1. Explain how a hedge fund manager might appear to be able to beat the market for several years, and yet have no privileged information whatsoever. (7 marks)

2. The M² ratio for a portfolio P is positive. Explaining each step, what therefore can you infer about the Sharpe ratio, the Treynor ratio, and the Jensens alpha of portfolio P relative to those of the market portfolio? (9 marks)

3. Your portfolio has a two-factor structure with a beta of 0.5 with respect to the first factor and a beta of 0.8 with respect to the second factor. This data is incorporated in the table along with the return on the risk free asset and on two pure factor portfolios, the first having a beta of 1 with respect to the first factor, and the second having a beta of 1 with respect to the second factor.

Portfolio	b1	b2	Return
Portfolio i	0.5	0.8	10.30
Pure factor 1 portfolio	1		7.00
Pure factor 2 portfolio		1	10.00
risk free asset			4.00

Suppose you wish to immunise your portfolio from factor risk. Show how this might be done. What is the expected return on the immunised portfolio?

(9 marks)