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Market & Funding Liquidity Brunnermeier & Pedersen Capital Constraint & Model Market Liquidity and Funding Liquidity Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Markus K. Brunnermeier Lasse Heje Pedersen Commonality Flight to Quality Liquidity Risk Princeton, CEPR, NBER NYU, CEPR, NBER Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Motivation Brunnermeier & Pedersen Capital Constraint & • Market liquidity Model Capital • ease of trading an asset Model • asset-speciﬁc Time-series Fragility • Funding liquidity Liquidity Spirals • availability of funds Cross- Sectional • agent-speciﬁc Commonality Flight to Quality • these liquidity concepts are mutually reinforcing Liquidity Risk • funding liquidity to dealers, hedge funds, investment banks Skewness ∂m0 etc. > 0 ∂|Λ0 | Literature ⇒ enhances trading and market liquidity • market liquidity improves collateral value, i.e. lowers margins ⇒ eases funding restriction Market & Funding Liquidity Stylized Facts on Market Liquidity Brunnermeier & Pedersen Capital Constraint & Model Capital Model 1 Sudden liquidity “dry-ups” Time-series 2 Correlated with volatility Fragility Liquidity Spirals • cross section Cross- • time series Sectional Commonality Flight to Quality 3 Flight to quality Liquidity Risk 4 Commonality of liquidity Skewness • within asset class (e.g. stocks) ∂m0 ∂|Λ0 | > 0 • across asset classes Literature 5 Moves with the market Market & Funding Liquidity Outline Brunnermeier & Pedersen Capital 1 Capital Constraint - Model Setup Constraint & Model Capital Model 2 Time-series Properties Time-series Liquidity Dry-ups/ Fragility Fragility Liquidity Spirals Liquidity Spirals Cross- Sectional Commonality 3 Cross-Sectional Properties Flight to Quality Commonality of Market Liquidity Liquidity Risk Skewness Flight to Quality ∂m0 > 0 ∂|Λ0 | Literature 4 Risk of Liquidity Crisis Skewness and Kurtosis 5 Related Literature Market & Funding Liquidity Leverage and Margins Brunnermeier j+ & Pedersen • Financing a long position of xt > 0 shares at price j Capital pt = 100: Constraint & Model • Borrow 90 dollars per share; j+ Capital • Margin/haircut: mt = 100 − 90 = 10 Model j+ Time-series • Capital use: 10xt Fragility j− Liquidity Spirals • Financing a short position of xt > 0 shares: Cross- • Borrow securities, and lend collateral of 110 dollars per Sectional Commonality share Flight to Quality • Short-sell securities at price of 100 dollars Liquidity Risk j− • Margin/haircut: mt = 110 − 100 = 10 Skewness ∂m0 > 0 • Capital use: 10xtj− ∂|Λ0 | Literature • Margins/haircuts must be ﬁnanced with capital: j+ j− xtj+ mt + xtj− mt ≤ Wt j where xtj = xtj+ − xtj− Market & Funding Liquidity Capital Brunnermeier & Pedersen Capital Constraint & Model Capital Model • Capital Wt : Time-series • Equity capital Fragility Liquidity Spirals • LLP: NAV, subject to lock up • LLC: equity, reduced by assets that cannot be readily Cross- Sectional employed (e.g. goodwill, intangible assets, property) Commonality Flight to Quality • Long-term unsecured debt Liquidity Risk • line of credit (material adverse change clause) Skewness • bonds/ loans: diﬃcult to get for smaller securities ﬁrms ∂m0 ∂|Λ0 | > 0 • Short term debt: not counted Literature • short-term loans, commercial paper, demand deposits Market & Funding Liquidity Cross-Margining Brunnermeier & Pedersen Capital Constraint & Model • Margins/haircuts must be ﬁnanced with capital, Capital Model Time-series j+ j− xtj+ mt + xtj− mt ≤ Wt , (1) Fragility Liquidity Spirals j Cross- Sectional Commonality where xtj = xtj+ − xtj− Flight to Quality • Alternative: perfect cross-margining Liquidity Risk Skewness net out all oﬀsetting risks, including diversiﬁcation ∂m0 ∂|Λ0 | > 0 beneﬁts, leading to a portfolio constraint: Literature Mt xt1 , . . . , xtJ ≤ Wt (2) Market & Funding Liquidity Regulatory Capital Requirements Brunnermeier & Pedersen Capital Constraint & Model Capital Model • Basel Accord: banks Time-series • regulatory capital subject to constraint similar to (1) Fragility Liquidity Spirals • alternatively, a bank can use its own model similar to (2) Cross- • SEC Net Capital Rule: brokers Sectional Commonality • net capital = capital minus haircuts (compare to (1)) Flight to Quality • net capital must exceed a certain fraction of aggregate Liquidity Risk debt Skewness ∂m0 ∂|Λ0 | > 0 • Regulation T: customers of brokers trading US equity Literature • initial margin must be at least 50% Market & Funding Liquidity Model Setup Brunnermeier & Pedersen Capital • Time: t = 0, 1, 2, 3 Constraint & Model • J assets: Capital Model • fundamental value vtj = Et [v j ] with ﬁnal payoﬀ v j at t = 3 Time-series • stochastic volatility with ARCH structure Fragility Liquidity Spirals Cross- vtj = vt−1 + ∆vtj = vt−1 + σt εjt , where εjt ∼iid N (0, 1) j j Sectional j Commonality σt+1 = σ j + θ|∆vtj | Flight to Quality Liquidity Risk • Market participants Skewness ∂m0 > 0 1 risk-averse customers ∂|Λ0 | Literature 2 speculators (dealers, hedge funds, ...) 3 ﬁnanciers (set margins speculators face) • Competitive stable equilibria j • Let Λj := pt − vtj and |Λj | be a measure of illiquidity t t Market & Funding Liquidity Customers Brunnermeier & Pedersen Capital Constraint & • 3 diﬀerent types of customers k ∈ {0, 1, 2} Model Capital k k • CARA utility function: u(W3 ) = − exp{−γW3 } Model 2 Time-series • endowment shock zk in t = 3 s.t. k=0 z k =0 Fragility Liquidity Spirals • become aware of t = 3-endowment shocks zk Cross- Sectional • simultaneously at t = 0 [with prob. (1 − a)] Commonality Flight to Quality • sequentially at t = k ∈ {0, 1, 2} [with “small” prob. a < ¯] a Liquidity Risk k • wealth dynamics: Wt+1 = Wtk + pt+1 − pt (yk + zk ) t Skewness ∂m0 > 0 • customer k’s demand ∂|Λ0 | Literature j j v1 − p1 ytj,k = j − z j,k for t = 1, 2 γ(σt+1 )2 Market & Funding Liquidity Speculators/Dealers Brunnermeier & Pedersen Capital Constraint & Model Capital • risk-neutral Model • wealth dynamics: Wt+1 = Wt + pt+1 − pt xt + ηt+1 Time-series j+ j− xtj+ mt + xtj− mt Fragility Liquidity Spirals • margin constraint: j ≤ Wt Cross- Sectional • speculators’ demand for J = 1 Commonality Flight to Quality + Liquidity Risk Wt /mt if pt < vt − Skewness xti = −Wt /mt if pt > vt for t = 1, 2 ∂m0 − + > 0 ∈ −Wt /mt , Wt /mt if pt = vt ∂|Λ0 | Literature i x0 = ... Market & Funding Liquidity Financiers - Margin setting Brunnermeier & Pedersen Capital • Margins are set based on Value-at-Risk (VaR) Constraint & Model j j+ Capital π = Pr (−∆pt+1 > mt | Ftf ) Model Time-series Fragility • Informed ﬁnanciers (vt ∈ Ftf ): Liquidity Spirals j+ m1 −Λj Cross- j π = Pr (−∆v2 − Λj +Λj > m1 ) = 1 − Φ 2 1 j+ j 1 Sectional σ2 Commonality =0 Flight to Quality Liquidity Risk Skewness j+ j j m1 = Φ−1 (1 − π) σ2 + Λj = σ j + θ|∆v1 | + Λj 1 ¯ ¯ 1 ∂m0 > 0 j− j ¯ j j ∂|Λ0 | m = 1 ... = σ + θ|∆v | − Λ ¯ 1 1 Literature • Uninformed ﬁnanciers (for a → 0): j+ j− m1 = Φ−1 (1 − π) σ2 = σ j + θ|∆p1 | = m1 ¯ ¯ Market & Funding Liquidity Financiers - Margin setting Brunnermeier & Pedersen Capital • Margins are set based on Value-at-Risk (VaR) Constraint & Model j j+ Capital π = Pr (−∆pt+1 > mt | Fti ) Model Time-series Fragility • Informed ﬁnanciers ⇒ stabilizing margins j+ m1 −Λj Liquidity Spirals Cross- j π = Pr (−∆v2 − Λj +Λj > m1 ) = 1 − Φ 2 1 j+ j 1 Sectional σ2 Commonality =0 Flight to Quality Liquidity Risk Skewness j+ j m1 = σ j + θ|∆v1 |+Λj ¯ ¯ 1 ∂m0 j− ∂|Λ0 | > 0 m =σ ¯ j + θ|∆v j |−Λj ¯ Literature 1 1 1 • Uninformed ﬁnanciers (for a → 0) ⇒ destab. margins? j ¯ m1 = σ j + θ|∆p1 | ¯ Market & Funding Liquidity Brunnermeier 1 Capital Constraint - Model Setup & Pedersen Capital Constraint & 2 Time-series Properties Model Capital Liquidity Dry-ups/ Fragility Model Liquidity Spirals Time-series Fragility Liquidity Spirals Cross- 3 Cross-Sectional Properties Sectional Commonality Commonality of Market Liquidity Flight to Quality Flight to Quality Liquidity Risk Skewness ∂m0 ∂|Λ0 | > 0 4 Risk of Liquidity Crisis Literature Skewness and Kurtosis 5 Related Literature Market & Funding Liquidity Liquidity Dry-ups/Fragility Brunnermeier & Pedersen Capital Constraint & Model Deﬁnition 1 Capital ∗ Liquidity is fragile if the price correspondence pt (η1 , vt ) is Model Time-series discontinuous in ηt or vt . Fragility Liquidity Spirals Cross- Proposition 1 Sectional Commonality (i) With informed ﬁnanciers, the market is fragile at time 1 if Flight to Quality x0 is large enough. Liquidity Risk (ii) With uninformed ﬁnanciers, the market is fragile at time 1 Skewness ∂m0 > 0 if x0 large enough or if margins are increasing enough with ∂|Λ0 | Literature illiquidity Λ1 . The latter happens if θ is large enough (i.e. ARCH eﬀects are strong) and the ﬁnancier’s prior on a fundamental shock (1 − a) is large enough (i.e. a < ¯). a Market & Funding Liquidity Example: Informed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 (J = 1) Capital W1 W1 Constraint & Constraints: short: ¯ ¯ σ +θ|∆v1 |−Λ1 & long: ¯ ¯ σ +θ|∆v1 |+Λ1 Model Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Informed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & Model Short region (p1 > v1 ) & long region (p1 < v1 ) Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Informed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & Model Speculators’ demand Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Informed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & Model Add customers’ supply Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Informed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & Model ⇒ No fragility — “Cushioning eﬀect of margins” Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Uninformed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & W1 W1 Model Constraints: short: x1 ≥ − σ+θ|∆p | & long: x1 ≤ ¯ ¯ ¯ ¯ σ +θ|∆p1 | Capital 1 Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Uninformed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & Model Short region (p1 > v1 ) & long region (p1 < v1 ) Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Uninformed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & Model Speculators’ demand Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Uninformed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & Model Add customers’ supply — two stable equilibria Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Uninformed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Constraint & Model Add customers’ supply — fragility for η1 = −150 Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Example: Uninformed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 0 Capital Example: fragility due to destabilizing margins Constraint & Model Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature p1 as correspondence of η1 p1 as correspondence of ∆v1 Market & Funding Liquidity Example: Uninformed ﬁnancier, Brunnermeier & Pedersen ARCH & x0 = 10 > 0 Capital Constraint & Model Leveraged x0 -position — ‘tilted star’ & bankruptcy line Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Liquidity Spirals Brunnermeier & Pedersen Capital Constraint & Model Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Liquidity Spirals Brunnermeier & Pedersen Capital Proposition 2 Constraint & Model In a stable illiquid equilibrium with Z1 > 0, x1 > 0, and Capital Model Time-series ∂p1 1 = + . Fragility ∂η1 2 m+ + ∂m1 − x0 ∂p1 x1 Liquidity Spirals γ(σ2 )2 1 Cross- Sectional Commonality ∂m+ Flight to Quality A margin spiral arises if ∂p1 < 0, which can happen if 1 Liquidity Risk ﬁnaniers are uninformed and a is small. Skewness ∂m0 > 0 A loss spiral arises if speculators’ previous position is in the ∂|Λ0 | Literature opposite direction as the demand pressure x0 Z1 > 0. 1 1 l l2 = + 2 + 3 + ... k −l k k k Market & Funding Liquidity Example: 1987 Crash Brunnermeier & Pedersen Capital Constraint & • Increased volatility caused banks to require more margin Model Capital • funding problems for marketmakers Model Time-series • failures at NYSE, Amex, OTC, trading ﬁrms, etc. Fragility • “thirteen [NYSE specialist] units had no buying power” Liquidity Spirals Cross- because of their funding constraint (SEC (1988)) Sectional Commonality • ⇒ mutually reinforcing Flight to Quality Liquidity Risk • Fed response: Skewness “calls were placed by high ranking oﬃcials of the FRBNY ∂m0 ∂|Λ0 | > 0 to senior management of the major NYC banks, indicating Literature that ... they should encourage their Wall Street lending groups to use additional liquidity being supplied by the FRBNY to support the securities community” Market & Funding Liquidity Margin for S&P500 Futures Brunnermeier & Pedersen Capital Margin requirement for CME members Constraint & Model as a fraction of the S&P500 index level Capital Model 14% Time-series Fragility 12% Liquidity Spirals Cross- Black Monday 10/19/87 US/Iraq war LTCM Sectional 10% Commonality Flight to Quality 8% Liquidity Risk 6% Skewness ∂m0 > 0 ∂|Λ0 | 4% Literature 2% 1989 mini crash Asian crisis 0% Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06 Market & Funding Liquidity Example: 1998 Liquidity Crisis Brunnermeier & Pedersen Capital Constraint & Model Capital Model • Salomon closed down proprietary trading Time-series Fragility • η-shock: less aggregate funding of trading in certain Liquidity Spirals markets Cross- Sectional • Russian default Commonality Flight to Quality • ∆v -shock: adverse fundamental shocks Liquidity Risk • increased spreads & reduced market liquidity Skewness ∂m0 ∂|Λ0 | > 0 • increased margins/haircuts & reduced funding liquidity Literature Market & Funding Liquidity De-leveraging of I-Banks Brunnermeier & Pedersen Capital Constraint & esp. in Fall of 1998 — Source: Adrian-Shin (2008) Model Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Brunnermeier 1 Capital Constraint - Model Setup & Pedersen Capital Constraint & 2 Time-series Properties Model Capital Liquidity Dry-ups/ Fragility Model Liquidity Spirals Time-series Fragility Liquidity Spirals Cross- 3 Cross-Sectional Properties Sectional Commonality Commonality of Market Liquidity Flight to Quality Flight to Quality Liquidity Risk Skewness ∂m0 ∂|Λ0 | > 0 4 Risk of Liquidity Crisis Literature Skewness and Kurtosis 5 Related Literature Market & Funding Liquidity Multiple Assets - Speculators’ Optimal Strat Brunnermeier & Pedersen Speculator maximizes expected proﬁt per capital use Capital Constraint & • expected proﬁt j j v1 − p1 = −Λj or −(v1 − p1 ) = Λj 1 j j 1 Model j Capital • capital use m1 Model Time-series Shadow cost of capital, funding liquidity, Fragility Liquidity Spirals j j j j Cross- v1 − p1 −(v1 − p1 ) Sectional φ1 = 1 + max{max j+ , max j− } Commonality j m1 j m1 Flight to Quality Liquidity Risk speculators Skewness ∂m0 |Λj | ∂|Λ0 | > 0 • invest only in securities with highest ratio 1 j Literature m1 (speculators determine price) • do not invest in securities with lower ratio (customers determine price) (If funding is abundant, φ1 = 1 and Λj = 0 ∀j.) 1 Market & Funding Liquidity Equilibrium Brunnermeier & Pedersen Capital Constraint & Model either Capital Model • funding is abundant, φ1 = 1, and Time-series market illiquidity Λj = 0 for all j; 1 Fragility Liquidity Spirals or Cross- Sectional • funding is tight, φ1 > 1, and Commonality Flight to Quality Liquidity Risk j ¯ |Λj |(φ1 ) = min{(φ1 − 1)m1 , |Λj (Z1 , ·)|} 1 1 Skewness ∂m0 j j ∂|Λ0 | > 0 x1 =0 x1 =0 Literature Recall, j j Λj = p1 − v1 1 Market & Funding Liquidity Commonality of Market Liquidity Brunnermeier & Pedersen Proposition 3 Capital Constraint & Model (iii) (Commonality of Market Liquidity) The market Capital illiquidity |Λ| of any two securities k and l comove, Model Time-series Fragility Liquidity Spirals Cov0 |Λk |, |Λl1 | ≥ 0 1 Cross- Sectional Commonality and market illiquidity comoves with funding illiquidity, φ1 Flight to Quality Liquidity Risk Cov0 |Λk |, φ1 ≥ 0 1 Skewness ∂m0 > 0 ∂|Λ0 | Literature (iv) (Commonality of Fragility) Jumps in market liquidity occurs simultaneously for all assets for which speculators are marginal. • Intuition: Funding liquidity is the driving common factor. Market & Funding Liquidity Commonality and Flight to Quality Brunnermeier & Pedersen Capital Constraint & Two asset example: σ 2 = 7.5 > 5 = σ 1 (Hint: asset 2 = light blue curve) Model Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Flight to Quality Brunnermeier & Pedersen Capital Constraint & Proposition 3, continued Model Capital Model (i) (Quality=Liquidity) Assets with lower fundamental Time-series volatility have better market liquidity. Fragility Liquidity Spirals (ii) (Flight to Quality) The market liquidity diﬀerential Cross- between high- and low-fundamental-volatility securities is bigger Sectional Commonality when speculator funding is tight, that is, σ l < σ k implies that Flight to Quality |Λk | increases more then |Λl1 | with a negative funding shock, 1 Liquidity Risk Skewness ∂m0 ∂|Λl1 | ∂|Λk | 1 ∂|Λ0 | > 0 ≤ , Literature ∂(−η1 ) ∂(−η1 ) Cov0 [|Λl1 |, φ1 ] ≤ Cov0 [|Λk |, φ1 ] . 1 Market & Funding Liquidity Commonality and Flight to Quality Brunnermeier & Pedersen Capital Constraint & Tow asset example: σ 2 = 7.5 > 5 = σ 1 (Hint: asset 2 = light blue curve) Model Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Brunnermeier 1 Capital Constraint - Model Setup & Pedersen Capital Constraint & 2 Time-series Properties Model Capital Liquidity Dry-ups/ Fragility Model Liquidity Spirals Time-series Fragility Liquidity Spirals Cross- 3 Cross-Sectional Properties Sectional Commonality Commonality of Market Liquidity Flight to Quality Flight to Quality Liquidity Risk Skewness ∂m0 ∂|Λ0 | > 0 4 Risk of Liquidity Crisis Literature Skewness and Kurtosis 5 Related Literature Market & Funding Liquidity Risk of Liquidity Crisis - t = 0 Brunnermeier & Pedersen Capital Constraint & Model Capital Model 1 pricing kernel depends on future funding liquidity, φt+1 Time-series Fragility Liquidity Spirals 2 funding liquidity risk can matter even before margin Cross- requirements actually bind Sectional Commonality 3 conditional skewness of price p1 due to the funding Flight to Quality Liquidity Risk constraint Skewness 4 margins m0 and illiquidity Λ0 can be positively related due ∂m0 > 0 ∂|Λ0 | to liquidity risk even if ﬁnanciers are informed. Literature Market & Funding Liquidity Risk of Liquidity Crisis - t = 0 Brunnermeier & Pedersen Capital • Pledgable capital interpretation of Wt Constraint & Model • if Wt < 0, losses have to be covered with unpledgable Capital capital Model • speculators’ “utility” φ1 W1 (also for W1 < 0) Time-series Fragility • weakest assumption that curbs speculators’ risk taking, Liquidity Spirals since objective function linear. Cross- Sectional Commonality Flight to Quality 1 Pricing kernel reﬂects funding liquidity (shadow cost) φt+1 . Liquidity Risk φ1 Skewness ∂m0 p0 = E0 [ p1 ], if φ0 = 1 (unconstrained case). ∂|Λ0 | > 0 E0 [φ1 ] Literature kernel φ1 p0 = E0 [φ1 ]E0 [p1 ] + Cov0 [ , p1 ] E0 [φ1 ] Market & Funding Liquidity p0 and E0 [p1 ] Brunnermeier & Pedersen Capital Constraint & Model Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Conditional Skewness and Kurtosis Brunnermeier & Pedersen Capital Constraint & Model Capital Model Time-series Fragility Liquidity Spirals Cross- Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Conditional Skewness in FX Brunnermeier & Pedersen Capital Brunnermeier, Nagel, Pedersen (NBER Macro Annual 2008) Constraint & Model Skewness Risk Reversals Capital JPY Model 1 1 Time-series Fragility Liquidity Spirals Cross- .5 .5 Sectional CHF Commonality NOK JPY EUR Flight to Quality Liquidity Risk CHF EUR NOK GBP 0 0 Skewness GBP CAD ∂m0 CAD > 0 ∂|Λ0 | Literature AUD NZD AUD NZD -.5 -.5 -.01 -.005 0 .005 .01 -.01 -.005 0 .005 .01 i*-i i*-i Market & Funding Liquidity Margins m0 can increase with |Λ0 | Brunnermeier & Pedersen • in t = 1: margins, m1 , are only increasing in |Λ1 | if • ﬁnanciers are uninformed Capital Constraint & • fundamentals follow ARCH structure Model Capital • in t = 0: margins, m0 , can be increasing with |Λ0 | even Model when ﬁnanciers are informed. Time-series • decline in W0 leads to Fragility Liquidity Spirals • increase in |Λ0 | Cross- • increase in m0 since p1 is more volatile Sectional Commonality Flight to Quality Liquidity Risk Skewness ∂m0 > 0 ∂|Λ0 | Literature Market & Funding Liquidity Related Theoretical Literature Brunnermeier & Pedersen This Paper: Related Theoretical Literature: Capital Constraint & Model Cushioning Eﬀect Gromb-Vayanos (2002), Geanakopolos (2003) Capital Model Conditions for Time-series destabilizing margins — Fragility Liquidity Spirals Fragility Asym. info: Gennotte-Leland (1990) Cross- Sectional Loss Spiral Grossman (1988), Kiyotaki-Moore (1997), Commonality Shleifer-Vishny (1997), Xiong (2001), Flight to Quality Gromb-Vayanos (2002), Morris-Shin (2004) Liquidity Risk Skewness Margin Spiral Vayanos (2004) ∂m0 > 0 ∂|Λ0 | Flight to Quality — Literature Commonality of Liquidity Contagion: Allen-Gale(2000b), Kyle-Xiong(2001) Paper links literatures on: asset pricing, microstructure, limits of arb, corporate ﬁnance, macro, GE Market & Funding Liquidity Conclusion Brunnermeier & Pedersen Capital Constraint & 1 Sudden liquidity “dry-ups” Model • fragility Capital Model • liquidity spirals Time-series • due to destabilizing margins (ﬁnanciers imperfectly informed + ARCH) Fragility Liquidity Spirals 2 Market liquidity correlated with volatility: Cross- Sectional • volatile securities require more capital to ﬁnance Commonality Flight to Quality 3 Flight to quality / ﬂight to liquidity: Liquidity Risk • when capital is scarce, traders withdraw more from Skewness “capital intensive” high-margin securities ∂m0 > 0 ∂|Λ0 | 4 Commonality of liquidity: Literature • these funding problems aﬀect many securities 5 Market liquidity moves with the market • because funding conditions do

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posted: | 11/19/2011 |

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