Economic indices of absolute and relative riskiness

Schreiber, Amnon

doi:10.1007/s00199-013-0784-9

Cited by 13 publications

(4 citation statements)

References 11 publications

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“…However, if the individual places the initial wealth in the risky asset, then the risk becomes a multiplicative risk. For a multiplicative risk, such as AS’s approach, Schreiber (2014) defined an economic index of relative riskiness for a risky asset as the reciprocal of the positive risk aversion parameter of an individual with constant relative risk aversion who is indifferent between taking and not taking the risky asset. Under this setup, the index of relative riskiness satisfies the following equation: …”

Section: Riskiness Index and Performance Measurementioning

confidence: 99%

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Do lump-sum investing strategies really outperform dollar-cost averaging strategies?

Hoang

Wong

2020

SEF

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Purpose The literature has demonstrated that lump-sum (LS) outperforms dollar-cost averaging (DCA) in uptrend markets while DCA outperforms LS only when the asset price is mean-reverted or downtrend. To bridge the gap in the literature, this study aims to use both Sharpe ratio (SR) and economic performance measure (EPM) to compare the performance of DCA and LS under both accumulative and disaccumulative approaches when the asset price is simulated to be uptrend. Design/methodology/approach This study uses both disaccumulative and accumulative approaches to compare DCA with LS and uses both SR and EPM to evaluate their performance when the asset price is simulated to be uptrend. Instead of using the annualized returns that are commonly used by other DCA studies, we compute the holding-period returns in the comparison in this paper. Findings The simulation shows that no matter which approach is used, DCA outperforms LS in nearly all the cases in the less uptrend markets while DCA still performs better than LS in many cases of the uptrend markets, especially when the market is more volatile and investment horizon is long, regardless which approach the authors used. The authors also find more evidence supporting DCA over LS by using EPM, which is more suitable in the analysis because the returns generated by DCA are positive skewed and flat-tailed that are ignored when SR is used. Research limitations/implications The authors conclude that DCA is a better trading strategy than LS for investment even in the uptrend market, especially on high risky assets. Practical implications Investors could consider choosing DCA instead of LS as their trading strategy, especially when they prefer long term investment and investing in high-risk assets. Social implications Fund managers could consider recommending DCA to their customers, especially when they prefer long term investment and investing in high-risk assets. Originality/value This is the own study and, as far as the authors know, this is the first study in the literature uses both SR and EPM to compare the performance of DCA and LS under both accumulative and disaccumulative approaches when the asset price is simulated to be uptrend.

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Section: Riskiness Index and Performance Measurementioning

confidence: 99%

“…Schreiber (2014) adopted a power utility and derived the index of relative riskiness, which, in fact, is equal to the AS index applied to the log return instead of the absolute return. Thus, the index of relative riskiness, RS ( S t ), is defined implicitly as shown in the following equation: …”

Section: Riskiness Index and Performance Measurementioning

confidence: 99%

Do lump-sum investing strategies really outperform dollar-cost averaging strategies?

Hoang

Wong

2020

SEF

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“…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%

“…In some sense, the difference between multiplicative and additive returns is only a matter of presentation: if one invests x dollars in a multiplicative gamble r, one's payoff will be x(1 + r) dollars, and this is just the same payoff as if one invests in an additive return of x • r dollars. Nevertheless, we think that presenting the results for multiplicative returns is important for two reasons: first, as argued in Schreiber (2014), each investment might have two different aspects of riskiness, absolute and relative; given two assets, one of them might be riskier in relative terms but less risky in absolute terms. Therefore it is worthwhile to study the difference between multiplicative and additive returns in our setup.…”

Section: A Multiplicative Gamblesmentioning

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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Riskiness for sets of gambles

Michaeli

2014

Econ Theory

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Economic indices of absolute and relative riskiness

Cited by 13 publications

References 11 publications

Do lump-sum investing strategies really outperform dollar-cost averaging strategies?

Do lump-sum investing strategies really outperform dollar-cost averaging strategies?

Short-Term Investments and Indices of Risk

Riskiness for sets of gambles

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