# Risk neutral preferences

In economics and finance, risk neutral preferences are preferences that are neither risk averse nor risk seeking. 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, 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.[1]

Portfolio theory

In portfolio choice,[2][3][4] 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, 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 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 derivative. 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 the expectation of a linear function of wealth, and maximizing it is equivalent to maximizing expected wealth itself.

References

1. ^Sandmo, Agnar. “On the theory of the competitive firm under price uncertainty,” American Economic Review 61, March 1971, 65-73.
2. ^Edwin J. Elton and Martin J. Gruber, “Modern portfolio theory, 1950 to date”, Journal of Banking and Finance 21, 1997, 1743-1759.
3. ^Markowitz, H.M. Portfolio Selection: Efficient Diversification of Investments, 1959. New York: John Wiley & Sons. http://cowles.econ.yale.edu/P/cm/m16/index.htm. (reprinted by Yale University Press, 1970, ISBN 978-0-300-01372-6; 2nd ed. Basil Blackwell, 1991, ISBN 978-1-55786-108-5)
4. ^Merton, Robert. “An analytic derivation of the efficient portfolio frontier,” Journal of Financial and Quantitative Analysis 7, September 1972, 1851-1872.

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