Risk-Management Lessons from Bonus Schemes

Management compensation packages typically include some form of bonus payment; these payments shall provide incentives for effort, but recently they were heavily criticized for their perceived excessive risk-taking incentives. This paper presents a continuous-time model in which the manager decides on the risk and effort level of the bank. A single-period model is nested into continuous-time; for this we confirm prior results on risk and effort levels and show that they misrepresent actual risks taken in our dynamic continuous-time setup. Furthermore, we show that with current bonus schemes risk and effort levels are typically of bang-bang type: the manager takes either maximal or minimal risk and either maximal or minimal effort. The bonusmalus scheme is believed by the public to limit risk-taking; we show that before the deferral date it behaves like a call option type bonus scheme and thereafter considerably hampers risk and effort. We also discuss how a bonus scheme should look like that incentivizes the manager to pick a target risk level. Finally, we illustrate our results quantitatively.