Consider an economy with three assets and two dates (t=0,1) and three states at t=1.

Let X=[1,2,3; 2,1,4; 1,3,1] (a 3x3 matrix) and p=[1.4; 1.8; 1.2] (a 3x1 matrix)

be the matrix of asset payoffs at t=1 and p the vector of asset prices at t=0.

(a) Does an arbitrage portfolio exist?

(b) Can you create a portfolio with payoff of (70, 140, 130) at t=1 and what is the t=0 price of such a portfolio?

(c) Determine the (implicit) risk free rate in this economy.