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

For an investor with utility U(w) = -e^{-0.02w}, what is the coefficient of absolute risk aversion A(w) = -U''(w)/U'(w)?

The coefficient of absolute risk aversion is a constant 0.02. The first derivative is 0.02e^{-0.02w} and the second is -0.0004e^{-0.02w}, so their negative ratio is 0.02 regardless of wealth, which is the defining feature of exponential utility.

  1. A0.02w
  2. B0.02, constantCorrect
  3. C0.02/w
  4. D50, constant
  5. -0.02

Explanation

U'(w)=0.02e^{-0.02w} and U''(w)=-0.0004e^{-0.02w}. So A(w)=0.0004/0.02=0.02, independent of w. The exponential utility therefore shows constant absolute risk aversion.

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