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Risking Other People’s Money: Gambling, Limited Liability, and Optimal Incentives

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NES 20th Anniversary Conference, Dec 13-16, 2012 …

NES 20th Anniversary Conference, Dec 13-16, 2012
Risking Other People’s Money: Gambling, Limited Liability, and Optimal Incentives (based on the article presented by Alexei Tchistyi at the NES 20th Anniversary Conference).
Authors: Peter DeMarzo, Dmitry Livdan, Alexei Tchistyi

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  • 1. Risking Other People’s Money:Gambling, Limited Liability, and Optimal IncentivesPeter DeMarzo, Dmitry Livdan, Alexei Tchistyi Stanford University U.C. Berkeley
  • 2. Motivation• Financial meltdown 2008 • Ex ante unlikely outcome • Ex post AIG, Lehman, Citi, Merrill Lynch, etc. suffered high losses • Losses were caused by divisions trading highly risky securities • Investors were unable to either monitor or understand actions taken by managers• Managers enjoy limited liability and their compensation is performance based
  • 3. Moral Hazard and Optimal Contracting• Managers may seek private gain by taking on tail risk • Earn bonuses based on short-term gains • Put firm at risk of rare disasters • Limited liability leaves them insufficiently exposed to downside risk • Is this the result of inefficient contracting?• Standard contracting models • Focus on effort provision • Static and dynamic models • Rewards for high cash flows can be optimal • But does this contract lead to excessive risk-taking?
  • 4. One-Period Model• Principal/Investor(s) • Risk-neutral • Owns the company • Value of the company without project is A (large)• One period risky project with payoff: 1, with probability   q   Y (q)  0, with probability 1    q(    ). - D, with probability q • Project risk • Low risk q = 0 • High risk q = 1 • High risk is suboptimal: ρ – δD < 0
  • 5. One-Period Model• Principal hires agent/manager to run the project• New output Y, subject to two-dimensional agency problem: • Divert output / shirk for private benefit (l) • Gamble ( <  D)  1• How does the possibility of gambling Y l  affect contracting? 1  0  -D
  • 6. One-Period Model• Contract specifies payoffs (w0, w1, wd) • wd = 0 • w1  w0 + l• No Gambling: •  (w1 – w0)   w0  w0   l /  • Agent must receive sufficient rents to prevent gambling • Exp. payoff = w0 +  l   l /  +  l = l ( +  / )  ws• Gambling: • Reduce agent rents: w0  0 • Exp. payoff = w0 + ( + ) l  l ( + )  wg < w s • Suffer expected loss:  D –   D
  • 7. One-Period Model• Low risk is more profitable to principal than high risk if  - ws   – D  wg D  l (/  ) • For small  principal would prefer to implement high risk project or not to undertake any project• Gambling is more costly to prevent when probability of disaster is low • Limited liability prohibits harsh punishment of agent for gambling, • Expected loss w0 is low when  is low, • Unless agent’s compensation w0 and ws are high
  • 8. Contract Conditional on Disaster• If we cannot punish agent for gambling it may be cheaper to reward him for not gambling ex post• Can the agent be rewarded for not gambling ex post? • Oil spills • Absence does not mean gambling did not occur – perhaps we just got lucky? • Earthquakes • If the building survives an earthquake, that is evidence that the builder did not cut corners • Financial crisis • If a bank survives it while other banks fail, that is evidence that the bank did not gamble
  • 9. Bonus for not Gambling• No gambling: pay bonus b if no loss ( - D ) given disaster  (w1 – w0)   (w0 + b)• Contract without gambling that maximizes principal payoff: wd = 0, w0 = 0, w1 = l, b = l  / . • Bonus b may be large, but expected bonus payment is not b=l • Exp. payoff for Agent = l  +  b = l  +  l  wg• In that case, no gambling is always optimal
  • 10. Implementation Using Put Options• Agent is given out-of-money put options on companies that are likely to be ruined in the "disaster" state • Caveat: Agent can collect the payoff from the options only if his company remains in a good shape• Potential downside of using put options • Creates incentives to take down competitors• Comprehensive cost-benefit analysis is needed
  • 11. Dynamic Model• A simple model (DS 2006) • Cumulative cash flow: dY =  dt + s dZ • Agent can divert cash flows and consume fraction λ ∈ (0, 1] • Alternative interpretation: drift  depends on agent’s effort • Earn private benefits at rate l per unit reduction in drift• Gambling with tail risk • Gambling raises drift to  + : dY = ( + ) dt + s dZ • Disaster arrives at rate , destroying the franchise and existing assets D if the agent gambled
  • 12. Basic Agency Problem• Interpretations • Cash Flow Diversion • Costly Effort (work/shirk) 70 Cumulative Output per Unit 60 Diverted 50 Funds 40 30 20 10 0 -10 0 1 2 3 4 5 -20 Time
  • 13. The Contracting Environment• Agent reports cash flows• Contract specifies, as function of the history of cash flows: • The agent’s compensation dCt  0 • Termination / Liquidation • Agent’s outside option = 0 • Investors receive value of firm assets, L < /r• Contract curve / value function: p(w) = max investor payoff given agent’s payoff w • Provide incentives via cash dCt or promises dwt • Tradeoff: Deferring compensation eases future IC constraints, but costly given the agent’s impatience
  • 14. Solving the Basic Model Investors’ payoff p(w)• First-Best Value Function • pFB(w) = /r – w /r First Best• Basic Properties • Positive payoff from stealing/shirking  p(0) = L • Public randomization  p(w) is weakly concave • Liquidation is inefficient  p(w) + w  /r L• Cash Compensation •  p (w)  -1 0 wc /r • Pay cash if w > wc Promises Cash • Use promises if w  wc Agent’s Payoff w
  • 15. Basic Model cont’d Boundary Conditions: • Termination: p(0) = L • Smooth pasting: p (wc) = -1 • Super contact: p (wc) = 0• Agent’s Future Payoff w p • Promise-keeping  – (g - r) wc /r p(wc) + wc = • E[dw] = g w dt r • Incentive Compatibility • w / y  l -g/r  dw = g w dt + l (dy – E[dy]) = g w dt + l s dZ L• Investor’s Payoff: HJB Equation r p =  + g w p + ½ l2s2p 0 wc w Req. E[FCF] E[dp] Promises Cash Return Agent’s Payoff w
  • 16. The Gambling Problem• Agent may increase profits by taking on tail risk • E.g. selling disaster insurance / CDS / deep OTM puts – earn  dt • Risk of disaster that wipes out franchise – arrival rate  dt, loss D 70 Cumulative Output per Unit 60 Put 50 Premia 40 30 20 10 0 -10 0 1 2 3 4 5 -20 Time
  • 17. The Gambling Problem• Agent’s incentives • Gain from gambling: l  dt • Potential loss: wt, with probability  dt • Agent will gamble if l  >  wt or w t < ws  l  /  • Agent will gamble if not enough “skin in the game”• Gambling region • Contract dynamics: dw = (g  ) w dt + l (dy – E[dy]) • Value function: (r  ) pg = (    D) + (g  ) w pg + ½ l2s2pg • Increased impatience • Smooth pasting: p(ws) = pg(ws), p’(ws) = pg’(ws)
  • 18. 100 ws wcExample 90 80• First Best = 100 •  = 10, r = 10%, g = 12%, 70 s = 8, L = 50, l = 1• Cash if w > 56 Investor p(w) 60 • wc = 56 50• Gamble if w < 40 •  = 2,  = 5%, ws = 40, D = 0 40• Compare to pure cases 30 • Longer deferral of compensation 20 LT debt • Greater use of credit line 10 vs. debt (more financial slack) Credit line 0 0 20 40 60 80 100 Agent w
  • 19. Ex-Post Detection and Bonuses• Suppose disaster states are observable • Earthquakes, Financial Crises, … • Can we avoid gambling by offering bonuses to survivors ex-post?• How large a bonus? • If wt ≥ ws : no bonus is needed to provide incentives • If wt < ws : increase wt to ws if firm survives disaster : bt = ws - wt• Bonus region • Contract dynamics: dw = [(g  ) w –  ws ] dt + l (dy – E[dy]) • Value function: (r  ) pb = (   pb(ws)) + [(g  ) w –  ws ] pb + ½ l2s2pb • Smooth pasting …
  • 20. 100 wb wsOptimal Bonuses 90 Investor p(w)• Bonus payments: 80 • substantially improve 70 investor payoff 60 • reduce need for deferred comp / 50 p(ws) financial slack / harsh 40 / – D penalties (no jumps) 30• For low enough wt, 20 gambling is still optimal 10 0 0 20 40 60 80 Agent w
  • 21. Summary• The double moral hazard problem is likely to be important in firms where risk-taking can be easily hidden• Risk-taking is likely to take place • Probability of disaster is low • After a history of poor performance, when the agent has little “skin” left in the game• As a result, optimal policies will have increased reliance on deferred compensation• When the “safe” practices can be verified ex-post, we can mitigate risk-taking via bonuses• When effort costs are convex, we should expect reductions in effort incentives as a means to limit risk- taking, with a jump to high powered incentives in the gambling region