Do Hedge Funds Supply or Demand Immediacy?
Petri Jylhä, Kalle Rinne and Matti Suominen*
April, 2012
Abstract
Regressing hedge funds’ returns on a measure of the returns from providing immediacy, we find
that hedge funds typically supply immediacy in the stock market. In the cross-section, the funds
with lengthy lockups and large funds have a higher propensity to supply immediacy compared to
other funds. Although the hedge funds typically supply immediacy, we find that the most extreme
cross-sectional return reversals are associated with stocks where hedge funds (at that point in time)
demand immediacy. Given that hedge funds typically supply immediacy, we study how the capital
flows into the hedge-fund industry affect the stock market. We show that increases in the amount of
speculative capital improve market liquidity, reduce the amount of short-term return reversal and
volatility. Finally, increases in the amount of speculative capital reduce the liquidity premium in
stock returns.
Key words: Hedge Funds, Speculative Capital, Liquidity, Immediacy, Volatility
JEL Classifications: G12, G23
_________________________________________________________________________________
* All authors are from the Aalto University (former Helsinki School of Economics). Contact: Matti Suominen. Address:
P.O. Box 21230, Aalto 00076, Finland, e-mail matti.suominen@aalto.fi; tel.: +358-50-5245678; fax: +358-9-43138678.
We thank Thierry Foucault, Juha Joenväärä, Si Li, Raghu Rau, Dale Rosenthal and the participants at Aalto University,
Bank of Finland, 2011 European Financial Management Alternative Investments Symposium in Toronto, 2011 London
School of Economics Alternative Investments Research Conference, Luxembourg School of Finance, and University of
Cambridge for their comments.
Electronic copy available at: http://ssrn.com/abstract=1629773
Introduction
It is well established that there are significant stock return reversals at one-week and one-month
horizons (see e.g. Jegadeesh, 1990, and Lehmann, 1990). Finance literature, see e.g. Jegadeesh and
Titman (1995), links the short-term return reversals with imperfect liquidity in financial markets. In
illiquid markets, return reversals emerge from transitory investors’ portfolio imbalances due to
imperfect risk bearing ability of market makers (Grossman and Miller, 1988), In such markets, the
market makers act as contrarian traders and make returns from supplying immediacy to other
investors (Hendershott and Seasholes, 2007).
In this paper, we study hedge funds’ role in the supply and demand of immediacy. Hedge funds can
act as contrarian traders and, along with the market makers, participate in the supply of immediacy
in the stock market (see Scholes, 2004, for discussion on hedge funds’ role in the supply of
immediacy). Alternatively, it can be that hedge funds typically demand immediacy in the stock
market as many of their equity market strategies, such as momentum, require frequent trading.
Our proxy for the returns to hedge funds from providing immediacy in the stock market is the
returns to a contrarian zero-investment long-short trading strategy that buys stocks with positive
expected weekly excess return, evaluated using past estimates of short-term return reversal, and
sells short stocks with negative expected excess return. Our approach to estimating the returns from
providing immediacy is closely related to that in Khandani and Lo (2011a), Nagel (2011), and
Rinne and Suominen (2011). In order to investigate whether hedge funds typically supply or
demand immediacy, we regress hedge fund returns on the returns from providing immediacy and
controls. If the regression coefficient for the returns from supplying immediacy is significantly
positive (negative), we conclude that the fund typically supplies (demands) immediacy.
2
Electronic copy available at: http://ssrn.com/abstract=1629773
Our main finding is that hedge funds typically supply immediacy in the stock market. In fact as
many as 18% of all hedge funds have a statistically significant positive exposure to our measure of
the returns from providing immediacy. We find that in the cross-section the funds with lengthy
lockups and large funds have a higher propensity to supply immediacy compared to other funds.
There are also time-varying factors that affect the hedge funds’ propensity to supply immediacy:
According to our results, hedge funds reduce their supply of immediacy when market liquidity is
high and, consistent with Nagel (2011), when credit market is tightening. Although the hedge funds
typically supply immediacy in the stock market, and perhaps exactly because of that, we find
evidence that the most extreme cross-sectional return reversals are associated with stocks where
hedge funds (at that point in time) demand immediacy.
Given the evidence that hedge funds typically supply immediacy in the stock market, we study how
the capital flows into the hedge fund industry affect the stock market. Consistent with Brunnermeier
and Pedersen (2009) and Gromb and Vayanos (2010), we find that increases in the amount of
speculative capital that hedge funds employ (either in assets under management or debt) improve
market liquidity, reduce the amount of short-term return reversal and volatility. Related to Acharya
and Pedersen (2005), we find that increases in the amount of speculative capital reduce the liquidity
premium in stock returns.
Previous empirical research on hedge funds’ role in the supply of immediacy is scarce. The only
other paper that focuses on the hedge fund’s role in supplying immediacy is, to our knowledge,
Aragon and Strahan (2011). They show that following Lehman Brothers’ bankruptcy, stocks traded
by the Lehman-connected hedge funds experienced greater declines in market liquidity than other
stocks.
3
More commonly researchers have studied the linkages between liquidity and hedge fund returns.
For instance, Sadka (2010) shows that hedge funds are exposed to unexpected market wide liquidity
shocks. He argues that this exposure is due to hedge funds’ portfolio allocations, where long
positions are commonly taken in more illiquid securities than short positions. As an example, he
refers to the case of convertible arbitrage, where long positions are taken in illiquid convertible
bonds, while short positions are taken in more liquid stocks. Second, however, he points out that
hedge funds’ exposure to market wide liquidity changes could result from the use of trading
strategies that require immediacy due to their frequent trading interval, such as the momentum
strategy. In all our tests of whether hedge funds supply or demand immediacy, we include the
unexpected shocks to liquidity, as measured in Sadka (2010), as a control. It turns out that the two
phenomena co-exist: several hedge funds, or hedge fund style categories as aggregate, have a
statistically significant exposure to the returns from providing immediacy. In addition several hedge
funds have a significant exposure to unexpected changes in liquidity.
In addition to Sadka (2010), there are a few other papers that present evidence of hedge funds’
exposure to the level of liquidity. For instance, Getmansky, Lo, and Makarov (2004) explore
reasons for high autocorrelation in hedge fund returns and argue that exposure to illiquid securities
is one likely explanation. Also Boyson, Stahel, and Stulz (2010) show evidence that liquidity
shocks are the main drivers of hedge fund returns and that liquidity affects the probability of
contagion in hedge funds. Gibson and Wang (2010), in turn, show that hedge funds’ return
predictability (documented by e.g. Avramov, Kosowski, Naik and Teo, 2011) is, at least partially,
driven by the funds’ exposure to liquidity risk. Other papers in this stream of literature include
Aragon (2007), Cao, Chen, Liang, and Lo (2009), Aragon, Liang and Park (2011), Khandani and
Lo (2011b), and Teo (2011). Kang, Kondor and Sadka (2011) is also related. They study the effect
of hedge fund activity on idiosyncratic volatility. One of their main findings is that the downward
4
trend in the volatility of low idiosyncratic volatility stocks can be attributed to long/short equity
hedge fund activity.
The rest of the paper is organized as follows. In Section 1, we describe our method for estimating
the returns from providing immediacy. In section 2, we present our main empirical results regarding
hedge funds’ propensity to supply immediacy. In Section 3, we analyze the effect of hedge fund
trading on short-term return reversals, liquidity, liquidity premium, and volatility. In Section 4, we
show that our main result, that hedge funds typically supply immediacy, is robust to several
alternative methods for estimating the returns from providing immediacy. Section 5 looks at the
case of extreme return reversals, while Section 6 concludes the paper.
1. Measuring the returns from providing immediacy
1.1. Data
When estimating return reversal patterns, our sample includes all stocks listed in the daily CRSP
file from the 1st of January 1990 to 31st December 2008, which fulfill the following requirements:
1) the security is an ordinary common stock, 2) the company is incorporated in the US, 3) the stock
is listed in the NYSE or the Amex, and 4) the company’s SIC code is available and it is included in
the Fama and French 48 industries, excluding the industry Other. Further, when estimating the
returns from providing immediacy, we make additional data restrictions to reduce noise in our
estimates. First, we remove from our sample all stocks that belong to the smallest decile of all USincorporated common stocks listed on NYSE or Amex. Second, we eliminate penny stocks by
removing from our sample all stocks that have a share price below five dollars. Finally, we require
that a stock must have a positive trading volume during each day when a position in the stock is
presumably opened.
5
1.2. Short-term return reversal
To estimate return reversal patterns in excess returns, we perform for each day a cross-sectional
regression, in which we regress the stocks’ (indexed by i) next 5-days’ (one week) excess returns
following the close on day t, Ri ,t  5 , on each of the stocks’ past 20 days’ (one month) excess returns,
Ri ,t  , where τ ∈ {0,..19}, and vector of controls Ci,t:
∑
(1)
Here αt is the intercept in the regression, while  i ,t is a stock specific error term. As controls in the
baseline regression we use two variables that are constructed by multiplying the past months’ (20days’) excess returns with either the stocks’ monthly (log of) trading volume or the firms’ (log of)
market capitalization at time t.1
An estimate of the short-term expected excess returns due to return reversals, following day t, is
then obtained by combining the estimated coefficients ̂
and ̂
from (1), estimated with data up
to period t, with the last 20-days’ returns and the values of the controls at time t.
When estimating (1) we calculate the excess returns by deducting from stocks’ returns the returns to
a corresponding equal-weighted Fama and French 48 industry index. We define our excess returns
relative to industry indexes as in this case the excess returns for stocks are more likely due only to
1
These two controls are motivated by the findings presented Campbell, Grossman, and Wang (1993), Pastor and
Stambaugh (2003), and Khandani and Lo (2011a).
6
price pressure from trading and not information. Our approach is similar to that of Hameed, Huang
and Mian (2010) who also define excess returns relative to industry indexes.2, 3
Suominen and Rinne (2011) show that the model’s explanatory power to forecast short-horizon
returns improves significantly when we include each of the past twenty days’ returns in a
forecasting regression instead of just the past month’s (roughly twenty days) return as is commonly
done. In addition, they show evidence that mean reversion in excess returns is gradual, suggesting
that optimal contrarian trading strategies that provide immediacy might have longer trading horizon
than one day (as is assumed in Khandani and Lo, 2011a). This turns out indeed to be the case,
motivating our choice to forecast 5-days’ as opposed to one day’s returns in regression (1).
Additional motivation for the 5-day forecasting period is given in Sections 1.3 and 2.6.
The estimated average coefficients ˆ t  from regression (1) are all negative and statistically highly
significant, showing that there is a large amount of mean reversion in the data. In addition, the
coefficients for the two controls are significant and have the expected sign: the coefficient of
volume interacted with past month’s return is negative, while the coefficient of market
capitalization interacted with past month’s return is positive. The regression results are presented in
Table 1 below.
2
As we show in Section 4 our main results are highly similar if excess returns are calculated relative to an equal-
weighted CRSP index as in Lehmann (1990), Lo and MacKinlay (1990), Khandani and Lo (2007, 2011a), and Nagel
(2011), or value-weighted CRSP index as in Pastor and Stambaugh (2003). One additional motivation for defining our
excess returns relative to industry indexes is that, amongst these alternatives, our method leads to the highest Sharpe
ratio for the returns from providing immediacy (returns from trading based on expected return reversals), suggesting
that in practice hedge funds would define excess returns in this context relative to industry indexes.
3
In the cross-sectional regressions of (1) at any given date t, we include only stocks that belong to the same Fama and
French industry index during the entire 25-day estimation interval.
7
[Insert Table 1]
Next, we use these results to estimate the available returns from providing immediacy.
1.3. Estimating the returns from providing immediacy
Similarly as Khandani and Lo (2011a), Nagel (2011), and Rinne and Suominen (2011), we proxy
for the available returns from providing immediacy, RIMM, by the monthly return to a zeroinvestment contrarian long-short trading strategy that utilizes short-term return reversals. More
precisely, our proxy for RIMM is the monthly return to a zero-investment long-short trading strategy
where every day a long position is opened in stocks with a positive expected 5-day return and a
short position in stocks with a negative expected 5-day return. After 5 days, such positions are
closed. We focus on an immediacy providing trading strategy where all positions are closed after 5days (one week) as this, using our portfolio rule, results in a higher Sharpe-ratio after accounting for
estimated transaction costs than otherwise similar trading strategies where positions are closed after
one day (as in Khandani and Lo, 2011a) or one month, as shown in Table A1 in the Appendix. We
do not experiment with other holding periods.
Lehman (1990), Khandani and Lo (2011a) and Nagel (2011) analyze the returns to contrarian
trading strategies where portfolios are formed by using the negative of the stocks’ past returns as
portfolio weights. Given the evidence on return reversal, these portfolio weights effectively
correspond with stocks’ expected excess returns. In line with their approach, we also use the stocks’
8
expected 5-day excess returns evaluated at time t, denoted by E t Ri ,t 5  , as portfolio weights when
forming the long and the short portfolios. 4
Next, before estimating the returns from providing immediacy, we trim the sample by always
excluding one percent of stocks with the highest and the lowest short-term expected returns. We do
so mainly as many of the extreme returns seem to be associated with block trades in small
capitalization firms with very poor liquidity—trades where hedge funds’ ability to provide
immediacy can be limited.5 In Section 5 we nevertheless include also these omitted stocks and find
additional results.
Now, given N stocks in the universe of potential stocks where positions can be taken on day t (the
trimmed sample), the assumed portfolio weights  iL,t in the long and  iS,t in the short portfolios on
day t are
(
∑
|
(
)
(
)
(
)
)|
(2)
(
∑
|
(
)
(
)
)
(
)|
Here IZ denotes an indicator function that equals one if Z is true and zero otherwise.
4
Besides corresponding with the common portfolio rule in similar contexts in the literature, this approach can be
motivated theoretically. Under the assumptions that the short-horizon returns are solely due to price pressure and
independent across securities, and the assumption that investors have CARA utility functions, the investors’ optimal
portfolio allocations are linear in the expected returns of the assets.
5
Avramov, Chordia and Goyal (2006) presents related evidence that the largest return reversals occur amongst the most
illiquid stocks.
9
When setting the portfolio weights in (2) we assume that the hedge funds’ time t estimates of
stocks’ expected 5-day excess returns are based on 120 past days’ (i.e., the past 6 months’) cross
sectional regressions of (1) up to time t-6, the last day for which there is five-day return data at time
t. The expected five-day returns at time t, Et ( Ri ,t 5 ) , can then be calculated using the stocks’ past
twenty days’ returns up to time t, past month’s trading volume and firms’ market capitalizations at
time t.
Our proxy for the returns from providing immediacy, RIMM, is the weighted average return on all
open positions to the zero-investment long-short trading strategy described above. Table 2
documents the pre-transaction cost returns on our immediacy providing trading strategy. As is
evident from Table 2, the returns from providing immediacy are high, even after controlling for
standard risk factors.
[Insert Table 2]
Figure 1, in turn, shows the time series evolution of the monthly returns from providing immediacy.
[Insert Figure 1]
2. Do hedge funds supply or demand immediacy?
It is not clear in advance whether hedge funds on average act as market makers and supply
immediacy, or demand immediacy in the stock market. While there appears to exist returns from
10
providing immediacy, as documented above, many other profitable dynamic trading strategies
employed by hedge funds, such as momentum, demand immediacy. In addition, it is not clear
whether the returns from providing immediacy that we documented above even exist after the
inclusion of transaction costs (see Avramov, Chordia and Goyal, 2006). In this section, we explore
these issues by regressing the hedge funds’ returns on our measure of the returns from providing
immediacy. If the mean of the regression coefficients for all funds is statistically significantly
positive we conclude that hedge funds typically supply immediacy (evidence that the returns from
providing immediacy are positive even after transaction costs), if the mean regression coefficient is
negative, we conclude that the hedge funds typically demand immediacy.
2.1. Data on hedge funds
The data on individual hedge funds are from the TASS database. Our sample includes all 5,703
hedge funds and funds of hedge funds in the TASS database that report their returns in U.S. dollars
and have a minimum of 36 monthly return observations between January 1994 and December 2008.
Table 3 provides the basic summary statistics of variables used in this study.
[Insert Table 3]
2.2. Controlling for liquidity shocks
The analysis regarding whether hedge funds’ demand or supply immediacy is complicated by the
finding in Sadka (2010) that hedge funds have exposure to unexpected shocks to the level of
liquidity. This empirical finding can be understood by looking at some of the strategies that hedge
funds employ. For instance, convertible arbitrage hedge funds are long in illiquid convertibles and
short in liquid stocks, see e.g. Agarwal, Fung, Loon, and Naik (2007). Also in the stock market,
hedge funds may take long positions in illiquid small stocks while shorting the more liquid large
11
stocks to benefit from liquidity premium in returns. Unexpected liquidity shocks that increase the
liquidity premium affect adversely the returns on both of these long-short investment strategies. As
the level of liquidity, the amount of short-term return reversal, and the returns from providing
immediacy are all closely related, see e.g. Avramov, Chordia and Goyal (2006), we control for
liquidity shocks in all the regressions that examine whether hedge funds supply or demand
immediacy in the stock market. As in Sadka (2010), we use the permanent-variable component of
price impact constructed in Sadka (2006) as our measure of liquidity. Also, following Sadka (2010)
we calculate the liquidity shocks as the residuals of an AR(3) model of changes in the level of
liquidity.6 The correlation between the liquidity shock series and our measure of the returns from
providing immediacy is -0.36.
2.3. Hedge funds’ exposure to the returns from providing immediacy
We start our empirical analysis by examining whether hedge fund returns are dependent on the
returns from providing immediacy. To do so, we regress fund by fund the hedge funds’ returns on a
number of previously used risk factors related to hedge funds, liquidity shocks, as well as the
returns from providing immediacy variable, RIMM, described earlier. More precisely, we extend the
seven hedge fund risk factor model of Fung and Hsieh (2004) by adding the returns from providing
immediacy and the unexpected changes in liquidity to the model.7 Table 4 presents the crosssectional means of the coefficients of the returns from providing immediacy, together with the
6
7
Data for the Sadka (2006) liquidity factors is obtained from WRDS.
The seven factors used by Fung and Hsieh (2004) are three trend following factors (for bonds, currencies and
commodities; Fung and Hsieh, 2001), an equity market factor (S&P 500), a size spread factor (Russell 2000 minus S&P
500), a bond market factor (monthly change in the 10-year treasury constant maturity yield), and a credit spread factor
(monthly change in the Moody’s Baa yield minus 10-year treasury constant maturity yield). Data for the trend
following factors are available on David Hsieh’s website: http://faculty.fuqua.duke.edu/~dah7/DataLibrary/TFFAC.xls.
12
proportion of coefficients that are statistically significant negative or positive at the five-percent
level. In addition to the whole sample of 5,703 hedge funds, the results are presented separately for
long/short equity funds (1,559 funds), equity market neutral funds (241), and other funds (3,903).
[Insert Table 4]
The results presented in Table 4 uniformly support a conclusion that hedge funds, on average
supply immediacy in the stock market. First, the average coefficient of the returns from providing
immediacy in the hedge fund return regression is positive (0.16) and statistically very significant
(associated t-statistic 26.9).8 Second, the amount of individual funds that have a statistically
significant exposure at a five-percent confidence level to the returns from providing immediacy is a
staggering 18% of all funds. This figure is statistically very significantly higher than the threshold
figure of 2.5%, which is the percentage of funds that we would expect to find to be statistically
significantly positive (negative) under the assumption that all funds in reality have a zero loading
on the returns from providing immediacy. Third, the fraction of negative coefficient funds, i.e.
funds that demand immediacy, is only 2%, which also is statistically significantly less than the
amount expected under zero exposure. Finally, these results are uniform across different fund types.
The average coefficient is significantly positive for long/short equity funds, equity market neutral
funds, as well as the other funds category. The amount of positive coefficients ranges between 14%
and 19% depending on the fund category and the fraction of negative coefficients varies between
2% and 3%.
8
Note that we include the Sadka (2006) liquidity shocks in the regressions. Hence the reported exposures to returns
from providing immediacy are not driven by the funds’ liquidity risk exposure. It seems that these are two separate
phenomena as, similar to Sadka (2010), we also find that hedge funds, on average, have a significant positive exposure
to the unexpected liquidity shocks beyond their exposures to the returns from providing immediacy.
13
In the robustness checks section of the paper (Section 4) we investigate, using several different
measures of the returns from providing immediacy, the robustness of these results. We
systematically come to the same conclusion: on average, hedge funds supply immediacy in the
stock market. With one measure of the returns from providing immediacy (otherwise similar
measure but now assuming that there is one day in between the estimation of expected returns and
trading) the percentage of funds that statistically significantly supply immediacy is as high as 28%.
It should also be noted that our approach of estimating whether hedge funds demand or supply
immediacy in the stock market can underestimate the overall role of these funds in the supply of
immediacy. This is so because each of the funds may over time act in both roles, as immediacy
demanders and as immediacy suppliers. In addition these funds may act simultaneously in different
roles in different markets. For instance, a fixed-income fund trading pricing discrepancies between
stocks and bonds may alter between supplying and demanding immediacy in the stock market
depending on whether the other investors at that time require more immediacy in the bond as
compared to the equity markets. Same is true also for the convertible arbitrage funds. In addition,
pure equity funds may alternate between supplying and demanding immediacy depending on the
immediacy needs of their other strategies. Given such problems in detecting the full extent to which
funds are involved in supplying immediacy, our finding that so many funds have systematically
statistically significant positive exposure to the returns from supplying immediacy is clear evidence
that supply of immediacy is an important strategy for hedge funds.
2.4. Fund characteristics and the supply of immediacy
Next we explore the sources of cross-sectional variation in hedge funds’ decision to supply
immediacy in the stock market. We approach this question by regressing at the fund-level the
coefficient of the returns from providing immediacy on various fund-level characteristics related to
14
the funds’ use of leverage, redemption limitations, capital flows, size, and style category. We start
from a broad model with all explanatory variables and exclude non-significant variables. Table 5
presents the results.
[Insert Table 5]
After excluding non-significant explanatory variables, only length of the lockup period and average
size significantly explain the cross-sectional variation in the funds’ tendency to supply or demand
immediacy. Funds with longer lockup periods and larger funds are more likely to supply immediacy
than funds with short lock-up periods or no lockups and funds with smaller assets under
management. These findings make sense as both the lockup period and large fund size decrease the
risk of facing sudden redemptions that are large compared to the funds’ assets under management.
Thus, the funds with long lockup periods and large asset bases can more systematically supply
immediacy as compared to the other funds in the market who at times of large redemptions must
demand immediacy in the market.
2.5. Time variation in hedge funds’ supply of immediacy
Next, we explore the time variation in hedge funds’ decision and ability to supply immediacy. Our
approach is to regress at the fund level hedge funds’ returns on the returns from providing
immediacy interacted with several time varying conditioning variables, in order to find if they affect
hedge funds’ propensity to supply immediacy. As before, we include the Fung and Hsieh (2004)
factors and the Sadka (2006) liquidity shocks as controls in the regressions.
Our first conditioning variable is the change in the Treasury-over-Eurodollar spread, the TED
spread. This variable is the change in the difference between the three-month interbank interest rate
15
and the three-month T-bill rate. Along with the previous literature, see e.g. Brunnermeier, Nagel
and Pedersen (2009), we use this measure as a proxy for the changes in hedge funds’ funding
conditions. An increase in the TED spread results in higher cost of leverage and thus presumably
lower leverage for the hedge funds. For instance Brunnermeier and Pedersen (2009) and Gromb and
Vayanos (2011) stress the importance of funding capital in arbitrageurs’ ability to provide
immediacy. Our second conditioning variable, that we expect to affect (negatively) funds’ decision
to supply immediacy, is the level of liquidity. We measure liquidity using the Pastor and
Stambaugh (2003) measure of stock market liquidity as this is readily available, in contrast to Sadka
(2006) level of liquidity for which we only have the shocks. The higher the value of the Pastor and
Stambaugh (2003) measure of stock market liquidity, the more liquid the US stock market is.
Table 6 presents the average coefficients of the interaction between returns from providing
immediacy and the above mentioned conditioning variables. Figure 2, in turn shows graphically the
relation between these variables and the hedge funds’ average propensity to supply or demand
immediacy.
[Insert Table 6 and Figure 2]
As is evident from Table 6 and Figure 2, hedge funds decrease their supply of immediacy when the
TED spread increases, i.e. the funds’ cost of leverage increases (and the availability of leverage
decreases). This result is consistent with Brunnermeier and Pedersen (2009) and Gromb and
Vayanos (2011).9 This finding is also consistent with Ben-David, Franzoni, and Moussawi (2011)
analysis of hedge funds’ behavior during the recent 2008 financial crisis and Nagel (2011). Second,
9
We also used the net flow of capital to hedge funds as a conditioning variable, but these results were not statistically
significant and are hence not reported.
16
as expected we find that higher stock market liquidity leads hedge funds to decrease their supply of
immediacy in the stock market (presumably as the available returns from supply of immediacy
decrease while the costs of immediacy of other immediacy demanding trading strategies decrease).
2.6. Slow moving capital and the five-day investment horizon
We now explore the timing of hedge funds’ immediacy providing trades. The evidence in Duffie
(2010) suggests that arbitrageurs, such as hedge funds, may need time to release capital from their
existing positions and hence may not be able to rapidly react to all emerging trading opportunities.
Under such circumstances it would be understandable that reversals occur only gradually. Below
we probe the timing of hedge funds’ exposures to the opportunities to provide immediacy that
arrive on any given day t, by studying the future exposure of hedge funds to the same stocks where
our returns from providing immediacy trading strategy assumes positions are taken on day t. More
precisely, we perform regressions where hedge funds’ returns are regressed on the returns to a longshort portfolio that is identical to our time t returns from providing immediacy long-short portfolio,
but where the 5-day returns are calculated after skipping n ∈ {0,..9} days. The results are presented
in Table 7.10
[Insert Table 7]
The results show, as the percentage of funds exposed to these stocks initially grows, that hedge
funds are indeed somewhat slow to react to the emerging trading opportunities, consistent with
Duffie (2010). That is, capital moves slowly also in our context. It seems to take one week before
10
We look at returns during 5-day intervals instead of one day returns in order to be able to better identify hedge funds’
exposures to this portfolio.
17
hedge funds exposure to the time t returns from providing immediacy portfolio reaches its
maximum (the same conclusion is obtained if we used daily returns instead of the 5-day returns in
these regressions as we have done).
It is also interesting to note that consistent with our assumption of a 5-day investment horizon for
hedge funds, more than than 60% of the hedge funds that have a significant exposure to our returns
from providing immediacy portfolio formed on day t, no longer have such exposure after five days,
that is from day t+5 onwards. Only one percent of such funds have any significant exposure to the
original long-short portfolio after eight days. Given these observations, it seems that the 5-day
investment horizon is appropriate. The fact that hedge funds seem to enter the market only
gradually after trading opportunities emerge is additional evidence that the returns from providing
immediacy are strictly positive even after transaction costs, in contrast to the arguments presented
in Avramov, Chordia, and Goyal (2006).
3. Hedge funds and stock market liquidity
3.1. Overview
In this section we study the effect of hedge funds on 1) short-term return reversals, 2) liquidity, 3)
liquidity premium and 4) volatility. We are especially interested in the effects of two measures of
hedge fund industry capital on these four variables of interest. These results help us evaluate further
the role that hedge funds play in the supply of immediacy in the stock market.
Our first proxy for changes in hedge fund industry speculative capital is the flow of funds to the
hedge funds industry (scaled by the US stock market capitalization).11 We use the flow, rather than
change in AUM, because of the non-stationarity of the latter. We believe that using the fund flows
11
Our estimates for hedge fund industry flows are from Jylhä and Suominen (2011).
18
is relatively free of endogeneity problems as hedge funds typically require a notification period of
up to several months prior to subscriptions and redemptions.
Second, we need a proxy for the changes in the total funding capital that hedge fund industry
employs. To build such a proxy, we first use the difference between the three month Eurodollar and
the three month Treasury interest rates, i.e. TED spread, as a measure of hedge funds’ funding cost.
Higher TED spread indicates higher cost of funding and lower leverage. The total amount borrowed
by hedge funds (industry leverage) depends not only on the cost of leverage but also on the level of
hedge funds’ equity. Hence, we multiply the TED spread by the hedge fund industry AUM
(normalized by the market capitalization of the US equity market) to obtain a measure of hedge
fund industry’s total cost of leverage, a variable that proxies for the total amount borrowed by
hedge funds (relative to the US equity market). We use the changes in the hedge fund industry’s
total cost of leverage as our proxy for the changes in total borrowed speculative capital, and as our
second proxy for changes in hedge fund industry speculative capital.
3.2 Hedge funds and return reversals
An increase in the amount of capital allocated to hedge funds that provide immediacy should
decrease the returns available from such activity. In our context, this means that we should expect
that hedge fund flows reduce the degree of short-term return reversals.
The inclusion of controls in regression (1) improves our estimates of short-term returns, but makes
inference on the amount of return reversal difficult. Hence, to obtain an estimate of the degree of
return reversal, we first repeat the daily regressions (1) but now without controls. The time series of
the negative of the coefficient for the past day’s return,
amount of short-term return reversal. The time series for
19
, is then a time-varying measure of the
is presented in Figure 3.
[Figure 3]
To study the effect of hedge funds on short-term return reversals, we now regress the monthly
averages of the
estimates on our two measures of changes in hedge fund industry capital. The
results are presented in Table 8.
[Insert Table 8]
These results show that hedge fund flows reduce the amount of short-term return reversal as
expected. The effect of hedge fund leverage is statistically insignificant, however.
3.3. Hedge funds and liquidity
In Table 9 we report the results of regressing changes in the level of liquidity on hedge fund flows
and changes in the cost of leverage. We use two measures of liquidity in this regression. First, we
measure liquidity shocks as shocks to the Sadka (2006) permanent-variable (PV) price impact.
Second, we look at the liquidity shocks as defined in Pastor and Stambaugh (2003). In both cases, a
positive coefficient for hedge fund flows would indicate that hedge fund flows increase liquidity.
[Insert Table 9]
The results presented in Table 9 show that hedge fund flows are associated with improvements in
liquidity. This means that speculative capital affects liquidity in the stock market, as predicted e.g.
by Gromb and Vayanos (2010), and our results that hedge funds play a significant role in the supply
20
of immediacy in the stock market. Also, changes in the cost of leverage are negatively associated
with market liquidity, consistent with our expectation.
3.4. Hedge funds and the liquidity premium
Table 10 presents the results of regressing the monthly liquidity premium on hedge fund flows. We
estimate the liquidity premium like Acharya and Pedersen (2005) as the monthly return of illiquid
stocks minus the return of liquid stocks.
[Insert Table 10]
We find that hedge fund flows lead to a positive contemporaneous return on a portfolio exposed to
the liquidity premium. These results are consistent with the idea that positive hedge fund flows
reduce the expected future liquidity premium. The cost of leverage has also the expected sign: an
increase in the cost of leverage leads to negative returns on a portfolio exposed to the liquidity
premium, leading potentially to larger expected future returns on such a portfolio. Also here, these
results are consistent with the important role of hedge funds in the supply of immediacy
documented in section 2.3.
3.5. Hedge funds and volatility
Several papers, see e.g. Brunnermeier and Pedersen (2009), link volatility with the level of
liquidity. The idea is that in illiquid markets investors’ order imbalances cause additional short-term
price volatility. Naturally, volatility is lower when arbitrageurs have abundant capital to supply
immediacy in the stock market.
21
In Table 11 we report the results of regressing the monthly changes on the average stock return
volatility of NYSE and Amex stocks on our proxies for changes in speculative capital. Given the
role of hedge funds in the supply of immediacy, we expect that hedge fund flows have a negative
effect and the changes in cost of leverage have a positive effect on volatility.
[Insert Table 11]
The effect of hedge fund flows lacks statistical significance. The effect of the change in the cost of
leverage is positive however, as predicted, and statistically highly significant. This result supports
the idea that the availability of speculative capital, more precisely the availability of funding capital
to hedge funds affects the stock market volatility, as argued by Brunnermeier and Pedersen (2009).
These findings are consistent with the findings in Kang, Kondor, and Sadka (2011).
4. Alternative measures of the returns from providing immediacy
In this section we show that our main result, that hedge funds, on average, provide immediacy in
the stock market, is robust to several alternative methods for estimating the returns from providing
immediacy. We consider the following changes to our approach of estimating the returns from
providing immediacy:
1. No trimming: In our standard way of calculating returns from providing immediacy, we exclude
one percent of stocks with the highest or lowest short term expected returns. In the first robustness
check we include also these extreme observations in return calculation.
2. Skip-a-day: We consider using returns from providing immediacy where in the estimation of the
return reversal (1) we do not include day t’s excess returns as an explanatory variable in the
22
regression. This practice of “skipping a day” (in order to allow the hedge fund managers some time
to think before forming their positions) lowers our estimates of return reversal, and our estimates of
the returns from providing immediacy, but does not have a major qualitative impact on our results.
In fact, as shown in Table 12, more funds than in the base case have a statistically significant
exposure to this measure of the returns from providing immediacy.
3. We consider using the value-weighted and equally weighted CRSP indexes, instead of the
industry indexes, as benchmarks when calculating stocks’ excess returns.
Table 12 presents the equivalent of the entire sample result in Table 4 for these alternative measures
of the returns from providing immediacy.
[Insert Table 12]
As Table 12 shows, our main result that hedge funds supply immediacy is very robust.
5. Extreme returns and hedge funds’ demand of immediacy
In estimating the returns from providing immediacy we trim the sample by excluding one percent of
stocks with the highest and lowest short-term expected return. In this section, we study separately
hedge funds exposure to the returns from providing immediacy within these extreme return stocks.
More precisely, we augment our baseline fund-level regression by adding the returns from
providing immediacy to the excluded stocks as an additional factor along with the seven Fung and
Hsieh (2004) factors, Sadka (2006) liquidity factor, and our former measure of the returns from
providing immediacy, RIMM. The returns from providing immediacy series for the excluded stocks is
23
constructed similarly as in Section 2, but in this case having only the stocks with one percent of
extremely positive and negative expected returns as the investment universe (as opposed to rest of
the stocks as in the calculation of RIMM). The aggregate results are reported in Table 13.
[Insert Table 13]
It seems that hedge funds, on aggregate, are exposed negatively to the returns of the extreme
expected reversal stocks (although not shown, these stocks also have the largest realized return
reversals). Also, the fraction of significantly negatively exposed funds is relatively high (7.4%),
whereas the fraction of positive coefficients is 2.6% and not significantly different from the
expected value under no exposure. This indicates that hedge funds act as immediacy demanders in
these extreme reversal cases. Table 13 also provides a robustness check of the results presented in
Table 4. Inclusion of the extreme reversal factor does not significantly change the average
coefficient or the fractions of negative and positive coefficients for the returns from providing
immediacy, RIMM.
How should we interpret these results? It seems that for the majority of the stocks (99% of stocks)
hedge funds systematically supply immediacy, but for a small fraction of stocks (1%) they demand
immediacy. Why are they demanding immediacy in the extreme returns stocks? We believe the
answer is simply that the extreme return stocks, where hedge funds demand immediacy, experience
extreme returns precisely for the reason that many hedge funds (who commonly supply immediacy)
demand immediacy in those stocks. When other investors demand immediacy, the price effects
remain subdued because hedge funds supply immediacy on those stocks (as is documented by our
previous findings). But when hedge funds collectively demand immediacy in some stocks (due to
execution of some common trading strategies, for instance momentum) there exists few
24
counterparties willing to supply immediacy and hence the costs of immediacy are high (i.e., those
stocks experience extreme positive or negative returns).
Earlier we noted that we excluded the 1% of extreme expected return stocks on the grounds that
these stocks are on average significantly smaller and less liquid based on the Amihud (2002)
measure of illiquidity than other stocks in our sample.12 Therefore many of these stocks are such
where it is difficult for hedge funds to provide immediacy. Similarly, many of these stocks are such
where hedge funds’ demand of immediacy should not materially affect their portfolio returns. The
fact that we nevertheless find that hedge funds on average demand immediacy in these extreme
return stocks is evidence that the costs of immediacy that hedge funds suffer when they collectively
demand immediacy are even higher than what our estimates suggest.
5. Conclusion
In this paper we study whether hedge funds demand or supply immediacy in the stock market by
regressing hedge fund returns on the returns to a contrarian trading strategy. Our main finding is
that typically hedge funds supply immediacy in the stock market.
We find also that large funds and funds with long lock up periods have a higher propensity to
supply immediacy in the stock market compared to other hedge funds. We find two time-varying
factors that affect hedge funds’ propensity to supply immediacy. First, hedge funds are more likely
to supply immediacy when liquidity is low and, second, when credit market is easing (TED spread
declining). Although the hedge funds typically supply immediacy in the stock market, we find
12
When compared to average company in the trimmed sample, the companies in the extreme percentiles are on average
69% smaller, have 31% smaller trading volume and four times larger Amihud (2002) measure of illiquidity.
25
evidence that the most extreme cross-sectional returns are associated with stocks where hedge funds
(at that point in time) demand immediacy.
We find support for the theories set forth in Brunnermeier and Pedersen (2009) and Gromb and
Vayanos (2010) that link market liquidity with the amount of speculative capital and funding
liquidity to speculators. In particular, we show that the amount of speculative capital (either hedge
fund flows or the amount of funding credit) affects the level of liquidity, the amount of short-term
return reversal, liquidity premium and stock return volatility.
26
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30
Table 1: Pattern of return reversal.
This table shows the average coefficients, b̂t-t , from daily cross-sectional regressions (Equation 1 in the text)
where stocks’ 5-day future excess returns Rt+5 are regressed on each of the stocks’ past twenty days’ excess
returns, Rt-τ , where τ ∈ {0,1,2,3,…,19} and controls Ln(Volume)xRt,t-19 and Ln(Market Capitalization)x Rt,t-19. Here
Rt,t-19 refers to past 20 days’ excess return. The excess returns are calculated relative to the corresponding equalweighted Fama-French 48 industry index returns. Sample period is from 1/1990 through 12/2008. T-statistics
based on Fama-Macbeth standard errors adjusted for first order autocorrelation are shown next to coefficients in
parenthesis. All coefficients that are statistically significant at the 5% level are bolded.
Rt+5
Rt
-0.182
(-39.27)
Rt-10
-0.045
(-10.21)
Rt-1
-0.110
(-23.68)
Rt-11
-0.043
(-9.71)
Rt-2
-0.089
(-19.87)
Rt-12
-0.041
(-9.66)
Rt-3
-0.077
(-17.44)
Rt-13
-0.042
(-10.22)
Rt-4
-0.068
(-15.35)
Rt-14
-0.041
(-9.84)
Rt-5
-0.062
(-13.39)
Rt-15
-0.040
(-9.04)
Rt-6
-0.056
(-13.14)
Rt-16
-0.038
(-8.73)
Rt-7
-0.055
(-12.66)
Rt-17
-0.037
(-8.83)
Rt-8
-0.049
(-11.53)
Rt-18
-0.036
(-8.88)
Rt-9
-0.046
(-10.72)
Rt-19
-0.034
(-9.05)
-0.001
(-11.09)
Ln(Volume)xRt,t-19
-0.003
(-2.30)
Ln(Market Capitalization)xRt,t-19
0.007
(4.74)
Number of daily regressions
4767
Average number of observations
2033
Intercept
Controls:
Average Adjusted R
2
0.064
31
Table 2: Return statistics for the immediacy providing trading strategy.
This table shows the statistics of daily and monthly returns from providing immediacy. Sample period is from 8/1990
through 12/2008. The returns from providing immediacy are pre-transaction cost returns on zero-investment long-short
trading strategy in which expected excess returns are used as portfolio weights when forming long and short portfolios
(Equation 2). These expected returns are calculated using six month moving averages of coefficients for mean reversion
(Equation 1), until six days prior to taking positions. Return statistics are based on averages of the returns of all open
positions. Fama and French / Carhart 4-factor alpha is calculated using data from Kenneth French’s website.
Daily
0.06
-0.09
0.05
0.2
0.33
60.2%
0.18
0.04
(8.20)
Mean
25th percentile
Median
75th percentile
Volatility
Positive return %
Sharpe ratio
4-factor alpha
t-statistics for alpha
32
Monthly
1.28
0.27
1.19
2.18
1.92
80.1%
0.67
1.00
(5.71)
Table 3. Descriptive statistics.
This table presents the descriptive statistics of the variables used in the paper. The sample period is from January 1994
through December 2008. All data are on a monthly frequency.
Mean
St.dev.
25%
Median
75%
1.00%
1.90%
0.10%
0.90%
2.00%
96.3
201.7
0.0
0.0
90.0
105.9
277.8
8.9
29.3
93.5
Return from providing immediacy
1.01%
1.91%
0.11%
0.91%
1.96%
Liquidity shock (Sadka)
0.0002
0.0053
-0.0023
0.0012
0.0030
Hedge fund specifics
Return
Lockup, days
AUM average, million USD
Time series
Liquidity shock (Pastor&Stambaugh)
-0.0009
0.0707
-0.0336
0.0014
0.0366
Hedge fund flow (% of AUM)
0.78%
1.57%
-0.02%
0.94%
1.67%
Hedge fund flow ($, scaled by US equity market cap)
0.03%
0.11%
0.00%
0.04%
0.08%
Change in TED spread
0.01%
0.39%
-0.10%
-0.01%
0.10%
Change in cost of leverage
0.0004
0.0376
-0.0038
-0.0003
0.0038
0.126
0.062
0.088
0.123
0.175
Change in stock market volatility
0.02%
0.44%
-0.15%
0.00%
0.13%
Monthly liquidity premium
0.05%
0.83%
-0.41%
0.05%
0.53%
Return reversal
33
Table 4. Hedge funds’ exposure to the returns from providing immediacy.
This table presents summary statistics of the coefficients of the returns from providing immediacy from regressions of
hedge fund returns on the seven Fung and Hsieh (2004) risk factors, returns from providing immediacy and unexpected
change in the level of liquidity. Mean gives the average of the coefficients for each hedge fund category, Negative
(Positive) gives the proportion of coefficients that are significantly negative (positive) at a 5% level using
autocorrelation and heteroskedasticity consistent standard errors (Newey and West, 1987). For means, the t-statistics
for the test of zero mean are given in parenthesis. For the proportion of negatives and positives, the figures in
parenthesis are z-statistics testing whether the proportion is equal to 2.5% which it would be under no exposure to
provision of immediacy. Figures significant at a 5% level are bolded. There are a total of 5,703 hedge funds in the
sample out of which 1,559 are classified as for long/short equity funds, 241 as equity market neutral funds, and 3,903 as
other funds.
All funds
Long/short equity
Equity market neutral
Other
Mean
0.161
(26.91)
0.164
(12.35)
0.104
(5.35)
0.163
(23.88)
34
Negative
2.0%
(-2.59)
2.9%
(0.98)
1.7%
(-0.84)
1.6%
(-3.54)
Positive
17.6%
(73.15)
14.0%
(29.20)
14.1%
(11.54)
19.3%
(67.09)
Table 5. Fund characteristics and provision of immediacy.
This table presents the results of regressing the fund-level estimates of immediacy provision on the length of funds’
lockup period and (logarithm of) the funds’ average assets under management and fund category dummies. The
dependent variable is the coefficient of returns from providing immediacy in a regression where fund returns are
regressed on the seven Fung and Hsieh (2004) risk factors, returns from providing immediacy and unexpected change
in the level of liquidity. Positive (negative) value means that the fund supplies (demands) immediacy. Lockup is the
length of the lockup period in years and Size is the (log of) average assets under management of the fund over the
sample period. Fund style dummies are included in all specifications. Heteroscedasticity consistent t-statistics are
reported in parenthesis. Figures significant at a 5% level are bolded.
Lockup
(1)
0.036
(2.50)
Size
Adjusted R2
Observations
0.124
5,703
35
(2)
0.015
(3.72)
0.115
4,934
(3)
0.043
(2.78)
0.014
(3.57)
0.117
4,934
Table 6. Time-variation in hedge funds’ supply of immediacy .
This table presents average coefficients for the returns from providing immediacy and the interaction of the returns
from providing immediacy and several conditioning variables in a regression of hedge fund returns on the seven Fung
and Hsieh (2004) risk factors, returns from providing immediacy, liquidity shocks, and the conditioning variable. The
conditioning variables are the change in TED spread (Treasury-over-Eurodollar) which proxies for the cost of leverage
and the one-month lagged Pastor and Stambaugh (2003) liquidity which proxies the level of stock market liquidity. The
t-statistics for the test of zero mean are given in parenthesis. Figures significant at a 5% level are bolded. The sample
size in each specification is 5,703 fund-level time series regressions.
Returns from
providing
immediacy
0.138
(23.02)
0.142
(24.11)
z = change in TED spread
z = Pastor-Stambaugh liquidity
36
z × Returns
from providing
immediacy
-0.128
(-4.30)
-0.454
(-4.56)
Table 7. Hedge funds’ future exposure to the returns from providing immediacy stocks.
This table presents the summary statistics of the coefficients from a regression where hedge funds’ monthly returns are
regressed on the monthly returns to a long-short portfolio where 5-day investments are made to our time t returns from
providing immediacy portfolio, but where the investments are made after skipping n days. In this way, we try to explore
the timing of the hedge funds supply of immediacy. In these regressions, we use as controls the seven Fung and Hsieh
(2004) risk factors and the unexpected change in the level of liquidity. Mean gives the average of the coefficients for all
funds, Negative (Positive) gives the proportion of coefficients that are significantly negative (positive) at a 5% level
using autocorrelation and heteroskedasticity consistent standard errors (Newey and West, 1987). For means, the tstatistics for the test of zero mean are given in parenthesis. For the proportion of negatives and positives, the figures in
parenthesis are z-statistics testing whether the proportion is equal to 2.5%, which it would be under no exposure to
provision of immediacy. Figures significant at a 5% level are bolded. Last column shows the percentage of those funds
that on day t statistically significantly provide immediacy (17,6% of all funds), which also have a statistically
significant exposure at a 5% level to that same long-short portfolio in the five days that follow after skipping n days.
0 days
1 day
2 days
3 days
4 days
5 days
6 days
7 days
8 days
9 days
10 days
Mean
0.161
(26.91)
0.187
(31.68)
0.185
(30.86)
0.198
(32.56)
0.211
(34.22)
0.210
(32.02)
0.162
(25.68)
0.076
(14.24)
0.038
(7.71)
0.043
(8.54)
0.030
(5.69)
Negative
2.0%
(-2.59)
1.4%
(-5.22)
1.7%
(-3.87)
1.8%
(-3.27)
1.9%
(-2.85)
1.9%
(-3.02)
2.1%
(-2.17)
2.0%
(-2.25)
1.9%
(-2.93)
1.7%
(-3.78)
2.5%
(0.12)
37
Positive
17.6%
(73.15)
22.2%
(95.20)
23.2%
(100.12)
25.8%
(112.76)
26.3%
(115.05)
22.7%
(97.74)
12.4%
(48.04)
6.2%
(17.93)
4.1%
(7.75)
4.2%
(8.18)
5.6%
(14.79)
%
100%
83%
72%
63%
51%
39%
14%
3%
1%
1%
1%
Table 8. Speculative capital and return reversals
This table presents the results of regressing the monthly return reversal estimate on measures of changes in speculative
capital and controls. As measure of return reversal, we use monthly averages of 5-day return reversal estimates, βt,0,
from daily cross-sectional regressions where stocks’ 5-day future excess returns Rt+5 are regressed on each of the
stocks’ past twenty days’ excess returns, Rt-τ, where τ ∈ {0,1,2,3,…,19}. The excess returns are calculated relative to
the corresponding equal-weighted Fama-French 48 industry index returns. Hedge fund flow is the net flow of capital
into the hedge fund industry divided by the market capitalization of the U.S. equity market. Change in cost of leverage
is calculated as the change in the difference between the three month Eurodollar and the three month Treasury interest
rates, multiplied by the lagged hedge fund AUM relative to stock market capitalization. The sample period is from
1/1994 to 12/2008. Autocorrelation and heteroscedasticity consistent t-statistics are reported in parenthesis. Coefficients
significant at a 5% level are bolded.
Intercept
0.132
(16.45)
Hedge fund flow1
-17.149
(-2.60)
Change in cost of leverage
0.029
(0.21)
2
Adjusted R
Monthly observations
1
0.077
180
Coefficients of hedge fund flows are divided by 109.
38
Table 9. Speculative capital and liquidity.
This table presents the results of regressing the monthly liquidity innovations on measures of changes in speculative
capital. As measures of liquidity, we use the permanent-variable component of price impact of Sadka (2006) and the
Pastor& Stambaugh (2003) liquidity factor. Hedge fund flow is the net flow of capital into the hedge fund industry
divided by the market capitalization of the U.S. equity market. Change in cost of leverage is calculated as the change in
the difference between the three month Eurodollar and the three month Treasury interest rates, multiplied by the lagged
hedge fund AUM relative to stock market capitalization. The sample period is from 1/1994 to 12/2008. Autocorrelation
and heteroscedasticity consistent t-statistics are reported in parenthesis. Coefficients significant at a 5% level are
bolded.
Sadka Pastor&Stambaugh
0.000
-0.005
Intercept
Hedge fund flow1
Change in cost of leverage
Adjusted R2
Monthly observations
1
(-0.83)
(-1.00)
1.711
12.632
(3.32)
(2.93)
-0.067
-0.447
(-10.70)
(-5.60)
0.243
180
0.057
180
Coefficients of hedge fund flows are divided by 109.
39
Table 10. Speculative capital and the liquidity premium.
This table presents the results of regressing the monthly liquidity premium on measures of changes in speculative
capital. As Liquidity premium we use the monthly liquidity premium constructed similarly as in Acharya and Pedersen
(2005). Hedge fund flow is the net flow of capital into the hedge fund industry divided by the market capitalization of
the U.S. equity market. Change in cost of leverage is calculated as the change in the difference between the three month
Eurodollar and the three month Treasury interest rates, multiplied by the lagged hedge fund AUM relative to stock
market capitalization. In the second specification, we also include the Fama and French (1993) risk factors Mkt-rf, SMB,
and HML. The sample period is from 1/1994 to 12/2008. Autocorrelation and heteroscedasticity consistent t-statistics
are reported in parenthesis. Coefficients significant at a 5% level are bolded.
Intercept
0.000
(0.10)
Hedge fund flow1
1.275
(2.70)
Change in cost of leverage
-0.010
(-0.68)
0.000
(-1.50)
0.609
(2.35)
-0.011
(-2.07)
Mkt-rf
0.000
(-0.03)
SMB
0.218
(13.06)
HML
0.102
(7.13)
Adjusted R2
Monthly observations
1
0.015
180
Coefficients of hedge fund flows are divided by 109.
40
0.803
180
Table 11. Speculative capital and volatility.
This table presents the results of regressing the monthly change in stock return volatility on measures of changes in
speculative capital. Volatility is measured as an equal weighted average of standard deviations of individual stocks’
daily returns. Hedge fund flow is the net flow of capital into the hedge fund industry scaled by the market capitalization
of the U.S. equity market. Change in cost of leverage is the change in the difference between the three month
Eurodollar and the three month Treasury interest rates, multiplied by the lagged hedge fund AUM relative to stock
market capitalization. The sample period is from 1/1994 to 12/2008 Autocorrelation and heteroscedasticity consistent tstatistics are reported in parenthesis. Coefficients significant at a 5% level are bolded.
Intercept
0.000
(1.23)
1
Hedge fund flow
-0.787
(-1.52)
Change in cost of leverage
0.040
(7.53)
2
Adjusted R
Monthly observations
1
0.105
180
Coefficients of hedge fund flows are divided by 109.
41
Table 12: Robustness checks.
This table shows the whole sample results of Table 4 using alternative measures of returns from providing immediacy
explained in the text. Mean gives the average of the coefficients for all hedge funds, and Negative (Positive) gives the
proportion of coefficients that are significantly negative (positive) at a 5% level using autocorrelation and
heteroskedasticity consistent standard errors (Newey and West, 1987). For means, the t-statistics for the test of zero
mean are given in parenthesis. For the proportion of negatives and positives, the figures in parenthesis are z-statistics
testing whether the proportion is equal to 2.5% which it would be under no exposure to provision of immediacy.
Figures significant at a 5% level are bolded.
Average
Negative
Positive
0.040
(9.62)
3.3%
(4.02)
6.4%
(19.03)
Skip-a-day
0.188
(34.28)
1.8%
(-3.61)
27.5%
(120.90)
EW CRSP index
0.106
(26.13)
2.4%
(-0.56)
18.3%
(76.45)
0.110
2.3%
18.8%
(25.64)
(-0.98)
(78.66)
No trimming
VW CRSP index
42
Table 13. Hedge funds’ exposure to the extreme return reversals.
This table presents summary statistics of the coefficients of the returns from providing immediacy (that is, RIMM) and
returns from providing immediacy to stocks with extreme expected reversals from regressions of hedge fund returns on
the seven Fung and Hsieh (2004) risk factors, returns from providing immediacy, returns from providing immediacy to
stocks with extreme expected reversals, and unexpected change in the level of liquidity. Mean gives the average of the
coefficients, Negative (Positive) gives the proportion of coefficients that are significantly negative (positive) at a 5%
level using autocorrelation and heteroskedasticity consistent standard errors (Newey and West, 1987). For means, the tstatistics for the test of zero mean are given in parenthesis. For the proportion of negatives and positives, the figures in
parenthesis are z-statistics testing whether the proportion is equal to 2.5% which it would be under no exposure to
provision of immediacy. Figures significant at a 5% level are bolded. There are a total of 5,703 hedge funds in the
sample.
Average
Negative
Positive
Returns from providing immediacy
0.172
(27.37)
1.9%
(-3.02)
19.1%
(80.44)
Returns from providing immediacy
-0.012
7.4%
2.6%
to extreme expected reversal stocks
(-11.17)
(23.87)
(0.46)
43
Figure 1: Monthly returns from the immediacy providing trading strategy.
This figure presents the quarterly average of monthly returns during our sample period 8/1990-12/2008 from the
immediacy providing trading strategy. The returns from providing immediacy are returns on a zero-investment longshort trading strategy in which expected excess returns are used as portfolio weights when forming the long and the
short portfolios (Equation 2). These expected returns are calculated using six month moving averages of coefficients for
mean reversion from regression (1), until six days prior to taking positions. Portfolio returns are based on averages of
the returns of all open positions. There is no consideration for transaction costs.
6%
5%
4%
3%
2%
1%
0%
-1%
1990
1993
1995
1998
2000
44
2003
2005
2008
Figure 2: Time variation in hedge funds’ provision of immediacy.
This figure presents average coefficient of the returns from providing immediacy, conditional on conditioning variables,
in a regression of hedge fund returns on the seven Fung and Hsieh (2004) risk factors, returns from providing
immediacy, liquidity shocks, and the interaction of the returns from providing immediacy with a conditioning variable.
The figure is based on results reported in Table 5. The conditioning variables are the Change in TED spread (Treasuryover-Eurodollar) which proxies for the cost of leverage, and the one-month lagged Pastor and Stambaugh (2003)
liquidity which proxies the level of stock market liquidity. The dotted lines present the 95% confidence interval of the
average coefficient.
45
Figure 3: Semiannual estimates of the 5-day return reversal.
This figure shows the semi-annual estimates of 5-day return reversal between 1990 and 2008. Our 5-day return reversal
estimate is the coefficient for the past return on day t, ˆt from daily regressions where stocks’ five day future excess
returns are regressed on each of the stocks’ past 20 day’s excess returns (Equation 1 described in the text without
controls). Excess returns are calculated relative to the corresponding equal-weighted Fama and French industry indices.
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00
1990
1993
1996
1999
46
2002
2005
2008
Appendix:
The effect of holding period on the returns from providing immediacy
Table A1: Return statistics for the immediacy providing trading strategy with broker commissions
Monthly return statistics for an immediacy providing trading strategy with different holding periods (1, 5 and 20 days)
are calculated for the period 8/1990- 12/2008 using following estimates for broker commissions: 5 basis points per trade
during the 1990s and 3 basis points per trade after 2000. Estimates are based on de Groot, Huij and Zhou (2011). The
returns from providing immediacy are the returns to a zero-investment long-short trading strategy similar to that
described in Section 2, in which expected holding period excess returns are used as portfolio weights when forming
long and short portfolios (as in Equation 2). These expected returns are calculated using six month moving averages of
coefficients for return reversal, from regressions similar to Equation 1 but with stocks’ one day, 5-day or 20-day future
excess return as dependent variables, until two, six or 21 days prior to taking positions. Return statistics are based on
averages of the returns of all open positions.
Mean
25th percentile
Median
75th percentile
St.dev.
Positive return %
Sharpe ratio
1 day
-2.51
-4.15
-2.46
-1.26
3.05
15.4%
-0.82
5 days
0.59
-0.38
0.53
1.42
1.86
62.9%
0.32
20 days
0.19
-0.34
0.25
0.74
1.25
63.2%
0.15
As Table A1 shows, the Sharpe ratio is the highest assuming a 5-day holding period.
47