Concept/Decision Theory/No. 0860
Risk Aversion
Risk aversion is a preference for a certain sum over a gamble with the same expected monetary value. In decision theory, it is represented by a concave utility function: each extra dollar adds less value. Daniel Bernoulli described this logic in 1738.
- Evidence
- Well established
- Read
- 6 min
- Links
- 16 connections
- Useful when
- Deciding under uncertainty · Money and investing · Negotiating · Risk and safety
01You've seen this when…
- in life
You leave your house deposit in an insured savings account, while a stock fund offers a higher expected return. The purchase is six months away.
- at work
A client offers a flat fee or a success bonus with a higher average payout. Your team chooses the flat fee to keep payroll predictable.
- out in the world
A town pays for flood insurance even though its premiums exceed the average annual claim. One uninsured flood would consume its emergency reserve.
02The idea
Suppose a fair coin decides whether you receive $100 or nothing. The gamble’s expected monetary value is $50: half of $100, plus half of zero. A guaranteed $50 has the same expected value. Someone who strictly prefers the guarantee is risk-averse for that choice.
The reasoning becomes clearer when money has different uses at different levels of wealth. The dollars that cover rent can matter more than the dollars that upgrade a vacation. With diminishing marginal utility, each additional dollar adds less value than the previous one. A shortfall can therefore hurt more than an equal-sized windfall helps.
In expected utility theory, people evaluate each possible outcome by its utility, meaning its value within their preferences, and weight that utility by the outcome’s probability. A utility curve that rises while bending downward is called concave. It represents risk aversion.
Two terms make the preference measurable. The certainty equivalent is the guaranteed amount someone values as highly as the gamble. The risk premium, in this sense, is the gap between the gamble’s expected monetary value and that certainty equivalent.
03Why it matters
Averages leave out what happens when the unfavorable outcome arrives. A business can have a profitable contract on average and still struggle to meet payroll if payment depends on success. A household can face a modest average annual loss while one accident threatens its savings.
Risk aversion helps explain why people pay insurance premiums above expected claims, accept lower returns for safer investments, and favor predictable income. These choices can fit coherent preferences. Their quality depends on the price paid for security and the consequences of the remaining risk.
It also directs attention to cheaper ways of reducing exposure. Diversification spreads investments across sources of return; insurance pools losses across policyholders. Both can preserve more expected value than avoiding every uncertain opportunity. The useful comparison is how much expected payoff each route costs for the reduction in exposure it buys.
04A worked example
Consider an invented consultant with $10,000 in savings. A client offers two contracts: a guaranteed $13,000 fee, or an even chance of receiving either $30,000 or nothing. The uncertain fee averages $15,000.
For this simplified illustration, treat the consultant’s savings and fee as the entire financial resource being modeled. Suppose utility equals the square root of the final balance. This is an assumed preference used to show the calculation.
What it looks like The consultant accepts $2,000 less than the uncertain contract’s average payout. Someone comparing only expected dollars would favor the bonus contract.
What’s actually going on The uncertain contract leaves final balances of $10,000 or $40,000. Their square roots are 100 and 200, so expected utility is 150. The guaranteed contract leaves $23,000, with utility of about 151.7. Under this preference, the guarantee ranks higher.
A guaranteed final balance of $22,500 would have utility of exactly 150. Subtract the original $10,000, and the uncertain fee’s certainty equivalent is $12,500. Its risk premium is therefore $2,500: the difference between the $15,000 expected fee and the $12,500 certainty equivalent. The offered guarantee clears that threshold.
What would have helped Making the tradeoff explicit. The consultant can compare the guarantee with a minimum acceptable certain fee, then check whether savings, payment timing, or a partial upfront payment change the exposure. Different preferences or greater resources can change the choice.
05Where people trip up
- Treating caution as a reasoning error. Preferring a lower average payout can be consistent with expected utility. The relevant question is whether the security gained justifies its price for the person bearing the consequences.
- Merging distinct kinds of discomfort. Risk aversion concerns uncertain outcomes. Loss aversion concerns losses weighing more heavily than equivalent gains relative to a reference point. Ambiguity aversion concerns uncertainty about the probabilities themselves. These can influence the same decision, but they describe different preferences.
- Buying certainty at any price. A warranty may cost far more than the expected repair bill. When replacing the item would barely affect the household budget, the protection may add little utility. Deductibles and self-insurance can reserve expensive coverage for losses that threaten essential spending or create a risk of ruin.
- Calling an option safe without naming the risk. Cash can protect a near-term purchase from market swings while losing purchasing power over time. A fixed salary can stabilize monthly income while leaving a worker dependent on one employer. Specify the outcome being protected, the time horizon, and the other exposures already present.
06Where it doesn’t explain every cautious choice
A preference for certainty alone cannot identify its cause. Someone may favor a fixed fee because the client seems unreliable, because a late payment triggers penalties, or because estimating the odds takes time. Those facts can change the expected payoff or the costs of the choice. Establishing risk aversion requires comparing options on a common footing.
Nor does one choice establish a stable personality trait. People buy insurance and lottery tickets, and their choices shift with stakes, framing, and whether outcomes appear as gains or losses. Prospect theory describes some of these patterns through reference points and probability weighting.
The concave-utility model gives a precise account of one kind of preference. Applying it to a person requires assumptions about the resources that matter, the probabilities they believe, and the alternatives they see.
07Roots
Daniel Bernoulli’s 1738 paper confronted a troublesome coin-toss game. The prize doubled as play continued, and the game ended at the first head. Its mathematical expected payout was infinite, yet people would pay only a modest amount to enter. Expected money alone gave an implausible answer to the question of what the game was worth.
Bernoulli proposed evaluating wealth by its usefulness. He used logarithmic utility, under which an additional dollar matters more to someone with little wealth. His discussion also reached the merchant shipping goods by sea: dividing cargo between ships could make the prospect more attractive by reducing exposure to a complete loss. The puzzle connected gambling, wealth, and insurance through the same reasoning.
In the 1960s, Kenneth Arrow and John Pratt developed standard measures of risk aversion based on the curvature of utility. These made it possible to compare how strongly different preferences resisted risk and how that resistance changed with wealth. The idea became a central tool in insurance, finance, and economic decision theory.
08How solid is this?
Within expected-utility theory, concave utility formally represents risk aversion. Behavioral research also shows that choices shift with framing and reference points, limiting a fixed concave utility function as a complete description of a person’s behavior.
09Connections
- Often confused with Loss Aversion, Probability Neglect, Ambiguity Aversion (Ambiguity Effect), Risk of Ruin
- Can lead toRisk Premium, Diversification
- Can follow from Diminishing Marginal Utility
- Part ofExpected Utility Theory, Prospect Theory
- See also Adverse Selection, BATNA, Framing Effect, Moral Hazard, Option Value, Certainty Equivalent, Risk vs. Uncertainty
+ 6 more in the list
10Origin and sources
Daniel Bernoulli supplied an early utility-based account in 1738. Kenneth Arrow and John Pratt developed standard measures of risk aversion in the 1960s.
- [1]Bernoulli, D. (1954). Exposition of a New Theory on the Measurement of Risk. Econometrica, 22(1), 23–36. English translation of the 1738 paper.
- [2]Pratt, J. W. (1964). Risk Aversion in the Small and in the Large. Econometrica, 32(1/2), 122–136.
- [3]Arrow, K. J. (1971). Essays in the Theory of Risk-Bearing. Markham Publishing Company.
- [4]Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), 263–291.
Suggest an edit· Updated 2026-10-02