LEVERAGE AND LIQUIDITY DRY-UPS: A FRAMEWORK AND POLICY IMPLICATIONS. Denis Gromb LBS, LSE and CEPR. Dimitri Vayanos LSE, CEPR and NBER

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1 LEVERAGE AND LIQUIDITY DRY-UPS: A FRAMEWORK AND POLICY IMPLICATIONS Denis Gromb LBS, LSE and CEPR Dimitri Vayanos LSE, CEPR and NBER June 2008 Gromb-Vayanos 1

2 INTRODUCTION Some lessons from recent crisis: Intermediary capital matters for market liquidity. Relevant intermediaries include investment banks and primary dealers. Intermediary capital is linked to prices of traded assets. Liquidity dry-ups and amplification effects. Standard theories (Arrow-Debreu): Asset markets are efficient. Liquidity is as good as it gets. No rationale for policy intervention or regulation. Practice: Regulators are concerned with market liquidity and intermediary solvency. Similar concerns as in previous crises (e.g., 1998). June 2008 Gromb-Vayanos 2

3 This Paper Theoretical framework that Emphasizes intermediary capital and importance for market liquidity. Can be used for welfare analysis. Key assumptions: Intermediaries are special. Better investment opportunities than other participants. Provide liquidity to other participants. Intermediaries face financial constraints. Questions: How much of their capital do intermediaries put at risk? Is intermediary risk taking socially optimal? Simplified version of Gromb and Vayanos (2002). Enlarge set of intermediary assets. June 2008 Gromb-Vayanos 3

4 Results Dynamics Following intermediary losses: Market liquidity declines. Prices are driven away from fundamental values. Price changes amplify intermediary losses. Contagion across otherwise unrelated assets. Welfare Intermediaries can fail to take socially optimal level of risk. Fail to internalize that changes in their positions affect prices. Pecuniary externality. Matters in world of financial constraints and incomplete markets. Implications for capital requirements and IO of intermediation sector. (Preliminary) June 2008 Gromb-Vayanos 4

5 A MODEL OF MARKET LIQUIDITY BASED ON INTERMEDIARY CAPITAL Two dates: t = 1, 2. Riskfree asset with return 0. Two zero net supply risky assets A and B with same payoff at t = 2: δ A,2 = δ B,2 = δ + ǫ A,2 with ǫ A,2 [ ǫ A,2, +ǫ A,2 ]. Liquidity demand: Segmented markets for assets A and B Different prices. Price wedge reflects unsatisfied demand for liquidity. Liquidity supply: Arbitrageurs: Specialists uniquely able to serve unsatisfied liquidity demand. Financial constraints Role for arbitrage capital. June 2008 Gromb-Vayanos 5

6 Liquidity Demand Segmented markets i = A, B: i-investors: Competitive, initial wealth w i,1. Can only invest in risky asset i and riskfree asset. Maximize: E 1 exp ( α i w i,2 ). Endowments At t = 2, i-investors receive: u i ǫ A,2. Gains from trade Endowments are opposites for A- and B-investors: u A = u B > 0. In the absence of arbitrageurs, prices of assets A and B can differ. June 2008 Gromb-Vayanos 6

7 Liquidity Supply Arbitrageurs can invest across markets. Exploit AB price wedge. Provide the liquidity A- and B-investors crave. Financial constraint: Position (long or short) in a risky asset Margin account. m x i,1 units of riskfree collateral for position of x i,1 shares of asset i: W 1 m x i,1. i=a,b Arbitrageur wealth W 1 : Inside capital. Smart external capital accessed frictionlessly. June 2008 Gromb-Vayanos 7

8 Equilibrium Notation and basic properties: Risk premium of asset i at date t: φ i,t E t [δ i ] p i,t. Risk premia are opposites: φ A,t = φ B,t > 0. Price wedge 2φ A,1 measures market liquidity. Arbitrageurs enter spread trades: x A,t = x B,t. Proposition 1: If W 1 < Ŵ1: Markets are not perfectly liquid: (φ A,1 > 0) Market liquidity increases with arbitrage capital: φ A,1 / W 1 < 0. If W 1 Ŵ1: Markets are perfectly liquid: (φ A,1 = 0) Remarks: Link between arbitrage capital and market liquidity. Liquidity dries up when arbitrage capital is low. Crucial to know: Is arbitrage capital is put at risk in a socially optimal way? June 2008 Gromb-Vayanos 8

9 ADDITIONAL INVESTMENT OPPORTUNITY Additional date t = 0. Additional asset C paying off at t = 2: δ C = δ + ǫ C,1 + ǫ C,2 with ǫ A,t [ ǫ A,t, +ǫ A,t ] revealed at t. C-investors: Competitive, initial wealth w C,1. Can only invest in risky asset C and riskfree asset. Maximize: E 0 exp ( α C w C,2 ). Endowments: At t = 2, receive u C (ǫ C,1 + ǫ C,2 ) with u C > 0. Arbitrageurs buy asset C to share risk with C-investors. Interpretation: Asset C: Mortgages. Assets A, B: Intermediaries other liquidity provision activities. June 2008 Gromb-Vayanos 9

10 Equilibrium at t = 1 Arbitrage capital allocated between AB spread trade (liquidity) and asset C (risksharing). Proposition 2: If W 1 < W 1 : Markets are not perfectly liquid: (φ A,1 > 0) Market liquidity increases with arbitrage capital: φ A,1 / W 1 < 0. Price of asset C increases with arbitrage capital: φ C,1 / W 1 < 0. If W 1 W 1 : Markets are fully liquid: (φ A,1 = 0) Price of asset C is independent of arbitrage capital: φ C,1 / W 1 = 0. Corollary: Following bad news on asset C: Arbitrage capital decreases. Price drop of asset C is amplified. (Amplification) Liquidity of assets A and B decreases. (Contagion) June 2008 Gromb-Vayanos 10

11 Equilibrium at t = 0 Risksharing between arbitrageurs and C-investors. Arbitrageur risk management: After realizing losses, investment opportunities become more attractive. Arbitrageurs can invest more conservatively, preserving scarce capital for bad times. Is arbitrageur risk management socially efficient? June 2008 Gromb-Vayanos 11

12 WELFARE ANALYSIS Experiment: Change arbitrageurs position in asset C at t = 0. Let the model run. Note: Respect financial constraints (i.e. constrained efficiency). Welfare: Sum of agents certainty equivalents at t = 0: W CEQ i + CEQ arb. i=a,b,c Proposition 3: Arbitrageurs position in asset C at t = 0 can fail to be socially optimal. June 2008 Gromb-Vayanos 12

13 Intuition Suppose that arbitrageurs take less risk at t = 0. More capital at t = 1 in bad state Transfer from arbitrageurs to A- and B-investors Welfare increases if A- and B-investors are sufficiently risk-averse. Asset C becomes cheaper at t = 0 Transfer from C-investors to arbitrageurs Welfare increases because arbitrageurs can use capital more productively. More generally: Change in arbitrageurs position affects prices. Price changes redistribute wealth across agents. Pecuniary externality. Matters in world of financial constraints and incomplete markets. June 2008 Gromb-Vayanos 13

14 POLICY (Preliminary) Conjecture 1: Constraining arbitrageurs investment in asset C can be welfare-improving. Intuition: Suppose arbitrageurs are overinvested at t = 0. Constraining them reduces their positions at t = 0. In essence, force them to do better risk management. Remarks: Implementation: Risk-based capital requirement? Here, regulation is not about default risk. Conjecture 2: Reducing the intensity of competition between arbitrageurs can be welfare-improving. Intuition: Imperfect competition Arbitrageurs (partly) internalize price effects. June 2008 Gromb-Vayanos 14