Risk Preference

Risk Preference Definition

Before we get to the definition of risk preference, we need to understand what risk is. Nobody can predict the future. Therefore, when making decisions, we have to understand that there is uncertainty about the future outcomes of our decisions. That is the definition of risk.

Now that we know what risk is, let's talk about risk preference. In the above example, some people would definitely stay in their current job, some people would analyze the situation and take some time to decide, and some people would jump at the opportunity without a second thought. These different decisions are based on risk preference or how much risk a person is willing to take to achieve an expected outcome.

Expected utility is the expected satisfaction someone would get from taking on a certain amount of risk. Since we don't know the outcome for certain, we have to estimate what the outcome might be along with the resulting satisfaction.

We can calculate the expected utility with the following equation:

\(E(U) = P_A \times U_A + P_B \times U_B \)

\(\hbox{Where:}\)

\(E(U) = \hbox{Expected Utility}\)

\(P_A = \hbox{Probability of Outcome A}\)

\(U_A = \hbox{Utility of Outcome A}\)

\(P_B = \hbox{Probability of Outcome B}\)

\(U_B = \hbox{Utility of Outcome B}\)

Now that we have defined risk, risk preference, and expected utility, and given a couple of examples, let's get into a little more detail about risk preference types.

Risk Preference Types

There are three risk preference types; risk-averse, risk-neutral, and risk-loving. Let's take a look at each.

Risk preference types: risk-averse

A risk-averse person prefers a certain outcome to an uncertain outcome with the same expected utility. A risk-averse person exhibits diminishing marginal utility. That is, for every $1 increase in income, the increase in utility from that extra income is less.

For most people, the more income one has, the less additional happiness comes with it. In other words, at a very low income, an extra dollar provides a lot of happiness, but if you are very rich, an extra dollar is really nothing to you. The risk-averse type is the most common risk preference type. Think about it. Almost everyone buys health, life, home, or car insurance, and most people prefer a job with stable wages compared to one with variable income. For the risk-averse type, avoiding losses is more important than receiving gains. That is, it is more important to avoid losing $10,000 than it is to gain $10,000.

Risk preference types: risk-neutral

A risk-neutral person is indifferent between a certain outcome and an uncertain outcome with the same expected utility. A risk-averse person exhibits constant marginal utility. That is, for every $1 increase in income, the increase in utility from that extra income is the same. For the risk-neutral type, avoiding losses is equally as important as receiving gains. That is, it is equally as important to avoid losing $10,000 as it is to gain $10,000.

Risk preference types: risk-loving

A risk-loving person prefers an uncertain outcome to a certain outcome, even if the expected utility of the uncertain outcome is less than that of the certain outcome. A risk-loving person exhibits increasing marginal utility. That is, for every $1 increase in income, the increase in utility from that extra income is higher. For the risk-loving type, the chance of winning big versus losing it all is worth more than a certain outcome. Losses are not a concern to them. The thrill of the chase, and the dopamine rush that comes with it, bring them more happiness than accepting a certain result.

Risk preference types: different risks and types

This brings up another point. The same person can have different risk preferences, depending on what risks they are taking. The worst that can happen when you make a risky decision to buy a lottery ticket is losing $2. However, the worst that can happen when you make a risky decision to go without home insurance is the entire value of your home! Big difference! Thus, depending on the type of risk and the amount that could potentially be lost, the same person can have different risk preferences.

Risk Preference Theory

The risk preference theory is based on expected utility. The assumption behind the theory is that, when faced with uncertain outcomes, people want to maximize their expected utility. Most people are risk-averse, which means their utility is very sensitive to changes in income. A less risk-averse person is less sensitive to changes in income. A risk-neutral person is not sensitive to changes in income at all.

Lower-income people are more risk-averse than higher-income people. This is because when you have little income, a given increase in income will mean a lot more to you than it will to someone with a lot more money. The diminishing level of additional happiness of a $1 increase in income as income grows is known as diminishing marginal utility.

While risk-averse people, which is most people, exhibit diminishing marginal utility, some people, who are risk-neutral, exhibit constant marginal utility, while even fewer people, who are risk-loving, exhibit increasing marginal utility. It is these differences in the marginal utility that determine a person's risk preference type and upon which the risk preference theory is based.

Risk Preference Measurement

Risk preference measurement can be done in several ways. First, there is marginal utility. If a person exhibits diminishing marginal utility, that is, less additional satisfaction as income grows, they are considered risk-averse. If a person exhibits constant marginal utility, that is, the same additional satisfaction as income grows, they are considered risk-neutral. If a person exhibits increasing marginal utility, that is, additional satisfaction grows as income grows; they are considered risk-loving.

Second, there are indifference curves. Indifference curves are used to compare satisfaction obtained from a certain combination of goods, a certain combination of risk and expected return, or a certain combination of risk and expected income.

Any combination on the same indifference curve brings the same amount of utility or satisfaction. In regards to combinations of risk and expected income, a strongly risk-averse person will have very steep indifference curves, meaning for a given increase in risk taken, they will expect a very high increase in expected income. A slightly risk-averse person will expect a smaller increase in expected income, so their indifference curves will be flatter. These indifference curves are shown in Figure 2 below. The slope of the indifference curves (higher for strongly risk-averse people, lower for slightly risk-averse people) can help to measure a person's risk preference.

Fig. 2 - Indifference Curves

Third, the risk premium, or the amount a person is willing to pay to avoid risk, can help to measure a person's risk preference. A risk-averse person will want to do whatever they can to avoid risk, so they will be willing to pay a very high risk premium. A less risk-averse person will not be willing to pay such a high risk premium as they are willing to take on more risk. Thus, looking at risk premiums can help to measure a person's risk preference.

Finally, risk preferences can be measured by a risk preference questionnaire.

Risk Preference and Expected Utility

We will explain risk preference and how it relates to the expected utility using a graph. Figure 3 below shows a utility function of a person who is risk-averse. As you can see, as income gets larger, this person's utility continues to rise, but at a slower and slower rate, until it finally stops rising altogether. This is known as diminishing marginal utility. For each $1 increase in income, utility rises at a diminishing rate.

Now, let's look at an example to demonstrate the expected utility.

Fig. 3 - Risk-Averse Utility Function