2. (30 points) The representative investor's utility function is given as follows: u(W) = In(W) There is one risky stock with random return f defined as follows (0.1, p=9/10 0,1-p=1/10 and one risk-free asset with return r; = 0.08. The investor has an initial wealth of W, =1, and will allocate 1 portion of this wealth to the risky stock and (1-2) portion of the wealth to the risk-free asset to maximize her expected utility defined on her end-of-period wealth. Show that investing all money in the risky stock (i.e., i =1) is not the optimal decision for this investor. How can the investor reallocate her wealth to increase her expected utility? (Note: if f(x)= In(x), then f'(x) = _) X 2. (30 points) The representative investor's utility function is given as follows: u(W) = In(W) There is one risky stock with random return f defined as follows (0.1, p=9/10 0,1-p=1/10 and one risk-free asset with return r; = 0.08. The investor has an initial wealth of W, =1, and will allocate 1 portion of this wealth to the risky stock and (1-2) portion of the wealth to the risk-free asset to maximize her expected utility defined on her end-of-period wealth. Show that investing all money in the risky stock (i.e., i =1) is not the optimal decision for this investor. How can the investor reallocate her wealth to increase her expected utility? (Note: if f(x)= In(x), then f'(x) = _) X