If you are like most people, you do not particularly enjoy uncertainty when it comes to making decisions. You would rather know for certain what the outcome of your decision will be. Why is that so? Why is it that you would likely prefer a comfortable job paying a certain income rather than a job where your income is not certain, even if there is a chance you could make a lot of money? Why is it that you would pay for health insurance rather than save the money and just hope that nothing bad happens to you? Why are some people less worried about uncertainty than others?
If you would like to know more about risk aversion and risk preference and how these influence the decisions people make, continue reading! Don't worry, there's no risk involved!
Fig. 1 - Skydivers
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.
Risk is the uncertainty about future outcomes.
For example, let's say you have a good job right now, but you are just not that thrilled about it. You want something better. You find a posting for a great opportunity, but it's in another city. The salary is much better than your current salary, but you'll have to move to take advantage of the opportunity.
This is a risky situation because you don't know what the outcome will be if you move. If things go well, great! You'll have a better job, a higher salary, and likely some new co-workers and friends.
However, what if things don't go so well? What if, after six months, you either don't like the job, don't like your boss, don't like your co-workers, or simply don't do well and are let go? Oh boy, now you are talking about having to find yet another job, but all the hassle and moving expenses you incurred went for nothing.
So how does one make such a decision? Continue reading to find out!
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.
Risk preference is defined as how much risk a person is willing to take based on the expected utility or satisfaction of the 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.
Expected utility is the probability-weighted average of total utility given uncertain outcomes.
We can calculate the expected utility with the following equation:
\(E(U) = P_A \times U_A + P_B \times U_B \)
\(\hbox{Where:}\)
\(E(U) = \hbox{Expected Utility}\)
\(P_A = \hbox{Probability of Outcome A}\)
\(U_A = \hbox{Utility of Outcome A}\)
\(P_B = \hbox{Probability of Outcome B}\)
\(U_B = \hbox{Utility of Outcome B}\)
In some cases, we can measure utility as a monetary value, like income. In other cases, we cannot measure utility in monetary terms (the satisfaction of being able to visit your grandmother or going to the beach has no monetary value). In these cases, we measure satisfaction in utils, a theoretical measure of satisfaction or happiness gained from a certain outcome. The util has no real meaning other than to compare satisfaction between outcomes.
For example, getting back to the job decision. Suppose we have the following estimates:
Current income: $50,000
Outcome A: Things don't go well, and you lose your new job in six months, so your annual income is zero in six months, and you are faced with the burden of finding yet another job. The probability that this will happen is 30%.
Outcome B: Things go great, and you keep your new job, which pays $80,000. The probability that this will happen is 70%.
In this case, we can measure utility in monetary terms using income.
\(\hbox{Thus we have the following:}\)
\(P_A = 30\%\)
\(U_A = $0\)
\(P_B = 70\%\)
\(U_B = $80,000\)
\(\hbox{Then:}\)
\(E(U) = P_A \times U_A + P_B \times U_B \)
\(E(U) = 0.3 \times $0 + 0.7 \times $80,000 = $56,000\)
Your expected utility, or income, if you take the new job in another city is $56,000. Since this is higher than your current income of $50,000, the wise decision would be to take the new job.
Of course, there are other factors involved in a decision as big as this, such as moving costs, the hassle of putting all of your belongings onto a truck, cleaning your current dwelling, moving away from family and friends, different weather, figuring out a new city, and so on. But to make it simple, we have ignored these other factors for this analysis.
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.
Unsure about utility and would like to learn more?Dive into these articles for further knowledge:- Utility Functions
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.
A risk-averse person prefers a certain outcome to an uncertain outcome with the same expected utility.
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.
A risk-neutral person is indifferent between a certain outcome and an uncertain outcome with the same expected utility.
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.
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.
Consider a lottery ticket. The jackpot is $100 million, and the probability of winning is 1 in 100 million. The cost of the lottery ticket is $2. What is the expected utility or value of buying the lottery ticket?
\(\hbox{We have:}\)
\(\hbox{Outcome A} = \hbox{Win the jackpot}\)
\(\hbox{Outcome B} = \hbox{Don't win the jackpot}\)
\(U_A = $100,000,000\)
\(P_A = 0.00000001\)
\(U_B = $0\)
\(P_B = 0.99999999\)
\(\hbox{Then:}\)
\(E(U) = P_A \times U_A + P_B \times U_B \)
\(E(U) = 0.00000001 \times $100,000,000 + 0.99999999 \times $0\)
\(E(U) = $1 + $0 = $1\)
In this case, since the cost of the lottery ticket ($2) is more than the expected value ($1), this is a losing bet. However, millions of people buy lottery tickets anyway. If most people are risk-averse, why do they buy lottery tickets if it's a losing bet? Again, it's the thrill of the chase, the excitement, the dream of that mansion and high-end sports car that comes with the tiny chance of winning. In addition, even for people with meager incomes, a $2 lottery ticket is not much of a sacrifice. If, on the other hand, the lottery ticket costs $100, there would likely be a lot less demand for lottery tickets!
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.
Diminishing marginal utility means that, as income grows, the additional utility gained from a given increase in income becomes smaller.
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.
Learn more in our article - Marginal Utility!
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.
Confused about the indifference curves and what they mean?Don't worry, we got you covered! Just click here:- Indifference Curve
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.
The risk premium is the amount a person is willing to pay to avoid risk.
Finally, risk preferences can be measured by a risk preference questionnaire.
When a person goes into an investment manager's office for the first time, often the investment manager will have that person fill out a questionnaire that asks them several questions.
An example question might be: 'What percentage of your portfolio are you willing to lose before you get concerned?'
Another example might be: 'Would you rather take a sure thing or a risky bet with the same expected value?'
Another question might be: 'How long do you plan to hold this investment?'
These questions helps to determine someone's ability to weather the ups and downs of the market. Questions like these help investment managers measure a person's risk preference, thereby helping them to put their clients into investments that best fit their risk tolerance.
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.
Suppose a risk-averse person named Jim currently has a job that pays $60,000 per year. Jim is getting a little bored with his job and is considering taking a sales job. However, this sales job has variable income. Jim will not know how much money he will make in any given month or year.
A good year will bring in $80,000, while a bad year will only bring in $40,000. These possible outcomes are equally probable, meaning there is a 50% chance for a bad year and a 50% chance for a good year.
The utility, or satisfaction, Jim gets from his current job is 13 utils, shown at Point B in Figure 3 below. If he takes the sales job and has a bad year, his utility will be 10 utils, shown at Point A, and if he has a good year, his utility will be 15 utils, shown at Point C.
We can calculate Jim's expected utility of the sales job with the following formula:
\(\hbox{Expected Utility of Sales Job} = P_A \times U_A + P_C \times U_C\)
\(\hbox{Expected Utility of Sales Job} = 0.5 \times 10 + 0.5 \times 15 = 12.5\)
Since the utility provided by Jim's current job, 13 utils, is greater than the expected utility of the sales job, which we calculated as 12.5 utils, Jim would be better off keeping his current job. This falls in line with the fact that risk-averse people prefer less variability of outcomes.
As you can see in Figure 3 below, going from $40,000 per year at Point A to $60,000 per year at Point B leads to an increase in utility of 3 utils. However, going from $60,000 per year at Point B to $80,000 per year at Point C leads to an increase in utility of just 2 utils. This is an example of diminishing marginal utility, which is characteristic of people who are risk-averse.
Fig. 3 - Risk-Averse Utility Function
To learn more on similar topics, check out our articles:- Consumer Choice- Risk-Return Trade-Off
- Risk Reduction
- Risk Asset
Risk Preference - Key takeaways
- Risk preference is defined as how much risk a person is willing to take based on the expected utility or satisfaction of the outcome.
Expected utility is the probability-weighted average of total utility given uncertain outcomes.
Risk-averse people exhibit diminishing marginal utility.
Risk-neutral people exhibit constant marginal utility.
Risk-loving people exhibit increasing marginal utility.
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