided by the
National Center for Supercomputing Applications, University of Illinois at
Urbana-Champaign .
Abstract
This paper examines the price impact of institutional stock trading,
using a unique data set which reports the transactions (large and small) made
by 37 large institutional money management firms. The direction of each trade
and the identity of the management firm behind each trade are known. While
institutional trades are associated with some price pressure, we find that the
average price impact is small. There is also a marked asymmetry between the
price impact of buys versus sells. We relate our findings to various
hypotheses on the elasticity of the demand for stocks, the cost of executing
transactions and the determinants of market impact. While market
capitalization and relative trade size influence the market impact of a trade,
the dominant influence is the identity of the money manager behind the trade.
This paper uses a unique data set to examine the effects of
institutional trading on stock prices. This data set reports the transactions
made by a sample of 37 large institutional money management firms over the
course of two and a half years. Each transaction is explicitly identified as
a purchase or sale by the money management firm in question; in addition, we
are able to distinguish between the trades of different management firms.
There are more than one million transactions, both small and large, involving
issues listed on the New York and American Stock Exchanges. These
transactions account for 5 percent of the dollar value traded on these two
exchanges over the sample period. We compare the price at which each
transaction is executed with a variety of benchmark price measures on the date
of the trade. Tracking the intra-day behavior of prices around institutional
trades allows us to evaluate the price impact of institutional trades and
helps us to disentangle alternative explanations for the sources of such
market impact.
Trading on equity markets has become increasingly dominated by
institutional investors. Schwartz and Shapiro (1990) estimate that in 1989
about seventy percent of trading volume on the New York Stock Exchange is
accounted for by member firms and institutional investors. In light of their
importance, the impact of institutional trading on stock prices has been the
subject of increased attention. Some have suggested, for example, that the
increased concentration of trading increases intra-day price swings (Report of
the New York Stock Exchange's Panel on Market Volatility and Investor
Confidence, 1990).
Trades in a particular stock may be generated under a variety of
investment styles (active or passive, value or growth) as well as a variety of
order placement strategies (market or limit orders), on the part of both
buyers and sellers. Most of these factors are not directly observable at the
time of the trade. Nonetheless, the general perception is that institutional
investors on average trade frequently in large amounts with accordingly large
price impact.
Early studies on the effects of institutional trading are unable to
distinguish between institutional and non-institutional transactions. Hence,
2
they focus on block trades, trades over 10,000 shares (e.g., Kraus and Stoll
(1972)). These and later studies (Holthausen, Leftwich and Mayers (1987,
1990), Ball and Finn (1989)) also suggest several reasons why trades might
affect prices. An impact of trades on prices is consistent with the presence
of new information conveyed by transactions (Kyle (1985), Easley and O'Hara
(1987)), or with the existence of various kinds of market frictions. Such
frictions might reflect the existence of different forms of liquidity costs,
including the costs of processing orders (Demsetz (1968)) or compensation for
inventory imbalances (Amihud and Mendelson (1980), Ho and Stoll (1987)).
Alternatively, the market price of a stock may be affected by shifts in excess
demand because investors do not recognize the existence of close substitutes
for an individual stock. Measuring the impact of trades on prices thus allows
an evaluation of the importance of these different effects on the flow
demand/supply schedules for stocks.
Numerous studies document the inability of portfolio managers to out-
perform various passive benchmarks, despite the considerable effort to analyze
and select stocks (Brinson, Singer and Beebower (1991), Fama (1991),
Lakonishok, Shleifer and Vishny (1992)). This "implementation shortfall" may
be due to the costliness of actually executing trades (Perold (1988)).
Indeed, the heavy expenditure of resources by institutions on trading
facilities and personnel suggests that execution costs might be non-negligible
and, moreover, that they are potentially controllable (Bodurtha and Quinn
(1990)). There is, accordingly, great interest in comparing the execution
performance of different money management firms. In evaluating the
profitability of various trading rules, researchers also find it necessary to
adjust for the costs of trading.
In comparison with the literature on block trades, our results provide
evidence from a distinctive sample of trades. Previous studies use the tick
test to classify trades as buyer- or seller-initiated. Block trades at a
price below (above) the price prior to the block are considered to be seller-
(buyer-) initiated. Zero tick trades are in general not classified.
Holthausen, Leftwich and Mayers (1987) find that the tick rule properly
classifies only 52.8 percent of a sample of trades known to be buyer-
initiated. Lee and Ready (1991) also explore the accuracy of the tick test.
The earlier studies thus measure the impact of large trades from the
perspective of the relatively more impatient party (i.e., the one willing to
trade on an uptick or downtick) . There are, of course, varying shades to a
trader's impatience to trade. Our results capture the traces of institutional
trading activity on stock prices, across the spectrum of degrees of impatience
to trade, incorporating many different trading strategies and many different
investment styles. What we are after in this paper, therefore, is the average
market impact incurred by institutions when altering the composition of their
portfolios. Moreover, our study of differences across managers can shed some
light on the impact of the degree of impatience on execution costs.
Our findings suggest that both institutional purchases and sales are
accompanied by some price pressure relative to the opening price on the trade
date. However, there is a marked asymmetry between the behavior of prices
after purchases and after sales. After buys, the stock price continues to
appreciate; in contrast, the price almost fully recovers to its prior level.
As a result, the average price change weighted by the dollar size of the trade
(the principal-weighted average) from the open to the close on the trade day
for buys is 0.34 percent, while the corresponding average price change for
sells is -0.04 percent. This asymmetry is intriguing, and we provide several
conjectures as to its source. The price impact of transactions is related to
the market capitalization of the stock, and to the relative difficulty of the
trade. But an even more dominant influence on the trade's price impact is the
identity of the money management firm behind the trade, suggesting
considerable differences across management firms.
While our findings indicate that institutional trades are associated
with some impact on stock prices, the magnitude of the effect pales in
comparison to the figures reported by previous authors. Kraus and Stoll
(1972), for example, find that large buy blocks are associated with a price
change (from the prior closing price to the close on the trade date) of
1.41 percent, while our findings (based on both small and large transactions)
suggest that the open-to-close average price change for buys is only
0.34 percent. The low magnitude of the price impact also has strong
implications for the much-debated issue of the market impact cost of executing
trades. A manager who gives up only an eighth of a point each way would incur
a round-trip cost of 0.68 percent on a typical stock. In contrast, we are
hard-pressed to find a round-trip market impact cost, in the aggregate over
all trades, exceeding 0.36 percent. The modest estimates of market impact
costs attest to the keenly competitive nature of the investment industry.
The remainder of the paper is organized as follows. Section 1 outlines
alternative explanations for the price impact of trades, and describes the
data. The empirical results are described in Section 2. Section 3 relates
our results on the price impact of trades to the question of measuring the
costs of executing trades. A final section provides the conclusions.
1 . Preliminaries
1.1. Reasons for Price Impact
Scholes (1972), Mikkelson and Partch (1985), Harris and Gurel (1986),
Shleifer (1986), Loderer, Cooney and Van Drunen (1991) examine the elasticity
of the demand for stocks. Three potential explanations for price changes
triggered by large trades are suggested in the literature: (i) short run
liquidity costs, (ii) imperfect substitution, and (iii) information effects.
Short run liquidity costs arise because of the difficulty in finding
immediately willing buyers or sellers. Efforts to attract buyers or sellers
translate into price concessions. In many large trades, block traders provide
some of the liquidity, and are compensated at least in part by a price
concession. A timely return of prices following a trade to the prior
equilibrium is consistent with this explanation.
Prices will also change around large trades if there are no perfect
substitutes for a particular stock. Hence, a seller faces a downward sloping
demand curve and a buyer an upward sloping supply curve. Thus, the seller in
a large transaction has to offer a discount to induce buyers to absorb the
extra shares. Similarly, a premium has to be offered by the buyer in a large
transaction. It stands to reason that the slope of the demand and supply
curves will depend on the length of the horizon, although this point has not
been emphasized in the literature. The imperfect substitution hypothesis is
consistent with permanent price changes or much slower reversals following the
trade, compared to the predictions of the short run liquidity hypothesis.
Permanent price changes caused by large trades are also expected if the
trades reveal private information that is subsequently impounded into the new
equilibrium price. Informed sellers believe that the stock is overpriced, and
informed buyers that the stock is underpriced. The information effect depends
on the identity of the buyer or seller and in many studies the size of a
transaction is used as a proxy for the information content of the trade.
1.2. Transaction Data
The data set used in this study consists of the transactions made by 37
large money management firms from July 1986 until the end of 1988. The data
are provided by SEI Corp. , a large consulting firm in the area of financial
services for institutional investors. For each transaction, the CUSIP number
of the stock is recorded, along with the trade date, the number of shares, the
dollar amount of the trade and dollar commissions. Each trade is identified
as a purchase or a sale, and there is an indicator for the money management
firm behind the trade. Each money management firm is identified to us only by
a numeric code.
We match up the SEI data on trades with the record of transaction prices
provided by the Francis Emory Fitch Co. Since the SEI data do not contain a
time stamp, we cannot identify the transaction prices immediately before or
after a specific trade by a money manager. In order to understand how trades
are executed, however, what we would actually like to know are the market
conditions when the portfolio manager actually decided to trade (which could
be much earlier than the actual execution of the trade). Such information, of
course, is not generally available.
Table 1 provides some description of our sample. We analyze 1,215,387
transactions, amounting to a value traded of 387.6 billion dollars. The
sample is very large when compared to those used in previous studies and
accounts for about 5 percent of the dollar value traded on the NYSE and AMEX.
As Lakonishok, Shleifer, Thaler and Vishny (1991) find, most of the trading
activity of institutions is in the largest stocks. The top decile by market
capitalization accounts for 48 percent of the trades and 61 percent of the
dollar value traded. In contrast, the bottom 40 percent of the stocks by
market capitalization account for 3.7 percent of the trades and only
0.6 percent of the dollar value traded.
Previous studies on price impact focus on trades exceeding 10,000
shares. Our results indicate that many of the institutional trades are
actually quite small. From Panel A of Table 2, the average number of shares
per trade is only 8400 for buys and 9100 for sells, and the medians are 2400
and 2700 for buys and sells, respectively. Moreover, 25 percent of the
trades involve less than 1000 shares, and only about 20 percent of the trades
involve more than 10,000 shares. The small size of a typical trade is
surprising, given that our data come from large money managers who are
expected to be involved in larger trades. The small trade sizes relative to
typical holdings are consistent with the view that managers trade
strategically in order to reduce the influence of short run liquidity costs,
or information effects.
Previous studies find that the number of blocks traded on a downtick
substantially exceeds the number of blocks traded on an uptick. One
explanation suggested for this phenomenon is that it is easier to sell large
amounts than to buy large amounts. Therefore, we expect to find that sells
are larger than the corresponding purchases. This is indeed the case,
although the differences are quite small. For example, in the largest stocks,
the mean number of shares traded is 8200 and 8700 for buys and sells,
respectively.
Panel B (Table 2) presents the distribution of the dollar value of
trades. The median trade is less than $100,000 and only about 6 percent of
the trades exceed $1,000,000. As the company size increases, the trades also
get large. In Panel C, we report the distribution of trade size relative to
normal daily trading volume. The median is only 2 percent, indicating that a
typical institutional trade is not a major event. However, as the size of the
companies decreases, the typical institutional trade becomes a more
significant event. For example, the median for buys is 0.24 in group 1,
relative to 0.01 in group 4. The largest 1 percent of trades are many times
larger than the typical daily volume in small stocks, whereas in the largest
stocks such trades are typically less than 40 percent of the daily volume.
Many studies focus on trades which are larger than the typical trading volume.
Our results indicate that such trades are very uncommon, at least in the more
liquid stocks where most institutional holdings are concentrated.
2 . Empirical Results
2.1. The Price Impact of Institutional Purchases and Sales
Table 3 summarizes the price impact of institutional purchases
(panel (A)) and institutional sales (panel (B)), together with the percentage
commission cost. For each transaction, the percentage return is calculated
from the day's opening price to the trade, and from the trade to the closing
price; the percentage return from the opening to the closing is also
reported.1 These correspond, respectively, to the total, temporary and
permanent effects on the stock price on the trade date, as discussed in
Holthausen et al . (1987). Further, to determine whether a typical
institutional trade is fundamentally distinguishable from other trades, we
compare the transaction price in a stock to the volume-weighted average of all
transaction prices in the same stock on the trade date. In the subsequent
discussion, we focus on the principal-weighted average of each price impact
measure. This procedure follows the norm in the investment industry, and
permits evaluation of the overall dollar amount of the price impact.
Prices for institutional purchases are 0.22 percent higher than the
opening price on the trade date on a principal-weighted average basis. Such a
difference amounts to eight cents per share, less than one tick, on a stock
with a price of $36.50 (the volume-weighted average price over our sample
period) . The price increase from the open to the trade is consistent with all
three hypotheses outlined in section 1.1. In part, the rise also reflects the
average daily upward drift in prices, although this component is small — the
mean total percentage change from the open to the close on the Standard and
Poor's Composite Index over this period is 0.06 percent. A final
interpretation of the price movement from the open to the trade is that
8
institutional money managers may be responding passively to changes in the
stock price before initiating transactions.
Sharply at odds with the reversal predicted by the short-run liquidity
hypothesis, we find that there is a further principal-weighted average price
increase of 0.12 percent from the trade to the closing price. It is possible
that the price pressure after the trade is a result of follow-up trades in the
same stock. These additional trades might be initiated by the same manager as
part of a larger trading program, or by other managers, to the extent that
they engage in "herding" behavior.
For institutional purchases, the permanent principal-weighted price
change from the open to the close is 0.34 percent. The simple mean price
change is lower (0.26 percent), and is considerably less than previous
estimates of the price impact of block purchases. Kraus and Stoll (1972) and
Holthausen et al. (1990) find that the average permanent price change is
around one percent. There are several reasons why it is not surprising that
earlier papers document larger price effects. These studies focus only on
large block transactions. In addition, their reliance on the tick test to
infer trade direction results in the exclusion of blocks associated with zero
price ticks. Finally, it is also quite probable that the remaining
transactions (those associated with an up or down tick) represent trades
initiated by relatively less patient investors (i.e., those willing to pay a
larger price concession in exchange for greater immediacy). Accordingly, the
average price impact is likely to be larger in the case of purchases or sales
selected on the basis of a non-zero tick, compared to purchases or sales in
general (whether initiated by the investor or not). Another possible reason
why we find lower price impact is that past studies of block trading use data
from earlier periods (no later than 1983). Dramatic changes have since
occurred in equity markets with respect to trading volume and technology,
commission rates, and the growth of hedging instruments.
Table 3 also reports the median and other percentiles for each measure
of price impact. Relative to the open or the close, the median impact for
buys is zero while the median permanent change for buys is also zero.
Evidently, the typical institutional purchase has little or no impact on
prices. However, the percentiles of the distribution of returns indicate that
there is substantial dispersion across trades with respect to their price
impact .
Another perspective on the price impact of institutional orders is
obtained by comparing the trade price to an average of transaction prices from
the same day. Berkowitz, Logue and Noser (1988) interpret the price impact
relative to the volume-weighted average price as a measure of execution cost.
Using this benchmark, the dollar-weighted average impact is very small, at
0.02 percent. Similar values are obtained if the calculation of the volume-
weighted price excludes the trade under consideration, or if the simple
average price is used as the benchmark. Indeed, the simple average impact is
slightly negative, which would imply, under the interpretation of Berkowitz,
Logue and Noser (1988), a negative execution cost on average to buying!
Turning to institutional sales (panel (B) of Table 3), there is a
principal-weighted average drop in prices of 0.14 percent from the open to the
trade. Many of the same factors as in the case for buys can account for this
change. In marked contrast to the behavior of prices after buys, however, the
initial price decline is almost fully reversed. As a result, there is only a
small permanent change of -0.04 percent. The post-trade behavior of prices in
the case of sells is thus more supportive of effects due to short-term
liquidity costs, rather than imperfect substitution or information.
The results in panel (B) are reminiscent of the findings in Kraus and
Stoll (1972) and Holthausen et al. (1990). However, we find much smaller
price impacts than reported in these earlier studies. Overall, the evidence
suggests that institutional sales are associated with some downward price
pressure, although the market impact is generally small and temporary.
It might be argued that the differences between the findings in Table 3
and the findings of earlier research are due to differences in commission
rates. If the specialist or block trader on the other side of the trade is
compensated by a commission as well as a price concession, then a lower
concession might be exchanged for a higher commission. Similarly, differences
between the commission rates for purchases and sales might account for the
differential price impact. In Table 3, however, the principal-weighted
10
commission rate is the same for buys and sells, at 0.17 percent of trade value
(six cents per share on a stock with the average price of $36.50). Moreover,
the simple average commission rate, 0.23 percent, is much smaller than the
mean commission rate of 1.01 percent for the largest stocks over the period
1960 to 1979, reported by Stoll and Whaley (1983).
2.2. The Asymmetric Response of Prices to Purchases and Sales
A key puzzle emerges from Table 3: there is a marked asymmetry between
the effect of institutional buying and selling activity on stock prices.2
Purchases of a stock are accompanied by an increase in its price, which
continues to rise after the trade; sales of a stock are accompanied by a drop
in its price, but there is subsequently an almost complete recovery in the
price.
Several factors, not mutually exclusive, might account for the
differences between the effects of buying and selling activity. "Street
wisdom" suggests that brokers are willing to accommodate customers' sales by
purchasing shares and holding them in inventory in exchange for a short-term
price concession. On the other hand, brokers are more reluctant to
accommodate customers' purchases by undertaking short positions. Since an
intermediary is less likely to be involved on the other side of an
institutional purchase, it is less likely that the transaction price in the
case of a buy incorporates a fee to the intermediary in the form of a
temporary price concession.
Information effects might also be stronger for purchases than for sales.
Since an institutional investor typically does not hold the market portfolio,
the choice of a particular issue to sell, out of the limited alternatives in a
portfolio, does not necessarily convey negative information. Rather, the
stocks which are sold may already have met the portfolio's objectives, or
there may be other mechanical rules, unrelated to expectations about future
performance, for reducing a position. As a result, there are many liquidity-
motivated reasons to dispose of a stock. In contrast, the choice of one
specific issue to buy, out of the numerous possibilities on the market, is
likely to convey favorable firm-specific news.'* The information content of
11
purchases might be diluted insofar as the portfolio receives net cash inflows.
However, Table 1 suggests that purchases and sales by our sample of money
managers are roughly equal. Moreover, net cash inflows to the typical money
manager are a very small percentage relative to the manager's turnover.
The larger, positive impact of institutional purchases could also arise
if institutions are positive feedback traders for buys but not for sells,
i.e., they intensify their buying behavior on days when the market rises.
This explanation, however, is not compatible with the data. For every day in
the sample period, we measure the rate of return from the open to the close on
the S&P 500 index. Moreover, for every day, we know the dollar value of
buying and selling activity by our sample of money managers. We then
calculate the dollar-weighted average return for buys and sells separately.
This produces a principal-weighted average return on the index of 0.05 percent
for buys, and 0.08 percent for sells. If anything, this finding suggests that
money managers might stabilize markets through negative feedback strategies.
In summary, the price impact of sales is not merely the reverse of the
impact of purchases. While the behavior of the stock price after buys
reflects new information or inelastic excess demand curves, the price behavior
after sells is more indicative of a liquidity-related reversal. In any case,
the average and median price effects are not large, and execution prices for
institutional trades do not differ very much from average prices over the
course of the day.
2.3. Firm Size, Trade Difficulty and Price Impact
Prior theoretical and empirical research suggests that the price impact
of a trade is affected by firm size (Loeb (1983), Stoll and Whaley (1983),
Keim and Madhavan (1991)), and by the size of the transaction (Easley and
O'Hara (1987), Glosten (1989)). Table 4 examines the behavior of the price
impact of trades as both firm size and trade complexity (trade size relative
to normal daily volume) vary. Within each of the four categories of firm size
(described in Table 1), trades are divided into four groups by trade
complexity, using the quart iles of the distribution of trade complexity (as
reported in Table 2, panel c) . In addition, the bottom panel of the table
12
aggregates across complexity groups within each size group, and the last
column in the table aggregates across size groups. The table reports the
principal-weighted averages.
In the bottom panel of Table 4, the return from the open for buys rises
monotonically as firm size declines, except for the smallest firms. ■ The
price continuation is also stronger after purchases of smaller firms. Taken
together, the average price change from open to close for institutional
purchases is positive and tends to be higher for smaller firms, ranging from
0.29 percent for the largest firms to 0.49 percent for the smallest. For sell
orders, the drop from the opening price to the execution price is also
stronger for smaller firms. However, the subsequent recovery is also stronger
for smaller firms. As a result, there is no clear pattern across the four
size groups with respect to the permanent price change — the price remains
roughly unchanged or declines slightly from the open to the close for sells.
The larger permanent price change associated with purchases of smaller
firms could be due to several reasons. Even a minor institutional stake in a
small stock might involve several successive trades, so that the market impact
of a purchase might be spread out over several days before a reversal occurs.
Further, the market might interpret institutional purchases of smaller stocks
as more reliable indicators of favorable private information. Unless an
investment manager specializes in lower-capitalization stocks, the decision to
purchase a small stock is generally risky for the manager. If the stock's
performance is disappointing, the manager may be asked to account for his
decision to depart from the norm and invest in small stocks (Lakonishok,
Shleifer, Thaler and Vishny (1991)). Hence, a manager must have strong
favorable beliefs about a small stock to justify its purchase. Sales by
institutional money managers, on the other hand, need not convey much new
information to the market, even for the smallest stocks. Such sales might
represent "window dressing, " attempts by managers to avoid potentially
embarrassing questions from their clients by removing poorly performing small
stocks from their portfolios. Investment policies regarding minimum levels of
market capitalization, dividend yield, or the number of analysts following a
13
stock may prompt a manager to sell stocks even in the absence of unfavorable
information.
When transactions are divided into four categories by complexity (the
last column of Table 4), the results are generally similar to those obtained
for trades ordered by firm size. In particular, the principal-weighted
average permanent price change for purchases increases monotonically with
trade complexity, rising from 0.17 percent for the easiest trades to 0.39
percent for the hardest trades. The permanent price change for sales is
generally small, even in the category of the hardest trades.
The two polar cases in the body of Table 4 provide further detail on the
association between price impact, firm size and trade complexity. In the case
of the easiest trades in the largest firms, the price changes are small: the
permanent impact for purchases (sales) is 0.11 percent (0.05 percent). At the
other end of the scale, the permanent price change for the hardest purchases
of the smallest stocks is 0.72 percent, comprising a return of 0.23 percent
from the open and a price continuation of 0.49 percent after the trade. Sell
transactions in this category are associated with a drop of 0.57 percent from
the opening price, but there is a subsequent reversal of 0.71 percent to the
close. Nonetheless, the price changes associated with even the hardest trades
in the smallest stocks are not particularly large, compared to other
researchers' estimates of the costs of trading small stocks in general. In
particular, since the average stock price of trades in this group is only
about $10, even a change of 0.72 percent is substantially less than one tick.
If the volume-weighted price is used as the benchmark, the price impact
provides little basis for discriminating between trades with different
characteristics: the average impact of the easiest purchases in the largest
stocks is -0.02 percent, while the average impact of the most difficult
purchases of the smallest stocks is, surprisingly, even more favorable at
-0.08 percent. For the smallest firms, however, the size of the price impact
of both buys and sells is sensitive to whether the trade is included in, or
excluded from, the volume-weighted average. In the category of the most
difficult trades in the smallest stocks, for example, excluding the trade from
14
the calculation of the volume-weighted average price yields a price impact of
0.01 percent for buys and -0.53 percent for sells.
The results in Table 4 confirm the asymmetry between buys and sells
across every category of firm size and trade complexity. The positive
permanent impact of buys is consistent with information effects or downward
sloping demand curves due to imperfect substitution. In contrast, sell
transactions are associated with only minor permanent price changes. Any
initial downward pressure on prices is generally reversed by the end of the
trading day, suggesting the existence of short-term liquidity costs.
2.4. Differences in Price Impact Across Money Managers
The market impact of a transaction can vary with the style of the money
manager and the performance of the trading desk responsible for the trade. A
central determinant of execution performance is the portfolio manager's
instructions to the trading desk as to how an order is to be filled. For
example, a value-oriented manager with low turnover will typically give much
latitude to the trading desk, since urgency is not considered critical. On
the other hand, a manager pursuing a short-term technical trading strategy
will insist on speedy execution, thereby constraining the trading desk. Given
the constraints imposed by the money manager, the trading desk still has
considerable flexibility as to how a trade is carried out (Wagner (1989)).
Its choices include: whether or not to employ a broker who is willing to
commit capital to facilitate trades (a capital broker); how many brokers to
employ; how much of an order to expose to each broker; the time frame within
which the trade is to be executed; as well as the leeway given to the broker
as to how to complete the trade (a market order, limit order or market-not-
held order, for example) or how much information about an order is displayed
to the public (as in a "sunshine trade"). In such a complicated process,
different managers with varying styles and levels of expertise are likely to
turn in different levels of execution performance.
An extended characterization of the various styles and trading
strategies adopted by different money managers, together with their resulting
impact on stock prices, is beyond the scope of this paper (see Lakonishok,
15
Shleifer and Vishny (1991, 1992)). Here we adopt the less ambitious tack of
only documenting the existence of dispersion across money management firms
with respect to the price impact of their trades. In Table 5, summary
statistics are presented for the distribution across management firms of three
of our measures of price impact. For each of the 37 money management firms,
the different returns are calculated and then averaged (using trade principal
as weights) across all the firm's trades. The summary statistics in Table 5
are based on these 37 observations for each price impact measure.
Considerable variation exists across managers for both buys and sells
under each measure of price impact. The variation cannot be attributed simply
to noise — the average price impact of each manager is based on tens of
thousands of trades, so that the precision of each estimate is high. For
example, the execution performance for buys relative to the opening price
varies from -0.46 percent in the tenth percentile to 0.54 percent in the
ninetieth percentile, yielding a difference of a full percentage point per
transaction. The corresponding difference for sells is very similar, at
0.98 percent per transaction. Insofar as the opening price is known if and
when a manager chooses to trade, the differences across managers in their
execution performance relative to the open might reflect several sources:
their differential skill in seeking out liquidity; ability in trading before
the release of information; as well as differences in their responses to price
movements subsequent to the opening. The dispersion across managers, in terms
of the post-trade return till the close, is also notable but substantially
lower. For buys (sells), the tenth percentile is -0.01 percent (0.01 percent)
and the ninetieth percentile is 0.25 percent (0.26 percent), giving rise to a
difference of 0.26 percent (0.27 percent) per transaction. Given that the
manager has already traded, and given that a trading strategy cannot be based
on the as yet unknown closing price on the trade date, the dispersion in
managers' post-trade returns should be expected to be smaller than the
dispersion in their pre-trade execution performance.
Our confidence that the differences across managers can be ascribed to
differences in styles and trading strategy, rather than noise, would be
heightened if a manager who obtains favorable execution for buys also fares
16
well for sells. This is indeed the case: the rank correlation across managers
between performance for buys and sells relative to the opening price is -0.84,
-0.10 for performance relative to the closing price and -0.74 for the
permanent price change. In other words, a manager who buys low relative to
the opening price (or relative to the closing price) also tends to sell high
relative to the opening price (or relative to the closing price).
As another step in tracing the sources of the cross-sectional
differences in price impact, we also obtained data from SEI on a subset of
sixteen of the management firms in our sample. In particular, data are
available on each of these managers' average turnover rate, and investment
style (each manager is classified as pursuing either a value-oriented or
growth-oriented style). Other things equal, a portfolio manager with low
turnover would tend to be a more patient investor and would thus tend to have
low price impact. In addition, an investor for whom timing is more critical
(such as a growth-oriented manager) would be expected to have a larger impact.
Based on the data for sixteen managers, a cross-sectional regression confirms
that the principal-weighted average price impact relative to the open for buys
increases with the turnover rate and is higher for a growth-oriented manager:
the estimated intercept is -0.32, while the coefficient for turnover rate is
0.37 and the coefficient for the dummy variable representing the manager's
style (zero for a value-oriented style and one for a growth-oriented style) is
0.31. The principal-weighted average price drop from the open for sells also
tends to be larger for a manager with high turnover and with a growth-oriented
style: the estimated intercept is 0.35, and the coefficients for turnover and
style are -0.26 and -0.27, respectively.6 Similar results are obtained if
the principal-weighted return from the open to the close is used as the
dependent variable. While the results from these regressions are only
suggestive (given the small number of managers), they are consistent with the
notion that the degree of urgency to trade, as reflected in different
investment style or trading strategies, is associated with the level of price
impact .
17
2.5 Regression Results
Following the lead of prior research, the previous sections confirm the
influence of firm size and trade difficulty on the price impact of a trade.
The unique features of our dataset enable us to suggest another potential
influence, namely the identity of the manager behind each trade. It is thus
natural to ask whether, after controlling for firm size and trade difficulty,
the manager's identity is an important determinant of a trade's price impact.
There may also be a trade-off between the commission cost and the market
impact of the trade. These various influences are accommodated in the
following regression model:
3 4 36
a + Pci + E 8Jsij + E YjDij + E <PiMii + ei
~1 j-1 J-l
For each trade i, rj is one of the three measures of price impact that we
focus on: the percentage return from the open to the trade, from the trade to
the close, and from the open to the close. The commission cost for the ith
trade is denoted by c-, and following the common practice in the investment
industry, is measured in cents per share (Marshall, 1988). It is likely that
the manager's trading desk perceives the trade-off (if any) in terms of the
dollar commission cost, rather than in terms of the commission rate. In the
U.S., unlike other countries, the commission cost for institutional investors
is on a cents per share basis, irrespective of the stock price level, rather
than in terms of the total value of the trade. Thus, for the same trade, a
broker charging four cents per share will be cheaper than a broker charging
eight cents per share. However, the cheaper broker, if assigned trades in
lower-priced stocks, will appear to have a high percentage commission rate.
In evaluating the relation between commission cost and price impact across
trades with different prices, therefore, it is necessary to express the
commission cost on a dollar basis rather than on a percentage basis.
Expressing the commission cost relative to the trade price would also confound
the effect of commissions with the effect of market capitalization (since
smaller stocks tend to have lower prices). The effects of market
18
capitalization, trade difficulty and managerial strategy are captured by the
dummy variables, S--, D-. and M- ■ , respectively. For example, M- ■ takes the
value of one if the ith trade is executed by the jth manager and is zero
otherwise. To permit identification, the coefficients for the dummy variables
for managers are normalized relative to the first manager in the data set.
Similarly, the coefficients for the trade difficulty variables are expressed
relative to the impact of trades in the first category (the easiest trades),
while the coefficients for firm size are expressed relative to the impact of
trades in the largest firms.
Separate regressions are fit for buy transactions and sell transactions.
In addition, the marginal explanatory power of each set of dummy variables is
assessed by excluding each set, one at a time, from the full model (1).
Panel A of Table 6 reports the adjusted R2 for each specification of the
regression model. Most of the explanatory power of the model comes from the
identity of the money manager behind the trade. In contrast, excluding the
dummy variables for firm size and trade complexity has little or no effect on
the R. In light of the importance of the manager dummies, it is perhaps not
surprising that the model provides the best fit in the equation for the return
from the open to the trade. This measure of price impact, to a larger extent
than the others, reflects the effects of managerial trading strategy.
In panel B, the coefficients of the full model are reported for each of
the three measures of price impact. Given the very large sample size, nearly
all of the estimated coefficients are large relative to their standard errors.
Therefore, the focus of the discussion will be on the economic significance of
the coefficients.
One presumption is that favorable execution (lower price impact) is
purchased from a broker in exchange for a higher commission fee. However, the
coefficient for the commission cost variable for both buys and for sells (in
parentheses) is very small. The most favorable evidence on substitution
between the price impact of a trade and its commission cost emerges in the
equation for the price impact of sells relative to the closing price. Even in
this case, however, an increase in the commission of one cent per share (in
itself a large jump in commissions) lowers the post-trade price reversal by
19
0.007 percent, yielding a dollar savings of only 0.3 cents per share on a
stock with the average price of $36.50. We also estimated the regression with
the commission cost measured relative to the trade price — as in the results
reported in Table 5, no relation can be detected between price impact and
commission rates. As Beebower (1989) points out, however, the commission
includes payment for research services and other plan expenses. The presence
of such services, not related to trade execution, would blur any association
between price impact and the total commission cost. In addition, some brokers
may be willing to commit their own capital to accommodate managers' trades,
while others may simply process transactions.
With respect to the influence of firm size and complexity, the results
in panel B confirm the findings of the previous sections. What is
particularly noteworthy, however, is that the coefficients of the dummy
variables for money managers still display considerable dispersion — for
example, the spread between the tenth and ninetieth percentiles is 0.72 (0.85)
when returns are measured from the open to the trade. While somewhat
attenuated relative to the findings of Table 5, these spreads are still
considerable.
3. The Execution Cost of Institutional Trades
The temporary and total price impact of institutional trades, and the
impact relative to various intra-day averages, reported in the previous
section, can also be interpreted as average execution costs for purchases and
sales. In particular, the difference between the price at which an order is
executed and the underlying true value of the stock amounts to a price
concession which is a cost of trading, in addition to brokerage commissions.
While considerable resources are expended within the investment community on
monitoring and controlling such trading costs, there is little consensus as to
the magnitude of execution costs. In practice, part of the disagreement stems
from the different choices of a benchmark price; the closing price of the
stock on the trade date, the opening price and the volume-weighted average
price are all used. In Table 3, average round-trip costs include commissions
(which are 0.34 percent of trade value), and market impact costs: these range
20
from 0.09 percent relative to the volume-weighted price to 0.36 percent
relative to the opening price. If the closing price is used as the benchmark,
the cost of sells is roughly offset, on average, by a benefit for buys, since
there is a post-purchase average price continuation. Further, if the
estimates of trading cost are disaggregated by market capitalization and trade
complexity, the average market impact costs are smaller than the corresponding
figures in Loeb (1983) or Stoll and Whaley (1983). In addition, the costs
relative to the open tend to move with market capitalization and trade
complexity in the expected direction. Assuming that the decision to trade is
made before the open, and thus using the opening price as the benchmark, the
round-trip cost, including commissions, for the hardest trades in the smallest
stocks is 1.90 percent (from Table 4); the corresponding cost for the easiest
trades in the largest stocks is 0.29 percent. Costs relative to the volume-
weighted price, however, display very little variation across trades in large
and small stocks, or across difficult and easy trades.
The various measures of execution cost are not without shortcomings.
The opening price may not be a relevant benchmark price if the order is not
submitted to the trader before trading begins. To one degree or another, each
cost measure can be gamed by traders who are being evaluated. A trader can
postpone trading until close to the end of the trading day and then choose to
execute only those transactions whose prices are better than the open or the
intra-day average price; the remaining orders are deferred. Similarly, a
trader who carries out a large transaction will have a major influence on the
volume-weighted price, distorting the cost calculation. None of these cost
measures addresses the issue of opportunity cost (including the cost of
unexecuted orders), or the potential adverse selection problem (the
possibility that the trader may be "bagged" by buying cheaply a stock that
subsequently experiences negative performance) . It would thus seem advisable,
in evaluating execution performance, to consider a broad range of cost
measures, rather than a single number.
21
4 . Summary and Conclusion
Analysis of the price impact of institutional trades sheds light on the
elasticity of the excess demand curve for stocks, and on the magnitude of the
cost of executing transactions. Previous studies on the price impact of
trades, however, have focussed on the effects of block trades and in some
cases, have considered only the largest blocks. In these studies, moreover,
the change in the transaction price itself is used to infer whether a trade is
initiated by the buyer or by the seller. In contrast, our sample covers a
more recent period and contains more than one million trades, both large and
small, by 37 large institutional money managers. Each trade is explicitly
identified as a purchase or sale by the money manager, who is also identified.
The distinctive features of our data set enable us to generalize and
extend previous studies on the price impact of block trades. Overall, the
evidence suggests that institutional purchases and sales of a stock are
associated with some pressure on prices. Relative to the opening price on the
trade date, for example, buy transactions are associated with a principal-
weighted average price increase of 0.22 percent while sell transactions are
associated with a principal-weighted average price decline of 0.14 percent.
The behavior of prices from the open to the trade can be attributable to
short-run liquidity costs, prior release of information or positive feedback
trading behavior by managers.
The post-trade behavior of prices is more perplexing, and displays a
sharp difference between buys and sells. Specifically, the price continues to
rise after purchases — the principal-weighted average return from the trade to
the closing price is 0.12 percent — while the price tends to correct itself
after sales — the reversal is 0.10 percent. The post-trade reversal for sells
is consistent with the existence of short-run liquidity costs, while the post-
purchase behavior of prices is consistent with information effects, or
imperfectly elastic demand curves.
We find that institutional purchases are associated with a principal-
weighted permanent price change from the open to the close on the trade date
of 0.34 percent, while there is only a very small permanent impact
(-0.04 percent) from institutional sales. The asymmetry is also noted in
22
Kraus and Stoll (1972) and Holthausen et al. (1987). The difference between
the price impact of buys and sells cannot be attributed to managers
concentrating their buying (selling) behavior on days when the market goes up
(down) . Rather, an analysis of the open-to-close price change on the Standard
& Poor's Index provides some evidence that money managers might trade in a
contrarian fashion.
Several conjectures are offered to account for the asymmetry between the
price impact of buys versus sells. Institutional sales are more likely to
involve an intermediary broker, compared to purchases. Hence the price impact
of sells is more likely to reflect a temporary discount as compensation for
the intermediary. In contrast, institutional purchases might be a stronger
signal of favorable information, whereas there are many liquidity-motivated
reasons to dispose of a stock. Further research, however, is called for to
account for the differences between the effects of buys and sells.
Considerable attention in previous research has focused on the effects
of market capitalization and relative trade size as determinants of the market
impact of a trade. We find that the market impact of a trade is indeed
related to these influences, although its magnitude is much smaller than in
previous work on large block trades. For example, the principal-weighted
average return from the open to the trade for the hardest trades in the
smallest stocks is only 0.23 percent for buys and -0.57 percent for sells. In
a multiple regression, the importance of market capitalization and trade
difficulty pales in comparison to the influence of the money manager who is
behind the trade. Considerable differences exist across managers with respect
to the price impact of their trades. A preliminary analysis suggests that
these differences are related to investment styles and trading strategies.
The results on the price impact of institutional trades provide some
insight on the much debated topic of the cost of executing trades. Our
highest estimates of round-trip costs are obtained if the opening price is
used as the benchmark. Even in this case, however, the round-trip market
impact cost is only 0.36 percent, which is definitely on the low side of
previous estimates. To put this cost estimate in perspective, suppose that
each purchase or sale results in giving up only one tick, so that round-trip
23
costs equal twenty-five cents. For a typical stock (price $36.50) the round-
trip market impact cost should be in this case 0.68 percent; almost double our
estimate. Keim (1989) finds that the relative bid-ask spread for the top
decile of NYSE stocks is 0.58 percent on average. Given the competitiveness
of the investment industry and the substantial resources expended on trading
facilities, it should not come as a total surprise that money managers are
loath to give up as much as an eighth every time they execute a trade.
H-LC.7-21
24
Footnotes
Since some of the trades occur at the open or at the close, we may be
biased towards finding no price impact relative to these two benchmarks. In
general, however, trading at the open or close represents a small fraction of
daily volume. For a sample of large NYSE-listed firms, for example, Forster
and George (1991) find that volume at the open is on average about 6% of daily
volume, while volume at the close is on average 3% of daily volume.
2Wood, Mclnish and Ord (1985), Harris (1989) document that returns on the
closing transaction are on average positive and relatively large; Harris
(1989) also finds an increase in both closing bid and ask prices, as well as
an increase in the frequency of ask prices at the close. The day-end pattern
in transaction prices may thus account for part of the post-trade price
change. However, there is still evidence of a price continuation subsequent
to buys and a reversal subsequent to sells when the next-to-closing price is
used as the benchmark: the principal-weighted average is 0.09 percent for
buys and 0.07 percent for sells.
It is also possible that the pool of counterparties facing a buyer is
more concentrated than the pool of possible counterparties facing a seller.
Sellers can thus exploit the potential competition among a larger group of
counterparties to obtain a smaller price concession, while buyers have a more
limited set of parties on the other side (namely, existing shareholders). It
may also be the case that existing holders of a stock tend to be more
optimistic about its future prospects, relative to other investors. Shleifer
and Summers (1990) argue that limitations on arbitrage can lead to differences
between the price of a stock and its true value. The buyer of a stock must
thus offer a higher premium to induce current holders to part with their
shares.
Another behavioral interpretation, suggested by money managers, is that
most managers target for purchases stocks that they believe are undervalued.
A slight increase in the price of such a stock might engender fears that the
stock will "run away" from those managers interested in the stock. Hence the
price increase might not deter managers from buying, perhaps contributing
further price pressure. On the other hand such managers display more patience
in selling; if the stock price falls, they are likely to defer selling,
feeling that the price will ultimately rebound to its higher value.
5Trading strategies in the smallest stocks are likely to differ from
trading strategies in larger stocks. Specifically, institutions that
predominately trade in low capitalization stocks may choose to buy only if a
favorable, inexpensive opportunity presents itself. Sellers of small stocks,
on the other hand, are more likely to come from a larger, more diffuse group
of institutions who do not specialize in small stocks. These managers may be
selling stocks whose market values have declined in past periods.
6The t-statistics for the estimated coefficients are as follows. In the
equation for buys, the t-statistic is -1.05 for the intercept; 0.80 for the
coefficient for turnover rate and 1.06 for the coefficient for the manager's
style. In the equation for sells, the intercept has a t-statistic of 1.62,
while the t-statistics for turnover and style are -0.81 and -1.33,
respectively. Note, however, that these t-statistics are based on a very
small sample.
25
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Table 3
Mean, standard deviation and fractiles of distribution of
price impact and commission cost for institutional purchases
(Panel A) and institutional sales (Panel B)
Sample comprises all trades of NYSE and AMEX stocks made by 37 institutional
money management firms from July 1, 1986 to December 30, 1988 (excluding
October 1987). Price impact is measured as the return (in percent): from the
opening price on the trade date to the trade; from the trade to the closing
price on the trade date; from the opening to the closing price on the trade
date; and from the volume-weighted average of all transaction prices in the
stock on the trade date to the trade.
Return (in percent) from:
Opening
Price
to trade
Trade to Opening
Closing to
Price Closing
Same
Day
Volume-
Weighted
Price
to trade
Commission
Cost, %
Panel A: Purchases
Principal-weighted average 0.22
Mean
Standard deviation
Proportion > 0
Median
10-percent ile
25-percentile
75-percentile
9 0-percent ile
Principal-weighted average -0.14
Mean
Standard deviation
Proportion < 0
Median
10-percent ile
25-percentile
75-percentile
90-percentile
0.22
0.12
0.34
0.02
0.17
0.10
0.16
0.26
-0.01
0.23
1.46
1.39
2.02
0.81
0.25
0.44
0.38
0.48
0.49
0.99
0.00
0.00
0.00
0.00
0.17
-1.33
-1.20
-1.85
-0.78
0.07
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-0.44
-0.78
-0.31
0.11
0.68
0.71
1.22
0.30
0.26
1.61
1.61
2.60
0.75
0.43
Panel
B: Sales
-0.14
0.10
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-0.07
0.17
-0.06
0.08
0.02
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0.23
1.52
1.44
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0.86
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0.46
0.46
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0.17
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-2.10
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-0.38
0.11
0.50
0.67
1.00
0.28
0.26
1.42
1.55
2.30
0.75
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Table 5
Mean, standard deviation and fractiles of distribution
across managers of measures of price impact, for
buys and sells (in parentheses)
Price impact is the return (in percent): from the opening price to the trade,
from the trade to the closing price, and from the opening to closing. Data
are all trades of NYSE and AMEX stocks made by 37 institutional money
management firms from July 1, 1986 to December 30, 1988 (excluding October
1987). For each money manager, the weighted average price impact (using the
dollar value of trades as weights) is calculated for all the manager's trades;
summary statistics for each measure of price impact are based on this sample
of 37 observations.
Return (in percent) from;
Principal-weighted average
Mean
Standard deviation
Median
10-percentile
25-percentile
7 5 -percentile
90-percent ile
Range between
10 and 90 percentiles
Opening
Trade to
Opening
price
closing
to
to trade
P*
ice
closinq
0.22
:-o.i4)
0.12
[ 0.10)
0.34
(-0.04)
0.13
-0.04)
0.12
! 0.12)
0.24
0.08)
0.45
0.37)
0.13
' 0.09)
0.42
I 0.42)
0.20
-0.09)
0.13
0.11)
0.32
0.04)
-0.46
-0.46)
-0.01
0.01)
-0.39
-0.36)
0.01
-0.31)
0.04
0.05)
0.04
-0.22)
0.37
0.14)
0.17
0.15)
0.53
0.27)
0.54
0.52)
0.25
0.26)
0.75
0.78)
1.00 ( 0.98)
0.26 ( 0.27) 1.14 ( 1.14)
Regression estimates of the model,
36
j7! j-l j-l
where r- is the return (in %) from: the open to the trade, from the trade to the close,
^nd from the open to the close. Cj is the dollar commission cost; Sj - is a dummy variable
for the trade's classification by market capitalization; D- ■ is a dummy variable for the
trade's classification by complexity; M- ■ is a dummy variable for the money manager. The
equation is estimated separately for buys and for sells. The sample comprises all trades
of NYSE and AMEX stocks made by 37 institutional money management firms from July 1, 1986
to December 30, 1988 (excluding October 1987). The 4 classifications by market
capitalization are: firms in the bottom 40% when ranked by market capitalization of NYSE
and AMEX stocks; firms ranked between 40% and 80%; firms ranked in the ninth decile; firms
ranked in the top decile. The 5 classifications by trade complexity are: trades
accounting for less than 10% of normal volume; trades between 10% and 2 5%; trades between
25% and 40%; trades between 40% and 80%; and trades accounting for above 80% of normal
volume.
A. Adjusted R (in percent) for full model, and models with each set of
dummy variables excluded one set at a time. Results from the
equation for sells are in parentheses.
Return (in %) from:
Opening price Trade to Opening to
to trade Closing price closing
Full model 3.45
Excluding manager effects 0.43
Excluding size effects 3.45
Excluding complexity effects 3.33
( 3.36) 0.70 ( 0.53)
( 0.26) 0.35 ( 0.17)
( 3.31) 0.48 ( 0.51)
( 3.34) 0.70 ( 0.42)
1.74 ( 1.39)
0.36 ( 0.10)
1.61 ( 1.34)
1.70 ( 1.38)
B. Estimated coefficients for full model for buys and for sells (in
parentheses)
Return (in %) from:
Explanatory variable
Intercept
Commission
Size 1 (smallest)
2
3 (large)
Complexity 2 (easy)
3
4
5 (hardest)
Manager
10-percent ile
25-percentile
Median
7 5 -percent ile
90-percentile
Range between
10 and 90 percentiles
Opening price Trade to Opening to
to trade Closing price closing
17
00
01
02
00
0.08
0.15
0.20
0.22
-0.52
■0.25
-0.12
03
20
-0.32) 0.00
-0.00) -0.00
-0.21) 0.30
-0.04) 0.16
-0.00) 0.07
-0.03) -0.02
-0.07) -0.06
-0.09) -0.05
-0.11) -0.00
-0.15)
-0.04)
0.15)
0.44)
0.70)
0.00
0.07
0.12
0.22
0.26
0.15
-0.01
-0.07
-0.04
0.01
0.05
0.12
0.13
0.29
-0.34
-0.26
-0.18
-0.09
0.00
0.18
(-0.18)
0.00
(-0.01)
0.30
(-0.28)
0.18
i-0-01)
0.07
' 0.01)
0.06
r 0.02)
0.10
0.05)
0.15
0.04)
0.22 <
0.17)
0.41 |
-0.33)
0.14 |
-0.19)
0.01 |
0.03)
0.20 |
0.22)
0.28 (
0.54)
0.72 ( 0.85) 0.26 ( 0.34) 0.69 ( 0.87)
")
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