Francesco Franzoni Swiss Finance Institute - University of ...

Empirical Asset Pricing

Francesco Franzoni

Swiss Finance Institute - University of Lugano

Limits of Arbitrage

c 2014 by F. Franzoni Page 1 - 109

Lecture Outline

1. Limits of arbitrage: the theory

2. Empirical evidence

Relevant readings:

� Gromb and Vayanos , 2010, Limits of arbitrage:the state of the theory, Working Paper

� Take a look at: DeLong, Shleifer, Summers, Wald-man (DSSW, JPE 1990), Shleifer and Vishny (JF

1997), Gromb and Vayanos (2002), Abreu and

Brunnermeier (JFE 2002), Abreu and Brunner-

meier (Econometrica, 2003), Brunnermeier and

Pedersen (RFS 2009)

� Brunnermeier and Nagel (JF 2004), Coval and

Sta�ord (JFE 2007), Hammed, Kang, and Viswanathan

(JF 2010), Nagel (2012, RFS), Aragon and Stra-

han (2012, JFE)


� Ben-David, Franzoni, Moussawi, Hedge fund stocktrading in the �nancial crisis of 2007-2009 (RFS,

2012)

� Ben-David, Franzoni, Landier, Moussawi, Do hedgefunds manipulate stock prices? (Journal of Fi-

nance, 2013)


1. Limits of arbitrage: the theory


A simple model

� Based on Gromb and Vayanos (2010)

� Two periods: 1 and 2

� Two assets with correlated payo�s: A and B

� Arbitrageurs are risk averse with CARA utility andrisk aversion �

� Arbitrageurs trade at time 1 and receive dividendsat time 2

� Normally distributed random dividends: dA and

dB , with mean �di and variance �i, i = A;B

� Asset B's price is set to the expected dividendpB = �dB

� There are exogenous demand (=liquidity) shocksin asset A: u

� Arbitrageurs provide liquidity: take the oppositeside of liquidity demand


� The equilibrium price of asset A is

pA = �dA + ��2A

�1� �2

�u

where � is the correlation between the dividends

of the two assets

� Notice: demand shocks u a�ect the price

� That is: arbitrageurs earn a premium from pro-

viding liquidity

� Assets with more risk (�A) and fewer substitutes(lower �) are more subject to demand shocks be-

cause arbitrageurs are less able to hedge risks

� Similarly, higher risk aversion (�) gives rise to alarger price impact

� Notice that if � = 1 there exists a perfect substi-tute of asset A. So, arbitrage is riskless and price

equals fundamentals

� In all other cases, arbitrage is not riskless


Fundamental vs. non-fundamental

risk

� Assume that there is a period 0 in which tradingoccurs

� At time 0, even the expectations of the dividends( �di) are random (e.g. think of a coarser informa-

tion set about fundamentals at time 0)

� And the demand shock u at time 1 is randomfrom the point of view of time 0

� Then, at time 0 arbitrageurs who need to liquidateat time 1 (short horizon) bear two sources of risk

1. Fundamental risk: related to uncertainty about�dA and �dB

2. Non-fundamental risk: related to uncertainty

about demand shocks u

� So, arbitrageurs with short horizons at time 0,may refrain from trading against time 0 demand

shocks because of non-fundamental risk


� As a result, the volatility of pA at t=1 as of t=0is

�A

�1 + �2�2A

�1� �2

�2�2u

�1=2and the correlation between pA and pB is

��1 + �2�2A

�1� �2

�2�2u

�1=2� That is, demand shocks create volatility and lowerthe correlation between the two assets

� As a result of this volatility and reduced correla-tion, arbitrageurs require a higher premium and

prices diverge further from fundamentals

� DSSW generate divergence from fundamentals in

a model with two identical assets, but with auto-

correlated demand shocks for one asset

� Crucial assumptions:

{ arbitrageurs with �nite horizons

{ in�nite horizon economy


� They call this: noise trader risk

� Short horizons can be endogenized as a form of

�nancial constraints (e.g. Shleifer and Vishny

1997, see below)

� Bottom line: non-fundamental risk can a�ect as-

set prices if arbitrageurs have short horizon


Short-selling costs

� In case of positive demand shocks, arbitrageurswould like to short the asset

� Short-selling is not free. Arbitrageurs need to postcash as collateral

� The interest rate earned on the collateral can bebelow the market interest rate

� This is a short-selling cost

� You can model the short-selling cost as c

� In this case, the equilibrium price of asset A at

time 1 is

pA = �dA + ��2A

�1� �2

�u if u � 0

pA = �dA + ��2A

�1� �2

�u+ c if u > 0

� In case u > 0, arbitrageurs are selling short assetA, and the price has to rise by c to compensate

them for short selling costs


� So, two assets with identical payo�s (� = 1) thatare subject to demand shocks can have di�erent

prices if there are short-selling costs. That is

pA = �dA + c

pB = �dA

� This result can explain the Palm-3Com anomaly

� In March 2000, 3Com announced that it would

spin o� its remaining stake in Palm by distributing

1.525 shares of Palm for each share of 3Com

� Palm was trading at $95.06 and 3Com was trad-

ing at $81.81

� The law of one price was violated because

$81:81 < 1:525� $95:06 = $145

� Why were investors willing to buy Palm at $95.95

while they could buy them at lower cost through

3Com shares?

� Positive sentiment for dot-com stocks


� However, you need to introduce limits of arbitrageto explain why rational investors did not arbitrage

it away

� Short selling costs do the job if large enough


Leverage constraints

� The ability to correct deviations from fundamen-

tals due to demand shocks requires capital

� In current model arbitrageurs' wealth does notappear because of CARA utility

� In general, wealth increases risk bearing capacity

� The constraints on arbitrageurs' ability to increasetheir wealth are labeled `�nancial constraints'

� One version of �nancial constraints is limits onleverage

� Gromb and Vayanos (2002), Brunnermeier andPedersen (2009) and others model these limits as

margin constraints

� Buying on margin: to buy a security, investorsborrow money from broker, and post the security

as collateral


� The value of the security is discounted (haircut).So, you cannot borrow 100% of the value of thesecurity

� You still need your own capital (margin require-ment)

� The broker wants to minimize the risk of this op-eration. So, the margin is the larger the morerisky the security is

� Similarly, to short sell a security, you need to postcash (margin) that exceeds the proceeds from theshort sale because the broker wants to be pro-tected against upward movements in the price

� So, arbitrageurs need to have at least some equitycapital in the presence of limits on leverage

� If there are demand shocks (u) arbitrageurs wouldlike to take the other side

� However, it's possible that their capital is notenough, so that they cannot borrow enough toenforce the law of one price

� That is: when arbitrageurs capital is small, theleverage constraint is binding, and arbitrageurs'liquidity provision is not perfect


Ampli�cation

� Suppose arbitrageurs enter period 1 with wealththat is invested in period 0

� There is a negative demand shock that lowers thevalue of the assets in arbitrageurs' portfolio

� This makes the leverage constraint binding in pe-riod 1

� Arbitrageurs receive margin calls from their bro-

kers and they are forced to liquidate

� Arbitrageurs' sales reinforce the negative demandshock

� Arbitrageurs are consuming liquidity in this case

� Ampli�cation


Contagion

� In a multi-asset setting, a demand shock to oneasset may force liquidation of other securities in

the portfolio

� For example, arbitrageurs may choose to liquidatethe more liquid securities �rst

� Or, they can choose to liquidate the most volatilesecurities that impose higher capital charges ( ight

to quality)

� In any case, a shock to one security can propagateto other securities because of leverage constraints


Funding liquidity and market

liquidity

� Brunnermeier and Pedersen (2009) use leverageconstraints in a multi-asset setting to generate

ampli�cation and contagion

� They talk about funding liquidity : the availabilityof capital for arbitrageurs, which depends on the

performance of their portfolio

� And market liquidity : the divergence of securitiesprices from fundamentals due to demand shocks

� The two forms of liquidity a�ect each other inwhat the authors label `loss spirals' and `liquidity

spirals'

� The action comes from forced liquidations after

initial losses, which reinforce the negative price

impact, and cause further losses


� The paper also predicts ` ights to quality': afternegative shocks, arbitrageurs sell high volatility

stocks and buy low volatility stocks to reduce the

amount of collateral that they need to post

� This e�ect reinforces the initial shocks because inthe model conditional volatility depends positively

on past returns (GARCH)


Constraints on equity capital

� These constraints operate similarly to leverageconstraints

� If capital is limited, arbitrage ability is limited, andliquidity provision is not perfect

� They can emerge if arbitrageurs' wealth belongsto other investors (agency problems)

� Shleifer and Vishny (1997) postulate that mu-tual/hedge fund investors redeem their capital fol-

lowing losses

� This fact constraints arbitargeurs' ability to cor-rect mispricing, triggers liquidations, and ampli�-

cation

� S&V show that these constraints limit liquidity

provision not only when they are binding, but also

when there is a chance that they will bind in the

future


� That is, arbitrageurs fear that future losses willcause forced liquidations. So, they limit their ex-

posure to risky assets

� Risk management emerges as a response to cap-ital constraints

� Next step: endogenize leverage and equity con-straints


Synchronization risk

� Abreu and Brunnermeier (2002) postulate that ar-bitrageurs have limited capital

� So, a single arbitrageur cannot correct mispricingalone

� Also, arbitrageurs are not simultaneously awareabout pro�t opportunities

� So, they do not necessarily jump in together tocorrect mispricing

� Finally, there are `holding costs'. That is, it is

costly to hold open positions in the expectation

that mispricing will be corrected

� As a result, mispricing can last for some time be-cause arbitrageurs fail to coordinate in entering

the market (synchronization risk)

� Kondor (JF, 2009) similarly generates persistentprice divergence from the dynamic choices of ar-

bitrageurs that need to decide when to enter the

market


� In Abreu and Brunnermeier (2003), given theseassumptions, it can make sense for arbitrageurs

to trade in the direction of the mispricing (ride

the bubble) in anticipation that the bubble will

continue for some time


2. Empirical evidence


Brunnermeier and Nagel (JF, 2004)

� Technology stocks on Nasdaq rose to unprece-dented levels during the two years leading up to

March 2000

� Valuations were implicitly assuming growth ratesof earnings exceeding what was previously expe-

rienced even by the fastest growing stocks

� Also valuations were implicitly assuming zero dis-count rates


� High price-to-sales (P/S) stocks (mostly high techstocks) experienced a four-fold price increase and

a huge correction after March 2000

� These valuations appear to be another exampleof asset price bubble


Question

� This seems a manifestation of investor irrational-ity

� However, this cannot survive without limits to ar-bitrage

� What were arbitrageurs doing during this period?

� They look at the trading behavior of the mostsophisticated investor class: hedge funds (HFs)

� They draw data from 13F �lings: all institutions

with more than $100M in U.S. equity have to

report their end-of-quarter long positions

� No data on short positions

� Did HFs attack or ride the bubble?


The weights of HFs in the tech

sector

� They use HFs' long portfolio holdings of high P/Sstocks and compare to weight of the same stocksin the market portfolio

� HFs were overweight (larger weight than the mar-ket weight) in tech stocks at least until the peakof the Nasdaq (March 2000)

� So, they did not attack the bubble, rather theywere riding it


How about the short side?

� HFs could also have increased their short positionsin tech stocks

� In this case, the impression of riding the bubblewould be mitigated

� But shorts not reported in the 13F

� So, look at style regressions for returns:

Rt = �+ �RM;t + �RT;t �RM;t

�+ "t

where RM;t is the market return and RT;t is the

tech sector return (high P/S stocks)

� captures the exposure to tech stocks on top ofwhat you get through the exposure to the market

portfolio

� For a long only fund replicating the market port-folio: � = 1 and = 0


� For most funds (except for short-selling special-ists), there is an over-exposure to the tech sector

� Short positions were used, but only to reduce ex-posure to the market (� < 1)

� To summarize, the results strengthen the evidencefrom the previous table that HFs were riding the

bubble


Evidence for individual HFs

� So far, aggregate data

� Did some funds behave di�erently? What were

the consequences on their performance?

� What about the money ows from investors? Theseare relevant for the limits of arbitrage

� Focus on a few selected funds, especially Soros

and Tiger


� Soros was riding the bubble especially after June1999

� Tiger was a value manager, de�nitely not ridingthe bubble. Exposure to tech stocks went to zero

in June 1999

� Diverging paths

� Look at fund ows:

� Soros did well during the bubble. So, investorskept pouring in money


� As Tiger's performance was poor during the bub-ble, it su�ered from redemptions

� Eventually, the Tiger fund was liquidated in March2000 because its asset base eroded too much.

Just before the bubble burst!


Conclusions

� B&N also show that at the stock level, HFs man-aged to time the the market correctly

� On average, they got out of stocks before theydeclined

� Evidence is consistent with `synchronization risk'theories (Abreu and Brunnermeier, 2002 and 2003)

� Not only do we observe that arbitrageurs do notcorrect mispricing (as predicted by �nancial con-

straints)

� But also we see that arbitrageurs ride the bub-ble, possibly because they anticipate that it will

continue for some time

� The example about Tiger is consistent with thelimits on equity capital, as described by Shleifer

and Vishny (1997)

� That is, temporary losses trigger redemptions thatprevent arbitrageurs to hold on to a strategy that

would pay o� in the longer run


Coval and Sta�ord (JFE 2007)

� Focus on �re sales

� A �re sale occurs when a distressed �rm/investorhas to liquidate its assets. Because the assets are

specialized, few buyers are present in the market.

Then, the price has to decline enough to attract

buyers to the market (see Shleifer and Vishny,

JEP, 2011)

� The evidence of price pressure from �re sales is

indirect evidence of limits of arbitrage

� The price deviates from fundamentals for an ex-

tended period of time and no other investor jumps

in immediately to provide liquidity

� Possibly because the other investors in that se-curity are also experiencing �nancial distress and

limits on their capital

� The authors focus on stock sales by mutual fundsthat experience signi�cant capital out ows (re-

demptions)


� Reason: identify an exogenous reason for the �resale

� That is: a reason that is unrelated to the valueof the asset that is sold


Identifying �re sales

� They show that mutual funds experiencing out-

ows reduce their positions more than other funds

� Symmetrically, funds experiencing in ows increasetheir positions

� Then, de�ne a ow induced trade for stock i in

quarter t as:

� That is, sum the positive change in stock hold-

ings for the funds that are top decile in ows and

substract the sum of the negative change in hold-

ings for the funds that are in the bottom decile of

ows

� Fire sale stocks are those that rank in the lowestdecile of the PRESSURE 1i;t variable


Price behavior of �re sale stocks

� One would like to disentangle the e�ect of sellingdue to negative information on the stock from the

e�ect of �re sales

� The assumption is that price pressure induced by�re sales is going to revert

� Instead, for information driven sales, the priceshould remain permanently at the lower level

� Here's the price pattern for stocks with ow in-

duced sales (bottom decile stocks by PRESSURE 1i;t).

They average across stocks and then across quar-

ters


� You see that the price eventually reverts, consis-tent with price pressure and lack of liquidity

� Magnitude: over the two quarters through montht the abnormal stock returns is -7.9% (t-stat=-

3.45)

� Prices revert over the following 18 months

� Instead, for stocks that are subject to voluntarysales (that is, construct Pressure variable without

conditioning on ows) the price pattern is


� Consistent with information driven sales

� Notice that also in the case of ow driven sales

the price starts declining before the quarter of the

�re sale

� Possible explanations:

{ Out ows are persistent. So mutual funds were

already selling that stock because of prior out-

ows


{ The prior price declines cause the negative per-

formance of the fund which receives redemp-

tions and is ultimately obliged to sell


Two pro�table trading strategies

� Liquidity provision:

{ Buy the stocks that have been subject to a

�re sale in the past year (skipping last quarter

for informational reason) and short the stocks

that are subject to positive price pressure

{ They show that alpha is 0.45% (monthly) from

four-factor model (t-stat=2)

� Front running:

{ Based on past fund performance, predict fu-

ture fund ows in a regression framework

{ Short the stocks that are mostly held by funds

with high expected out ows and go long the

stocks by funds with high expected in ows

{ That is, trade before and in the same direction

as the funds that receive high out/in ows

{ The alpha of this strategy from four-factor

model is 0.65% (monthly) with t-stat=2.51%


Conclusions

� Evidence of predictable price pressure e�ects from�re sales

� This suggests that liquidity does not ow imme-diately into the market

� That is, mispricing survives for an extended periodof time

� Indirect evidence of limits of arbitrage

� Possible story: the arbitrageurs that are special-ized in these assets are also su�ering from capital

constraints because of losses

� Other story: the arbitrageurs need to gather in-formation about these stocks and it takes time

(information cost story by Merton 1987)


Hameed, Kang, and Viswanathan

(JF 2010)

� The theory suggests that liquidity supply (marketliquidity) depends on arbitrageurs' capital (fund-

ing liquidity, Brunnermeier and Pedersen 2009)

� However, arbitrageurs' capital is hard to measurebecause the actual identity of liquidity providers

is not clear

� Hence, encompassing approach where they iden-tify declines in arbitrageurs' capital using declines

in the stock market

� Underlying assumption: a decline in the marketbrings about losses for arbitrageurs who have to

withdraw their liquidity provision

� Focus on:

{ Time-series and cross-sectional variation in liq-uidity

{ Commonality in liquidity

{ Returns from providing liquidity


Time-series variation in liquidity

� Weekly frequency

� At the stock level, the regress the weekly changein relative bid-ask spread on lagged market returns

and control variables

� They report the mean and median estimated slopesacross stocks

� Liquidity (the bid-ask spread) is positively (neg-atively) related to lagged market returns up to

three weeks in the past

� Next, they look for asymmetric e�ect of negativeand positive market returns


� Conjecture: negative shocks should matter morebecause �nancial constraints become binding

� Ddown is a dummy variable for negative marketreturns

� It turns out that in week t� 1, the lagged marketreturn has a more negative impact on the bid-ask

spread if the market is going down

� Overall, evidence consistent with losses in arbi-trageurs' trading capital having an e�ect on mar-

ket liquidity because of capital constraints


Supply or Demand

� The e�ect that they identify is also consistentwith increase in demand for liquidity

� For example, in a panic selling investors dumpstocks and consume market liquidity

� The story they want to tell is about a decrease inthe supply of liquidity by �nancial intermediaries

� To identify a supply e�ect they use variables thatcapture a deterioration in arbitrageurs' capital

{ Return on portfolio of investment banks and

broker-dealers listed on NYSE

{ Volume of repos (Adrian and Shin 2008): more

repos, bigger balance sheet of �nancial inter-

mediaries

{ The spread in Commercial Paper yields over

T-Bill rate: bigger spread, lower liquidity

� DCAP is a dummy variable based on each of thethree variables above to capture periods when in-

termediaries are constrained


� They run the regression:

� Results:


� For each of the three variables, the negative rela-tion between market return and the bid-ask spread

is reinforced during periods when the arbitrageurs

are likely to be constrained

� Supply e�ect


Other results

� Cross-sectional e�ects:

{ The negative relation between bid-ask spreads

and market return is stronger for high volatility

stocks

{ Consistent with ight to quality

{ That is, arbitrageurs' exposure to high volatil-

ity assets decreases in bad times

� Commonality in liquidity

{ Sensitivity of stock liquidity to market liquidity

is stronger in down markets

{ Consistent with view that when constraints are

binding the systematic component of liquidity

becomes more important

{ That is, arbitrageurs withdraw from all mar-

kets when constraints are binding

� Returns from providing liquidity


{ Contrarian strategies (buy stocks after nega-

tive returns and sell stocks after positive re-

turns) earn higher returns in down markets

(1.18% per week)

{ Consistent with reduced supply of liquidity in

down markets (also see Nagel 2011)


Conclusions

� Evidence that liquidity deteriorates after negativemarket returns

� Evidence that this e�ect results from a decrease

in the supply of liquidity

� Consistent with theories that postulate �nancialconstraints for arbitrageurs that become binding

after losses


Nagel: Evaporating liquidity (2012,

RFS)

� During the recent crisis liquidity evaporated inmany markets

� In ABS markets trading activity came to a com-plete stop

� It could be the case that the crisis ampli�ed theasymmetric information problems

� But also that market makers' capital deterioratedand they could no longer provide liquidity

� The paper focuses on this second (liquidity sup-ply) story, which is related to the limits of arbi-trage

� Focus mostly on Nasdaq stocks

� Di�erent from NYSE because on NYSE specialistshave stringent obligations to provide liquidity

� Di�erent from previous paper: focus on �nancialcrisis

� Also, use the VIX as a predictor of market stress


Returns to providing liquidity

� Compute the returns from reversal strategies

� Buy stocks that went down over the prior �vedays and sell stocks that went up over the prior

�ve days

� The weight in each stock (wRit) is proportionalto the negative of the abnormal return (over the

market return) in the prior period

� Weights are normalized so that they add up to $1on the long and $1 on the short side

� Assuming 50% margins on both sides, the pro�ts

from this strategy give the returns on a $1 invest-

ment


Why reversal strategies?

� The author shows that reversal strategies approx-imate the returns from liquidity provision

� This strategy replicates the actions of a marketmaker who buys when the public sells and vice

versa

� A market maker wants to earn a positive return

to be compensated for inventory risk

� That is, market makers are risk averse (limitedrisk bearing capacity). So, if they have to increase

exposure to risky assets they require compensa-

tion

� Then, the price has to go down when the publicsells so that in the next period the market maker

earns positive return

� Notice that price changes dictated by informationbased trades do not revert

� Reversion occurs only if price changes occur be-cause of the non-information related components

of transaction costs (inventory, search costs)


Predict returns using the VIX

� Focus of the paper is on predictable time variationin returns from liquidity provision

� That is, the author wants to relate returns fromliquidity provision to aggregate phenomena that

cause deterioration of market makers' capital

� He uses the VIX as predictor

� Rationale:

{ Brunnermeier and Pedersen (2009) argue that

when volatility is high �nancial constraints on

arbitrageurs are tighter

{ Adrian and Shin (2010) show that in periods

of high VIX the risk appetite of broker-dealers

goes down because of risk management con-

straints

{ Ben-David, Franzoni, and Moussawi (2011)

show that at the peak of the �nancial crisis

(when the VIX was high) hedge funds liqui-

dated their equity portfolios


Results

� Condition on prior �ve day returns. Buy at closingprice of day t� 1. Hedge market exposure

� Report 3-month moving average of daily returnsfrom the strategy

� Returns are close to 1% per day during the LTCM

crisis (Summer 1998)

� But then, until 2007, they go down to 0.2% per

day


� During the last crisis returns surpassed the levelsfrom the LCTM default

� There is no single three-month period with nega-tive returns

� So, downside risk is not likely to be behind thesehigh returns

� The skewness is also positive

� Volatility is low (0.59% daily) and Sharpe Ratio

are huge (about 11 annual vs. 0.26 for the Market

in this sample)

� So, volatility of this strategy is not likely to bedeterring other investors from providing liquidity

� More likely, the �xed-costs for entering in the liq-uidity provision market are keeping investors away

� But the focus of the paper is on time-variation inthe return, not on the level of the (net) returns


Time-variation in returns

� Notice the extreme correlation with the VIX index

� In regressions, the VIX predicts the returns on thestrategy

� He shows that predictability persists when returnsare standardized by their conditional volatility

� That is, it is the conditional Sharpe Ratio of thestrategy that is predictable

� In other words, the price for risk on this strategy(and not just the expected return) increases in

times of high VIX


Further results

� In the cross-section, reversal strategies are morepro�table during the crisis for high volatility stocks

� Consistent with ight to quality (Brunnermeierand Pedersen 2009)

� Comparison with NYSE

{ Returns from reversal strategies on NYSE are

much lower, almost zero

{ However, they peak at 0.50% per day during

the crisis

{ Conjecture for why NYSE more similar to NAS-

DAQ over time: electronic and algorithmic

trading has decreased the importance of the

specialists on NYSE

� Separate supply e�ect from demand e�ect

{ Higher demand for liquidity could be behind

increased returns from liquidity provision (al-

though not necessarily behind increased Sharpe

Ratio)


{ Identi�cation: If demand e�ect, volume should

increase. If supply e�ect, volume should de-

crease

{ Predict aggregate volume (turnover) with VIX

{ Find a negative coe�cient

{ Volume decreases on Nasdaq in periods of mar-

ket stress

{ Supply e�ect!


Conclusions

� Returns from liquidity provision increase in peri-

ods of market stress

� Not only, but also the price per unit of risk (SharpeRatio) increases

� Consistent with limits of arbitrage theories thatsuggests that market makers are constrained in

their liquidity provision by risk management and

other concerns at times of market stress

� Stock markets are more liquid than other markets

� So, you should expect this supply e�ect to bemagni�ed in other markets (e.g. ABS)


Aragon and Strahan (2012, JFE)

� Do hedge funds provide liquidity?

� Same as: are HFs bene�cial to �nancial markets?

� Test of Brunnermeier and Pedersen (2009)

� Funding liquidity impacts market liquidity

� But feedback e�ect (market liquidity ! funding

liquidity) complicates identi�cation

� Need an exogenous shock to funding liquidity

� Also, HFs' strategy is to get into illiquid positionsto provide liquidity and get out when liquidity im-

proves

� So, there is correlation between HF presence inan asset and the evolution of liquidity

� Need exogenous variation in HF presence in themarket

� Lehman bankruptcy (September 15, 2008) pro-vides this natural experiment


The prime-broker

� Lehman Brothers, among other activities, oper-ated as prime broker to many HFs

� A prime-broker for a HF acts as: custodian for

securities, security lender (short sales), �nancier

(buying on margin), risk manager (for smaller

funds)

� The authors focus on re-hypothecation activitiesof prime-broker

� Re-hypothecation: a broker is allowed to lend aclient's securities to another client who wants to

do short sales

� Re{hypothecation can have many layers

� Counterparty risk: if the prime-broker goes bank-rupt, the lent-out securities may never return to

their original owner

� This is a problem for the original HF that loses

part of its capital


� The paper uses the bankruptcy of Lehman as anexogenous shock to the HF's capital, for the HFs

that had Lehman as a prime-broker

� Data on prime-brokers from TASS

� Then, they look at the liquidity of the stocks thatwere largely owned by the HFs which had Lehman

as a broker around its bankruptcy

� Did liquidity decrease?

� Data on ownership from 13F �lings


E�ect of Lehman's bankruptcy on

HFs

� First, they want to show that Lehman's bank-ruptcy had a negative impact on the connectedHFs

� Estimate hazard rate models

� These are econometric models that estimate theimpact of covariates on the failure probability

� Failure proxied by disappearance of HF from TASS

� Explanatory variable of interest: 2008 dummy *Lehman fund dummy

� Estimated coe�cient > 1 positive e�ect


� In all speci�cations, the variable of interest (be-ing a Lehman connected fund, in year of Lehman

bankruptcy) is > 1

� Magnitude: 2.42 means that Lehman funds in2008 were 2.42 times as likely to fail compared

to Lehman funds before the crisis

� Bottom line: the bankruptcy of the prime-broker

had a negative impact on connected funds


E�ect on liquidity

� Next, they want to show that connected HFs de-creased their liquidity provision

� Notice �rst that liquidity decreased across theboard in the stock market after Lehman's collapse

� Next, use regression analysis to show that liquiditydecreased for stocks owned by connected funds

(as de�ned in June 2008)

� Pre-crisis and Post-crisis: 3 months before and 3months after September 15, 2008


� Excluded category from regression is holdings by

non-institutional investors (notice that you can-

not have this variable in the regression because

of perfect collinearity with the other ownership

variables, as they add up to 1)

� Relevant tests:

{ 1 = 0, test if Lehman connected HF own-

ership e�ect is di�erent from non-institutional

ownership

{ 1 = 2, test if Lehman connected HF own-

ership had same e�ect as other HF

{ 1 = 3, test if Lehman connected HF owner-

ship had same e�ect as other non-HF-institution


� Lehman connected HF ownership increased illiq-uidity in most speci�cations (and decreased re-

turns)

� The three null hypotheses above are rejected

� It turns out that ownership by other HFs and in-stitutions mitigated the drop in liquidity due to

Lehman connected HF ownership (negative coef-

�cient)

� The negative impact on returns of Lehman con-nected HF ownership suggests �re sales by these

HFs


Robustness: Bear Stearns

� They want to show that it is the disappearanceof the brokerage services that caused the drop inliquidity, as opposed to the news that a majorbank went bust

� Compare with Bear Stearns failure

� BS was bailed out by JP Morgan, which took overits activities

� No disruption to BS-connected HFs

� Focus on March 2008


� No e�ect on liquidity of connected HF ownership

� Consistent with their conjecture


E�ect by liquidity groups

� The increase in illiquidity due to Lehman con-nected HF ownership was larger for stocks that

were already illiquid

� Consistent with liquidity betas (�2 in Acharyaand Pedersen 2005) being larger for more illiquid

stocks


Which dimension of liquidity

deteriorated?

� Following Sadka (2006) they decompose liquidityinto two dimensions

� Using transaction data, they estimate price im-pact components that are due to:

{ Information asymmetry (permanent impact of

order ow on prices)

{ Transaction costs (transitory impact of order

ow on prices)

� For stocks owned by Lehman connected HFs they�nd that:

{ Permanent price impact # (improvement in liq-uidity)

{ Transitory price impact " (deterioration in liq-uidity)

� Interpretation:


{ HFs are liquidity providers, they trade patiently,

and take the other side of liquidity demand (u)

{ But HFs are also informed traders. So they

increase the cost of trading for their counter-

parties (the market-makers)


Conclusions

� The authors �nd a plausible source of exogenousvariation in arbitrageurs' ability to provide liquid-

ity

� They �nd evidence that when funding liquiditydeteriorates also market liquidity deteriorates

� They cannot trace the continuation of the liquid-ity spiral in Brunnermeier and Petersen (2009)


Ben-David, Franzoni, Moussawi

(2012, RFS)

� Hedge funds (HFs) resemble the textbook arbi-trageurs

{ Sophisticated: trade across assets and markets

{ Use leverage

{ Engage in short selling

� However, HFs depend on outside �nancing

{ Vulnerable to investor redemption of capital

{ Vulnerable to margin calls

� Did HFs continue to provide liquidity in the crisisof 2007-2009 or did they run into �nancial con-

straints?

� Evidence that liquidity provision was hampered:Aragon and Strahan (2010), Nagel (2010)


The data (long positions)

� HFs long equity holdings in U.S. stocks at quar-terly frequency:

{ Thomson 13F Institutional Ownership

{ No survivorship/self-reporting biases

{ All management companies with more than

$100 million in U.S. equity

� Match with proprietary HF identi�cation list pro-vided by Thomson

� Using ADV �lings, keep pure-play HF (e.g., no

Goldman Sachs)

� Manually match a subset with TASS for returnsand characteristics

� Sample period: 2004Q1{ 2009Q4


Equity portfolioTotal AUM ($m, TASS match)

Year 13F TASS match in TASS ($bn) Mean(1) (2) (3) (4)

2004 436 104 93 4662005 530 124 112 5972006 606 133 147 7472007 693 136 189 9102008 696 114 149 6102009 612 98 147 521

Number of Mgrs.


The data (short interest)

� Hedge fund short positions not reported in 13F

� Use short interest from the exchanges at stock

level

� Assume that short interest is mostly driven byhedge funds

� Boehmer and Jones (2008): 55% to 70% of short

interest is by institutions

� Goldman Sachs (2010): up to 85% of short inter-

est by hedge funds


The data (mutual funds and clients)

� We compare hedge funds to mutual funds

{ CRSP Mutual Funds data: ows, returns

� We analyze the ownership structure of hedge funds

{ ADV ownership data: coarse ownership struc-

ture

{ Became mandatory in 2009, therefore may in-

duce survivorship bias

� Summary statistics on aggregate data:

N Mean St.Dev. Min Median MaxHF holdings over mkt cap (%) 24 2.420 0.549 1.460 2.500 3.190∆ HF Holdings (%, share of equity holdings) 24 3.390 8.010 16.700 4.500 13.900∆ HF Holdings (%, share of mkt cap) 24 0.066 0.199 0.489 0.118 0.336MF holdings over mkt cap (%) 24 13.400 0.799 12.200 13.500 14.700∆ MF Holdings (%, share of mkt cap) 24 0.077 0.096 0.094 0.067 0.296Other inst. holdings over mkt cap (%) 24 40.900 2.010 34.100 40.600 44.500∆ Other inst. holdings (%, share of mkt cap) 24 0.005 0.934 2.370 0.202 1.620Retail holdings over mkt cap (%) 24 43.300 2.130 39.900 43.100 50.800∆ Retail holdings (%, share of mkt cap) 24 0.138 0.879 1.360 0.331 2.330Short interest ratio (SIR) (%) 24 2.740 0.515 2.090 2.660 3.830∆ Short interest ratio (∆ SIR) (%, share of short interest) 24 1.180 8.740 20.700 1.340 19.800∆ Short interest ratio (∆ SIR) (%, share of shares outstanding) 24 0.041 0.260 0.605 0.029 0.676


Results: HF trading

1.5

2

2.5

3

3.5

% o

f tot

al m

arke

t cap

italiz

atio

n

2004

q1

2004

q2

2004

q3

2004

q4

2005

q1

2005

q2

2005

q3

2005

q4

2006

q1

2006

q2

2006

q3

2006

q4

2007

q1

2007

q2

2007

q3

2007

q4

2008

q1

2008

q2

2008

q3

2008

q4

2009

q1

2009

q2

2009

q3

2009

q4

Quarter

Quant MeltdownAugust 2007

Lehman CollapseSeptember 2008

� Drastic declines in the fraction of the stock mar-ket owned by HFs around two critical events

� Look at actual trades evaluated at prior periodprices (to �lter out the change in prices during

the quarter)


� The sello�s took place in four quarters: Q3/Q4of 2008 and 2009


What about the short side?

2

2.5

3

3.5

4

% o

f tot

al m

arke

t cap

italiz

atio

n

2004

q1

2004

q2

2004

q3

2004

q4

2005

q1

2005

q2

2005

q3

2005

q4

2006

q1

2006

q2

2006

q3

2006

q4

2007

q1

2007

q2

2007

q3

2007

q4

2008

q1

2008

q2

2008

q3

2008

q4

2009

q1

2009

q2

2009

q3

2009

q4

Quarter

Quant MeltdownAugust 2007

Lehman CollapseSeptember 2008

� High correlation of short interest with HF longequity holdings (42%)

� The correlation is 79% during the crisis period

� Long and short positions move in tandem


Net e�ect?

� Do the changes in short positions cancel out withthe changes in long position, so that net e�ect onliquidity is zero?

� At the stock level, regress change in HF long po-sition onto the change in short interest

� Correlation is at most 9%

� Liquidity is removed from stocks that hedge fundshold (\undervalued"), and added to stocks thathedge funds short sell (\overvalued").

� Hence, the exit of hedge funds and short-sellersleads to greater mispricing


Who bought?

Mutual funds Other institutions Retail investors(1) (2) (3)

Precrisis 2004Q12007Q2 0.1 0.1 0.3Crisis 2007Q32009Q1 0.0 0.4 0.5Postcrisis 2009Q22009Q4 0.1 0.8 1.1

Selloff quarter 2007Q3 0.1 1.6 1.4Selloff quarter 2007Q4 0.1 2.4 2.3

2008Q1 0.1 0.2 0.32008Q2 0.1 1.1 1.0

Selloff quarter 2008Q3 0.0 0.3 0.8Selloff quarter 2008Q4 0.1 0.9 0.5

2009Q1 0.1 1.8 1.4

Avg Qtr ∆ Holdings (% of total mkt cap)

� Stocks sold by hedge funds are absorbed by

{ Other institutions (excluding mutual funds):

Q3 of 2007 and Q4 of 2008

{ Retail investors: Q4 of 2007 and Q3 of 2008


Why did HFs sell?

� Balance sheet of a HF

Assets Liabilities

U.S. Stocks Equity (AUM)

Other investments Debt(including Cash) (including Short positions)

�U:S:Stocks = �AUM+�Debt��OtherInvestments

� We can construct fund ows (�AUM) using TASS

� But. . .

{ No time-series dimension on leverage

{ No direct information on other investments

{ No fund level information on short positions

� We need empirical proxies to identify channelsother than �AUM


Financial constraints

� We test whether the large sello�s were due to�nancial constraints in the form of:

{ Investor redemptions

{ Margin calls

{ Risk management constraints


Investor redemptions

Selloff quarter 11.529*** 6.516(4.130) (1.718)

Fund flows 0.160(0.874)

lead(Fund flows) 0.396***(3.892)

lead2(Fund flows) 0.157*(2.036)

Observations 2053 2053Adj R2 0.009 0.038

Dependent variable: ∆ HF equity portfolio (%)

� Fund-quarter level regressions

� Dependent variable: % change in equity portfolio

value

� Sello� quarter dummy: Q3/Q4 of 2007 and 2008

� Future fund ows explain 43% of sello� dummy

� Most direct evidence of selling motive


Margin calls + Risk limits

Selloff quarter 12.118*** 6.991 2.653(4.445) (1.564) (0.544)

× Avg. leverage 5.982** 5.711***(2.281) (2.903)

Fund flows 0.193(1.461)

lead(Fund flows) 0.384**(2.400)

lead2(Fund flows) 0.060(0.954)

Avg. leverage 4.476*** 4.326***(4.293) (4.382)

Observations 1332 1332 1332Adj R2 0.009 0.016 0.039

Dependent variable: ∆ HF equity portfolio (%)

� Conjecture: higher leverage ! higher likelihood

of forced deleveraging

� Con�rmed by the data

� Financial constraints (Redemptions + Leverage):

explain 78% of sello�s


Which stocks are sold?

� Analysis of stock characteristics can reveal mo-tives of sello�s

� We �nd that during the crisis HFs sold:

{ High volatility stocks rather than low volatility

stocks

� Consistent with margin calls and risk man-agement (Brunnermeier and Pedersen 2009)

{ Low price impact stocks rather than high price

impact stocks

� Consistent with management of price im-pact during �re sales

� Also, short interest is mostly closed on high volatil-ity stocks

� Overall, evidence is consistent with �nancial con-straints channel


HFs vs. Mutual Funds

� Use mutual funds as benchmarks for hedge fundbehavior

� Similarities:

{ Investment in the equity market

{ Active investing

� Major di�erences:

{ Hedge funds use high leverage and short posi-

tions

{ Hedge funds have restrictions on capital with-

drawals

{ Hedge fund investors are more sophisticated

(institutional investors)


Di�erence in behavior

� Compared to MFs, HFs had:

{ Higher redemptions

{ Higher sales of stocks (MF almost did not sell)


Performance- ow sensitivity

� It has to be the case that investors of the twotypes of funds react di�erently to negative per-

formance

� Prior literature:

{ Mutual fund investors exhibit convex performance-

ow sensitivity

� Strong in ows following good past perfor-mance

� Weak out ows following bad past perfor-mance

� Hedge fund investors exhibit linear ow-performancesensitivity (Li, Zhang, Zhao 2011)

� Hedge funds' ow-performance relation is moresensitive when liquidity restrictions are stricter (Ding,

Getmansky, Liang, and Wermers 2010)

� Liquidity restrictions:


{ Lockup period

{ Redemption notice

{ Redemption frequency

� Sophisticated investors react more strongly to pastperformance (Calvet, Campbell, and Sodini 2009)


Performance- ow sensitivity: MFs vs

HFs

� TRank i (i=1,2,3): is a dummy that categorizesprior-quarter performance in three terciles

� The dependent variable is the Flows into the fundas a fraction of AUM

Ranking / sample:Sample period: All qtrs NonCrisis Crisis All qtrs NonCrisis Crisis

TRank1 0.072** 0.116** 0.036 0.094*** 0.129*** 0.010(2.067) (2.715) (0.929) (3.146) (3.353) (0.393)

× I(Hedge fund) 0.133*** 0.147*** 0.111* 0.120*** 0.123** 0.115**(3.601) (3.062) (1.970) (3.425) (2.618) (2.542)

TRank2 0.049** 0.091*** 0.057 0.050** 0.093*** 0.056(2.061) (3.661) (1.941) (2.093) (3.723) (1.865)

× I(Hedge fund) 0.099*** 0.118*** 0.038 0.117*** 0.154*** 0.020(3.831) (3.691) (0.967) (3.771) (4.004) (0.649)

TRank3 0.538*** 0.593*** 0.402*** 0.523*** 0.584*** 0.372***(11.253) (11.001) (4.832) (10.851) (10.716) (4.783)

× I(Hedge fund) 0.096* 0.159** 0.060 0.124** 0.192*** 0.042(1.744) (2.721) (0.562) (2.137) (3.077) (0.402)

Calendar Quarter FE Yes Yes Yes Yes Yes YesObservations 204240 145262 58978 204240 145262 58978Adj R2 0.082 0.080 0.084 0.080 0.078 0.081Controls: I(Hedge fund), log(AUM)

Absolute ranking Withinstyle rankingDependent variable: Flows (q+1) / AUM (q)

� Hedge funds have higher sensitivity of ows tobad performance


Performance- ow sensitivity:

liquidity restrictions

� Create a dummy variable for HFs with high liq-uidity restrictions: I(HF with constraints)

Ranking / sample:Sample period: All qtrs NonCrisis Crisis All qtrs NonCrisis Crisis

TRank1 0.072** 0.117** 0.035 0.095*** 0.130*** 0.011(2.077) (2.720) (0.910) (3.155) (3.358) (0.406)

× I(Hedge fund) 0.091** 0.091* 0.100 0.086** 0.070 0.123*(2.264) (1.776) (1.420) (2.175) (1.363) (2.219)

× I(HF with constraints) 0.070** 0.100** 0.009 0.062** 0.101*** 0.020(2.128) (2.406) (0.189) (2.162) (2.987) (0.435)

TRank3 0.538*** 0.593*** 0.401*** 0.522*** 0.583*** 0.371***(11.234) (10.999) (4.813) (10.835) (10.711) (4.765)

× I(Hedge fund) 0.118* 0.202** 0.094 0.155** 0.247*** 0.071(1.759) (2.833) (0.754) (2.327) (3.699) (0.567)

× I(HF with constraints) 0.050 0.084* 0.044 0.060 0.104** 0.053(1.336) (1.884) (0.661) (1.596) (2.579) (0.766)

Calendar Quarter FE Yes Yes Yes Yes Yes YesObservations 204240 145262 58978 204240 145262 58978Adj R2 0.082 0.080 0.085 0.080 0.079 0.081Controls: I(Hedge fund), log(AUM), I(HF with constraints), TRank2 + interactions

Absolute ranking Withinstyle rankingDependent variable: Flows (q+1) / AUM (q)

� Hedge funds with liquidity restrictions have highersensitivity of ows to bad performance

� During crisis: no sensitivity (evidence of gate rais-ing?)


HF behavior and investor base

� Are individual investors less sensitive than institu-tional investors to bad performance?

� Exploit heterogeneity in HF investor base

� Dependent variables: � HF equity holdings or

Flows into the fund

� Explanatory variable of interest: Fraction of fundowned by institutions*Crisis dummy

I(Crisis) defined as: 07Q309Q1 Selloff Qtrs 07Q309Q1 Selloff QtrsI(Crisis) 0.117 3.321 1.678 16.458**

(0.034) (1.622) (0.196) (2.480) × Institution ownership 2.633*** 1.137** 2.491** 0.034

(4.995) (2.586) (2.410) (0.119) × I(Lockup period) 3.903 0.380 4.039 1.508

(0.554) (0.120) (0.552) (0.417) × I(Redemption period > 90) 12.358 7.790* 12.496 8.510**

(1.344) (2.016) (1.400) (2.131)

Observations 1474 1477 1474 1477Adj R2 0.043 0.057 0.043 0.060Controls: Institutional ownership, I(Lockup period), I(Redemption period > 90), constant

Flows (q+1) / AUM (q)∆ HF equity portfolio (%)


� High institutional ownership! higher sales, greater

out ows during the crisis

� Potential driving factors:

{ Institutional investors more sophisticated, hence

more reactive

{ Risk management controls in the institutions

that force them to sell

{ Career concerns for managers within the insti-

tutions that need to justify poor performance


Conclusions

� Hedge funds drastically decreased their equity hold-ings during the last crisis

� Main driving force is capital withdrawals and pres-sure by lenders

� Hedge funds are di�erent because:

{ Investors react aggressively to past losses

{ Reaction is stronger when capital restrictions

are in place

{ Stronger sello�s and redemptions for hedge

funds with high institutional investors

� Strong support for limits to arbitrage in bad times(Brunnermeier and Pedersen, 2009)

� For the most part, HFs liquidity provision seemsto be pro-cyclical

� This result compounds with evidence that broker-dealers expand/contract their balance sheets in a

pro-cyclical manner (Adrian and Shin 2010)


Ben-David, Franzoni, Landier,

Moussawi (2013, JF)

� HFs are considered to be liquidity providers

{ Correct mispricing

{ Make markets e�cient

� However, evidence suggests that this is not alwaysthe case (limits of arbitrage)

� For example: Brunnermeier and Nagel (2004),Ben-David, Franzoni, Moussawi (2011)

� Another potential dimension is: moral hazard inthe relationship with their clients

� They could take actions to manipulate the re-ported performance and earn higher fees

� For example: pump up stock prices to in ate port-folio returns

� Consequence: market prices contain noise

� Question: do HFs distort market prices to `game'their compensation scheme?


Performance evaluation and fees

� HFs earn management fees: typically 2% of assets

under management (AUM)

� They also earn a performance fee: typically 20%of return above a hurdle rate

� They earn performance fee only for returns thatare above a high watermark, that is, the highest

level of AUM ever reached

� HFs report performance monthly

� Investors, when making investment decisions, typ-ically evaluate funds based on year-to-date (YTD)

performance, and compare them to other funds

� HFs have incentive to manipulate performance to:

{ Earn more management fees, by retaining the

clients

{ Earn more performance fees, if returns above

high watermark

{ Attract new clients and increase AUM


What kind of manipulation?

� HFs could pump up the prices of the stocks intheir long portfolio

� They can do that by buying more of these stocks

� And push down the prices of stocks in their shortpositions

� Blocher, Engelberg, and Reed (2010) show that

short sellers push down prices of short stocks at

the end of the year

� Manipulation is likely to have an impact on monthlyreturns if it happens at the end of the month

� ...Actually at the end of the day

� This is temporary price pressure: it should revertquickly


Evidence of manipulation?

� Look at daily returns and create a dummy forstocks with above median HF ownership

� That is, stocks that are held by HFs more thanothers

� On the last day of the month, high HF ownershipstocks earn 18bps more than other stocks (riskadjusted returns)

� This e�ect reverts over the next two days (mostlyon the �rst day of the next month)

� Consistent with HFs pumping up the price of stocksthey own


End-of-day?

� Action is strongest at the end of the last day ofthe month


Incentive to manipulate: stock level

� Which stocks are more likely to be manipulated?

� Those for which:

{ Price impact is larger (less liquid): look at

Amihud measure

{ Have a bigger weight in the HF portfolio

� At the stock level, create incentive groups basedon: Amihud * Weight in aggregate HF portfolio

� More incentive, bigger blip (=end-of-month jumpin price and reversal on the next day)


Fund level evidence

� Are these blips in stock returns re ected in blipsin HFs' returns?

� Fund level analysis using total returns

� Strong blip on last day of the month, in all quar-ters


Which funds manipulate?

� Incentives are stronger for funds:

{ which want to avoid a very bad month

{ which are having a very good YTD perfor-

mance and can beat their pears

{ less costly for concentrated funds

� Predictions are con�rmed


Tighter predictions

� YTD E�ect higher for young funds

{ Higher returns from being noticed

{ Beliefs of investors more elastic (Bayesian)

� YTD E�ect higher for funds with previous poor

ranking

{ Bene�t more from recategorization

� YTD E�ect higher in March

{ Elasticity of relative YTD ranking to monthly

performance is higher

� All predictions are con�rmed in the data


Conclusions

� The agency relation between HFs and their clientsgenerates another dimension along which HFs are

limited in their ability to make markets more e�-

cient

� The paper �nds that HFs add noise to monthlyprices

� Monthly prices are a very important signal in theeconomy (performance evaluation, derivative con-

tracts, etc.)

� So, in this case, it's not just about HFs failing tocorrect mispricing, it is more serious than that:

HFs distort the e�ciency of market prices


Francesco Franzoni Swiss Finance Institute - University of ...

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