IAI Actuarial Core Principles · Economic Modelling · Rational choice theory and utility
An investor has utility U(w) = w - 0.0005 w^2 (w in Rs thousands, in the range where U is increasing). What is her coefficient of absolute risk aversion A(w) = -U''(w)/U'(w) at w = 500?
The absolute risk aversion is 0.0020. At w = 500 the first derivative is 0.5 and the second derivative is -0.001, so A = 0.001 divided by 0.5. Forgetting to divide by marginal utility gives the wrong value of 0.0010.
- A0.0010
- B0.0020Correct
- C0.0005
- D0.0100
- 0.0013
Explanation
U'(w) = 1 - 0.001w = 1 - 0.5 = 0.5. U''(w) = -0.001. A = 0.001/0.5 = 0.002. Using U'' alone (0.001) ignores the division by marginal utility.
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