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CFA Level I · CFA Level I Exam · The Return and Risk of a Financial Portfolio

An investor who is risk averse is offered a fair gamble with an expected payoff of zero and positive variance. Which statement best describes how the investor most likely views the gamble?

The risk-averse investor rejects the fair gamble. Because utility is concave, the expected utility of a zero-mean risky payoff is lower than the utility of receiving zero for certain. Indifference would apply to a risk-neutral investor, and acceptance would apply to a risk seeker.

  1. AThe investor rejects it because it lowers expected utility relative to a certain outcome of zero.Correct
  2. BThe investor accepts it because variance is rewarded with higher utility.
  3. CThe investor is indifferent because the expected payoff is zero.

Explanation

A risk-averse investor has a concave utility function, so the expected utility of a fair gamble is below the utility of its expected value received with certainty. The gamble is therefore rejected. Indifference would describe a risk-neutral investor.

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