financial economics

Question 12. Consider the single index model. Suppose there exists aportfolio P that has apositive alpha and a beta between 0 and 1. Suppose also that this portfolio is welldiversied, that is, the rmspecic component of risk has been completely diversied away (i.e., cp = 0(cp) = 0). Show that by choosing weights wp on portfolio P and 1 wp on the market portfolio you can construct a portfolio Q that has a beta of 0 (these weights will be expressions in terms of p). 'What's the alpha of this portfolio Q? Is it positive, negative, or zero? Explain how you could use this portfolio for an arbitrage opportunity. (Hint: What are the variance and risk premium of this portfolio Q?)