Suppose an Asset Has a Risky Return Given By $x \sim N\left(\mu, \sigma^{2}\right)$

Multiple Choice

Suppose an asset has a risky return given by $x \sim N\left(\mu, \sigma^{2}\right)$ . Gus believes the return on the asset is given by $\hat{x} \sim N\left(\mu, \hat{\sigma}^{2}\right)$ , where $\hat{\sigma}>\sigma$ . Lulu believes the return on the asset is given by $x \sim N\left(\mu, \sigma^{2}\right)$ . Gus and Lulu have the same risk averse preferences. Which of the following is true?

A) Gus requires a larger risk premium on the asset than Lulu.
B) Lulu requires a larger risk premium on the asset than Gus.
C) Gus is more likely to purchase the asset.
D) Gus and Lulu require the same risk premium.