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Lesson 8 of 13 · 13 min

Risk aversion and utility

A utility function turns each investor's attitude to risk into one number per investment, so investments can be ranked: $U = E(r) - \tfrac{1}{2}A\sigma^2$ .

In short

Offered a sure amount or a gamble with the same expected value: the risk-averse investor takes the sure amount, the risk-neutral investor is indifferent, the risk seeker takes the gamble.
Markets price assets as if the typical investor is risk averse; we assume risk aversion from here on.
Risk tolerance is the opposite of risk aversion: more tolerance, more willingness to take risk.
Utility $U = E(r) - \tfrac{1}{2}A\sigma^2$ : $A > 0$ risk averse, $A = 0$ risk neutral, $A < 0$ risk seeking.
Utility only ranks choices for one investor; it cannot be compared or added across people.
A risk-free asset ( $\sigma = 0$ ) gives the same utility to everyone: its return.

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