Options can induce risk taking for arbitrary preferences

Abstract

Summary.It is widely believed that call options induce risk-taking behavior. However, Ross (2004) challenges this intuition by demonstrating the impossibility of inducing managers with arbitrary preferences to always act as if they were less risk averse. If preferences and price distributions are unknown, risk-taking behavior cannot be always induced by an option contract. Here, we prove a new result showing that, with no information about preferences and some knowledge about prices, one can write a call option that makes all managers prefer riskier projects to safer ones. This points out that in order to design options that induce risk taking it is sufficient to have information about price distributions.

Do executive stock options induce excessive risk taking?

“…Section 5 concludes. 2 The theoretical literature on this issue is unsettled; whether stock options can induce more risk taking depends on characteristics of options (moneyness) and the utility function, risk aversion, and outside wealth of managers (see, e.g., Lambert et al, 1991;Carpenter, 2000;Ju et al, 2003;Ross, 2004;Tian, 2004;Braido and Ferreira, 2006 Harvey and Graham (2001) also present survey-based evidence that most firms have an optimal or target debt-to-equity ratio. 6 Strictly speaking, stock holdings contribute to vega as well, since stock can be considered as a call option written on total firm value and its value rises with firm risk.…”

Terrorist choice: a stochastic dominance and prospect theory analysis

“…Past the intersection of the two distributions, the cumulative distribution for G is located to the right of the cumulative distribution for F. An incentive structure that censures the two probability distributions such that positive payoffs are received only at or beyond the level of outcome associated with the intersection of the two cumulative probability distributions will ensure that the more risky of the two alternatives is always chosen, regardless of the preferences of the decision-maker. Braido and Ferreira (2006) provide a proof of this in their analysis of risk-taking behaviour and options-based compensation schedules, where those compensation schedules are defined by a particular 'strike price' at which payoffs become positive. Braido and Ferreira (2006) show that there is a 'strike price' (trigger point) that will always entice the decision-maker who has been granted an option to choose the more risky of two alternatives.…”

“…Braido and Ferreira (2006) provide a proof of this in their analysis of risk-taking behaviour and options-based compensation schedules, where those compensation schedules are defined by a particular 'strike price' at which payoffs become positive. Braido and Ferreira (2006) show that there is a 'strike price' (trigger point) that will always entice the decision-maker who has been granted an option to choose the more risky of two alternatives. Braido and Ferreira (2006, 516) state the familiar stochastic dominance criteria (above).…”

“…Braido and Ferreira (2006) note that this assumption applies to all standard distributions. They follow with their main proposition, the proof of which is their main result.…”

Does Negotiating with Terrorists Make Them More Risk Seeking?

“…A mathematical approach would build upon the types of results found in Carpenter (2000), Ross (2004) and Braido and Ferreira (2006). In particular, it would be interesting to prove that the results contained in Ross (2004) apply in situations where a terrorist group dynamically accumulates actual payoffs and concessions over time in a series of terrorist actions.…”