Comparing Local Risks by Acceptance and Rejection

Schreiber, Amnon

doi:10.1111/mafi.12054

Cited by 9 publications

(6 citation statements)

References 15 publications

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“…In this context, two papers are close to the present paper: Shorrer (2014) and Schreiber (2016). Shorrer (2014) shows that there exist risk indices that are, essentially, consistent with the acceptance/rejection decisions of all risk-averse agents with respect to bounded discrete gambles with sufficiently small support.…”

Section: Related Literature and Contributionsupporting

confidence: 61%

“…The acceptance function has already been used to study risk indices in various papers (e.g., Hart, 2011;Aumann & Serrano, 2008;Foster & Hart, 2009, 2013. In particular, our analysis of this decision function extends the analysis of Schreiber (2016), by showing the similarity between this function in the mean-variance setup and the corresponding decision function in the continuous-time setup.…”

Section: Decision Functionsmentioning

confidence: 62%

“…The case of the the acceptance/rejection function f AR has been analyzed in Schreiber (2016). As the function f AR has only two feasible values (0 or 1), it cannot admit of consistent risk indices, as in many cases in which one gamble is riskier than another, an agent may choose to reject both gambles (and his value of f AR of both gambles would be zero).…”

Section: Weak Consistency For Acceptance/rejectionmentioning

confidence: 99%

“…As the function f AR has only two feasible values (0 or 1), it cannot admit of consistent risk indices, as in many cases in which one gamble is riskier than another, an agent may choose to reject both gambles (and his value of f AR of both gambles would be zero). Nevertheless, one can define the milder notion of weak consistency, and show that a corollary to Schreiber's (2016) result is that the risk index Q l V M is weakly consistent with the acceptance/rejection function f AR .…”

Section: Weak Consistency For Acceptance/rejectionmentioning

confidence: 99%

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Short-Term Investments and Indices of Risk

Heller

Schreiber

2019

SSRN Journal

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We study various decision problems regarding short-term investments in risky assets whose returns evolve continuously in time. We show that in each problem, all risk-averse decision makers have the same (problem-dependent) ranking over short-term risky assets. Moreover, in each problem, the ranking is represented by the same risk index as in the case of CARA utility agents and normally distributed risky assets. JEL Classification: D81, G32.We analyze four decision problems that are important in economic settings. In general, different risk-averse agents rank the desirability of gambles differently. However, our main result shows that in each of these problems, all risk-averse agents have the same (problem-dependent) ranking over short-term investments in risky assets whose returns evolve continuously. Moreover, in each problem, the ranking is represented by the same risk index obtained in the commonly used mean-variance preferences (e.g., Markowitz, 1952), which are induced by CARA utility agents and normally distributed gambles. Brief Description of the ModelWe consider an agent who has to make an investment decision related to a gamble. We think of a gamble as the additive return on a financial investment. We assume that the agent has (1) an initial wealth w, and (2) a von Neumann-Morgenstern utility u that is increasing and risk-averse (i.e, u ′ > 0 and u ′′ < 0). We assume that a gamble is represented by a random variable with (1) positive expectation, and (2) some negative values in its support. For each problem the agents' choices are modeled by a decision function that assigns a number to each agent and each gamble, where a higher number is interpreted as the agent finding the gamble to be more attractive (i.e., less risky) for the relevant decision problem.We study four decision problems in the paper: (1) acceptance/rejection, in which the agent faces a binary choice between accepting and rejecting the gamble (e.g., Hart, 2011);(2) capital allocation, in which the agent has a continuous choice of how much to invest in the gamble (e.g., Markowitz, 1952; Sharpe, 1964); (3) the optimal certainty equivalent, in which the agent evaluates how much an opportunity to invest in the gamble (according to the optimal investment level) is worth to the agent (e.g., Hellman & Schreiber, 2018); and (4) risk premium, in which the agent evaluates how much investing in the gamble is inferior to obtaining the gamble's expected payoff (Arrow, 1970). 1 A risk index is a function that assigns to each gamble a nonnegative number, which is interpreted as the gamble's riskiness. We say that a risk index is consistent with a decision function f over some set of agents and gambles, if each agent in the set ranks all gambles in the set according to that risk index; that is, f assigns for each agent a higher value for gamble g than for gamble g ′ iff the risk index assigns a lower value to g. A risk-aversion index is a function that assigns to each agent a non-negative number, which is interpreted as the agent's risk aversion. We sa...

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Section: Related Literature and Contributionsupporting

confidence: 61%

Section: Decision Functionsmentioning

confidence: 62%

Section: Weak Consistency For Acceptance/rejectionmentioning

confidence: 99%

Section: Weak Consistency For Acceptance/rejectionmentioning

confidence: 99%

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Short-Term Investments and Indices of Risk

Heller

Schreiber

2019

SSRN Journal

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“…A first element of innovation, for instance has been kept by [16] who introduced the measure of riskiness R FH : whereas R AS orders gambles (investments) looking at the utility function regardless of wealth, R FH examines the investments looking for the critical wealth regardless of utility. Extensions towards this direction include the contributions of [17] who show how to extend the definition of R FH to continuous random variables and to dynamic environments; [18] extends the definition of acceptance dominance order to risky assets whose values follow random processes, and using differential calculus shows that the acceptance dominance order is a complete order that can be represented by an index of local risk. On the other hand, [19] working on the original R AS concept, studied an extension of the stochastic dominance order, which is equivalent to the one introduced by the index of Aumann and Serrano.…”

Section: Introductionmentioning

confidence: 99%

On a New Index Aimed at Comparing Risks

Resta¹,

Marina²

2015

JMF

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This paper fits into the research stream started by Aumann and Serrano (2008) with their index R AS , and introduces a new index of riskiness called I θ. In particular, our intuition moves from the observation that the R AS index is defined over the set of gambles whose expected value of losses is lower than the one of gains. We then restrict the attention on investment opportunities in a proper relation with a benchmark value (] ∈ 0,1 θ and we build the index I θ. The mathematical features of the new index are discussed in deepest detail, providing evidence that I θ can be used by the investor in comparing risks: θ plays the role of a threshold value such that once fixed in the range (] 0,1 , I θ suggests to take into consideration a gamble (an investment, an asset) g only if the ratio between the expected value of its losses and the expected value of its gains is lower than such θ. Moreover, I θ nests R AS as special case when θ = 1, and it satisfies both homogeneity and duality properties. In the light of these features, I θ seems to satisfy the common need among practitioners for flexible index of riskiness.

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Economic indices of absolute and relative riskiness

Schreiber

2013

Econ Theory

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Comparing Local Risks by Acceptance and Rejection

Cited by 9 publications

References 15 publications

Short-Term Investments and Indices of Risk

Short-Term Investments and Indices of Risk

On a New Index Aimed at Comparing Risks

Economic indices of absolute and relative riskiness

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