Updated for the 2026-2027 CFA® Level I curriculum.
Every portfolio decision starts with a trade-off between risk and return. Risk aversion measures how an investor handles that trade-off. It explains why two investors looking at the same set of portfolios can choose differently, and it gives CFA Level I candidates a formula-based way to compare those choices. This note covers the utility function that quantifies risk aversion and shows how the risk-aversion coefficient shapes portfolio selection.
Quick Answer
Risk aversion describes an investor's preference for lower risk when expected returns are equal. A risk-averse investor requires higher expected return to accept higher risk.
CFA Level I represents this preference with the utility function , where is expected return, is the risk-aversion coefficient, and is variance of returns. Higher values mean stronger risk aversion and a stronger preference for lower-variance portfolios. This formula lets candidates rank portfolios by utility instead of by return or risk alone.
Key Takeaways About Risk Aversion and Portfolio Selection
Risk aversion is measured by coefficient in the utility function .
A higher value means the investor penalizes variance more heavily and prefers safer portfolios.
Risk-averse investors require compensation for taking on risk. Risk-seeking investors do not.
Indifference curves plot combinations of risk and return that give an investor equal utility.
Steeper indifference curves belong to more risk-averse investors.
The optimal portfolio sits where an investor's indifference curve is tangent to the set of available portfolios.
What You Need to Know for CFA Level I
Calculate utility using given expected return, variance, and .
Compare two or more portfolios for the same investor and identify the one with the highest utility.
Classify an investor as risk averse, risk neutral, or risk seeking based on behavior or stated preferences.
Explain why risk-averse investors demand a risk premium.
Recognize that indifference curves are convex for risk-averse investors and interpret their slope.
Connect a higher risk-aversion coefficient to a flatter position on the risk spectrum, meaning lower risk tolerance.
Risk Aversion and the Risk-Return Trade-Off
Risk aversion sits inside the broader topic of portfolio risk and return. Once you can calculate expected return and variance for a portfolio, the next question is which portfolio an investor should actually choose. That choice depends on how much risk the investor is willing to accept for additional return.
A risk-averse investor will not accept extra risk without extra expected return. Given two portfolios with equal expected returns, this investor always picks the one with lower variance. Given two portfolios with equal variance, this investor always picks the one with higher expected return. This is the foundation of mean-variance analysis on the exam.
Risk aversion is not the same as risk avoidance. A risk-averse investor still takes risk. They just require fair compensation for it. This distinction matters because CFA questions often test whether candidates confuse "averse" with "avoidant."
Utility and Indifference Curves
Utility theory converts an investor's risk-return preference into a number. Each portfolio has a utility score based on its expected return, its variance, and the investor's risk-aversion coefficient. An investor prefers the portfolio with the higher utility score, regardless of how return and risk are split between the choices.
An indifference curve plots every combination of expected return and standard deviation that produces the same utility score for a given investor. Points on the same curve are equally attractive to that investor, even though the risk and return numbers differ.
For a risk-averse investor, indifference curves slope upward and are convex. Moving northeast on the graph, from lower risk and return to higher risk and return, keeps utility constant. A steeper curve means the investor needs a larger return increase to accept the same increase in risk. Investors with higher values have steeper, more tightly curved indifference curves.
How the Risk-Aversion Coefficient Affects Portfolio Choice
The formula candidates need is:
Notation legend:
= utility value of the portfolio (unitless score, used for ranking only)
= expected return of the portfolio, expressed as a decimal or percentage
= risk-aversion coefficient (a positive number for risk-averse investors)
= variance of portfolio returns, expressed in decimal form (standard deviation squared)
Utility rises with expected return and falls with variance. The risk-aversion coefficient controls how much variance reduces utility. A larger means variance has a bigger negative effect on the score.
When increases, the penalty for variance grows. This pushes the investor's preferred portfolio toward lower-risk options, even if that means accepting lower expected return. When decreases toward zero, variance matters less, and the investor's choice depends almost entirely on expected return.
Risk Seeking, Risk Neutral, and Risk Averse Behavior
Investor Type | Risk-Aversion Coefficient | Behavior |
|---|---|---|
Risk averse | Requires higher expected return to accept higher variance. Prefers the portfolio with lower risk when returns are equal. | |
Risk neutral | Judges portfolios only on expected return. Variance does not affect the decision. | |
Risk seeking | Gains utility from higher variance. May choose a lower-return, higher-risk portfolio over a safer one with a higher return. |
Most CFA Level I material assumes investors are risk averse. Questions that test risk-neutral or risk-seeking behavior usually ask you to classify an investor based on a decision, not to calculate utility for them.
Worked Example: Comparing Two Investors
Maria and Tom are each choosing between two portfolios.
Portfolio X: Expected return = 10%, standard deviation = 20%
Portfolio Y: Expected return = 8%, standard deviation = 12%
Maria has a risk-aversion coefficient of . Tom has a risk-aversion coefficient of .
Step 1: Calculate variance for each portfolio.
Portfolio :
Portfolio :
Step 2: Calculate Maria's utility for each portfolio .
Maria prefers Portfolio . Her higher risk aversion penalizes Portfolio 's larger variance too heavily for the extra 2% return to compensate.
Step 3: Calculate Tom's utility for each portfolio .
Tom's utility scores are close, but he still prefers Portfolio , though by a smaller margin than Maria.
Both investors choose Portfolio here, but for different reasons. Maria's higher makes her reject Portfolio 's risk decisively. Tom's lower makes the decision closer, showing that a less risk-averse investor needs less return advantage to consider taking on more risk. If Portfolio offered a higher expected return, Tom would likely switch to it before Maria would.
Common Exam Traps
Treating risk averse as risk avoidant
A risk-averse investor still holds risky assets. They simply demand compensation. Do not assume risk aversion means choosing the lowest-risk option automatically, since expected return still matters.
Forgetting to square the standard deviation
The utility formula uses variance, not standard deviation. Candidates who plug in instead of will get the wrong utility score, especially when standard deviation is a two-digit percentage.
Assuming one portfolio fits every investor
The optimal portfolio depends on each investor's value. Two investors facing the same set of portfolios can rationally choose differently.
Confusing willingness with the coefficient itself
A stated willingness to take risk is not the same as a specific value. The coefficient is a calculation input, not a personality description.
Missing the 0.5 multiplier
Some candidates apply directly to variance without the 0.5 factor built into the formula. This changes the utility score and can flip the ranking between two close portfolios.
Practice Question
An investor has a risk-aversion coefficient of . She is choosing between two portfolios:
Portfolio 1: Expected return = 12%, standard deviation = 18%
Portfolio 2: Expected return = 9%, standard deviation = 10%
Based on utility, which portfolio should she choose?
Portfolio 1, because it has the higher expected return
Portfolio 2, because it produces the higher utility score
Portfolio 1, because standard deviation does not affect utility for risk-averse investors
Correct Answer: B
Portfolio 2 produces the higher utility score, so the investor should choose it despite its lower expected return.
Option A: This choice ignores variance entirely and assumes higher return always wins, which is only true for risk-neutral investors.
Option C: This choice misunderstands the utility formula. Standard deviation, through variance, directly reduces utility for any investor with .
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FAQs About Risk Aversion and Portfolio Selection
What does risk averse mean in simple terms?
A risk-averse investor prefers less risk when expected returns are the same. This investor will still accept risk, but only if the expected return is high enough to justify it.
What is a typical risk-aversion coefficient?
CFA Level I does not assign a single typical value. The coefficient varies by investor and is usually given in exam problems rather than assumed.
Is risk aversion the same as risk tolerance?
They are related but not identical. Risk aversion is captured mathematically through the coefficient in the utility formula. Risk tolerance is a broader concept that includes willingness and ability to take risk, covered in the Investor Risk Tolerance note.