EconPapers    
Economics at your fingertips  
 

Expected Shortfall, spectral risk measures, and the aggravating effect of background risk, or: risk vulnerability and the problem of subadditivity

Mario Brandtner

Journal of Banking & Finance, 2018, vol. 89, issue C, 138-149

Abstract: We analyze spectral risk measures (SRMs) including its most popular representative, Expected Shortfall (ES), with respect to Gollier and Pratt (1996)’s concept of risk vulnerability. We find that SRMs and risk vulnerability are mutually exclusive, owing to the property of subadditivity: while subadditivity is commonly regarded as the axiomatic cornerstone of SRMs, risk vulnerability, by contrast, prevails if and only if superadditivity holds. The lack of risk vulnerability yields questionable predictions in portfolio problems: SRM-decision makers who split their wealth between a risk free and a risky asset do constantly opt for an increase in the risky investment when their deterministic background wealth is complemented by some additional background risk. The more general setting where background wealth is already random and then becomes more risky is not as clear-cut: Any SRM-decision maker may both increase or decrease the risky investment, depending on the concrete instance of the portfolio problem. However, when random background wealth and the risky asset are jointly normally distributed, SRM-decision makers will again unambiguously increase their risky investment. We further conduct a data analysis and discuss possible implications of the findings for regulatory risk management.

Keywords: Spectral risk measures; Expected Shortfall; Risk vulnerability; Subadditivity (search for similar items in EconPapers)
JEL-codes: D81 G32 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378426618300268
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jbfina:v:89:y:2018:i:c:p:138-149

DOI: 10.1016/j.jbankfin.2018.02.002

Access Statistics for this article

Journal of Banking & Finance is currently edited by Ike Mathur

More articles in Journal of Banking & Finance from Elsevier
Bibliographic data for series maintained by Haili He ().

 
Page updated 2020-05-02
Handle: RePEc:eee:jbfina:v:89:y:2018:i:c:p:138-149