Consider the following statements for an investor regarding a quadratic utility function of the form U= E(r)-0.5*A*(SD)^2 Where, U= Utility; E(r)= expected return on the portfolio; A= coefficient of risk-aversion; (SD)^2= Variance of returns Statement (1) When the value of A=0, it suggests that the investor is risk-neutral Statement (2) When the value of A is negative, it suggests that the investor is risk-averse Statement (3) When the value of A is positive, it suggests that the investor is risk-lover Which of these above statements is (are) CORRECT? • a. Statement (1) only. • b. Statement (1) and statement (2) only. • c. Statement (2) and statement (3) only. • d. Statement (1) and statement (3) only. O e. Statement (1), statement (2) and statement (3).
Question
Consider the following statements for an investor regarding a quadratic utility function of the form U= E(r)-0.5A(SD)^2 Where, U= Utility; E(r)= expected return on the portfolio; A= coefficient of risk-aversion; (SD)^2= Variance of returns Statement (1) When the value of A=0, it suggests that the investor is risk-neutral Statement (2) When the value of A is negative, it suggests that the investor is risk-averse Statement (3) When the value of A is positive, it suggests that the investor is risk-lover Which of these above statements is (are) CORRECT? • a. Statement (1) only. • b. Statement (1) and statement (2) only. • c. Statement (2) and statement (3) only. • d. Statement (1) and statement (3) only. O e. Statement (1), statement (2) and statement (3).
Solution
a. Statement (1) only.
In the context of a quadratic utility function, when the coefficient of risk-aversion (A) is equal to zero, it suggests that the investor is risk-neutral. This is because the investor does not consider the risk (variance of returns) in their utility function, and only cares about the expected return.
However, statements (2) and (3) are incorrect. When the value of A is negative, it suggests that the investor is a risk-seeker or risk-lover, not risk-averse. This is because a negative A would mean the investor derives utility from taking on more risk. Conversely, when the value of A is positive, it suggests that the investor is risk-averse, not a risk-lover. This is because a positive A would mean the investor's utility decreases with increasing risk.
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