1. Assume that there are only three investors in the economy 1, 2 and 3, with tetal wealth of 500 , 1000,1500 billion poundh, respectively. There are only four assets in this economy, the risk free security, and ricky stocks A, 18 and C. The holdings of each invester in each asset (in billion pounds) are shown below: [Note that a negative amount imvested in the risk-free asset means borrowing at the risk-free rate] Answer the following questions, showing all relevant calculations. 1. Calculate the weights on each asset that constitute the market portfolio in this economy, and show that investors 1, 2 and 3 are in fact holding this portfolio. [15\\%] ii. Suppose that the expected retum of the market portfolio is \11 with a standard deviation of 23N. The risk free rate is \\( 1 \\mathrm{~K} \\). Assuming that imestors 1,2 and 3 have mean variance preferences, and gven their investment prodile in the table above, cakculate their ceefficient of risk aversion. [20\\%] Assume that the expected returns of well diversified portfolios in an economy are driven by a one factor model as follows \\( E[R]=\\alpha+r f+\\beta 1 \\) (E[RFactor 1\\( ] \\) ). Jane is a hedge fund manager, and she estimates that \\( \\beta 1 \\) of portfolio \\( A B C \\) is 1.2 , and for portfolio DEF it is 0.75 . The risk-free rate is \1 per year, and the expected return on the relevant factor, E[RFactor 1\\( ] \\), is \8 per year. Jane believes that the expected returns over the coming year on \\( A B C \\) is \13.8, and on DEF is \4.75. Design an arbitrage strategy that exploits Jane's expectations, and calculate the expected cash flow from this strategy. Assume that the short side of the trade is worth f1M. Also assume that Jane's broker charges fees for borrowing shares when shorting an asset. If an investor wants to sell short portfolio \\( A B C \\), then the shorting fees are \1.5 of the size of the short position. The equivalent short-sale cost for portfolio DEF is \2. These fees are paid when the position is closed and the trade is completed