Amplification Mechanisms in Liquidity Crises
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Transcript of Amplification Mechanisms in Liquidity Crises
Amplification Mechanisms in Liquidity Crises
Arvind KrishnamurthyNorthwestern University
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Amplification
• Losses on Subprime Mortgages (Fall 07 est.)– At most $500 bn
• Decline in world stock market (Sep 08 to Oct 08)– Close to $26,000 bn
• Expected output losses (IMF forecast)– $4,700 bn
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Amplification Mechanisms
• I am going to describe two financial mechanisms that have played an important role in the crisis1. Balance sheet amplification2. Uncertainty amplification
• I omit …– Subprime was the trigger for a real estate
bubble bursting– Aggregate demand effects
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Liquidity model
• Investors (continuum) A and B own one unit of an asset at date s
• Intermediary (bank/market-maker/trading desk) provides price support at date t>s:– Promises to provide liquidity to sellers at P=1– But, Bank has only 2 > L > 1 units of liquidity
• Investors may receive shocks that require them to liquidate:– φA , φB
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Fundamental equilibrium at date t
• One of four states– No shocks: P = 1– A shock: P = 1– B shock: P = 1– A and B shocks: P = L/2
• Date s price:– Ps = 1 – (1 – L/2) φA φB
– Liquidity discount = (1 – L/2) φA φB
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Balance Sheet Considerations• Define the “equity net worth” of an investor as
W = Pt – Ds
• Suppose date t holdings are subject to a capital/collateral constraint
m Θt < W• 1 – Θt is amount liquidated if constraint binds:
1 – Θt = 1 - (Pt – Ds) /m
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Pt = 1
Lt
Lt = 1 – (Pt - Ds)/2m
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Consider states (A) or (B)
• P = 1 is equilibrium if L is small
• If Ds is large, liquidation curve shifts up and right
• Or, larger fundamental liquidity shock, liquidation curve shifts up and right
• Or, m increases, twists liquidation function
• All cases, multiple equilibria
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Pt = 1
Lt
Lt = 1 – (Pt - ds)/2m
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E2
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Policy Response: Add liquidity (increase L)
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Pt = 1
Lt
Lt = 1 – (Pt - ds)/2m
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Policy Response: Discount loans at m* < m
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Pt = 1
Lt
Lt = 1 – (Pt - ds)/2m
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E2
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Policy Response: Buy distressed assets
Crisis Policy
1. Liquidity injection2. Buying troubled assets3. Discount lending4. Equity injections …
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Ex-ante Policy• If we push the model further (I wont here), there
is another policy that pops up:– Ex-post externalities that agents don’t
internalize ex-ante• Over-leveraging in the financial sector
• Ex-ante leverage limitation.
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Recap
• So far, liquidation model
• Next, Uncertainty and Crises
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Uncertainty
• Subprime crisis:– Complex CDO products, splitting cash flows in
unfamiliar ways– Substantial uncertainty about where the losses lie– But less uncertainty about the direct aggregate
loss (small)
• Knightian uncertainty, ambiguity aversion, uncertainty aversion, robustness preferences
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Modeling:
• Standard expected utility– max{c} EP u(c)
– P refers to the agent’s subjective probability distribution
• Modeling ambiguity/uncertainty/robustness:– max{c} min{Q ϵ Q } EQ u(c)
– Q is the set of probability distributions that the agent entertains
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Uncertainty in the baseline model• Recall, agents may receive liquidity
shocks that makes them sell assets at date t• Shock probabilities are φA , φB
• Suppose agents are uncertain about the correlation between their liquidity shocks of A and B.
• ρ (A,B) ϵ [0, 1]16
Worst-case decision rules
• max{c} min{Q ϵ Q } EQ u(c) Worst-cases for A (and B) is ρ (A,B) = 1• Agents subjective probs only consider two
states• No shocks: P = 1• A and B shocks together: P = L/2
• Date s price:• Ps = 1 – (1 – L/2) φ• Liquidity discount = (1 – L/2) φ
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Compare to baseline case• One of four states
– No shocks: P = 1– A shock: P = 1– B shock: P = 1– A and B shocks: P = L/2
• Date s price:– Ps = 1 – (1 – L/2) φA φB
– Liquidity discount = (1 – L/2) φA φB
• Uncertainty magnifies the importance of the liquidation event: order(φ) versus order(φ2)
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Crisis Policy
• LLR policy again• Inject liquidity into bank in the event that
both shocks hit. – Liquidity discount = (1 – L/2) φ – Larger effect on agent’s uncertainty, but CB
delivers only with probability φA φB
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Ex-ante Policy
• In liquidity externality model, it was to reduce date s leverage
• More generally, this is about incentivizing better ex-ante risk management
• But does the central bank really know better?– Especially when it comes to new financial
products– History … everyone is blindsided in the same way
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Ex-ante Policy
• Policing new innovations, these are the trouble spots– Regulations slow new innovations
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Summary
• Two financial amplification mechanisms– Interactions
• Crisis policies are similar• Ex-ante policies are different
– Regulate leverage of financial sector– Regulate growth in particular of financial
innovation
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