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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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