Chance-constrained portfolio selection is an approach to
portfolio selection under
loss aversion
In cognitive science and behavioral economics, loss aversion refers to a cognitive bias in which the same situation is perceived as worse if it is framed as a loss, rather than a gain. It should not be confused with risk aversion, which descri ...
.
The formulation assumes that (i) investor's preferences are representable by the
expected utility
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Ratio ...
of final wealth, and that (ii) they require that the probability of their final wealth falling below a
survival or safety level must to be acceptably low.
The chance-constrained portfolio problem is then to find:
:Max
w
jE(X
j), subject to Pr(
w
jX
j < s) ≤ ,
w
j = 1, w
j ≥ 0 for all j,
::where s is the survival level and is the admissible
probability of ruin; w is the weight and x is the value of the ''jth'' asset to be included in the portfolio.
The original implementation is based on the seminal work of
Abraham Charnes and
William W. Cooper on
chance constrained programming in 1959,
and was first applied to finance by
Bertil Naslund and
Andrew B. Whinston in 1962
and in 1969 by N. H. Agnew, et al.
For fixed the chance-constrained portfolio problem represents
lexicographic preferences and is an implementation of
capital asset pricing under loss aversion.
In general though, it is observed that no
utility function
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings.
* In a Normative economics, normative context, utility refers to a goal or ob ...
can represent the preference ordering of chance-constrained programming because a fixed does not admit compensation for a small increase in {{math, ''α'' by any increase in expected wealth.
For a comparison to
mean-variance and
safety-first portfolio problems, see; for a survey of
solution methods here, see; for a discussion of the
risk aversion
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more c ...
properties of chance-constrained portfolio selection, see.
[Pyle, D. H. and Stephen J. Turnovsky (1971), “Risk Aversion in Chance Constrained Portfolio Selection, Management Science,18, No. 3, 218-22]
Retrieved September 24, 2020.
See also
*
Capital asset pricing model
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a Diversification (finance), well-diversified Portfolio (f ...
*
Expected utility theory
*
Kelly criterion
*
Lexicographic preferences
*
Loss aversion
In cognitive science and behavioral economics, loss aversion refers to a cognitive bias in which the same situation is perceived as worse if it is framed as a loss, rather than a gain. It should not be confused with risk aversion, which descri ...
*
Portfolio optimization
*
Post modern portfolio theory
*
Roy's safety-first criterion
*
Stochastic programming
References
Portfolio theories
Stochastic optimization
Financial economics
Actuarial science