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.单项选择题
A
Neither of the statements are true (both are false)
B
Only statement 1 is true
C
Only statement 2 is true
D
Both statements are true (neither are false)

Question

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.单项选择题

A

Neither of the statements are true (both are false)

B

Only statement 1 is true

C

Only statement 2 is true

D

Both statements are true (neither are false)

BlackTom AI · Accepted Answer

Question restatement: Which of the following statements about the ‘What is Risk?’ section of the lecture material based on the diagram below are TRUE?

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.
2. A risk-averse individual would always prefer A to C because A has a significantly lower level of risk than C.

Option 1: 'Neither of the statements are true (both are false)'
- This option would be correct only if both 1 and 2 were false. To judge that, we need to compare the implied preferences with what the diagram shows.
- In the diagram, points A and B appear to have roughly the same expected value (EV) around 50, but A is at a lower risk than B. A risk-averse person typically prefers the option with the same EV but lower risk, so A would be preferred to B. Therefore statement 1 would be true, not false.

Option 2: 'Only statement 1 is true'
- This statement asserts that statement 1 is true and statement 2 is false.
- As noted, statement 1 is consistent with risk-averse behavior when EVs are equal and risk differs (A lower risk than B). This matches typical risk-averse preferences.
- Statement 2 claims A is preferred to C solely due to lower risk, implying EVs are equal or that lower risk dominates. However, the diagram shows C has a higher expected value than A. Since risk-averse agents trade off risk and expected reward, a higher EV at greater risk may still be preferred, so A would not be unambiguously preferred to C. Hence statement 2 is not necessarily true.

Option 3: 'Only statement 2 is true'
- This would require statement 2 to be true while statement 1 is false. As discussed, statement 1 aligns with the diagram (A and B have similar EVs with A lower risk), making it true. Therefore this option is incorrect.

Option 4: 'Both statements are true (neither are false)'
- This would require both 1 and 2 to be true. We have reason to doubt statement 2 because C offers a higher EV than A, and a risk-averse individual would weigh both risk and reward. With higher EV on C, risk-averse preferences do not automatically favor A simply due to lower risk. Thus this option is not supported.

Summary: The most consistent interpretation with the diagram is that statement 1 is true (A and B have similar EVs, A has less risk), while statement 2 is not guaranteed true because C offers a higher EV that may compensate for higher risk. Therefore, the correct choice corresponds to the option stating that only statement 1 is true.