Given the information on the XYZ stock: (S_{0}=$ 50, sigma=0.175, R=) (3 %, beta^{mathrm{S}}=0.35), and (Eleft(R_{mathrm{S}} ight)=-0.10),

Given the information on the XYZ stock: \(S_{0}=\$ 50, \sigma=0.175, R=\) \(3 \%, \beta^{\mathrm{S}}=0.35\), and \(E\left(R_{\mathrm{S}}\right)=-0.10\), determine the following characteristics of an XYZ 50 European put with an expiration of \(t\) \(=0.25\) :

a. Equilibrium OPM put price

b. Expected rate of return of the put

c. Standard deviation of the put

d. Beta of the put