Suppose that there are three dates, t = 0, 1, 2. There are two assets, a...

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Suppose that there are three dates, t = 0, 1, 2. There are two assets, a long-lived riskless asset and a short-lived risky asset. The long-lived asset is tradable at both t= 0 and t = 1. It has a riskless return of R between t = 0 and t = 1. Between t = 1 and t = 2 this asset has a riskless return of either R₁ or R2, with R₁ R₂. At t 0, the interest rate prevailing at t 1 (i.e. R₁ or R2 ) is not known. The two realizations of the period 1 interest rate are equally likely. The short-lived asset is tradable only at t = 0 and not at t = 1. Its rate of return between t = 0 and t = 1 is 2R if R₁ is realized and 0 otherwise. All interest rates are gross. = = (a) Consider a risk-averse agent with initial wealth Wo. Suppose the agent has a oneperiod horizon: he cares only about wealth at t = 1. What is the agent's demand for the risky asset? = (b) Consider an agent, with initial wealth Wo, who maximizes the utility function Eo where W₂ denotes wealth at t = 2 W-y 1 Y 2. Determine the agent's demand for the risky asset (expressed as a fraction of initial wealth Wo ). Explain why the agent would demand the risky asset. Suppose that there are three dates, t = 0, 1, 2. There are two assets, a long-lived riskless asset and a short-lived risky asset. The long-lived asset is tradable at both t= 0 and t = 1. It has a riskless return of R between t = 0 and t = 1. Between t = 1 and t = 2 this asset has a riskless return of either R₁ or R2, with R₁ R₂. At t 0, the interest rate prevailing at t 1 (i.e. R₁ or R2 ) is not known. The two realizations of the period 1 interest rate are equally likely. The short-lived asset is tradable only at t = 0 and not at t = 1. Its rate of return between t = 0 and t = 1 is 2R if R₁ is realized and 0 otherwise. All interest rates are gross. = = (a) Consider a risk-averse agent with initial wealth Wo. Suppose the agent has a oneperiod horizon: he cares only about wealth at t = 1. What is the agent's demand for the risky asset? = (b) Consider an agent, with initial wealth Wo, who maximizes the utility function Eo where W₂ denotes wealth at t = 2 W-y 1 Y 2. Determine the agent's demand for the risky asset (expressed as a fraction of initial wealth Wo ). Explain why the agent would demand the risky asset.