3. Consider a complete market, one period, two-state economy, where states u and

Question

3. Consider a complete market, one period, two-state economy, where states u and d are equiprobable at time 1. The aggregate endowment is Zu in state u and Zd in state d. The representative investor has power utility with relative risk aversion ndex y 1.e U(e) =F 1-1 The numeraire is the risk-free bond paying one unit of consumption at time 1, irrespective of the state of the world (a) What is the price of the state-u Arrow Debreu security? [15 marks] ith payoff R(u in state u equilibrium expected return of the stock? [15 marks]

Explanation / Answer

(a) Price of Arrow Debreu Security

Endowment vector = (Zu;Zd)

Utility for the endowment vector * probability at state u + Utility for the endowment vector at state d

(b) Equilibrium expected return of the stock

Weighted value of (payout - price) at the two states

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