There are three assets considered to be following two-index model perfectly, with zero residual risk. The model estimations of these three assets are shown in the following table.

Asset	Expected Return	b1i	b2i
A	4.5%	1	0.5
B	6%	3	0.2
C	4%	1	0.3

a) Find the weights of the assets in the zero-beta portfolio. [4 marks]

b) If the risk free rate is 2%, identify whether there is any arbitrage opportunities. If yes, what is the arbitrage strategy. If no, explain why. [4 marks]

c) If the three assets do not follow the model perfectly, i.e. there are non zero residual risks. Can you construct an arbitrage portfolio? If yes, how? If no, why? [2 marks]