Improving the Power of Tests of Stochastic Dominance

Donald, Stephanie Hemelryk; Hsu, Yu Chin

doi:10.1080/07474938.2013.833813

Cited by 54 publications

(66 citation statements)

References 17 publications

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“…from which one has the following typical results (for example, see Donald and Hsu (2013) converge to the same process as the limit process, conditional on the sample path with probability approaching 1. For further details, see Donald and Hsu (2013).…”

Section: Is a Function Of N Satisfying That M(n) → ∞ And N/(nmentioning

confidence: 99%

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A stochastic dominance approach to financial risk management strategies

Chang

Jiménez-Martín

Maasoumi

et al. 2015

Journal of Econometrics

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The Basel III Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one of a range of alternative risk models to forecast Value-at-Risk (VaR). The risk estimates from these models are used to determine the daily capital charges (DCC) and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realized losses exceed the estimated VaR. In this paper we define risk management in terms of choosing sensibly from a variety of risk models and discuss the optimal selection of financial risk models. A previous approach to model selection for predicting VaR proposed combining alternative risk models and ranking such models on the basis of average DCC. This method is based only on the first moment of the DCC distribution, supported by a restrictive evaluation function. In this paper, we consider uniform rankings of models over large classes of evaluation functions that may reflect different weights and concerns over different intervals of the distribution of losses and DCC. The uniform rankings are based on recently developed statistical tests of stochastic dominance (SD). The SD tests are illustrated using the prices and returns of VIX futures. The empirical findings show that the tests of SD can rank different pairs of models to a statistical degree of confidence, and that the alternative (recentered) SD tests are in general agreement.

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Section: Is a Function Of N Satisfying That M(n) → ∞ And N/(nmentioning

confidence: 99%

“…Assumption 2.1: Linton, Maasumi and Whang, (2005) (hereafter LMW), Linton, Song and Whang (2010) and Donald and Hsu (2013) for further details). In order to test if Y SD1 X, Donald and Hsu (2013) formulate their hypotheses as:…”

Section: Definitions and Hypothesis Formulationmentioning

confidence: 99%

A stochastic dominance approach to financial risk management strategies

Chang

Jiménez-Martín

Maasoumi

et al. 2015

Journal of Econometrics

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“…SuchĜ can be obtained by applying the technique of contact set estimation in the context of stochastic dominance testing. See Linton et al (2010) and Donald and Hsu (2016), as well as the literature on moment inequalities with moment selection (Andrews and Shi (2013), among others).…”

Section: Inference For Welfare Gainmentioning

confidence: 99%

Who should be treated? Empirical welfare maximization methods for treatment choice

Kitagawa

Tetenov²

2017

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One of the main objectives of empirical analysis of experiments and quasi-experiments is to inform policy decisions that determine the allocation of treatments to individuals with different observable covariates. We study the properties and implementation of the Empirical Welfare Maximization (EWM) method, which estimates a treatment assignment policy by maximizing the sample analog of average social welfare over a class of candidate treatment policies. The EWM approach is attractive in terms of both statistical performance and practical implementation in realistic settings of policy design. Common features of these settings include: (i) feasible treatment assignment rules are constrained exogenously for ethical, legislative, or political reasons, (ii) a policy maker wants a simple treatment assignment rule based on one or more eligibility scores in order to reduce the dimensionality of individual observable characteristics, and/or (iii) the proportion of individuals who can receive the treatment is a priori limited due to a budget or a capacity constraint. We show that when the propensity score is known, the average social welfare attained by EWM rules converges at least at n −1/2 rate to the maximum obtainable welfare uniformly over a minimally constrained class of data distributions, and this uniform convergence rate is minimax optimal. We examine how the uniform convergence rate depends on the richness of the class of candidate decision rules, the distribution of conditional treatment effects, and the lack of knowledge of the propensity score. We offer easily implementable algorithms for computing the EWM rule and an application using experimental data from the National JTPA Study.

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“…Three tests proposing different resampling procedures for estimating the critical values of a extended Kolmogorov-Smirnov (KS) test for SD are used, namely: (i) Barret and Donald (BD) (2003), who propose a standard bootstrap simulation method to mimic the asymptotic null distribution of the least favourable case (LFC); (ii) Linton, Maasoumi and Whang (2005) (LMW), who estimate the critical values using the subsampling method proposed in Politis and Romano (1994), which allow for general dependence amongst the prospects, and for observations not to be i.i.d., such that the critical values for this test does not rely on the (LFC); and (iii) the Donald and Hsu (2013) test that extends Hansen's (2005) recentering method to obtain critical values for the KS test, which increases power properties compared with the unadjusted test mounted at the composite boundary of the null and alternative spaces, the so-called Least Favorable Case (LFC).…”

Section: Test Statistics and Critical Valuesmentioning

confidence: 99%

“…The technical assumptions required for the underlying statistical theory include the following (see Linton, Maasoumi and Whang (2005) (hereafter LMW), Linton, Song and Whang (2010) and Donald and Hsu (2013) for further details): for all u with strict inequality for some u;…”

Section: Test Statistics and Critical Valuesmentioning

confidence: 99%

Choosing Expected Shortfall over VaR in Basel III Using Stochastic Dominance

Chang¹,

Jiménez-Martín²,

Maasoumi³

et al. 2017

Proceedings of the 2017 International Conference on Economics, Finance and Statistics (ICEFS 2017)

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Abstract.Bank risk managers follow the Basel Committee on Banking Supervision (BCBS) recommendations that recently proposed shifting the quantitative risk metrics system from Value-at-Risk (VaR) to Expected Shortfall (ES). The Basel Committee on Banking Supervision (2013, p. 3) noted that: "a number of weaknesses have been identified with using VaR for determining regulatory capital requirements, including its inability to capture tail risk". The proposed reform costs and impact on bank balances may be substantial, such that the size and distribution of daily capital charges under the new rules could be affected significantly. Regulators and bank risk managers agree that all else being equal, a "better" distribution of daily capital charges is to be preferred. The distribution of daily capital charges depends generally on two sets of factors: (1) the risk function that is adopted (ES versus VaR); and (2) their estimated counterparts. The latter is dependent on what models are used by bank risk managers to provide for forecasts of daily capital charges. That is to say, while ES is known to be a preferable "risk function" based on its fundamental properties and greater accounting for the tails of alternative distributions, that same sensitivity to tails can lead to greater daily capital charges, which is the relevant (that is, controlling) practical reference for risk management decisions and observations. In view of the generally agreed focus in this field on the tails of non-standard distributions and low probability outcomes, an assessment of relative merits of estimated ES and estimated VaR is ideally not limited to mean variance considerations. For this reason, robust comparisons between ES and VaR will be achieved in the paper by using a Stochastic Dominance (SD) approach to rank ES and VaR.

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Improving the Power of Tests of Stochastic Dominance

Cited by 54 publications

References 17 publications

A stochastic dominance approach to financial risk management strategies

A stochastic dominance approach to financial risk management strategies

Who should be treated? Empirical welfare maximization methods for treatment choice

Choosing Expected Shortfall over VaR in Basel III Using Stochastic Dominance

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