# How to Calculate Risk Aversion

Based on their level of risk aversion, certain investors choose different options when the expected payoff is similar. An investor is risk-averse if he prefers a lower certain cash flow to a similar expected payoff to avoid uncertainty. A risk-neutral investor is indifferent regarding investments that offer the same payoff and different levels of uncertainty, while an investor has an appetite for risk taking if she prefers the uncertain outcome with a similar payoff to a certain outcome.

We measure risk aversion in terms of both absolute terms and relative terms.

## Step 1.

Estimate the expected profit of an investment by multiplying the expected outcomes by their probabilities. For example, if you expect a profit of $10,000 or a loss of $5,000 with equal probability, the expected value of the profit will be [(10,000 * 0.5) + (- 5,000 * 0.5)] $2,500.

## Step 2.

Determine if a particular investor will prefer the certain amount of $2,500 to the above investment, or if the investor will instead prefer the above given investment.

## Step 3.

If an investor is indifferent between a choice of the above investment with a chance of making a profit or loss compared to an investment with an equal expected value, but a certain cash flow, the investor is said to be risk-neutral. In this case, it is said that the certainty equivalent of the investor is equal to the expected value.

## Step 4.

If an investor needs higher certain cash flow to prefer the $2,500 in the above example, than he is said to be risk-loving.

## Step 5.

If an investor will accept an even lower certain amount than the expected value of $2,500 in the above example, he is said to be risk-averse. Hence, a risk-averse investor has a certainty equivalent lower than the expected value of an investment alternative.

## Tip

Remember that, in general finance theory, a rational investor is said to be indifferent between two choices with an equal expected value and is assumed to be risk-neutral. However, in risk estimation scenarios, most individuals prefer an even lower amount with a lower expected value if the amount is certain to be received.

## Warning

Investors exhibit differing behaviours in different situations. Another experiment showed that many investors are loss-averse instead of risk-averse, and their preference for a certain cash flow payment to an uncertain cash flow in the above example is driven by the fact that they do not like loss in any form.