Consider an economy with three assets and two dates (t=0,1) and three states at t=1. Let [1 2 37 X = 2 1 4 1 3 11 p= 1.8 be the matrix of asset payoffs at t=l and p the vector of asset prices at t=0. Suppose pz=2. (a) Is there an arbitrage? [3p] (b) If yes, find an arbitrage portfolio. [3p] Suppose p3=1.2. (c) Does an arbitrage portfolio exist? [2p] Can you create a portfolio with payoff of (120, 190, 220) at t=1 and what is the t=0 price of such a portfolio? [4p) Determine the (implicit) risk free rate in this economy. [4p) Consider an economy with three assets and two dates (t=0,1) and three states at t=1. Let [1 2 37 X = 2 1 4 1 3 11 p= 1.8 be the matrix of asset payoffs at t=l and p the vector of asset prices at t=0. Suppose pz=2. (a) Is there an arbitrage? [3p] (b) If yes, find an arbitrage portfolio. [3p] Suppose p3=1.2. (c) Does an arbitrage portfolio exist? [2p] Can you create a portfolio with payoff of (120, 190, 220) at t=1 and what is the t=0 price of such a portfolio? [4p) Determine the (implicit) risk free rate in this economy. [4p)