Risk Aversion
What is Risk Aversion?
Risk aversion is a preference for a certain outcome over a gamble with the same expected value, shown by diminishing marginal utility of wealth.
A risk-averse person turns down a fair gamble, meaning one whose expected value equals its cost, and takes the sure amount instead. The reason is diminishing marginal utility of wealth: the extra utility from gaining $500 is smaller than the utility lost from dropping $500, so the downside outweighs the upside even at even odds. On a graph, a risk-averse person's utility of wealth curve is concave, bending toward the horizontal axis. It follows that their certainty equivalent, the sure amount that feels as good as the gamble, is less than the gamble's expected value, and the gap between the two is the risk premium they will pay to avoid the risk. That premium is why insurance can be priced above the expected payout and still be worth buying.
Risk Aversion: a worked example
Let utility be the square root of wealth, and offer a 50/50 gamble between ending with $10,000 and ending with $40,000. The expected value is 0.5 × $10,000 + 0.5 × $40,000 = $25,000. The expected utility is 0.5 × 100 + 0.5 × 200 = 150, since the square root of 10,000 is 100 and the square root of 40,000 is 200. A sure wealth giving utility 150 is 150 squared, or $22,500, so the certainty equivalent is $22,500, below the $25,000 expected value. The $2,500 gap is the risk premium, the most this person would pay to swap the gamble for cash.
The mistake students make with risk aversion
A common error is thinking risk aversion means refusing all risk. A risk-averse person will take a gamble whose expected value is high enough to cover the risk premium; they only reject bets that are merely fair or worse. The other slip is treating risk aversion as irrational. It follows directly from diminishing marginal utility of wealth, which is standard in consumer theory.
Risk Aversion questions
How can you tell if someone is risk averse from a utility curve?
A risk-averse person has a concave utility of wealth curve, one that rises but flattens as wealth grows. A risk-neutral person's curve is a straight line, and a risk-loving person's curve is convex and gets steeper. That curvature is exactly what makes losses hurt more than equal-sized gains help.
What is a risk premium?
A risk premium is the difference between a gamble's expected value and its certainty equivalent, the amount a person would give up to escape the risk. A risk-averse person has a positive risk premium, a risk-neutral person's is zero, and a risk-loving person's is negative. Insurance priced above the expected payout is the everyday version of this.
Why do risk-averse people buy insurance and also lottery tickets?
The same person can insure a house and buy a lottery ticket because the two involve very different stakes relative to their wealth, and a ticket sells entertainment along with the payout. Standard models explain insurance easily and treat lottery buying as a small-stakes exception, sometimes modeled with a utility curve that is concave over losses and convex over tiny gains. It is a known limit of the simple theory, not a knockdown of it.
Formula / Example
Related terms
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated