a) By considering the formulas for the expected return (pp) and standard deviation (Up) of a portfolio with :r: invested in the market asset and 1 x invested in the risk-free asset, show that it is possible to write: olEr r pp=p (:1 ')+rs. :3 Assume there are two assets: the Market Asset and a risk free asset, each with current value of 1. There are two future states of the world with equal probability, and the payos of the two assets are as follows: Asset 1 Asset 2 State 1 1.05 1.20 State 2 1.05 0.93 b) An investor, Thomson, who has a utility function U (W) = c_W, and a wealth of 1, is considering investments in the two assets. How much should he invest in the Market Asset? c) Another investor, Tom, who has the same amount wealth as Thomson but has a different utility function u(W) = e'w"'2, is also considering investments in the two assets. Will he invest more in the Market Asset? Explain. d) Another investor, Harry, who has the same utility function as Thomson but has more wealth (2). He is considering to invest all his money in the two assets- How much should he invest in the Market Asset? Explain