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Lecture 8: Financial contracting and incentives Minimizing the “lemons tax” Contracts shape incentives • Bad contracts create perverse incentives • Good contracts create good incentives and reduce the impact of asymmetric information (“the lemons tax”) • The idea of an optimal contract: Alice proposes Bob a contract that maximizes her utility, given Bob’s informational advantage. Thereby she even improves Bob’s lot. Contracting issues in banking • Wages, promotions, bonus schemes • Underwriting (conditions, fees) • Lending contracts – mortgage credits • Borrowing contracts – deposits – subordinated debt • Derivatives An example Alice needs $1 for an investment that yields $2. She promises Bob to repay $1.5 for a credit of $1. Bob has two options: “accept” or “reject”. Alice has two options: “pay back” or “default”. Bob does not know whether Alice is honest and will in fact repay. • Should Bob accept, i.e., lend? • Will Alice repay? • • • • • The game tree Bob accept reject Alice Payoff Bob Payoff Alice pay 0.5 0.5 default -1 2 0 0 The game tree Bob accept reject Alice Payoff Bob Payoff Alice pay 0.5 0.5 default -1 2 0 0 Backwards induction The game tree Bob accept reject Alice Payoff Bob Payoff Alice pay 0.5 0.5 default -1 2 0 0 Backwards induction The outcome Alice will not repay. Bob, therefore, should not lend. Both end up with payoff of $0. The outcome is not Pareto optimal! Both would be better off with “lend”+”repay”, yielding $0.5 to each. • Hence the idea of a contract: How could parties modify payoffs in a way that preserves incentives to repay and to lend? • • • • The idea of a contract • A mutual agreement defining payments (money or in kind) in different (observable) states of nature • X pays Y an amount of z if ... • Example: If Alice defaults on Bob’s loan she has to undergo a punishment: – unpaid work for the Red Cross, value: -$1.6 – "a pound of your fair flesh“ The game tree with a contract Bob accept reject Alice Payoff Bob Payoff Alice pay 0.5 0.5 default -1 2.0-1.6 = 0.4 0 0 The outcome • Alice will repay. • Bob will lend. • Both parties are better off! Contract design = turning switches (1) Where do I want to end up? Bob accept reject Alice Payoff Bob pay 0.5 default -1 0 Where do I want to end up? Contract design = turning switches (1) Where do I want to end up? Bob accept reject Alice Payoff Bob pay 0.5 default -1 0 Objective function Where do I want to end up? Contract design = turning switches (2) How can I make the other behave? Bob accept reject Alice Payoff Bob Payoff Alice pay default 0 0 0.5 -1 0.5 < 2 Problem Contract design = turning switches (2) How can I make the other behave? Bob accept reject Alice Payoff Bob Payoff Alice pay default 0 rej 0.5 -1 P(ap) ≥ P(ad) Incentive Constraint Contract design = turning switches (3) How can I make the other participate? Bob accept reject Alice Payoff Bob Payoff Alice pay 0.5 P(ap) default -1 ≥ 0 P(r) Participation Constraint Summing up: Optimal contracts • Contracting: a reaction to information problems. • Uncontingent contracts (“A will pay z") => Pareto sub-optimal results (agency cost). Example: Market for Lemons (Akerlof 1971). • Contingent contracts (“A will pay: z1 if w1, z2 if w2, ... ") => reduction of agency cost. • Optimal contracts maximizes principal’s utility subject to constraints. • Constrained Pareto Optimum Contracts can be written on observable outcomes Alice Bob 2 11 4 3 6 5 2 11 4 3 6 5 Contracts can be written on observable outcomes Alice Bob 2 1 4 3 6 5 2 1 4 3 6 5 Summing up: Principal-Agent-Models • Principal wants agent to do something • Background: asymmetric information – agent knows more than principal – information asymmetry is common knowledge. • Consequence: market may fail and produce inefficient results. • Contract may bridge the information gap and reduce “agency cost”. Summing up: The maximization problem • The principal maximizes expected utility (objective function), subject to constraints: – Participation Constraint: The agent accepts the contract. – Incentive Constraint: The agent acts as preferred by the principal. – Feasibility (or Wealth) Constraint: All payments are feasible. Two basic stories Story 1 t=0 Hidden Information t=1 P offers a contract t=2 Adverse Selection t=3 time The contract is executed A discovers his type A accepts or refuses Story 2 t=0 Hidden Action t=1 A accepts or refuses t=2 Moral Hazard t=3 time The outcome is realized and the contract is executed P offers a contract A exerts an effort or not Hidden information: Who moves first? • Signaling (agent moves first): – university diploma (cost to get diploma correlated with hidden ability) – capital ratio (owners signal low risk by retaining residual loss) • Screening (principal moves first) – franchise in health insurance (expected cost correlated with sickness probability) – mortgage collateral requirement (higher cost to bad debtors) Lack of screening in subprime crisis? “Given investors’ concerns, one might expect the capital markets to screen out the riskiest, predatory loans from securitized subprime loan pools. There is growing evidence, however, that securitizing entities perform inadequate screening.” ... “In many instances the mortgage loans in the statistical mortgage pool were acquired ... from sources, including mortgage brokers and other non-originators, that could not provide detailed information regarding the underwriting guidelines of the originators.” Engel&McCoy (2007, p. 102-3) Hidden action Story 2 t=0 Hidden Action t=1 A accepts or refuses t=2 Moral Hazard t=3 time The outcome is realized and the contract is executed P offers a contract A exerts an effort or not • Assumption 1: • Assumption 2: • Consequence: • Problem: Outcome is correlated with effort. Effort cannot be observed. Preserving incentives for effort: Optimal contract rewards the agent in good states, punishes in bad states. Conflict: incentives vs. feasibility Conflict: incentives vs. insurance Incentives in the subprime market “What were they thinking” (Rajan, 2007): • The bureaucratic motive (agent paid at fixed wage): – “the search for extra yield ... covering your rear end through the fig leaf of the rating.” Incentives in the subprime market “What were they thinking” (Rajan, 2007): • Chasing alpha (agent paid for risk-adjusted excess return): – stock picking, activism, financial engineering: difficult; rare ability – liquidity provision (hold long-term illiquid assets): “the poor manager’s source of alpha” – taking hidden risk (e.g., selling deep-out-of-themoney put options, like buying AAA CDO’s) Other examples • Limited liability (= feasibility constraint): Limits punishment to agent for bad outcomes – bonus systems – shareholders’ risk taking – put option on home for mortgage debtor • “Pro-cyclicality” of regulation: Banks cannot be punished in bad times – capital requirements Conclusions • Unobservable type or action lead to – adverse selection – moral hazard • Contracts address such information problems • Optimal contracts reduce, but do not eliminate agency cost • Trade-off between risk sharing and incentives