Establish the properties claimed for the risk-free return proxies:

(a) Show that var(R˜) ≥ var(R˜ p + bme˜p)for every return R˜.

(b) Show that cov(R˜ p,R˜ p +bze˜p) = 0.

(c) Prove (5.23), showing that R˜ p +bce˜p represents the constant bc times the expectation operator on the space of returns.