Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences
Abstract
Let us consider a financially constrained leveraged
financial firm having some divisions
which have invested into some risky assets. Using c
oherent measures of risk the sum of the
capital requirements of the divisions is larger tha
n the capital requirement of the firm itself,
there is some diversification benefit that should b
e allocated somehow for proper
performance evaluation of the divisions. In this pa
per we use cooperative game theory and
simulation to assess the possibility to jointly sat
isfy three natural fairness requirements for
allocating risk capital in illiquid markets: Core C
ompatibility, Equal Treatment Property and
Strong Monotonicity.
Core Compatibility can be viewed as the allocated r
isk to each coalition (subset) of divisions
should be at least as much as the risk increment th
e coalition causes by joining the rest of the
divisions. Equal Treatment Property guarantees that
if two divisions have the same stand�
alone risk and also they contribute the same risk t
o all the subsets of divisions not containing
them, then the same risk capital should be allocate
d to them. Strong Monotonicity requires
that if a division weakly reduces its stand�alone r
isk and also its risk contribution to all the
subsets of the other divisions, then as an incentiv
e its allocated risk capital should not
increase. Analyzing the simulation results we concl
ude that in most of the cases it is not
possible to allocate risk in illiquid markets satis
fying the three fairness notions at the same
time, one has to give up at least one of them