Given the following information on the XYZ stock: \(S_{0}=\$ 50, \sigma=\) \(0.175, R=3 \%\), and \(\beta^{\mathrm{S}}=0.35\), determine the following characteristics of an XYZ 50 European call with an expiration of \(t\) \(=0.25\) :

a. Equilibrium OPM call price

b. Expected rate of return of the call

c. Standard deviation of the call

d. Beta of the call Comment on relative sizes of the expected returns, standard deviations, and \(\beta\) of the XYZ call and stock.