Optimal margins and equilibrium prices

Transcription

1 Optimal margins and equilibrium prices Bruno Biais Florian Heider Marie Hoerova Toulouse School of Economics ECB ECB Bocconi Consob Conference Securities Markets: Trends, Risks and Policies February 26, 2016 The views expressed are solely those of the authors.

2 Research questions Counterparty risk concern in derivatives contracts One remedy proposed: higher margin requirements (Dodd-Frank, EMIR) Issue: margin calls can trigger fire-sales (BIS, 2010) Gromb and Vayanos (2002), Brunnermeier and Pedersen (2009), but there margins are exogenous What are the benefits and costs of optimal margin calls when asset prices are endogenous? are there instabilities? are privately optimal margins also socially optimal?

3 Main results Financial contracts enable risk-sharing but... may lead to risk-taking by counterparty to limit counterparty risk limit risk-sharing Margins enhance risk-sharing (Biais, Heider, Hoerova, 2015) ring-fence assets from moral hazard but forgo return (only safe, low-yield assets can be posted) Margin calls can generate downward-sloping supply curve in the asset market multiple equilibria (instability) Market equilibrium has over-margining (pecuniary externality)

4 Hedgers Mass 1 continuum of risk-averse identical hedgers (utility u over t=2 consumption) Each endowed with 1 unit of risky asset with random t=2 payoff θ Same risky asset for all: aggregate/systematic risk π 1 π θ θ

5 Investors Mass 1 continuum of sophisticated investors; risk-neutral Mass m continuum of unsophisticated investors; risk-averse Each endowed with 1 unit of cash Can invest fraction 1 β in an asset with random t = 2 payoff R per unit (independent of θ)

6 Investor moral hazard Can exert unobservable effort at t = 1 to control downside risk effort shirk R µ R 1 µ 0 Effort cost C per unit for sophisticated, C + δ for unsophisticated Assume: R C 1 R C δ

7 Information structure Public information s about the hedged risk θ becomes available at the beginning of t = 1 (before investor effort choice) The signal is informative: prob[θ s] > prob[θ] Observing s is bad news for investor who sold insurance against θ

8 Margin calls and asset sales Fraction α of investor s risky assets liquidated at t = 1 and cash proceeds deposited on margin account Margin call takes place after the signal and before investor effort choice Assets sold to market at price p asset supply at t = 1 Assets demand from mass m of unsophisticated investors

9 Market equilibrium at t = 1 α m/p α(p) 0 R C δ p

10 Sequence of events t=0 t=1 t=2 Invest cash Transfers τ( θ, s, R j ) Margins α( s) Signal s about θ observed Margin call α(s) Market clearing price p Effort or not θ and R j realize Transfers τ(θ, s, R j ) paid

11 First-best: no moral hazard Hedger request investor s effort: max τ,α E [u( θ + τ)] subject to: E [τ] E [β(r C 1) + (1 β)α(r C p)] In the first-best unsophisticated keep cash, sophisticated invest all cash full insurance: hedger consumes E [ θ] contract does not depend on the signal s margins are not used contract is actuarially fair, E [τ] = 0

12 Incentive constraint (depends on signal s) Two incentive compatibility (IC) conditions [ β + (1 β) α(s)p + (1 α(s))(r C ] 1 µ ) E [τ s] }{{} pledgeable return P

13 Economics of margins and cash After good signal, incentive constraint is slack (E [τ s] < 0) no margin call, α( s) = 0 After bad signal, possible relaxation of the incentive constraint: P + α (s) (p P)(1 β) + β(1 P) = E [τ s] }{{}}{{} incentive benefit of margin incentive benefit of cash But tightening of the participation constraint: E [β(r C 1) + (1 β)α(r C p)] = E [τ] }{{}}{{} opportunity cost of cash opportunity cost of margin

14 Optimal interior margin α (given the price p) Focus on margins (β = 0) cash is not used if extra cost for unsophisticated δ not too large Optimal interior margin is given by u (E [θ s] + E [τ s]) u (E [θ s] + E [τ s]) = 1 + R C p p P }{{}}{{} risk-sharing across signals opportunity cost/incentive benefit

15 Privately-optimal margin φ(0) 1 + R C p p P Opportunity cost of margin 1 u (α;p) ū (α) 0 α (s) 1 α Trades off opportunity cost of margins with incentives benefits

16 Higher price: better trade-off opp. cost / incentive benefit φ(0) 1 + R C p p P Opportunity cost of margin 1 u (α;p) ū (α) 0 α (s) 1 α Trades off opportunity cost of margins with incentives benefits

17 Higher price: better risk-sharing across signals φ(0) 1 + R C p p P Opportunity cost of margin 1 u (α;p) ū (α) 0 α (s) 1 α Trades off opportunity cost of margins with incentives benefits

18 Market equilibrium as risk-aversion ρ increases 1.0 D(p) S(p) p

19 Market price as a function of risk-aversion ρ: jumps p* best price worst price

20 Second-best equilibrium A hedger does not take into account the negative effect of his margining (lower asset price) on others The socially optimal amount of margins α SB internalizes this negative pecuniary externality Equilibrium not information-constrained efficient over-margining: α α SB

21 Two-way contagion From θ to R: when bad news hit hedger s asset margin calls on insurer s asset fire-sales (low p) excess volatility: Var(p) > than in the first-best correlation in volatility: high Var(θ) high Var(p) From R to θ: incentive problem in management of R limited insurance of θ risk risk premium for securities on θ

22 Concluding remarks Bad news about a hedged position hedge turns into a liability for sellers of insurance To maintain incentives call margins asset sales Market equilibrium instability and too much margining Scope to regulate margins