A joint analysis of the common ratio and common difference effects

Purpose The purpose of this paper is to examine the relationship and trade-off between delay and risk in the assessment of probabilistic dated prospects. Design/methodology/approach The framework of this paper is probabilistic intertemporal choice where recent studies argue that there is a close relationship between the nonstandard behaviour in the domains of risk and time. However, the correlation between these two fields has not yet been demonstrated. This paper presents a theoretical essay by using the discounted utility (DU) and the expected utility (EU) models, and considering some of their anomalies. Findings By taking into account the interaction between risk and time in the preference relations, the implications between some anomalies present in the DU and EU models have been identified. As a result of this, in Theorem 1 the common difference effect has been derived from the delay effect and reciprocally, in Theorem 2, the common ratio effect has been deduced from the common difference effect. Originality/value In this paper, it has been shown that one component of a probabilistic dated reward (amount, time or probability) may be transformed and incorporated into another component, thus demonstrating the trade-off between amount and time, amount and probability, and time and probability.