Worst-Case Value at Risk and Portfolio Management: A Simple Method Incorporating Model Uncertainty

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 - α) * 100% drawdowns. The CDD measure generalizes the notion of the drawdown functional to a multi-scenario case and can be considered as a generalization of deviation measure to a dynamic case. The CDD measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. Mathematical properties of the CDD measure have been studied and efficient optimization techniques for CDD computation and solving asset-allocation problems with a CDD measure have been developed. The CDD family of risk functionals is similar to Conditional Value-at-Risk (CVaR), which is also called Mean Shortfall, Mean Excess Loss, or Tail Value-at-Risk. Some recommendations on how to select the optimal risk functionals for getting practically stable portfolios have been provided. A real-life asset-allocation problem has been solved using the proposed measures. For this particular example, the optimal portfolios for cases of Maximal Drawdown, Average Drawdown, and several intermediate cases between these two have been found.

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Value at Risk Incorporating Dynamic Portfolio Management

SSRN Electronic Journal ◽

10.2139/ssrn.1932719 ◽

2000 ◽

Author(s):

Stephen Lawrence

Keyword(s):

At Risk ◽

Portfolio Management ◽

Value At Risk ◽

Dynamic Portfolio

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Risk-based constraints with correlated uncertainties for the optimal operation of an energy community

10.36227/techrxiv.14790252.v2 ◽

2021 ◽

Author(s):

Mihály Dolányi ◽

Kenneth Bruninx ◽

Jean-François Toubeau ◽

Erik Delarue

Keyword(s):

At Risk ◽

Value At Risk ◽

Measurement Data ◽

Real Life ◽

Optimal Operation ◽

Conditional Value At Risk ◽

Forecast Errors ◽

Worst Case ◽

Life Measurement ◽

Out Of Sample

<div>This paper formulates an energy community's centralized optimal bidding and scheduling problem as a time-series scenario-driven stochastic optimization model, building on real-life measurement data. In the presented model, a surrogate battery storage system with uncertain state-of-charge (SoC) bounds approximates the portfolio's aggregated flexibility. </div><div>First, it is emphasized in a stylized analysis that risk-based energy constraints are highly beneficial (compared to chance-constraints) in coordinating distributed assets with unknown costs of constraint violation, as they limit both violation magnitude and probability. The presented research extends state-of-the-art models by implementing a worst-case conditional value at risk (WCVaR) based constraint for the storage SoC bounds. Then, an extensive numerical comparison is conducted to analyze the trade-off between out-of-sample violations and expected objective values, revealing that the proposed WCVaR based constraint shields significantly better against extreme out-of-sample outcomes than the conditional value at risk based equivalent.</div><div>To bypass the non-trivial task of capturing the underlying time and asset-dependent uncertain processes, real-life measurement data is directly leveraged for both imbalance market uncertainty and load forecast errors. For this purpose, a shape-based clustering method is implemented to capture the input scenarios' temporal characteristics.</div>

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INTEGRATED MANAGEMENT OF MARKETING RISK AND EFFICIENCY / INTEGRUOTAS MARKETINGO RIZIKOS IR EFEKTYVUMO VALDYMAS

Journal of Business Economics and Management ◽

10.3846/16111699.2011.555357 ◽

2011 ◽

Vol 12 (1) ◽

pp. 5-23 ◽

Cited By ~ 9

Author(s):

Aleksandras Vytautas Rutkauskas ◽

Adomas Ginevičius

Keyword(s):

At Risk ◽

Risk Management ◽

Portfolio Management ◽

Value At Risk ◽

Integrated Management ◽

Management Strategies ◽

Optimization Methods ◽

Integrated Analysis ◽

Marketing Risk ◽

Marketing Efficiency

There are two principal problems arising for marketing management: first—the increase of marketing ability to use effectively its resources, and second—to inventory the risks influencing marketing activity in order to develop their management strategy. Considering exceptional riskiness of marketing, the solution of marketing efficiency problems is not separable from identification of risks, influencing marketing, and their management strategies development. Integrated analysis of marketing efficiency and risk management problems is performed in two ways. First, a marketing risks portfolio management situation is analysed in such a way that resources, intended for risk management, are distributed among the means of decreasing value at risk in such a manner that the overall value of risk, i.e. the resultant of all risk values, would be minimal. Second, based on the expert efficiency estimates for a unit of costs in every element of marketing structure, a distribution of costs is pursued which would uphold the best increase of marketinggenerated marginal utility. To find the solution, imitative modeling and stochastic optimization methods are used. Santrauka Kyla dvi pagrindines marketingo valdymo problemos: pirma—tai marketingo gebejimo efektyviai naudoti jam skirtus išteklius didinimas, antra—inventorizuoti marketingo veiklai itak daranèias rizikas, siekiant parengti ju valdymo strategij. Atsižvelgiant i išskirtini marketingo rizikingum, jo efektyvumo problemu sprendimas neatsiejamas nuo riziku, daranèiu poveiki marketingui, identifikavimo ir ju valdymo strategiju sukurimo. Straipsnyje marketingo efektyvumas ir rizikos valdymo problemos nagrinejamos dviem budais. Pirmas—nagrinejama marketingo riziku portfelio valdymo situacija, kai ištekliai, skirti rizikai valdyti, dalijami tarp priemoniu, skirtu riziku vertei mažinti (Value at Risk), taip, kad bendroji rizikos verte, t. y. visu rizikos verèiu atstojamoji, butu minimali. Antras—remiantis ekspertu efektyvumo iverèiais snaudu vienetui kiekviename marketingo strukturos elemente, ieškomas toks snaudu padalijimas, kuris puoseletu naudingiausi marketingo sukuriamo ribinio naudingumo prieaugi. Sprendimams rasti pasitelkti imitacinio modeliavimo ir stochastinio optimizavimo metodai.

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