A wealth-requirement axiomatization of riskiness

Foster, Dean P.; Hart, Sergiu

doi:10.3982/te1150

Cited by 19 publications

(8 citation statements)

References 16 publications

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“…Aumann and Serrano (2008) o¤er a set of axioms characterizing the AS riskiness measure. An axiomatization of the FH measure is o¤ered separately inFoster and Hart (2013).…”

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confidence: 99%

Performance evaluation with high moments and disaster risk

Kadan¹,

Liu²

2014

Journal of Financial Economics

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Traditional performance evaluation measures do not account for tail events and rare disasters. To address this issue, we reinterpret the riskiness measures of Aumann and Serrano (2008) and Foster and Hart (2009) as performance indices. We derive the moment properties of these indices and their sensitivity to rare disasters and show that they are consistent with the asset pricing literature. As applications, we show that "anomalous" investment strategies such as "momentum" or investment in private equity lose much of their glamour when accounting for high moments and rare events. Furthermore, using the indices to select mutual funds results in desirable high-moment properties out of sample.

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“…Aumann and Serrano (2008) o¤er a set of axioms characterizing the AS riskiness measure. An axiomatization of the FH measure is o¤ered separately inFoster and Hart (2013).…”

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confidence: 99%

Performance evaluation with high moments and disaster risk

Kadan¹,

Liu²

2014

Journal of Financial Economics

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“…That is, f AR ((u, w) , g) is equal to one if accepting the gamble yields a weakly higher expected payoff than rejecting it, and it is equal to zero otherwise. 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: 65%

“…In two influential papers, Aumann & Serrano (2008) and Foster & Hart (2009) presented two "objective" indices of riskiness of gambles, which are independent of the subjective utility of the agent. These indices are either based on reasonable axioms that an index of risk should satisfy (e.g., Artzner et al, 1999;Aumann & Serrano, 2008;Cherny & Madan, 2009;Foster & Hart, 2013;Schreiber, 2014;Hellman & Schreiber, 2018; see also the recent survey of Föllmer & Weber, 2015), or they are based on an "operative" criterion such as an agent never going bankrupt when relying on an index of risk in deciding whether to accept a gamble (Foster & Hart, 2009; and see also Meilijson, 2009 , for a discussion of operative implication of Aumann & Serrano's index of risk). 3 We argue that risk is a multidimensional attribute that crucially depends on the investment problem.…”

Section: Related Literature and Contributionmentioning

confidence: 99%

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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“…VaR has proved to have superior qualities than variance/standard deviation and, as such, is more suitable to characterize risky investments. Since its introduction, VaR has rapidly become the standard in the finance industry, although searching for alternatives, like coherent risk measures (Artzner et al ., ) or objective measures of risk (Aumann and Serrano, ; Foster and Hart, ; Marina and Resta, ; Resta and Marina, ) to cite some examples, has practically never ended. Indeed, alternatives have often superior mathematical features than VaR, but they have not (or not yet) conquered a great consensus among practitioners because they are harder to implement practically.…”

Section: Introductionmentioning

confidence: 99%

VaRSOM: A Tool to Monitor Markets' Stability Based on Value at Risk and Self‐Organizing Maps

Resta

2015

Intell. Sys. Acc. Fin. Mgmt.

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We introduce a variant of self-organizing maps (SOMs) termed VaRSOM that evaluates the similarity among inputs and nodes of the map employing value at risk (VaR). In this way we embed risk measurement within a machine-learning architecture, thus becoming particularly well-suited to analysing financial data. We tested the visualization capabilities and the explicative power of VaRSOM on data from the German Stock Exchange; we then evaluated the results in a comparative perspective, opposing the VaRSOM outcomes to those of SOM trained with more conventional similarity measures. The results lead to the conclusion that VaRSOM is a tool particularly well suited to visualize and exploit critical patterns in financial markets. This, in turn, opens perspectives for a general machine-learning framework sensitive to financial distress and contagion effects. than VaR, but they have not (or not yet) conquered a great consensus among practitioners because they are harder to implement practically.From a more general perspective, however, those measures are per se of limited help in monitoring the intrinsic riskiness and vulnerability of the financial system as a whole. Nevertheless, this is a crucial task, since the identification of vulnerabilities makes it possible to detect imbalances within a financial system that could signal future episodes of financial stress-in the past three decades, more than 20 countries have experienced banking or currency crises of different degrees of severity.Conceptually, a stress episode can involve one or more of the following phenomena: increased uncertainty about the fundamental value of assets and the behaviour of investors, greater uncertainty about exposures of counterparties and decreased willingness among market participants to hold risky and illiquid assets (Hakkio and Keeton, 2009). Since none of these phenomena can be observed directly, financial stress must be inferred from the behaviour of asset prices and other financial variables. This is generally conceived as the ground for pure stand-alone numerical tools, like early warning systems (EWSs) that attempt to model the complexity of financial relations by way of nonlinear techniques (e.g. Demyanyk and Hasan, 2010), or by developing proper combinations of observable factors, leading to imbalance indicators (Pasricha et al., 2013), distress indicators (Kaminsky, 1999) and to indicators discriminating between 'weak fundamentals' and 'investors' panic' (Zhuang and Dowling, 2002). EWSs, in turn, can be strengthened by way of visualization tools that amplify understanding through visual perception. Visumap (Li, 2004) is an example, although it is not specifically thought of for economic applications.Within this framework, the financial tsunami that originated from the USA in 2007-2008 dramatically highlighted the poor forecasting performance of existing EWSs; from the perspective of automatic systems design, this experience suggested the importance to develop new systems that are able to offer more readable and intuitive results to fac...

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A wealth-requirement axiomatization of riskiness

Abstract: We provide an axiomatic characterization of the measure of riskiness of gambles (risky assets) introduced by Foster and Hart (2009). The axioms are based on the concept of "wealth requirement."

Cited by 19 publications

References 16 publications

Performance evaluation with high moments and disaster risk

Performance evaluation with high moments and disaster risk

Short-Term Investments and Indices of Risk

VaRSOM: A Tool to Monitor Markets' Stability Based on Value at Risk and Self‐Organizing Maps

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