There are two states of nature (s1, s2) with probabilities 3/4 and 1/4 , respectively. Suppose there is a representative agent who is endowed with 2 units of consumption today, and (3,1) tomorrow. The agent has power utility u(c) = −(c − 5)^2 , c ≤ 5 and β = 1. In the asset market, there is a security with payoff (1,0) and a riskfree bond that pays (1,1).
(a) What are the risk-neutral probabilities?
(b) What is the gross return (Rf) of the riskfree bond?
(c) What is the expected gross return of the security with payoff (1,0)? Is the expected risk premium (also known as the risk correction) of this security positive or negative? Please explain intuitively.