economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...

and finance, risk neutral preferences are

preferences In psychology, economics and philosophy, preference is a technical term usually used in relation to choosing between alternatives. For example, someone prefers A over B if they would rather choose A than B. Preferences are central to decision the ...

that are neither risk averse nor

risk seeking In accounting, finance, and economics, a risk-seeker or risk-lover is a person who has a preference ''for'' risk. While most investors are considered risk ''averse'', one could view casino-goers as risk-seeking. A common example to explain ris ...

. A risk neutral party's decisions are not affected by the degree of uncertainty in a set of outcomes, so a risk neutral party is indifferent between choices with equal expected payoffs even if one choice is riskier. For example, if offered either

\$50

or a

50\%

chance each of

\$100

and

\$0

, a risk neutral person would have no preference. In contrast, a risk averse person would prefer the first offer, while a risk seeking person would prefer the second.

Theory of the firm

In the context of the

theory of the firm The theory of the firm consists of a number of economic theories that explain and predict the nature of the firm, company, or corporation, including its existence, behaviour, structure, and relationship to the market. Firms are key drivers in ec ...

, 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 choice,Merton, Robert. "An analytic derivation of the efficient portfolio frontier," ''

Journal of Financial and Quantitative Analysis The ''Journal of Financial and Quantitative Analysis'' is a peer-reviewed bimonthly academic journal published by the Michael G. Foster School of Business at the University of Washington in cooperation with the W. P. Carey School of Business at ...

'' 7, September 1972, 1851-1872. a risk neutral investor who is 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. 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 risk neutral utility function

Choice under uncertainty is often characterized as the maximization of

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 ...

. Utility is often assumed to be a function of profit or final portfolio wealth, with a positive first

derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...

. The utility function whose expected value is maximized is

concave Concave or concavity may refer to: Science and technology * Concave lens * Concave mirror Mathematics * Concave function, the negative of a convex function * Concave polygon, a polygon which is not convex * Concave set * The concavity of a ...

for a risk averse agent,

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

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 the expectation of a linear function of wealth, and maximizing it is equivalent to maximizing expected wealth itself.

Theory of the firm

Portfolio theory

The risk neutral utility function

References

See also