Risk neutral
Encyclopedia
In economics
and finance
, risk neutral behavior is between risk aversion
and risk seeking. If offered either €50 or a 50% chance of each of €100 and nothing, a risk neutral person would have no preference between the two options. In contrast, a risk averse
person presented with these options would accept some amount less than €50 in preference to the risky option, while a risk seeking person would accept a less than 50% chance of €100 in preference to the sure €50.
, a risk neutral firm facing risk about the market price of its product, and caring only about profit, would maximize the expected value of its profit (with respect to its choices of labor input usage, output produced, etc.). But a risk averse firm in the same environment would typically take a more cautious approach.
, a risk neutral investor able to choose any combination of an array of risky assets (various companies' stocks, various companies' bonds, etc.) would invest exclusively in the asset with the highest expected
yield, ignoring its risk features relative to those of other assets, and would even sell short
the asset with the lowest expected yield as much as is permitted in order to invest the proceeds in the highest expected-yield asset. In contrast, a risk averse investor would diversify
among a variety of assets, taking account of their risk features, even though doing so would lower the expected return on the overall portfolio. The risk neutral investor's portfolio would have a higher expected return, but also a greater variance of possible returns.
. The utility function whose expected value is maximized is concave
for a risk averse agent, convex
for a risk lover, and linear for a risk neutral agent. Thus in the risk neutral case, expected utility of wealth is simply equal to a linear function of expected wealth, and maximizing it is equivalent to maximizing expected wealth itself.
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, risk neutral behavior is between risk aversion
Risk aversion
Risk aversion is a concept in psychology, economics, and finance, based on the behavior of humans while exposed to uncertainty....
and risk seeking. If offered either €50 or a 50% chance of each of €100 and nothing, a risk neutral person would have no preference between the two options. In contrast, a risk averse
Risk aversion
Risk aversion is a concept in psychology, economics, and finance, based on the behavior of humans while exposed to uncertainty....
person presented with these options would accept some amount less than €50 in preference to the risky option, while a risk seeking person would accept a less than 50% chance of €100 in preference to the sure €50.
Theory of the firm
In the context of the theory of the firmTheory of the firm
The theory of the firm consists of a number of economic theories that describe the nature of the firm, company, or corporation, including its existence, behavior, structure, and relationship to the market.-Overview:...
, a risk neutral firm facing risk about the market price of its product, and caring only about profit, would maximize the expected value of its profit (with respect to its choices of labor input usage, output produced, etc.). But a risk averse firm in the same environment would typically take a more cautious approach.
Portfolio theory
In portfolio choiceModern portfolio theory
Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
, a risk neutral investor able to choose any combination of an array of risky assets (various companies' stocks, various companies' bonds, etc.) would invest exclusively in the asset with the highest expected
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
yield, ignoring its risk features relative to those of other assets, and would even sell short
Short selling
In finance, short selling is the practice of selling assets, usually securities, that have been borrowed from a third party with the intention of buying identical assets back at a later date to return to that third party...
the asset with the lowest expected yield as much as is permitted in order to invest the proceeds in the highest expected-yield asset. In contrast, a risk averse investor would diversify
Diversification
Diversification may refer to:* Diversification involves spreading investments* Diversification is a corporate strategy to increase market penetration...
among a variety of assets, taking account of their risk features, even though doing so would lower the expected return on the overall portfolio. The risk neutral investor's portfolio would have a higher expected return, but also a greater variance of possible returns.
The risk neutral utility function
Choice under uncertainty is often characterized as the maximization of expected utility. Utility is often assumed to be a function of profit or final portfolio wealth, with a positive first derivativeDerivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
. The utility function whose expected value is maximized is concave
Concave function
In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex.-Definition:...
for a risk averse agent, convex
Convex function
In mathematics, a real-valued function f defined on an interval is called convex if the graph of the function lies below the line segment joining any two points of the graph. Equivalently, a function is convex if its epigraph is a convex set...
for a risk lover, and linear for a risk neutral agent. Thus in the risk neutral case, expected utility of wealth is simply equal to a linear function of expected wealth, and maximizing it is equivalent to maximizing expected wealth itself.
See also
- Risk neutral valuation
- Risk-neutral measureRisk-neutral measureIn mathematical finance, a risk-neutral measure, is a prototypical case of an equivalent martingale measure. It is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market a derivative's price is the discounted...