Chance-constrained portfolio selection is an approach to
portfolio selection under
Loss aversion
Loss aversion is the tendency to prefer avoiding losses to acquiring equivalent gains. The principle is prominent in the domain of economics. What distinguishes loss aversion from risk aversion is that the utility of a monetary payoff depends o ...
.
The formulation assumes that investor’s preferences are representable by the
expected utility The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
of final wealth, and that they require to be acceptably low, the probability of their final wealth falling below a
survival or safety level.
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
stochastic programming
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. A stochastic program is an optimization problem in which some or all problem parameters are uncertain ...
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
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...
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
*
Portfolio optimization
*
Loss aversion
Loss aversion is the tendency to prefer avoiding losses to acquiring equivalent gains. The principle is prominent in the domain of economics. What distinguishes loss aversion from risk aversion is that the utility of a monetary payoff depends o ...
*
Stochastic programming
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. A stochastic program is an optimization problem in which some or all problem parameters are uncertain ...
*
Expected utility theory The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
*
Lexicographic preferences
*
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 well-diversified portfolio.
The model takes into ac ...
*
Post modern portfolio theory
References
Portfolio theories
Stochastic optimization
Financial economics
Actuarial science