Higher order elicitability and Osband’s principle

Fissler, Tobias; Ziegel, Johanna F.

doi:10.1214/16-aos1439

Cited by 323 publications

(364 citation statements)

References 34 publications

Supporting

Mentioning

335

Contrasting

Unclassified

Order By: Relevance

“…Rockafellar and Uryasev ([36] p. 22) further elaborate on some of these issues in their discussion of the 'fundamental risk quadrangle', and suggest a way round the issue of the non-elicitability of CVaR by utilising quantile regression, as pioneered by Koenker and Basset [37]. Fissler and Ziegel [38] further concur, in a discussion of higher order elicitability and Osbond's principle, and again mention quantile and expectile regression. They demonstrate that the pair (value at risk, expected shortfall) is elicitable, subject to mild regularity assumptions, which involve the relevant distributions consisting of absolutely continuous distributions with unique quantiles.…”

Section: Optimising Conditional Value At Riskmentioning

confidence: 99%

Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis

Allen

McAleer

Powell

et al. 2016

JRFM

View full text Add to dashboard Cite

Abstract:This paper features an analysis of the effectiveness of a range of portfolio diversification strategies, with a focus on down-side risk metrics, as a portfolio diversification strategy in a European market context. We apply these measures to a set of daily arithmetically-compounded returns, in U.S. dollar terms, on a set of ten market indices representing the major European markets for a nine-year period from the beginning of 2005 to the end of 2013. The sample period, which incorporates the periods of both the Global Financial Crisis (GFC) and the subsequent European Debt Crisis (EDC), is a challenging one for the application of portfolio investment strategies. The analysis is undertaken via the examination of multiple investment strategies and a variety of hold-out periods and backtests. We commence by using four two-year estimation periods and a subsequent one-year investment hold out period, to analyse a naive 1/N diversification strategy and to contrast its effectiveness with Markowitz mean variance analysis with positive weights. Markowitz optimisation is then compared to various down-side investment optimisation strategies. We begin by comparing Markowitz with CVaR, and then proceed to evaluate the relative effectiveness of Markowitz with various draw-down strategies, utilising a series of backtests. Our results suggest that none of the more sophisticated optimisation strategies appear to dominate naive diversification.

show abstract

Section: Optimising Conditional Value At Riskmentioning

confidence: 99%

Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis

Allen

McAleer

Powell

et al. 2016

JRFM

View full text Add to dashboard Cite

show abstract

“…A desirable property for a risk measure is the elicitability , which allows one to compare competitive forecasting methods, a property that VaR does have (see Gneiting, 2011 ). The lack of elicitability for CVaR has been adjusted via the joint elicitability , concept formalised in Fissler and Ziegel (2016) , but earlier flagged out by Acerbi and Székely (2014) . Robustness properties of a risk measure are also of great interest since they imply that the estimate is insensitive to data contamination.…”

Section: Introductionmentioning

confidence: 99%

Robust and Pareto Optimality of Insurance Contracts

et al. 2017

View full text Add to dashboard Cite

a b s t r a c tThe optimal insurance problem represents a fast growing topic that explains the most efficient contract that an insurance player may get. The classical problem investigates the ideal contract under the assumption that the underlying risk distribution is known, i.e. by ignoring the parameter and model risks. Taking these sources of risk into account, the decision-maker aims to identify a robust optimal contract that is not sensitive to the chosen risk distribution. We focus on Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR)-based decisions, but further extensions for other risk measures are easily possible. The Worst-case scenario and Worst-case regret robust models are discussed in this paper, which have been already used in robust optimisation literature related to the investment portfolio problem. Closed-form solutions are obtained for the VaR Worst-case scenario case, while Linear Programming (LP) formulations are provided for all other cases. A caveat of robust optimisation is that the optimal solution may not be unique, and therefore, it may not be economically acceptable, i.e. Pareto optimal. This issue is numerically addressed and simple numerical methods are found for constructing insurance contracts that are Pareto and robust optimal. Our numerical illustrations show weak evidence in favour of our robust solutions for VaR-decisions, while our robust methods are clearly preferred for CVaR-based decisions.

show abstract

“…While some authors interpret this to mean that ES cannot be back-tested (e.g., [5,6]), [7] argue that elicitability is relevant for relative comparisons between estimators, but not for absolute significance testing. Moreover, [8] show that the pair (VaR, ES) is jointly elicitable. Nevertheless, the question arises whether there are non-trivial coherent risk measures that are elicitable.…”

Section: Introductionmentioning

confidence: 91%

Dependence Uncertainty Bounds for the Expectile of a Portfolio

Jakobsons

Vanduffel

2015

SSRN Journal

View full text Add to dashboard Cite

Abstract:We study upper and lower bounds on the expectile risk measure of risky portfolios when the joint distribution of the risky components is not fully specified. First, we summarize methods for obtaining bounds when only the marginal distributions of the components are known, but not their interdependence (unconstrained bounds). In particular, we provide the best-possible upper bound and the best-possible lower bound (under some conditions), as well as numerical procedures to compute them. We also derive simple analytic bounds that appear adequate in various situations of interest. Second, we study bounds when some information on interdependence is available (constrained bounds). When the variance of the portfolio is known, a simple-to-compute upper bound is provided, and we illustrate that it may significantly improve the unconstrained upper bound. We also show that the unconstrained lower bound cannot be readily improved using variance information. Next, we derive improved bounds when the bivariate distributions of each of the risky components and a risk factor are known. When the factor induces a positive dependence among the components, it is typically possible to improve the unconstrained lower bound. Finally, the unconstrained dependence uncertainty spreads of expected shortfall, value-at-risk and the expectile are compared.

show abstract

Higher order elicitability and Osband’s principle

Abstract: This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016a).

Cited by 323 publications

References 34 publications

Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis

Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis

Robust and Pareto Optimality of Insurance Contracts

Dependence Uncertainty Bounds for the Expectile of a Portfolio

Contact Info

Product

Resources

About