3. Let R1 and R2 denote the (random) returns of Stocks 1 and 2, respectively. It is known that the randomness of R1 and R2 comes from a single factor, F, that captures the movement of the price of aluminium. The relationship between R1, R2 and F are as follows: = R1 = 0.018 +0.01F; R2 = 0.011 +0.02F. = Assume the arbitrage pricing theory holds for this question. (a) Calculate the risk-free rate. (b) Let R3 be the return of Stock 3 such that R3 = a -0.005F. Calculate the value of a such that there are no arbitrage opportunities in the market. (c) Let R4 be the return of Stock 4 such that R4 = 0.038 +0.006F. Describe how you may effect arbitrage using Stocks 1, 2, 4 and the risk-free asset. =