Which of the following statements about the ‘What is Risk?’ section of the lecture material based on the diagram below are TRUE: A risk-averse individual would always prefer A to B because they both offer the same expected reward while B has a higher level of risk than A. A risk-averse individual would always prefer A to C because A has a significantly lower level of risk than C.

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BlackTom AI · Accepted Answer

To tackle this question, I will break down each statement and compare it with the diagram and the concept of risk aversion.
Option 1: 'A risk-averse individual would always prefer A to B because they both offer the same expected reward while B has a higher level of risk than A.' The diagram shows A and B delivering similar or equal expected values, but B carries a higher risk than A. A risk-averse person prefers less risk when the payoff is the same, so this statement aligns with standard risk-averse preferences. This explanation supports why A would be preferred over B if the expected rewards are equal, highlighting the key idea that risk-averse individuals trade off higher risk for no additional gain.
Option 2: 'A risk-averse individual would always prefer A to C because A has a significantly lower level of risk than C.' Here, although A may have lower risk than C, the diagram indicates that C offers a higher expected value than A. A strictly risk-averse choice is not solely about minimizing risk; it also weighs the higher payoff. If C’s higher expected value is substantial, a risk-averse individual might still choose C to obtain the greater reward, especially depending on the exact utility framework. Therefore, this statement is not universally true and can be incorrect given the higher payoff associated with C.
Option 3: 'Neither of the statements are true (both are false)' This would mean that both the above claims about A vs B and A vs C are incorrect. Since statement 1 is consistent with risk-averse preferences when rewards are equal and B is riskier, this option would be false if statement 1 is actually true.
Option 4: 'Both statements are true (neither are false)' This would assert that A is preferred to B under equal rewards (true) and A is also preferred to C due to lower risk (which, as discussed, may not hold if C offers a significantly higher expected value that could justify the extra risk). Given the diagram, statement 2 does not hold universally, so this option is not correct.
In summary, the first statement matches the core principle of risk aversion for equal expected rewards, while the second statement fails to account for the trade-off between higher expected value and higher risk, making it not universally true.

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