The Risk and Incentives Trade-off in the Presence of Heterogeneous Managers

Abstract

Agency theory predicts a negative relationship between risk and incentives, yet recent empirical evidence has not consistently found such a relationship. In fact, some researchers have found a positive relationship. By introducing competition for heterogeneous managers, who differ in their degrees of risk aversion, into a standard agency model, this paper demonstrates that a negative or positive relationship is theoretically possible. Which arises depends on the relative risk aversion parameters of the managers and the absolute and relative riskiness of the environments. JEL Classification Numbers: L2

Performance pay, risk attitudes and job satisfaction

“…4 Similarly, Serfes (2005) and Wright (2004) use the classic agency model to develop Ackerberg and Botticini's (2002) hypothesis that less risk averse managers are hired by firms operating in more risky environments. Wright (2004) notes that in the matching equilibrium less risk-averse workers receive a rent if manager type and firm type are unobservable. 5 Milgrom and Roberts (1992: pp.…”

Optimal Incentives in a Principal–Agent Model with Endogenous Technology

“…Indeed, by applying the implicit function theorem to Equation (12), we obtain that 7 Note that the first two components of Equation (12) are positive, while the third one is negative. 8 For example, this is always the case if k is bounded and lim σ 2 →0 (−k ) = +∞.…”

“…As the second component of Equation (12) is nonnegative, a sufficient condition that guarantees that lim σ 2 →0 F(σ 2 ) > 0 is that lim σ 2 →0 (−k ) > lim σ 2 →0 rk 2 , i.e., that lim σ 2 →0 (−k /rk 2 ) > 1, so that the sum of the first and third component of F(σ 2 ) is strictly positive. 8 From lim σ 2 →σ 2 k = 0 and k ≡ k(σ 2 ) > 0 follows that the first two components of Equation (12) tend to zero as σ 2 reaches the upper boundσ 2 ; hence, lim σ 2 →σ 2 F(σ 2 ) = −rk 2 < 0.…”

“…Some recent contributions on the matching literature (e.g., Wright [8], Legros and Newman [9], Serfes [10,11], and Li and Ueda [12]) has attempted to offer a theoretical justification of the above cited results. The explanation provided has been based on the endogenous matching between principals and agents by introducing the heterogeneity on managers' degree of risk aversion (Wright [8]), on the assortative matching between risk-averse agents and riskier principals (Serfes [10]), or on the matching between agents and firms that differ, respectively, for the level of productivity and riskiness (Li and Ueda [12]).…”

“…In particular, by introducing competition for heterogeneous managers, who differ in their degrees of risk aversion, Wright [8] proves that a negative or positive relationship between agents' risk and incentives is possible and depends on the relative risk aversion of the managers and the riskiness of the environments. Serfes [10] shows that, whereas under efficient positive assortative matching (in which higher risk-averse agents are optimally matched with riskier principals) the traditional trade-off between risk and incentives holds, under efficient negative assortative matching (lower risk-averse agents are matched with riskier principals) this trade-off can fail to hold, in particular when matching curves are very steep.…”