Дилемма инвестора хедж


Дилемма инвестора и управляющего хедж-фонда
Definitions:
Assets under management A0Management fee: mfA0 (0<mf<1)
Performance fee: pfA1-A0=pfA0r (0<pf<1)
r – annual return for investments
W0 – amount of withdrawal
Model 1: Equilibrium for a managing director
Actions:
act aggressively, while investors withdraw W0payoff:
mfA0-W0+pfA0-W0raact conservative and investors do not withdraw money
payoff:
mfA0+pfA0rcIf the utility from both scenarios is the same, then
W0pfra+mf=pfA0(ra-rc)Introduce ω, where ω=W0A0 - fraction of assets withdrawn by investors
ω=pf(ra-rc)mf+pfraWe have a relationship between risky and conservative strategies linked to the proportion of withdrawal.
Model 2: equilibrium for an investor
Actions:
withdraw W0, while MD acts aggressively
-mfA0-W0+(1-pf)A0-W0rado not withdraw money, while MD act conservative
payoff:
-mfA0+(1-pf)A0rcSo, in the equilibrium:ω=(1-pf)(ra-rc)1-pfra-mfSince ω>0, 1-pfra>mf which logically constitute to the fact that return from the investments should outweigh the management costs.
Results:
In equilibrium investors accept lower return for their investments than MD, for every level of withdrawal.
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