Almost Stochastic Dominance and Efficient Investment Sets

Levy, Moshe

doi:10.4236/ajor.2012.23038

Cited by 17 publications

(3 citation statements)

References 26 publications

(30 reference statements)

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“…However, the relaxation of this assumption is conditional: The area of violation (i.e. the area where the cumulative probability distribution of B is above that of A) must be very small compared with the total area of the two distributions (Basu et al 2011;Levy 2009Levy , 2012. The SD decision-making criteria consider both risk and potential outcomes with the cumulative distribution function.…”

Section: Stochastic Dominance Decision-making Criteriamentioning

confidence: 99%

Life cycle versus balanced funds: An emerging market perspective

Louw

Schalkwyk

Reyers

2017

SAJEMS

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Background: Inadequate retirement savings is an international challenge. Additionally, individuals are not cognisant of how asset allocation choices ultimately impact retirement savings. Life cycle and balanced funds are popular asset allocation strategies to save towards retirement. However, recent research is questioning the efficacy of life cycle funds that switch to lower risk asset classes as retirement approaches.Aim: The purpose of this study is to compare the performance of life cycle funds with balanced funds to determine whether either dominates the other. The study compares balanced and life cycle funds with similar starting asset allocations as well as those where the starting asset allocations differ.Setting: The study has a South African focus and constructs funds using historical data for the main local asset classes; that is, equity, fixed income and cash, as well as a proxy for foreign equity covering the period 1986–2013.Method: The study makes use of Monte Carlo simulations and bootstrap with replacement, and compares the simulated outcomes using stochastic dominance as decision-making criteria.Results: The results indicate that life cycle funds fail to dominate balanced funds by first-order or almost stochastic dominance when funds have a similar starting asset allocation. It is noteworthy that there are instances where the opposite is true, that is, balanced funds dominate life cycle funds. These results highlight that while the life cycle funds provide more downside protection, they significantly suppress the upside potential compared to balanced funds. When the starting asset allocations of the balanced and life cycle funds differ, the stochastic dominance results are inconsistent as to the efficacy of the life cycle fund strategies considered.Conclusion: The study shows that whether one fund is likely to dominate the other is strongly dependent on the underlying asset allocation strategies of the funds. Additionally, the length of the glide path and the risk and return characteristics of the investable universe are also likely to influence the findings.

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Section: Stochastic Dominance Decision-making Criteriamentioning

confidence: 99%

Life cycle versus balanced funds: An emerging market perspective

Louw

Schalkwyk

Reyers

2017

SAJEMS

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“…The budget is assumed not to be a constraint. The hybrid solution data are summarized in Table 7 and its cumulative distribution [41] and several of interest are depicted in Figure 3.…”

Section: Hybrid Solution Examplementioning

confidence: 99%

Optimization of Critical Systems for Robustness in a Multistate World

Kujawski¹

2013

AJOR

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Critical systems are typically complex systems that are required to perform reliably over a wide range of scenarios, or multistate world. Seldom does a single system exist that performs best for all plausible scenarios. A robust solution, one that performs relatively well over a wide range of scenarios, is often the preferred choice for reduced risk at an acceptable cost. The alternative with the maximum expected utility may possess vulnerabilities that could be exploited. The best strategy is likely to be a hybrid solution. The von Neumann-Morgenstern Expected Utility Theory (EUT) would never select such a solution because, given its linear functional form, the expected utility of a hybrid solution cannot be greater than that of every constituent alternative. The continuity axiom and the independence axiom are assessed to be unrealistic for the problem of interest. Several well-known decision models are analyzed and demonstrated to be potentially misleading. The linear disappointment model modifies EUT by adding a term proportional to downside risk; however, it does not provide a mathematical basis for determining preferred hybrid solutions. The paper proposes a portfolio allocation model with stochastic optimization as a flexible and transparent method for defining choice problems and determining hybrid solutions for critical systems with desirable properties such as diversification and robustness.

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“…Some papers found that ASD rule can explain common practice in investments unanswered by SD rules (e.g., Bali et al, 2009;Levy, 2009;Bali et al, 2013) 3 . Moreover, researchers showed that investment efficient sets can be further improved by ASD rule (e.g., Levy, 2012).…”

Section: Introductionmentioning

confidence: 99%

Estimating the Critical Parameter in Almost Stochastic Dominance from Insurance Deductibles

et al. 2021

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Knowing how small a violation of stochastic dominance rules would be accepted by most individuals is a prerequisite to applying almost stochastic dominance criteria. Unlike previous laboratory-experimental studies, this paper estimates an acceptable violation of stochastic dominance rules with 939,690 real world data observations on a choice of deductibles in automobile theft insurance. We find that, for all policyholders in the sample who optimally chose a low deductible, the upper bound estimate of the acceptable violation ratio is 0.0014, which is close to zero. On the other hand, considering that most decision makers, such as 99% (95%) of the policyholders in the sample, optimally chose the low deductible, the upper bound estimate of the acceptable violation ratio is 0.0405 (0.0732). Our results provide reference values for the acceptable violation ratio for applying almost stochastic dominance rules. This paper was accepted by Manel Baucells, decision analysis.

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Almost Stochastic Dominance and Efficient Investment Sets

Cited by 17 publications

References 26 publications

Life cycle versus balanced funds: An emerging market perspective

Life cycle versus balanced funds: An emerging market perspective

Optimization of Critical Systems for Robustness in a Multistate World

Estimating the Critical Parameter in Almost Stochastic Dominance from Insurance Deductibles

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