Risk tolerance

In economics and finance, risk aversion is the behavior of humans (especially consumers and investors), when exposed to uncertainty, to attempt to reduce that uncertainty. It is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff. For example, a risk-averse investor might choose to put his or her money into a bank account with a low but guaranteed interest rate, rather than into a that may have high expected returns, but also involves a chance of losing value.

A person is given the choice between two scenarios, one with a guaranteed payoff and one without. In the guaranteed scenario, the person receives $50. In the uncertain scenario, a coin is flipped to decide whether the person receives $100 or nothing. The expected payoff for both scenarios is $50, meaning that an individual who was insensitive to risk would not care whether they took the guaranteed payment or the gamble. However, individuals may have different risk attitudes.

A person is said to be:

The average payoff of the gamble, known as its expected value, is $50. The dollar amount that the individual would accept instead of the bet is called the certainty equivalent, and the difference between the expected value and the certainty equivalent is called the risk premium. For risk-averse individuals, it is positive, for risk-neutral persons it is zero, and for risk-loving individuals their risk premium is negative.

In expected utility theory, an agent has a utility function u(x) where x represents the value that he might receive in money or goods (in the above example x could be 0 or 100).

Time does not come into this calculation, so inflation does not appear. (The utility function u(x) is defined only up to positive linear affine transformation - in other words a constant offset could be added to the value of u(x) for all x, and/or u(x) could be multiplied by a positive constant factor, without affecting the conclusions).

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