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CFA Level I Exam · Portfolio Risk and Return: Part I

Return Distributions and Investor Risk Preferences for CFA Level 1

Updated 7 October 2026 · Fact-checked

Risk preference describes how an investor trades expected return against risk. A risk-averse investor demands extra return for extra risk, a risk-neutral investor looks only at expected return, and a risk-seeking investor accepts lower return for a gamble. Over long periods, riskier asset classes have earned higher average returns.

Understand Return Distributions and Investor Risk Preferences

Start with a simple idea: investors want return but dislike uncertainty. Return is what you earn. Risk is how far the actual outcome can differ from what you expect. We usually measure it with variance or standard deviation of returns.

Historical data across markets shows a pattern. Cash and short-term government bills have had low returns and low volatility. Government bonds sit higher. Corporate bonds sit higher again. Equities have had the highest average returns and the highest standard deviation. Small-cap stocks and emerging market equities have often been more volatile than large-cap developed market stocks. This is the risk-return trade-off: higher expected return comes with higher risk. It is not a guarantee. Riskier assets can and do lose money, and past results do not fix future returns.

Return distributions are often not perfectly normal. Equity returns tend to show fat tails (excess kurtosis), and some assets show negative skew. So standard deviation alone can understate the chance of extreme losses. Keep this in mind when a question asks whether a risk measure is complete.

Now the investor side. A risk-averse investor prefers the less risky choice when expected returns are equal. To accept more risk, this investor needs a higher expected return. A risk-neutral investor ignores risk and ranks choices only by expected return. A risk-seeking investor (also called risk-loving) likes risk and may pick the riskier choice even at equal or lower expected return. Most investors are assumed to be risk averse.

Utility theory puts numbers on this. Each portfolio gets a utility score. A risk-averse investor's utility rises with expected return and falls with variance. The risk-aversion coefficient A shows how much utility is lost per unit of variance. A larger A means more risk-averse. Utility lets you rank portfolios: pick the highest score. The risk-free rate gives the same score as a risk-free portfolio, so it is the benchmark for judging whether a risky portfolio is worth holding.

Key formulas to remember

Utility of a portfolio (mean-variance)
U = E(r) − 0.5 × A × σ²
E(r) and σ² in decimals. A is the risk-aversion coefficient. A > 0 risk averse, A = 0 risk neutral, A < 0 risk seeking.
Utility of the risk-free asset
U = Rf
Variance is zero, so utility equals the risk-free rate.
Variance and standard deviation
σ = √σ²
Standard deviation is in the same units as return, so it is easier to compare.
Risk preference rule
Risk averse: needs higher E(r) for higher σ; risk neutral: ranks by E(r) only; risk seeking: may accept lower E(r) for higher σ
Compare assets at equal expected return first.

How to solve Return Distributions and Investor Risk Preferences questions

Use this method for any question on risk preferences, utility or the risk-return pattern of asset classes.

  1. 1Read the stem and identify what is asked: a preference type, a utility ranking, or a risk-return statement.
  2. 2Write down E(r), σ and A for each portfolio. Convert percentages to decimals.
  3. 3If a utility is needed, compute U = E(r) − 0.5 × A × σ² for each option and the risk-free rate.
  4. 4Rank by utility. The highest utility is preferred. Compare with Rf to decide if the risky portfolio beats the risk-free asset.
  5. 5For conceptual questions, match the investor to the rule: averse needs compensation for risk, neutral ignores risk, seeking likes risk.
  6. 6For asset class questions, order by risk: cash, government bonds, corporate bonds, equities, with small-caps and emerging markets typically more volatile.
  7. 7Eliminate the two wrong options by checking for absolutes such as always, guaranteed or no risk.

Quickest way: Utility shortcut

When to use it: When a question gives E(r), σ and A for two or three portfolios and asks which one an investor prefers.

  1. Square σ as a decimal, for example 20% gives 0.04.
  2. Multiply by 0.5 × A to get the risk penalty.
  3. Subtract the penalty from E(r).
  4. Pick the highest result.
  5. On the TI BA II Plus, key 0.2 [x²] × 0.5 × A = to get the penalty. For example, with A = 4, 0.2 [x²] × 0.5 × 4 = gives 0.08. Then 0.12 − 0.08 = 0.04.

Common mistakes in Return Distributions and Investor Risk Preferences

  • Using percentages instead of decimals in the utility formula

    Typing 20 for σ gives 400 for variance, which swamps the answer.

    Fix: Convert to decimals first: 20% is 0.20, variance 0.04.

  • Forgetting the 0.5 in U = E(r) − 0.5Aσ²

    Students remember the shape but drop the constant.

    Fix: Write the full formula at the top of your working every time.

  • Saying a risk-neutral investor dislikes risk

    Mixing up neutral with averse.

    Fix: Neutral means risk is irrelevant. Only expected return matters, so A = 0.

  • Thinking higher risk guarantees higher return

    The trade-off is taught as a rule.

    Fix: It is a pattern in expected and long-run average returns. Realized returns can be lower.

  • Treating standard deviation as the full picture of risk

    Return distributions are assumed normal.

    Fix: Remember skewness and kurtosis: fat tails mean extreme losses can be more likely than a normal curve suggests.

Worked examples

Example 1

An investor has a risk-aversion coefficient A = 4. Portfolio X has expected return 12% and standard deviation 20%. Portfolio Y has expected return 8% and standard deviation 10%. The risk-free rate is 3%. Which choice gives the highest utility? A) Risk-free asset B) Portfolio X C) Portfolio Y

Show the solution
  1. Utility of X = 0.12 − 0.5 × 4 × 0.20² = 0.12 − 2 × 0.04 = 0.12 − 0.08 = 0.04.
  2. Utility of Y = 0.08 − 0.5 × 4 × 0.10² = 0.08 − 2 × 0.01 = 0.08 − 0.02 = 0.06.
  3. Utility of the risk-free asset = 0.03.
  4. Compare: 0.03 < 0.04 < 0.06.

Answer: C) Portfolio Y, with utility of 0.06 (a certainty-equivalent return of 6%).

Example 2

Two investments have the same expected return of 9%. Investment 1 is certain. Investment 2 has an uncertain outcome with the same expected value. An investor strictly prefers Investment 2. What is the investor's risk preference? A) Risk averse B) Risk neutral C) Risk seeking

Show the solution
  1. The expected returns are equal, so return does not separate the choices.
  2. A risk-averse investor would prefer the certain outcome, so A is wrong.
  3. A risk-neutral investor would be indifferent between the two, so a strict preference for Investment 2 rules out B.
  4. Strictly preferring the uncertain outcome at equal expected return signals a liking for risk.

Answer: C) Risk seeking.

Exam tips

  • Utility questions are short calculations. Do them with decimals and check that the answer is plausible: utility should be below E(r) for a risk-averse investor.
  • When two options have the same expected return, the preference question is really a risk question. Decide using the three definitions.
  • For asset class statements, reject options with words like always or guaranteed.
  • Remember the risk-free asset has utility equal to Rf, which often decides the answer.
  • Numerical options go from smallest to largest, so check you picked the correct position after calculating.

Practice questions from Portfolio Risk and Return: Part I

Return Distributions and Investor Risk Preferences: frequently asked questions

What is the difference between risk averse, risk neutral and risk seeking?

A risk-averse investor needs extra expected return to take extra risk. A risk-neutral investor cares only about expected return. A risk-seeking investor is attracted to risk and may accept a lower expected return for it.

How do you measure the risk of an investment in CFA Level I?

The standard measures are variance and standard deviation of returns. Higher values mean outcomes are more spread out. Skewness and kurtosis add information about asymmetry and extreme outcomes.

Which asset classes have had the highest historical risk and return?

Equities have generally had the highest long-run average returns and volatility, ahead of bonds and cash. Small-cap and emerging market equities have often been more volatile still. This is a historical pattern, not a promise.

What does the risk-aversion coefficient A mean?

A measures how much utility an investor gives up per unit of variance. A higher A means a more risk-averse investor, who needs more return to hold the same risk.