Risk Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardShould you buy insurance for \200/year that covers a \5000 loss occurring with probability 0.03? Calculate expected value for both choices and discuss why someone might still buy the insurance.
Solution
- 1 Without insurance: expected loss = 0.03 \times 5000 = \150; no guaranteed cost but risk of \5000
- 2 With insurance: guaranteed cost = \200= \
- 3 EV comparison: without insurance has lower expected cost (\150 < \200), so insurance is negative EV for the buyer
- 4 Why buy anyway: risk aversion β a \5000 sudden loss may be catastrophic (can't afford); paying \200 converts uncertain catastrophe to manageable certain cost; utility of money is non-linear
Answer
Insurance has higher expected cost (\200 > \150), but risk aversion justifies buying it for certainty and catastrophe protection.
Expected value alone doesn't determine optimal decisions. Risk-averse individuals prefer a certain smaller loss over an uncertain larger one, even when EV is worse. Insurance converts variance into a fixed cost β valuable when losses would be catastrophic.
About Risk
Risk is the possibility of loss or negative outcome, quantified by combining the probability of the event with the severity of its impact: Expected Loss = P(loss) times amount of loss.
Learn more about Risk βMore Risk Examples
Example 1 medium
A business faces two possible disasters: (A) equipment failure β probability 0.10, cost [formula]500
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