6. Suppose that there are two assets in which I can invest. The first is a risk-free asset whose expected return is r > 0 and whose volatility is zero. The second is a risky asset whose return is normally distributed with mean >r and volatility > 0. Let (w) and o(u) denote the mean and variance of my portfolio's return, assuming 1 invest 100w% of my wealth in the risky asset. (a) Sketch o(u) and determine the variance-minimizing allocation. (b) Show that if X>0 is a constant, then (w) - 1o4(u) attains its minimum at i = 0 (c) Use your answer from (b) to explain why it is always optimal for a utility maximizer (witht exponential utility) to invest a positive amount in the risky asset, regardless of their degree of risk aversion or initial wealth. 6. Suppose that there are two assets in which I can invest. The first is a risk-free asset whose expected return is r > 0 and whose volatility is zero. The second is a risky asset whose return is normally distributed with mean >r and volatility > 0. Let (w) and o(u) denote the mean and variance of my portfolio's return, assuming 1 invest 100w% of my wealth in the risky asset. (a) Sketch o(u) and determine the variance-minimizing allocation. (b) Show that if X>0 is a constant, then (w) - 1o4(u) attains its minimum at i = 0 (c) Use your answer from (b) to explain why it is always optimal for a utility maximizer (witht exponential utility) to invest a positive amount in the risky asset, regardless of their degree of risk aversion or initial wealth