Bank Asset Choice and Liability Design. June 27, 2015

Transcription

1 Bank Asset Choice and Liability Design Saki Bigio UCLA Pierre-Olivier Weill UCLA June 27, 2015

2 a (re) current debate How to regulate banks balance sheet? Trade off btw: reducing moral hazard: over-issuance, over-lending, bailout reducing provision of money-like liabilities What we do today: a simple model of a bank s balance sheet abstract from moral hazard for now focus on incentives to provide liquidity services

3 a monopolistic bank Asset side: pays intermediation cost to attract depositors depositors bring heterogenous collateral assets some safe and liquid, others risky exposed to a lemon problem Liability side: issues liabilities used as means of payment security design Optimal asset and liability structure: safe collateral combined with risky collateral on the asset side safe collateral input for creating info insensitive liabilities the safest collateral is the best input liabilities expose safe depositors to risky assets

4 literature Banks as issuer of low info sensitivity liabilitities Gorton-Pennacchi (90) Dang-Gorton-Holmström-Ordonez (14) Security design DeMarzo-Duffie (99), Biais-Mariotti (04), many others Bundling vs. tranching in lemon markets Farhi-Tirole (14) New monetarist models Berentsen-Camera-Waller (07), Rocheteau (11)

5 the economic environment

6 one island Three dates, t {0, 1, 2} One island (sector, city, etc...) in the broader macroeconomy at t = 2, island productivity shock, ω {ω l, ω h }, proba π(ω) A continuum of risk-neutral producers who cannot commit each endowed with one tree paying off R j (ω) M j asset of type j {1, 2,..., J}, j M j = 1 At time t = 1, outside trading opportunity each producer learns ω and travels to different outside island anonymously meets a worker who is uninformed about ω workers supplies labor, cost c(q) = q at t = 1 output is r(ω) q at t = 2

7 maintained assumptions Gains from trade in the high state only: r(ω h ) > 1 = r(ω l ) Lemon problem for sufficiently info sensitive trees π(ω h )r(ω h ) < 1 Trees and productivity are positively correlated M j R j (ω h ) M j R j (ω l ) j j

8 benchmark: bilateral trade with the tree assume constrained optimal (i.e. constrained by asym info) trade If R j (ω l ) > R j (ω h ) liquid and trade at true value q(ω h ) = R j (ω h ) producer s ex ante value = U [R j ] = E [r R j ]

9 benchmark: bilateral trade with the tree assume constrained optimal (i.e. constrained by asym info) trade If R j (ω l ) > R j (ω h ) liquid and trade at true value q(ω h ) = R j (ω h ) producer s ex ante value = U [R j ] = E [r R j ] If R j (ω l ) R j (ω h ) and r(ω h )E [R j ] R j (ω h ) liquid but trade at discount q(ω h ) = q(ω l ) = E [R j ] producer s ex ante value = U [R j ] = E [r] E [R j ]

10 benchmark: bilateral trade with the tree assume constrained optimal (i.e. constrained by asym info) trade If R j (ω l ) > R j (ω h ) liquid and trade at true value q(ω h ) = R j (ω h ) producer s ex ante value = U [R j ] = E [r R j ] If R j (ω l ) R j (ω h ) and r(ω h )E [R j ] R j (ω h ) liquid but trade at discount q(ω h ) = q(ω l ) = E [R j ] producer s ex ante value = U [R j ] = E [r] E [R j ] If R j (ω l ) R j (ω h ) and r(ω h )E [R j ] R j (ω h ) fully illiquid, q(ω h ) = 0 producer s ex ante value U [R j ] = E [R j ]

11 a monopolistic bank A wealthless risk-neutral agent who can commit Incurs convex cost M j C ( µj M j ) to attract µ j type-j producers At t = 0, exchange trees for newly designed securities some liquid: can be used for bilateral trades at t = 1 some illiquid: remain at the bank until t = 2 Later: some preliminary results about realistic implementations

12 optimal liability design given assets

13 the bank s problem Suppose the banker has attracted producers µ = {µ 1, µ 2,..., µ J } Banker s problem: V (µ) = max E [c] w.r.t. c(ω), D j (ω), I j (ω) 0, and s.t. feasibility: c(ω) + j µ j [D j (ω) + I j (ω)] j µ j R j (ω) liquidity: j, D j (ω h ) r(ω h )E [D j ] participation: j, U [D j ] + E [I j ] U [R j ]. where, recall, U [D(ω)] is the value of trading with a security D

14 one contract fits all an aggregation property For liquid securities, the producer s value of trading, U [D j ] is positively homogenous and concave in the payoffs D j (ω) optimal to design the same liabilities for all, but give quantities optimal liabilities solve bank problem with representative depositor brings the aggregate tree R = j µ jr j has the aggregate outside value Ū = j µ ju [R j ]

15 finding optimal liabilities Guiding principle: liquid liabilities create more value than illiquid ones the bank should maximize issuance of liquid liabilities

16 finding optimal liabilities Guiding principle: liquid liabilities create more value than illiquid ones the bank should maximize issuance of liquid liabilities Step 1 : try to solve the bank s problem with a liquid liability only but if lemon problem too strong: no solution exist! liquidity constraint limits the size of liquid liabilities... feasible liquid liabilities too small to induce participation!

17 finding optimal liabilities Guiding principle: liquid liabilities create more value than illiquid ones the bank should maximize issuance of liquid liabilities Step 1 : try to solve the bank s problem with a liquid liability only but if lemon problem too strong: no solution exist! liquidity constraint limits the size of liquid liabilities... feasible liquid liabilities too small to induce participation! Step 2 : find the highest value liquid liability, D (ω) D (ω) alone does not induce participation pick the illiquid liability, I (ω), to satisfy participation

18 optimal liabilities when Step 1 fails: strong lemon problem on the island D(ωh ) 0 D(ω` )

19 optimal liabilities when Step 1 fails: strong lemon problem on the island D(ωh ) R (ωh ) 0 D(ω` ) R (ω` )

20 optimal liabilities when Step 1 fails: strong lemon problem on the island D(ωh ) liquidity constraint R (ωh ) 45 degree line 0 D(ω` ) R (ω` )

21 optimal liabilities when Step 1 fails: strong lemon problem on the island D(ωh ) liquidity constraint R (ωh ) 45 degree line iso E [D] 0 D(ω` ) R (ω` )

22 optimal liabilities when Step 1 fails: strong lemon problem on the island D(ωh ) liquidity constraint R (ωh ) iso E [D] 45 degree line 0 D(ω` ) R (ω` )

23 optimal liabilities when Step 1 fails: strong lemon problem on the island D(ωh ) iso E [D] liquidity constraint R (ωh ) 45 degree line 0 D(ω` ) R (ω` )

24 optimal liabilities when Step 1 fails: strong lemon problem on the island D(ωh ) liquidity constraint R (ωh ) 45 degree line 0 D(ω` ) R (ω` )

25 optimal liabilities when Step 1 fails: strong lemon problem on the island D(ωh ) liquidity constraint R (ωh ) optimal liability 0 45 degree line D(ω` ) R (ω` )

26 the optimal liabilities (ct d) when Step 1 fails: strong lemon problem on island The liquid liability, D (ω), is like defaultable debt with a face value R(ω l ) < D (ω h ) < R(ω h ) repays in full in high state, default in low state The illiquid security, I (ω), is like equity pays off only in the high state Bank s payoff is also like equity

27 when is there an illiquid liability? assume Rj (ωh ) Rj (ω` ) and normalize E [Rj ] = 1 R (ωh ) R (ω` ) 0 1 measure of lemon

28 when is there an illiquid liability? assume Rj (ωh ) Rj (ω` ) and normalize E [Rj ] = 1 R (ωh ) R (ω` ) I? (ω` ) > 0 I? (ω) = measure of lemon

29 implementation: realistic bank liabilities For holders of illiquid trees: collateralized loan R j (ω h ) D(ω h )(1 + interest rate) = I (ω h ) illiquid liability generated by haircut holder of trees pays off loan if ω h, default if ω l For holders of liquid trees: checking and saving deposits bank purchases the tree checking deposit, D(ω) (senior) saving deposit, I (ω) (junior)

30 optimal asset choice

31 properties of the bank s value, V (µ) Weakly increasing and concave in µ = {µ 1,..., µ J } Illiquid and liquid trees are complement in V (µ) If strong lemon problem: V µ j of liquid trees > 0 helps increase the value of D (ω), reduce I (ω) If weak lemon problem: V µ j of liquid trees = 0

32 the optimal asset choice problem max µ V (µ) C(µ) is a nice concave optimization problem When lemon problem is weak bank s problem solved with illiquid trees only do not attract any liquid trees create a single liquid liability, D (ω), from illiquid trees When lemon problem is strong bank s problem NOT solved with illiquid trees only attract liquid trees to reduce I (ω) create a single liquid liability, D (ω) from all trees sometimes also create an illiquid liability, I (ω)

33 attract trees with low info sensitivity first asset composition µ j M j 0 liquid trees illiquid trees info sensitivity R j (ω h ) R j (ω l )

34 asset composition attract trees with low info sensitivity first when intermediation cost drop: bank gets larger attracts more info sensitive assets, both liquid and illiquid µ j M j 0 liquid trees illiquid trees info sensitivity R j (ω h ) R j (ω l )

35 conclusion A simple model of a bank s balance sheet Purely driven by incentives to issue liquid liabilities Optimal balance sheet safe depositors are exposed to risky assets liquid liabilities are risky drop in intermediation cost bank attracts riskier assets Are there symptoms of moral hazard? curing them would reduce liquidity provision

36 optimal bilateral trade with the tree Consider a producer with asset in hand when meeting a worker Anonymity and lack of commitment tree is medium of exchange But private info creates a lemon problem Our approach: assume constrained optimal trade maximize production in the high state w.r.t allocation of tree and labor supplies in both states s.t. feasibility, individual rationality, and incentive compatibility