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IAI Actuarial Core Principles · Business Management · Decision-making process, attitude to risk and competition

The board of an Indian reinsurer must choose between two projects. Project X has a certain profit of Rs 50 crore. Project Y has a 50% chance of Rs 110 crore and a 50% chance of a Rs 0 outcome. The board chooses X. Which statement best explains this choice?

The board is risk-averse. Project Y's expected profit is Rs 55 crore, higher than X's certain Rs 50 crore, yet the board prefers certainty. Giving up expected value to avoid variability is the hallmark of risk-averse behaviour.

  1. AThe board is risk-seeking, because X has lower variance
  2. BThe board is risk-averse, preferring a certain Rs 50 crore to Y's higher expected Rs 55 croreCorrect
  3. CThe board is risk-neutral, since expected values are equal
  4. DThe board has misapplied expected value, because X's expected value is higher
  5. The board is risk-averse because Y's expected value is lower than X's

Explanation

Y's expected value is 0.5 x 110 = Rs 55 crore, above X's Rs 50 crore. Choosing the lower, certain amount shows risk aversion. Options claiming equal or higher expected value for X are arithmetically wrong.

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