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IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk

An investor has a utility of wealth function U(w) = ln(w). Which statement about this investor's attitude to risk is correct?

The investor is risk-averse because the second derivative of ln(w) is -1/w², which is negative. Concavity of the utility function means the investor prefers a certain outcome to a gamble with the same expected wealth, while the positive first derivative reflects non-satiation.

  1. ARisk-seeking, because U'(w) is positive
  2. BRisk-averse, because U''(w) is negativeCorrect
  3. CRisk-neutral, because U(w) is increasing
  4. DRisk-averse, because U''(w) is positive
  5. Risk-seeking, because U(w) is concave

Explanation

U'(w)=1/w>0 shows non-satiation, and U''(w)=-1/w²<0 shows concavity, which defines risk aversion. A positive second derivative would indicate risk-seeking, so options citing it or calling a concave function risk-seeking are wrong.

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