Consider the following single index specification: R_i = a_i + _i R_M + e_i.

Where R_i is the return on security i (X or Y), R_M is the return on index M (a broad market index) and e_i is a zero-mean white noise random variable not correlated with anything.

Assume that the single index specification correctly describes returns of all securities and the risk-free rate is constant at 4%. Furthermore, you have the following descriptive statistics for returns of Stock X, Y, and index M.

	Expected return	Return Standard Deviation	i
Stock X	13%	30%	1.5
Stock Y	9%	15%	0.5
Index M	10%	20%	1

Calculate Jensens alpha of Stock Y.

(3 marks)

Calculate the information ratio of Stock Y.

(5 marks)

In light of your answer in part a), design a zero net investment alpha capturing portfolio consisting of Stock X, Stock Y, and Index M. That is, design a portfolio that yields a positive expected return by capturing the alpha in part a) with i) no exposure to the index (zero beta) and ii) zero net investment. Use Stock Y as the numeraire i.e., express the investments (long or short) on Stock X and Index M based on a $1 investment (long or short) in Stock Y.

(8 marks)