Question9 Which of the following statements regarding risk-averse investors is true? They would always choose a lower risk investment over a higher risk investment They only invest in risk-free assets They have negative risk aversion coefficients They only accept risky investments if they have higher positive risk premiums They would always choose the investment with the highest return ResetMaximum marks: 3 Flag question undefined

Question

BlackTom AI · Accepted Answer

Risk-averse investors require compensation for bearing risk: they will accept a risky investment only if its expected return exceeds a safer alternative by a positive risk premium.

1. Relevant knowledge points and concepts
- Risk aversion: preferences that favor less uncertainty; utility functions are concave.
- Risk premium (π): the extra expected return over a risk-free rate required to make the investor indifferent to taking risk. π = E[R] − R_f.
- Arrow–Pratt absolute risk aversion: for risk-averse agents this coefficient is positive; a negative coefficient indicates risk-seeking behavior.

2. Step-by-step reasoning
- Compare a risky asset with expected return E[R] to a risk-free asset with return R_f.
- A risk-averse investor accepts the risky asset only if expected utility from the risky asset exceeds utility from the risk-free asset.
- In return terms, that typically requires E[R] − R_f > 0 (a positive risk premium) sufficient to compensate for the disutility of risk.

3. Calculational/intermediate step (simple representation)
- Let π = E[R] − R_f.
- Condition to accept risky asset: π > 0 and large enough such that E[U(R)] > U(R_f).
- No further numeric calculation is needed; the sign and sufficiency of π determine acceptance.

4. Why the correct answer is correct
- "They only accept risky investments if they have higher positive risk premiums" directly expresses that risk-averse investors demand extra expected return for additional risk. This aligns with utility-based and portfolio theory reasoning.

5. Why other options are incorrect
- "They would always choose a lower risk investment..." is false because a higher-risk asset may be chosen if compensated by a sufficiently higher expected return.
- "They only invest in risk-free assets" is false: risk-averse investors can hold risky assets when compensated.
- "They have negative risk aversion coefficients" is false: risk-averse implies positive coefficients; negative implies risk-seeking.
- "They would always choose the investment with the highest return" is false because highest return may come with unacceptable risk that a risk-averse investor avoids.

6. Conclusion
The correct choice is: They only accept risky investments if they have higher positive risk premiums. This matches the provided answer.

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