Chance-constrained portfolio selection is an approach toportfolio selection underloss aversion. The formulation assumes that: (i) investor's preferences are representable by theexpected utility of final wealth; and that (ii) they require that the probability of their final wealth falling below asurvival or safety level must be acceptably low.The chance-constrained portfolio problem is then to find:
The approach is typically applied only by sophisticatedquantitative investors.Hedge funds may use this given their needfor tightly controlled risk metrics, including probabilisticdrawdown control,Value-at-Risk-based optimization, andmodel uncertainty management.Pension fundsand insurance firms will sometimes apply this toliability-driven investing (LDI) to ensure a portfolio meets funding targets with a minimum probability.
The original implementation is based on the seminal work ofAbraham Charnes andWilliam W. Cooper onchance constrained programming in 1959,[1]and was first applied to finance byBertil Naslund andAndrew B. Whinston in 1962[2] and in 1969 by N. H. Agnew, et al.[3]
For fixedα the chance-constrained portfolio problem representslexicographic preferences and is an implementation ofcapital asset pricing under loss aversion.In general though, it is observed[4] that noutility function can represent the preference ordering of chance-constrained programming because a fixedα does not admit compensation for a small increase inα by any increase in expected wealth.
For a comparison tomean-variance andsafety-first portfolio problems, see;[5] for a survey ofsolution methods here, see;[6] for a discussion of therisk aversion properties of chance-constrained portfolio selection, see.[7]