Suppose you can invest in only the market index fund and 1-month Treasury bill because of some regulation. Assume E[r] = 10%. SD[r] = 20%. and rf = 2%. You become a new portfolio manager at Fidelity. You heard your predecessor chose w = 0.5 (= the weight on the market index fund) to please the CEO. You also need to construct the portfolio that will please the CEO, but now E[r] = 13%, SD[r] = 10%, and rf = 3%. So, w = 0.5 will not be the optimal portfolio for the CEO any more. What value of w should you pick, given the portfolio theory you learned if the CEO's risk preference (= price of risk) does not change?