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The model – setup
The model – setup
The model – setup
The model – setup
The model – setup
The model – setup
The model – setup
The model – setup
The model – setup
The model – setup
The model – payoff structure
The model – payoff structure
The model – payoff structure
The model – payoff structure
The model – payoff structure
The model – payoff structure
The model – payoff structure
The model – payoff structure
The equilibrium - benchmark
The equilibrium - benchmark
The equilibrium - benchmark
The equilibrium - benchmark
The equilibrium - benchmark
The equilibrium - benchmark
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T1/2
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
The full equilibrium: decisions at T0
A numerical example
A numerical example
A numerical example
A numerical example
The model implication
The model implication
The model implication
The model implication
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The Fragile Capital Structure of Hedge Funds and the Limits to Arbitrage

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1The Fragile Capital Structure of Hedge 10make notices to fund about redemption.
Funds and the Limits to Arbitrage Xuewen 11The model – payoff structure. Redeem:
Liu Antonio S. Mello Imperial College Stay:
Business School February 2009. 12The model – payoff structure.
2During a financial crisis, when 13The equilibrium - benchmark. The
markets most need liquidity and arbitrage trade-off In case ??X: liquidate 0 units
tradings, hedge funds often reduce their In case ?>X: liquidate The expectation
exposures and positions. Between July and of fund’s equity value at T2 : The unique
August in 2008 alone, the hedge fund optimal cash holding:
industry's cash holdings rose from $156 14The full equilibrium. Idea
billion to a record $184 billion, Coordination problem among late investors
equivalent to 11% of assets under causes ex-post potential run Fund mangers
management (The Economist, October 25, factor the ex-post run into ex-ante cash
2008). Facts and evidence. holding decision Procedure: backward
3Why it is puzzle? Micro perspective induction Investors’ redemption decisions
Hedge funds’ expertise would present them at T1/2 given the cash holding X The
with greater opportunity from the more fund's optimal cash holding decision at T?
frequent and more evident misalignment in 15The full equilibrium: decisions at
prices during a crisis. Why did they do T1/2. Late investor i’s decision rule: Two
the opposite? ---“Be fearful when others dominance regions of ? The lower dominance
are greedy and greedy when others are region : dominate strategy (?i ,X) ? stay
fearful” (Warren Buffett) Social Assumption: no discounting at fire sale
perspective Hedge funds' behavior had a (i.e. ?=1) The upper dominance region :
negative impact on the functioning of dominant strategy(?i ,X)? Withdraw where
financial markets. Without arbitrage, no solves WS(s)=WR(s) and To verify: , so
correct price signals, the vicious cycle that the upper region exists.
of lower price informativeness and less 16The full equilibrium: decisions at
liquidity. T1/2. The threshold equilibrium The
4The research questions. Research equilibrium where every late investor sets
questions: Why hedge funds, aggressive a threshold and uses the threshold
investors seeking high returns, hold strategy such that, given that all other
riskless assets? Why hedge funds quickly late investors set the threshold as , it
increase their cash holdings during a is optimal for a late investor himself to
crisis? What factors determine the cash do that. The unique threshold equilibrium.
holdings in hedge funds' balance sheets? 17The full equilibrium: decisions at
Cash is negative debt. Alternately, why T1/2. Step 1: Given the realized ? and the
hedge funds have lower leverage than threshold , the proportion of late
investment banks? investors running: Step 2: For the late
5Why these questions matter? To help investor i, his expected net payoff of
understand an important phenomenon – staying versus redeeming: Step 3: For the
limits to arbitrage Holding cash/riskless marginal late investor who receives the
assets is synonymous to hedge funds threshold signal :
limiting their arbitrage activities. The 18The full equilibrium: decisions at
limits-to-arbitrage is one of three key T1/2. When ??0, s(?, ?*) is uniformly
elements to understand financial crisis distributed within the interval [?*,1].
(Allen (2009)). Geometrically,
6Existing explanation. Shleifer and 19The full equilibrium: decisions at
Vishny (1997): Asymmetrical information: T1/2. The existence of The threshold
investors do not understand or perfectly increasing in X.
observe the trades and positions taken by 20The full equilibrium: decisions at T0.
arbitrageurs Investors might react with The total number of investors redeeming
their feet to short-term bad performance. Only consider the case of Equilibrium
Ex ante, professional fund managers decide selection : the unique threshold
to abstain from taking positions that equilibrium : staying-strategy equilibrium
might lose money in the short term, which Consider two regions of X, in order i) ii)
limits arbitrage. where.
7Our explanation. Strategic risk rather 21The full equilibrium: decisions at T0.
than fundamental risk causes the limits to The expectation of fund’s equity value at
arbitrage No information asymmetry: T2 : First order condition The trade-off
investors know perfectly the long-term First term: high return and costly fire
performance of hedge funds' position sale; the tradeoff in benchmark; being
Frictions result from market illiquidity negative when X is high Second term: the
and the fragile nature of the equity The effect of increasing surviving window ? on
frictions mean that investors care about fund value The unique optimal cash holding
both fundamentals and the actions of other X:
investors Both strategic risk (i.e. 22The full equilibrium: decisions at T0.
uncertain about what other investors will We check the change of WII(X) when X is
do) and fundamental risk cause redeem. slightly changed at X=X* The first term is
Hedge fund managers , in response to negative and the second term is positive.
ex-post possible run, decide to limit Overall, Run causes more cash holding: Two
arbitrage ex ante. Investors worry about effects of run on cash holing Response
both asset side and liability side of effect : the size of redemption is changed
balance sheets of hedge funds. Signalling effect: cash can assure
8Our Framework. We use global game inventors and reduces the probability of
techniques to model the asset allocation run.
decision of a hedge fund that is subject 23The full equilibrium: decisions at T0.
to the possibility of a run by its The expected fund value at the second
investors. Solve the unique optimal cash region of X Not optimal to hold cash in
holding with and without the run effect this region Intuitively, too much cash
The coordination problem and the panic run convinces investors not to run, but it is
induce hedge funds to hold more cash ex too costly.
ante Run is due to funding-liquidity 24A numerical example.
reasons rather than fundamental reasons 25The model implication. Suppose that
Brunnermeier (2009) discusses two reasons the hedge fund manager's reservation
The run can be fundamental-driven as in utility (opportunity cost) is C.
Goldstein and Pauzner (2005). WI(X*,R)?C and WII(X*,R)?C The limited
9Related Literature. Limits to arbitrage opportunity R such that
arbitrage: Schleifer and Vishny (1997), WI(X*,R)>C> WII(X*,R) Define.
Stein (2005) Coordination problem: Diamond 26Discussions. The difference between
and Dybvig (1983), Goldstein and Pauzner hedge funds and banks Both liability and
(2005), Chen, Goldstein and Jiang(2007) equity of hedge funds are fragile while
Applciaitons of global game: Bank run only debt is fragile for banks Capital
(Rochet and Vives (2004), Goldstein and fragility encourages micro-prudence
Pauzner (2005)); currency crises (Morris Investment decision: less risky investment
and Shin (1998), Corsetti, Dasgupta, Financing decision: lower leverage These
Morris, and Shin (2004)); contagion of conservative behaviors of hedge funds help
financial crises (Dasgupta (2004), them survive better Capital fragility
Goldstein and Pauzner (2004)); market limits arbitrage and implies
liquidity (Morris and Shin (2004), Plantin macro-unsoundness.
(2009)). 27Conclusions. A new explanation of
10The model – setup. Four dates: T0 : X limits to arbitrage Coordination risk in
in cash, 1-X in long-term illiquid asset addition to fundamental risk matters
T1 : ? proportion are ‘early’ investors Fragile equity structure plus low market
needing to redeem, ? uniformly Discounted liquidity leads to coordination risk
price at fire sale of illiquid asset: ?, Fragility encourages micro-prudence but
where ?<1. T2 : the illiquid asset leads to macro-unsoundness An unregulated
realizes gross return R, where R>1. : sector of the financial industry can be
each investor knows whether he is ‘early’ safer than a regulated sector because of
or not. Late investor i receives signal ; the nature of the financial contracts that
?i uniform in [- ? ,+ ?]. All investors exist in each case.
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