Risk Neutrality
Risk neutrality is the assumption that an individual or institution is indifferent to risk, evaluating uncertain prospects by their expected value alone. A risk-neutral agent prefers a prospect with a higher expected value and is neither willing to pay to avoid risk nor willing to accept risk for its own sake.
Definition and Comparison
Risk neutrality contrasts with risk aversion, in which an agent prefers a certain outcome to a risky prospect with the same expected value, and with risk seeking, in which an agent prefers the risky prospect. A risk-neutral agent is indifferent between a certain outcome and a risky prospect of equal expected value.
Risk neutrality requires that expected utility be linear in the outcome, so that the utility of a prospect equals the expected utility of the outcomes. Risk aversion corresponds to concavity of the utility function and risk seeking to convexity. The degree of risk aversion is captured by the curvature of the utility function.
Use in Economics and Finance
Risk neutrality is a convenient assumption in many models, since it simplifies the analysis by eliminating the need to specify risk preferences. In asset pricing, risk-neutral valuation uses a risk-neutral probability measure to price assets, exploiting the fact that prices can be represented as discounted expected payoffs under that measure, regardless of the true preferences of investors.
The technique is central to the pricing of derivatives and to the analysis of no-arbitrage conditions. It does not assume that investors are risk neutral; rather, it uses a change of measure to incorporate risk preferences into the probabilities, so that the pricing can be computed by taking expectations.
When Risk Neutrality Is Appropriate
Risk neutrality may be a reasonable approximation in some contexts. Large, well-diversified institutions may be approximately risk neutral with respect to idiosyncratic risks, since these can be diversified away. Firms maximising expected profit, rather than expected utility, act as if risk neutral, and this is a common assumption in the analysis of production and investment under uncertainty.
Risk neutrality is less appropriate for individuals facing risks that cannot be diversified, such as the risk of unemployment or illness, and for institutions whose survival is at stake. In these cases, risk aversion is important and cannot be neglected without losing important features of behaviour.
Risk Aversion in Practice
The prevalence of insurance, of diversification, and of risk premia in asset markets demonstrates that risk aversion is widespread and economically significant. The equity premium puzzle, the finding that the return on equities exceeds that on safe assets by more than standard models can explain with plausible risk aversion, indicates that risk preferences and market frictions remain incompletely understood.
The analysis of risk and risk preferences informs the design of contracts, of insurance, and of financial regulation. Understanding when risk neutrality is an appropriate simplification and when it must be abandoned is a central element of applied economic and financial analysis.
Expected Utility Theory
Risk neutrality is a special case of expected utility theory, in which preferences over uncertain prospects satisfy a set of axioms and can be represented by the expected value of a utility function. Linearity of the utility function corresponds to risk neutrality, while concavity corresponds to risk aversion and convexity to risk seeking.
The expected utility framework provides the foundation for the analysis of choice under uncertainty and for the measurement of risk aversion. It has been extended and criticised, with behavioural evidence documenting departures from its predictions, including loss aversion and probability weighting.
Risk Neutrality in Corporate Finance
In corporate finance, firms are often assumed to maximise expected profit rather than expected utility, effectively assuming risk neutrality. The assumption is justified by the argument that shareholders can diversify their portfolios, so that only systematic risk matters, and that firms should maximise the value of their shares, which reflects the market's valuation of that risk.
The assumption underlies the analysis of capital budgeting, of project evaluation, and of capital structure. Where shareholders cannot diversify, or where managers have different preferences from shareholders, the assumption may fail, and the analysis must account for risk preferences.
Risk Neutrality and Market Prices
In asset pricing, the risk-neutral approach does not assume that investors are risk neutral. Instead, it uses a change of measure, replacing the true probabilities with risk-neutral probabilities, so that prices can be computed as discounted expected payoffs under the risk-neutral measure. The risk preferences of investors are embedded in the difference between the true and risk-neutral probabilities.
The approach is central to the pricing of derivatives and to the analysis of no-arbitrage conditions. It allows the pricing of complex claims without specifying investor preferences, provided that the underlying risks can be traded and that arbitrage is absent.
Limitations and Extensions
The assumption of risk neutrality is a simplification that may fail in important contexts. Where risks are large relative to the resources of the agent, where risks are not diversifiable, or where survival is at stake, risk aversion is important and cannot be neglected.
Extensions of the analysis incorporate risk aversion into models of investment, of insurance, and of financial contracts, generating different predictions about behaviour and about prices. The choice between risk neutrality and risk aversion depends on the context and on the importance of the risks involved, and the analysis must be calibrated to the situation at hand.