TY - JOUR
T1 - Risk managing tail-risk seekers: VaR and expected shortfall vs S-shaped utility
AU - Armstrong, John
AU - Brigo, Damiano
PY - 2019/4/1
Y1 - 2019/4/1
N2 - We consider market players with tail-risk-seeking behaviour modelled by S-shaped utility, as introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in constraining such players, as such measures cannot reduce the traders expected S-shaped utilities. Indeed, when designing payoffs aiming to maximize utility under a VaR or ES risk limit, the players will attain the same supremum of expected utility with or without VaR or ES limits. By contrast, we show that risk management constraints based on a second more conventional concave utility function can reduce the maximum S-shaped utility that can be achieved by the investor. Indeed, product designs leading to progressively larger S-shaped utilities will lead to progressively lower expected constraining conventional utilities, violating the related risk limit. These results hold in a variety of market models, including the Black Scholes options model, and are particularly relevant for risk managers given the historical role of VaR and the endorsement of ES by the Basel committee in 2012--2013.
AB - We consider market players with tail-risk-seeking behaviour modelled by S-shaped utility, as introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in constraining such players, as such measures cannot reduce the traders expected S-shaped utilities. Indeed, when designing payoffs aiming to maximize utility under a VaR or ES risk limit, the players will attain the same supremum of expected utility with or without VaR or ES limits. By contrast, we show that risk management constraints based on a second more conventional concave utility function can reduce the maximum S-shaped utility that can be achieved by the investor. Indeed, product designs leading to progressively larger S-shaped utilities will lead to progressively lower expected constraining conventional utilities, violating the related risk limit. These results hold in a variety of market models, including the Black Scholes options model, and are particularly relevant for risk managers given the historical role of VaR and the endorsement of ES by the Basel committee in 2012--2013.
KW - Concave utility constraints
KW - Concave utility risk constraints
KW - Effective risk constraints
KW - Expected shortfall constraints
KW - Limited liability investors
KW - Optimal product design under risk constraints
KW - S-Shaped utility maximization
KW - Tail-risk-seeking investors
KW - Value at risk constraints
UR - http://www.scopus.com/inward/record.url?scp=85061594575&partnerID=8YFLogxK
U2 - 10.1016/j.jbankfin.2019.01.010
DO - 10.1016/j.jbankfin.2019.01.010
M3 - Article
VL - 101
SP - 122
EP - 135
JO - Journal of Banking and Finance
JF - Journal of Banking and Finance
SN - 0378-4266
ER -