We consider a market model, where the prices of the risk-free and risky assets are denoted by A(t) and S(t), respectively. Assume that A(0) = 100, A(1) = 110, S(0) = 10 dollars, and

S(1) = 12 with probability 1/2

11 with probability 1/4

10 with probability 1/4

(a) Is the model arbitrage free? If not, give an arbitrage opportunity.

(b) Find all portfolios (x, y) with positive initial capital and 11% expected return, where x and y denote the units of the risky and risk-free assets, respectively.

(c) Calculate σV /σS for the portfolios found in (b), where σV is the risk of such a portfolio and σS is the risk of the risky asset.