There are two states of nature (S1, S2) with equal probabilities. Suppose there is a representative...

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There are two states of nature (S1, S2) with equal probabilities. Suppose there is a representative agent who is endowed with 1 unit of consumption today, and (2, 1) tomorrow. The agent has quadratic utility u(c) (c-3)2, c <3 < and =1. In the asset market, there are three securities. Security 1 is a comprehensive stock index that is a claim to the entire endowment of the economy. By definition, the stock index is the market portfolio with payoffs (2,1). Security 2 has payoffs (1,0), security 3 has payoffs (0,1), and security 4 is a riskfree bond that pays (1, 1). < ) What are the risk-neutral probabilities? Explain intuitively why the risk- neutral probability in one state is higher than that in the other state. < ) What is the expected gross return (i.e. expected payoffs over price) of security 2? Is the expected risk premium (E[R2]-R) of this security positive or negative? Please explain intuitively why this is the case. There are two states of nature (S1, S2) with equal probabilities. Suppose there is a representative agent who is endowed with 1 unit of consumption today, and (2, 1) tomorrow. The agent has quadratic utility u(c) (c-3)2, c <3 < and =1. In the asset market, there are three securities. Security 1 is a comprehensive stock index that is a claim to the entire endowment of the economy. By definition, the stock index is the market portfolio with payoffs (2,1). Security 2 has payoffs (1,0), security 3 has payoffs (0,1), and security 4 is a riskfree bond that pays (1, 1). < ) What are the risk-neutral probabilities? Explain intuitively why the risk- neutral probability in one state is higher than that in the other state. < ) What is the expected gross return (i.e. expected payoffs over price) of security 2? Is the expected risk premium (E[R2]-R) of this security positive or negative? Please explain intuitively why this is the case.